"Lessons In Electric Circuits, Volume III -- Semiconductors"

FifthEdition,lastupdateMarch29,2009

LessonsInElectricCircuits,VolumeIII– 

Semiconductors 

ByTonyR.Kuphaldt 

FifthEdition,lastupdateMarch29,2009

c○2000-2013,TonyR.Kuphaldt 

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• SecondEdition:PrintedinSeptemberof2000.Illustrationsreworkedinstandardgraphic 

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• FourthEdition: PrintedinDecember2002. Newsectionsadded,anderrorcorrections 

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• FithEdition: PrintedinJuly2007. Newsectionsadded,anderrorcorrectionsmade, 

formatchange. 

i

Contents 

1 AMPLIFIERSANDACTIVEDEVICES 1 

1.1 Fromelectrictoelectronic................................ 1 

1.2 Activeversuspassivedevices .............................. 3 

1.3 Amplifiers ......................................... 3 

1.4 Amplifiergain. ...................................... 6 

1.5 Decibels .......................................... 8 

1.6 AbsolutedBscales .................................... 14 

1.7 Attenuators ........................................ 16 

2 SOLID-STATEDEVICETHEORY 27 

2.1 Introduction........................................ 27 

2.2 Quantumphysics..................................... 28 

2.3 ValenceandCrystalstructure ............................. 41 

2.4 Bandtheoryofsolids................................... 47 

2.5 Electronsand“holes”................................... 50 

2.6 TheP-Njunction ..................................... 55 

2.7 Junctiondiodes ...................................... 58 

2.8 Bipolarjunctiontransistors............................... 60 

2.9 Junctionfield-effecttransistors............................. 65 

2.10 Insulated-gatefield-effecttransistors(MOSFET) . ................. 70 

2.11 Thyristors ......................................... 73 

2.12 Semiconductormanufacturingtechniques ...................... 75 

2.13 Superconductingdevices................................. 80 

2.14 Quantumdevices ..................................... 83 

2.15 SemiconductordevicesinSPICE . ........................... 91 

Bibliography ........................................... 93 

3 DIODESANDRECTIFIERS 97 


3.2 Metercheckofadiode . ................................. 103 

3.3 Dioderatings . ...................................... 107 

3.4 Rectifiercircuits ..................................... 108 

3.5 Peakdetector . ...................................... 115 

3.6 Clippercircuits ...................................... 117 

iii

iv CONTENTS 

3.7 Clampercircuits ..................................... 121 

3.8 Voltagemultipliers .................................... 123 

3.9 Inductorcommutatingcircuits ............................. 130 

3.10 Diodeswitchingcircuits ................................. 132 

3.11 Zenerdiodes........................................ 135 

3.12 Special-purposediodes. ................................. 143 

3.13 Otherdiodetechnologies................................. 163 

3.14 SPICEmodels. ...................................... 163 

Bibliography ........................................... 171 

4 BIPOLARJUNCTIONTRANSISTORS 173 


4.2 Thetransistorasaswitch................................ 176 

4.3 Metercheckofatransistor ............................... 179 

4.4 Activemodeoperation . ................................. 183 

4.5 Thecommon-emitteramplifier ............................. 189 

4.6 Thecommon-collectoramplifier............................. 202 

4.7 Thecommon-baseamplifier ............................... 210 

4.8 Thecascodeamplifier . ................................. 218 

4.9 Biasingtechniques .................................... 222 

4.10 Biasingcalculations ................................... 235 

4.11 Inputandoutputcoupling................................ 247 

4.12 Feedback.......................................... 256 

4.13 Amplifierimpedances . ................................. 263 

4.14 Currentmirrors...................................... 264 

4.15 Transistorratingsandpackages . ........................... 269 

4.16 BJTquirks......................................... 271 

Bibliography ........................................... 278 

5 JUNCTIONFIELD-EFFECTTRANSISTORS 281 


5.2 Thetransistorasaswitch................................ 283 

5.3 Metercheckofatransistor ............................... 286 

5.4 Active-modeoperation . ................................. 288 

5.5 Thecommon-sourceamplifier–PENDING ...................... 297 

5.6 Thecommon-drainamplifier–PENDING ...................... 298 

5.7 Thecommon-gateamplifier–PENDING . ...................... 298 

5.8 Biasingtechniques–PENDING . ........................... 298 

5.9 Transistorratingsandpackages–PENDING .................... 299 

5.10 JFETquirks–PENDING ................................ 299 

6 INSULATED-GATEFIELD-EFFECTTRANSISTORS 301 


6.2 Depletion-typeIGFETs ................................. 302 

6.3 Enhancement-typeIGFETs–PENDING . ...................... 311 

6.4 Active-modeoperation–PENDING .......................... 311

CONTENTS v 

6.5 Thecommon-sourceamplifier–PENDING ...................... 312 

6.6 Thecommon-drainamplifier–PENDING ...................... 312 

6.7 Thecommon-gateamplifier–PENDING . ...................... 312 

6.8 Biasingtechniques–PENDING . ........................... 312 

6.9 Transistorratingsandpackages–PENDING .................... 312 

6.10 IGFETquirks–PENDING ............................... 313 

6.11 MESFETs–PENDING ................................. 313 

6.12 IGBTs ........................................... 313 

7 THYRISTORS 317 

7.1 Hysteresis ......................................... 317 

7.2 Gasdischargetubes ................................... 318 

7.3 TheShockleyDiode.................................... 322 

7.4 TheDIAC ......................................... 329 

7.5 TheSilicon-ControlledRectifier(SCR)......................... 329 

7.6 TheTRIAC ........................................ 341 

7.7 Optothyristors. ...................................... 344 

7.8 TheUnijunctionTransistor(UJT) ........................... 344 

7.9 TheSilicon-ControlledSwitch(SCS).......................... 350 

7.10 Field-effect-controlledthyristors . ........................... 352 

Bibliography ........................................... 354 

8 OPERATIONALAMPLIFIERS 355 


8.2 Single-endedanddifferentialamplifiers........................ 356 

8.3 The”operational”amplifier ............................... 360 

8.4 Negativefeedback .................................... 366 

8.5 Dividedfeedback ..................................... 369 

8.6 Ananalogyfordividedfeedback . ........................... 372 

8.7 Voltage-to-currentsignalconversion.......................... 378 

8.8 Averagerandsummercircuits ............................. 380 

8.9 Buildingadifferentialamplifier . ........................... 382 

8.10 Theinstrumentationamplifier ............................. 384 

8.11 Differentiatorandintegratorcircuits ......................... 385 

8.12 Positivefeedback ..................................... 388 

8.13 Practicalconsiderations ................................. 392 

8.14 Operationalamplifiermodels .............................. 408 

8.15 Data . ........................................... 413 

9 PRACTICALANALOGSEMICONDUCTORCIRCUITS 415 

9.1 ElectroStaticDischarge ................................. 415 

9.2 Powersupplycircuits–INCOMPLETE ........................ 420 

9.3 Amplifiercircuits–PENDING ............................. 422 

9.4 Oscillatorcircuits–INCOMPLETE .......................... 422 

9.5 Phase-lockedloops–PENDING . ........................... 424 

9.6 Radiocircuits–INCOMPLETE............................. 424

vi CONTENTS 

9.7 Computationalcircuits. ................................. 433 

9.8 Measurementcircuits–INCOMPLETE........................ 455 

9.9 Controlcircuits–PENDING .............................. 456 

Bibliography ........................................... 456 

10ACTIVEFILTERS 459 

11DCMOTORDRIVES 461 

11.1 PulseWidthModulation................................. 461 

12INVERTERSANDACMOTORDRIVES 465 

13ELECTRONTUBES 467 


13.2 Earlytubehistory .................................... 468 

13.3 Thetriode ......................................... 471 

13.4 Thetetrode ........................................ 473 

13.5 Beampowertubes .................................... 474 

13.6 Thepentode ........................................ 476 

13.7 Combinationtubes .................................... 476 

13.8 Tubeparameters ..................................... 479 

13.9 Ionization(gas-filled)tubes ............................... 481 

13.10Displaytubes . ...................................... 485 

13.11Microwavetubes ..................................... 488 

13.12TubesversusSemiconductors.............................. 491 

A-1ABOUTTHISBOOK 495 

A-2CONTRIBUTORLIST 499 

A-3DESIGNSCIENCELICENSE 507 

INDEX 511

Chapter1 

AMPLIFIERSANDACTIVE 

DEVICES 

Contents 

1.1 Fromelectrictoelectronic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 

1.2 Activeversuspassivedevices . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 

1.3 Amplifiers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 

1.4 Amplifiergain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 

1.5 Decibels......................................... 8 

1.6 AbsolutedBscales . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 

1.7 Attenuators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 

1.7.1 Decibels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 

1.7.2 T-sectionattenuator. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 

1.7.3 PI-sectionattenuator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 

1.7.4 L-sectionattenuator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 

1.7.5 BridgedTattenuator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 

1.7.6 Cascadedsections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 

1.7.7 RFattenuators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 

1.1 Fromelectrictoelectronic 

ThisthirdvolumeofthebookseriesLessonsInElectricCircuitsmakesadeparturefromthe 

formertwointhatthetransitionbetweenelectriccircuitsandelectroniccircuitsisformally 

crossed. Electriccircuitsareconnectionsofconductivewiresandotherdeviceswherebythe 

uniformflowofelectronsoccurs. Electroniccircuitsaddanewdimensiontoelectriccircuits 

inthatsomemeansofcontrolisexertedovertheflowofelectronsbyanotherelectricalsignal, 

eitheravoltageoracurrent. 

1

2 CHAPTER1. AMPLIFIERSANDACTIVEDEVICES 

Inandofitself,thecontrolofelectronflowisnothingnewtothestudentofelectriccircuits.Switchescontroltheflowofelectrons,asdopotentiometers,especiallywhenconnected 

asvariableresistors(rheostats). Neithertheswitchnorthepotentiometershouldbenewto 

yourexperiencebythispointinyourstudy.Thethresholdmarkingthetransitionfromelectric 

toelectronic,then,isdefinedbyhowtheflowofelectronsiscontrolledratherthanwhetheror 

notanyformofcontrolexistsinacircuit.Switchesandrheostatscontroltheflowofelectrons 

accordingtothepositioningofamechanicaldevice,whichisactuatedbysomephysicalforce 

externaltothecircuit.Inelectronics,however,wearedealingwithspecialdevicesabletocontroltheflowofelectronsaccordingtoanotherflowofelectrons,orbytheapplicationofastatic 

voltage.Inotherwords,inanelectroniccircuit,electricityisabletocontrolelectricity. 

ThehistoricprecursortothemodernelectronicserawasinventedbyThomasEdisonin 

1880whiledevelopingtheelectricincandescentlamp. Edisonfoundthatasmallcurrent 

passedfromtheheatedlampfilamenttoametalplatemountedinsidethevacuumenvelop. 

(Figure1.1(a))Todaythisisknownasthe“Edisoneffect”.Notethatthebatteryisonlynecessarytoheatthefilament.Electronswouldstillflowifanon-electricalheatsourcewasused. 

e -1 e -1 

- 

(a) (b) 

+ 

control 

Figure1.1: (a)Edisoneffect,(b)Flemingvalveorvacuumdiode,(c)DeForestaudiontriode 

vacuumtubeamplifier. 

By1904MarconiWirelessCompanyadviserJohnFlemmingfoundthatanexternallyappliedcurrent(platebattery)onlypassedinonedirectionfromfilamenttoplate(Figure1.1(b)),butnotthereversedirection(notshown).Thisinventionwasthevacuumdiode,usedtoconvertalternatingcurrentstoDC.TheadditionofathirdelectrodebyLeeDeForest(Figure1.1 

(c))allowedasmallsignaltocontrolthelargerelectronflowfromfilamenttoplate. 

Historically,theeraofelectronicsbeganwiththeinventionoftheAudiontube,adevice 

controllingtheflowofanelectronstreamthroughavacuumbytheapplicationofasmall 

voltagebetweentwometalstructureswithinthetube.Amoredetailedsummaryofso-called 

electrontubeorvacuumtubetechnologyisavailableinthelastchapterofthisvolumeforthose 

whoareinterested. 

Electronicstechnologyexperiencedarevolutionin1948withtheinventionofthetransistor. 

ThistinydeviceachievedapproximatelythesameeffectastheAudiontube,butin 

avastlysmalleramountofspaceandwithlessmaterial.Transistorscontroltheflowofelec- 

e -1 

- 

(c) 

+

1.2. ACTIVEVERSUSPASSIVEDEVICES 3 

tronsthroughsolidsemiconductorsubstancesratherthanthroughavacuum,andsotransistor 

technologyisoftenreferredtoassolid-stateelectronics. 

1.2 Activeversuspassivedevices 

Anactivedeviceisanytypeofcircuitcomponentwiththeabilitytoelectricallycontrolelectron 

flow(electricitycontrollingelectricity). Inorderforacircuittobeproperlycalledelectronic, 

itmustcontainatleastoneactivedevice. Componentsincapableofcontrollingcurrentby 

meansofanotherelectricalsignalarecalledpassivedevices.Resistors,capacitors,inductors, 

transformers,andevendiodesareallconsideredpassivedevices. Activedevicesinclude,but 

arenotlimitedto,vacuumtubes,transistors,silicon-controlledrectifiers(SCRs),andTRIACs. 

Acasemightbemadeforthesaturablereactortobedefinedasanactivedevice,sinceitisable 

tocontrolanACcurrentwithaDCcurrent,butI’veneverhearditreferredtoassuch. The 

operationofeachoftheseactivedeviceswillbeexploredinlaterchaptersofthisvolume. 

Allactivedevicescontroltheflowofelectronsthroughthem. Someactivedevicesallowa 

voltagetocontrolthiscurrentwhileotheractivedevicesallowanothercurrenttodothejob. 

Devicesutilizingastaticvoltageasthecontrollingsignalare,notsurprisingly,calledvoltagecontrolleddevices.Devicesworkingontheprincipleofonecurrentcontrollinganothercurrent 

areknownascurrent-controlleddevices.Fortherecord,vacuumtubesarevoltage-controlled 

deviceswhiletransistorsaremadeaseithervoltage-controlledorcurrentcontrolledtypes.The 

firsttypeoftransistorsuccessfullydemonstratedwasacurrent-controlleddevice. 

1.3 Amplifiers 

Thepracticalbenefitofactivedevicesistheiramplifyingability.Whetherthedeviceinquestionbevoltage-controlledorcurrent-controlled,theamountofpowerrequiredofthecontrollingsignalistypicallyfarlessthantheamountofpoweravailableinthecontrolledcurrent. 

Inotherwords,anactivedevicedoesn’tjustallowelectricitytocontrolelectricity;itallowsa 

smallamountofelectricitytocontrolalargeamountofelectricity. 

Becauseofthisdisparitybetweencontrollingandcontrolledpowers,activedevicesmaybe 

employedtogovernalargeamountofpower(controlled)bytheapplicationofasmallamount 

ofpower(controlling).Thisbehaviorisknownasamplification. 

Itisafundamentalruleofphysicsthatenergycanneitherbecreatednordestroyed.Stated 

formally,thisruleisknownastheLawofConservationofEnergy,andnoexceptionstoithave 

beendiscoveredtodate.IfthisLawistrue–andanoverwhelmingmassofexperimentaldata 

suggeststhatitis–thenitisimpossibletobuildadevicecapableoftakingasmallamountof 

energyandmagicallytransformingitintoalargeamountofenergy.Allmachines,electricand 

electroniccircuitsincluded,haveanupperefficiencylimitof100percent. Atbest,powerout 

equalspowerinasinFigure1.2. 

Usually,machinesfaileventomeetthislimit,losingsomeoftheirinputenergyintheform 

ofheatwhichisradiatedintosurroundingspaceandthereforenotpartoftheoutputenergy 

stream.(Figure1.3) 

Manypeoplehaveattempted,withoutsuccess,todesignandbuildmachinesthatoutput 

morepowerthantheytakein.Notonlywouldsuchaperpetualmotionmachineprovethatthe


P input 

Perfect machine 

Efficiency = P output 

P input 

= 1 = 100% 

P output 

Figure1.2:Thepoweroutputofamachinecanapproach,butneverexceed,thepowerinput 

for100%efficiencyasanupperlimit. 

P input 

Realistic machine 


P input 

< 1 = less than 100% 

P output 

P lost (usually waste heat) 

Figure1.3:Arealisticmachinemostoftenlosessomeofitsinputenergyasheatintransformingitintotheoutputenergystream.

1.3. AMPLIFIERS 5 

LawofConservationofEnergywasnotaLawafterall,butitwouldusherinatechnological 

revolutionsuchastheworldhasneverseen,foritcouldpoweritselfinacircularloopand 

generateexcesspowerfor“free”.(Figure1.4) 

P input 

Perpetual-motion 

machine 


P input 

P 

Perpetual-motion 

input machine 

> 1 = more than 100% 

P output 

P output 

P "free" 

Figure1.4:Hypothetical“perpetualmotionmachine”powersitself? 

Despitemucheffortandmanyunscrupulousclaimsof“freeenergy”orover-unitymachines, 

notonehaseverpassedthesimpletestofpoweringitselfwithitsownenergyoutputand 

generatingenergytospare. 

Theredoesexist,however,aclassofmachinesknownasamplifiers,whichareabletotakein 

small-powersignalsandoutputsignalsofmuchgreaterpower.Thekeytounderstandinghow 

amplifierscanexistwithoutviolatingtheLawofConservationofEnergyliesinthebehavior 

ofactivedevices. 

Becauseactivedeviceshavetheabilitytocontrolalargeamountofelectricalpowerwitha 

smallamountofelectricalpower,theymaybearrangedincircuitsoastoduplicatetheform 

oftheinputsignalpowerfromalargeramountofpowersuppliedbyanexternalpowersource. 

Theresultisadevicethatappearstomagicallymagnifythepowerofasmallelectricalsignal 

(usuallyanACvoltagewaveform)intoanidentically-shapedwaveformoflargermagnitude. 

TheLawofConservationofEnergyisnotviolatedbecausetheadditionalpowerissupplied 

byanexternalsource,usuallyaDCbatteryorequivalent. Theamplifierneithercreatesnor 

destroysenergy,butmerelyreshapesitintothewaveformdesiredasshowninFigure1.5. 

Inotherwords,thecurrent-controllingbehaviorofactivedevicesisemployedtoshapeDC 

powerfromtheexternalpowersourceintothesamewaveformastheinputsignal,producing 

anoutputsignaloflikeshapebutdifferent(greater)powermagnitude.Thetransistororother 

activedevicewithinanamplifiermerelyformsalargercopyoftheinputsignalwaveformout 

ofthe“raw”DCpowerprovidedbyabatteryorotherpowersource. 

Amplifiers,likeallmachines,arelimitedinefficiencytoamaximumof100percent.Usually,electronicamplifiersarefarlessefficientthanthat,dissipatingconsiderableamountsof 

energyintheformofwasteheat.Becausetheefficiencyofanamplifierisalways100percent


P input 

External 

power source 

Amplifier 

P output 

Figure1.5:Whileanamplifiercanscaleasmallinputsignaltolargeoutput,itsenergysource 

isanexternalpowersupply. 

orless,onecanneverbemadetofunctionasa“perpetualmotion”device. 

Therequirementofanexternalsourceofpoweriscommontoalltypesofamplifiers,electricalandnon-electrical. 

Acommonexampleofanon-electricalamplificationsystemwould 

bepowersteeringinanautomobile,amplifyingthepowerofthedriver’sarmsinturningthe 

steeringwheeltomovethefrontwheelsofthecar.Thesourceofpowernecessaryfortheamplificationcomesfromtheengine.Theactivedevicecontrollingthedriver’s“inputsignal”isa 

hydraulicvalveshuttlingfluidpowerfromapumpattachedtotheenginetoahydraulicpiston 

assistingwheelmotion.Iftheenginestopsrunning,theamplificationsystemfailstoamplify 

thedriver’sarmpowerandthecarbecomesverydifficulttoturn. 

1.4 Amplifiergain 

Becauseamplifiershavetheabilitytoincreasethemagnitudeofaninputsignal,itisusefulto 

beabletorateanamplifier’samplifyingabilityintermsofanoutput/inputratio.Thetechnical 

termforanamplifier’soutput/inputmagnituderatioisgain.Asaratioofequalunits(power 

out/powerin,voltageout/voltagein,orcurrentout/currentin),gainisnaturallyaunitless 

measurement.Mathematically,gainissymbolizedbythecapitalletter“A”. 

Forexample,ifanamplifiertakesinanACvoltagesignalmeasuring2voltsRMSand 

outputsanACvoltageof30voltsRMS,ithasanACvoltagegainof30dividedby2,or15: 

A V = V output 

V input 

A V = 

A V = 15 

30 V 

2 V 

Correspondingly,ifweknowthegainofanamplifierandthemagnitudeoftheinputsignal, 

wecancalculatethemagnitudeoftheoutput.Forexample,ifanamplifierwithanACcurrent

1.4. AMPLIFIERGAIN 7 

gainof3.5isgivenanACinputsignalof28mARMS,theoutputwillbe3.5times28mA,or 

98mA: 

I output = (A I)(I input) 

I output = (3.5)(28 mA) 

I output = 98 mA 

InthelasttwoexamplesIspecificallyidentifiedthegainsandsignalmagnitudesinterms 

of“AC.”Thiswasintentional,andillustratesanimportantconcept:electronicamplifiersoften 

responddifferentlytoACandDCinputsignals,andmayamplifythemtodifferentextents. 

Anotherwayofsayingthisisthatamplifiersoftenamplifychangesorvariationsininput 

signalmagnitude(AC)atadifferentratiothansteadyinputsignalmagnitudes(DC).The 

specificreasonsforthisaretoocomplextoexplainatthistime,butthefactofthematteris 

worthmentioning.Ifgaincalculationsaretobecarriedout,itmustfirstbeunderstoodwhat 

typeofsignalsandgainsarebeingdealtwith,ACorDC. 

Electricalamplifiergainsmaybeexpressedintermsofvoltage,current,and/orpower,in 

bothACandDC.Asummaryofgaindefinitionsisasfollows. Thetriangle-shaped“delta” 

symbol(∆)representschangeinmathematics,so“∆Voutput/ ∆Vinput”means“changeinoutput 

voltagedividedbychangeininputvoltage,”ormoresimply,“ACoutputvoltagedividedbyAC 

inputvoltage”: 

Voltage 

Current 

Power 

DC gains AC gains 

A V = V output 

V input 

A I = I output 

I input 

A P = 

P output 

P input 

A V = ∆V output 

∆V input 

A I = ∆I output 

∆I input 

A P = (∆V output)(∆I output) 

(∆V input)(∆I input) 

A P = (A V)(A I) 

∆ = "change in . . ." 

Ifmultipleamplifiersarestaged,theirrespectivegainsformanoverallgainequaltothe 

product(multiplication)oftheindividualgains.(Figure1.6)Ifa1Vsignalwereappliedtothe 

inputofthegainof3amplifierinFigure1.6a3Vsignaloutofthefirstamplifierwouldbe 

furtheramplifiedbyagainof5atthesecondstageyielding15Vatthefinaloutput.


Input signal Amplifier 

Amplifier 

Output signal 

gain = 3 

gain = 5 

Overall gain = (3)(5) = 15 

Figure1.6:Thegainofachainofcascadedamplifiersistheproductoftheindividualgains. 

1.5 Decibels 

Initssimplestform,anamplifier’sgainisaratioofoutputoverinput. Likeallratios,this 

formofgainisunitless.However,thereisanactualunitintendedtorepresentgain,anditis 

calledthebel. 

Asaunit,thebelwasactuallydevisedasaconvenientwaytorepresentpowerlossintelephonesystemwiringratherthangaininamplifiers.Theunit’snameisderivedfromAlexanderGrahamBell,thefamousScottishinventorwhoseworkwasinstrumentalindevelopingtelephonesystems.Originally,thebelrepresentedtheamountofsignalpowerlossduetoresistanceoverastandardlengthofelectricalcable.Now,itisdefinedintermsofthecommon 

(base10)logarithmofapowerratio(outputpowerdividedbyinputpower): 

A P(ratio) = P output 

P input 

A P(Bel) = log P output 

P input 

Becausethebelisalogarithmicunit,itisnonlinear.Togiveyouanideaofhowthisworks, 

considerthefollowingtableoffigures,comparingpowerlossesandgainsinbelsversussimple 

ratios: 

Table: Gain / loss in bels 

Loss/gain as 

a ratio 

P output 

P input 

100 

10 

1 

(no loss or gain) 

Loss/gain 

in bels 

log 

1000 3 B 

P output 

P input 

2 B 

1 B 

0 B 

Loss/gain as 

a ratio 

P output 

P input 

Loss/gain 

in bels 

log 

P output 

P input 

0.1 -1 B 

0.01 -2 B 

0.001 -3 B 

0.0001 -4 B 

Itwaslaterdecidedthatthebelwastoolargeofaunittobeuseddirectly,andsoitbecame

1.5. DECIBELS 9 

customarytoapplythemetricprefixdeci(meaning1/10)toit,makingitdecibels,ordB.Now, 

theexpression“dB”issocommonthatmanypeopledonotrealizeitisacombinationof“deci-” 

and“-bel,”orthatthereevenissuchaunitasthe“bel.” Toputthisintoperspective,hereis 

anothertablecontrastingpowergain/lossratiosagainstdecibels: 

Table: Gain / loss in decibels 

Loss/gain as 

a ratio 

P output 

P input 

1000 

100 

10 

1 

(no loss or gain) 

Loss/gain 

in decibels 

10 log 

30 dB 

20 dB 

10 dB 

0 dB 

P output 

P input 

Loss/gain as 

a ratio 

P output 

P input 

0.1 

0.01 

0.001 

Loss/gain 

in decibels 

10 log 

-10 dB 

-20 dB 

-30 dB 

0.0001 -40 dB 

P output 

Asalogarithmicunit,thismodeofpowergainexpressioncoversawiderangeofratioswith 

aminimalspaninfigures. Itisreasonabletoask,“whydidanyonefeeltheneedtoinventa 

logarithmicunitforelectricalsignalpowerlossinatelephonesystem?”Theanswerisrelated 

tothedynamicsofhumanhearing,theperceptiveintensityofwhichislogarithmicinnature. 

Humanhearingishighlynonlinear:inordertodoubletheperceivedintensityofasound, 

theactualsoundpowermustbemultipliedbyafactoroften.Relatingtelephonesignalpower 

lossintermsofthelogarithmic“bel”scalemakesperfectsenseinthiscontext:apowerlossof 

1beltranslatestoaperceivedsoundlossof50percent,or1/2.Apowergainof1beltranslates 

toadoublingintheperceivedintensityofthesound. 

AnalmostperfectanalogytothebelscaleistheRichterscaleusedtodescribeearthquake 

intensity:a6.0Richterearthquakeis10timesmorepowerfulthana5.0Richterearthquake;a 

7.0Richterearthquake100timesmorepowerfulthana5.0Richterearthquake;a4.0Richter 

earthquakeis1/10aspowerfulasa5.0Richterearthquake,andsoon. Themeasurement 

scaleforchemicalpHislikewiselogarithmic,adifferenceof1onthescaleisequivalentto 

atenfolddifferenceinhydrogenionconcentrationofachemicalsolution. Anadvantageof 

usingalogarithmicmeasurementscaleisthetremendousrangeofexpressionaffordedbya 

relativelysmallspanofnumericalvalues,anditisthisadvantagewhichsecurestheuseof 

RichternumbersforearthquakesandpHforhydrogenionactivity. 

Anotherreasonfortheadoptionofthebelasaunitforgainisforsimpleexpressionofsystemgainsandlosses.Considerthelastsystemexample(Figure1.6)wheretwoamplifierswere 

connectedtandemtoamplifyasignal.Therespectivegainforeachamplifierwasexpressedas 

aratio,andtheoverallgainforthesystemwastheproduct(multiplication)ofthosetworatios: 


P input 

Ifthesefiguresrepresentedpowergains,wecoulddirectlyapplytheunitofbelstothetask


ofrepresentingthegainofeachamplifier,andofthesystemaltogether.(Figure1.7) 

A P(Bel) = log A P(ratio) 

A P(Bel) = log 3 A P(Bel) = log 5 

Input signal 

Amplifier 

gain = 3 

Amplifier 

gain = 5 

Output signal 

gain = 0.477 B gain = 0.699 B 


Overall gain (Bel) = log 15 = 1.176 B 

Figure1.7:Powergaininbelsisadditive:0.477B+0.699B=1.176B. 

Closeinspectionofthesegainfiguresintheunitof“bel”yieldsadiscovery:they’readditive. 

Ratiogainfiguresaremultiplicativeforstagedamplifiers,butgainsexpressedinbelsadd 

ratherthanmultiplytoequaltheoverallsystemgain.Thefirstamplifierwithitspowergain 

of0.477Baddstothesecondamplifier’spowergainof0.699Btomakeasystemwithanoverall 

powergainof1.176B. 

Recalculatingfordecibelsratherthanbels,wenoticethesamephenomenon.(Figure1.8) 

A P(dB) = 10 log A P(ratio) 

A P(dB) = 10 log 3 A P(dB) = 10 log 5 

Input signal 

Amplifier 

gain = 3 

Amplifier 

gain = 5 

Output signal 

gain = 4.77 dB gain = 6.99 dB 


Overall gain (dB) = 10 log 15 = 11.76 dB 

Figure1.8:Gainofamplifierstagesindecibelsisadditive:4.77dB+6.99dB=11.76dB. 

Tothosealreadyfamiliarwiththearithmeticpropertiesoflogarithms,thisisnosurprise. 

Itisanelementaryruleofalgebrathattheantilogarithmofthesumoftwonumbers’logarithm 

valuesequalstheproductofthetwooriginalnumbers.Inotherwords,ifwetaketwonumbers 

anddeterminethelogarithmofeach,thenaddthosetwologarithmfigurestogether,then 

determinethe“antilogarithm”ofthatsum(elevatethebasenumberofthelogarithm–inthis 

case,10–tothepowerofthatsum),theresultwillbethesameasifwehadsimplymultiplied 

thetwooriginalnumberstogether. Thisalgebraicruleformstheheartofadevicecalleda 

sliderule,ananalogcomputerwhichcould,amongotherthings,determinetheproductsand 

quotientsofnumbersbyaddition(addingtogetherphysicallengthsmarkedonslidingwood, 

metal,orplasticscales). Givenatableoflogarithmfigures,thesamemathematicaltrick 

couldbeusedtoperformotherwisecomplexmultiplicationsanddivisionsbyonlyhavingto 

doadditionsandsubtractions,respectively. Withtheadventofhigh-speed,handheld,digital 

calculatordevices,thiselegantcalculationtechniquevirtuallydisappearedfrompopularuse. 

However,itisstillimportanttounderstandwhenworkingwithmeasurementscalesthatare


logarithmicinnature,suchasthebel(decibel)andRichterscales. 

Whenconvertingapowergainfromunitsofbelsordecibelstoaunitlessratio,themathematicalinversefunctionofcommonlogarithmsisused:powersof10,ortheantilog. 

If: 

A P(Bel) = log A P(ratio) 

Then: 

A P(ratio) = 10 A P(Bel) 

Convertingdecibelsintounitlessratiosforpowergainismuchthesame,onlyadivision 

factorof10isincludedintheexponentterm: 

If: 

A P(dB) = 10 log A P(ratio) 

Then: 

A P(ratio) = 10 

A P(dB) 

10 

Example: Powerintoanamplifieris1Watt,thepoweroutis10Watts.Findthepower 

gainindB. 

A P(dB)=10log10(PO/PI)=10log10(10/1)=10log10(10)=10(1)=10dB 

Example: FindthepowergainratioA P(ratio)=(PO/PI)fora20dBPowergain. 

A P(dB)=20=10log10A P(ratio) 

20/10=log10A P(ratio) 

10 20/10 = 10 log10(A P(ratio)) 

100=A P(ratio)=(PO/PI) 

Becausethebelisfundamentallyaunitofpowergainorlossinasystem,voltageorcurrent 

gainsandlossesdon’tconverttobelsordBinquitethesameway.Whenusingbelsordecibels 

toexpressagainotherthanpower,beitvoltageorcurrent,wemustperformthecalculation 

intermsofhowmuchpowergaintherewouldbeforthatamountofvoltageorcurrentgain. 

Foraconstantloadimpedance,avoltageorcurrentgainof2equatestoapowergainof4(2 2 ); 

avoltageorcurrentgainof3equatestoapowergainof9(3 2 ). Ifwemultiplyeithervoltage 

orcurrentbyagivenfactor,thenthepowergainincurredbythatmultiplicationwillbethe 

squareofthatfactor.ThisrelatesbacktotheformsofJoule’sLawwherepowerwascalculated 

fromeithervoltageorcurrent,andresistance:


P = E2 

R 

P = I 2 R 

Power is proportional to the square 

of either voltage or current 

Thus,whentranslatingavoltageorcurrentgainratiointoarespectivegainintermsofthe 

belunit,wemustincludethisexponentintheequation(s): 

AP(Bel) = log AP(ratio) 2 

AV(Bel) = log AV(ratio) 2 

AI(Bel) = log AI(ratio) Exponent required 

Thesameexponentrequirementholdstruewhenexpressingvoltageorcurrentgainsin 

termsofdecibels: 

AP(dB) = 10 log AP(ratio) 2 

AV(dB) = 10 log AV(ratio) 2 

AI(dB) = 10 log AI(ratio) Exponent required 

However,thankstoanotherinterestingpropertyoflogarithms,wecansimplifytheseequationstoeliminatetheexponentbyincludingthe“2”asamultiplyingfactorforthelogarithm 

function.Inotherwords,insteadoftakingthelogarithmofthesquareofthevoltageorcurrent 

gain,wejustmultiplythevoltageorcurrentgain’slogarithmfigureby2andthefinalresult 

inbelsordecibelswillbethesame: 

For bels: 

2 

AV(Bel) = log AV(ratio) . . . is the same as . . . 

AV(Bel) = 2 log AV(ratio) For decibels: 

2 

AI(Bel) = log AI(ratio) . . . is the same as . . . 

AI(Bel) = 2 log AI(ratio) 2 

AV(dB) = 10 log AV(ratio) 2 

AI(dB) = 10 log AI(ratio) . . . is the same as . . . . . . is the same as . . . 

AV(dB) = 20 log AV(ratio) AI(dB) = 20 log AI(ratio) Theprocessofconvertingvoltageorcurrentgainsfrombelsordecibelsintounitlessratios 

ismuchthesameasitisforpowergains:


If: 

A V(Bel) = 2 log A V(ratio) 

Then: 

A V(Bel) 

A V(ratio) = 10 2 

A I(Bel) = 2 log A I(ratio) 

A I(ratio) = 10 

Herearetheequationsusedforconvertingvoltageorcurrentgainsindecibelsintounitless 

ratios: 

If: 

A V(dB) = 20 log A V(ratio) 

Then: 

A V(ratio) = 10 

A V(dB) 

A I(Bel) 

A I(dB) = 20 log A I(ratio) 

20 20 

A I(ratio) = 10 

Whilethebelisaunitnaturallyscaledforpower,anotherlogarithmicunithasbeeninventedtodirectlyexpressvoltageorcurrentgains/losses,anditisbasedonthenaturallogarithmratherthanthecommonlogarithmasbelsanddecibelsare. 

Calledtheneper,itsunit 

symbolisalower-case“n.” 

A V(ratio) = V output 

V input 

AV(neper) = ln AV(ratio) AI(neper) = ln AI(ratio) Forbetterorforworse,neitherthenepernoritsattenuatedcousin,thedecineper,ispopularlyusedasaunitinAmericanengineeringapplications. 

Example: Thevoltageintoa600 Ωaudiolineamplifieris10mV,thevoltageacrossa600 

Ωloadis1V.FindthepowergainindB. 

2 

A I(dB) 

A I(ratio) = I output 

I input 

A (dB)=20log10(VO/VI)=20log10(1/0.01)=20log10(100)=20(2)=40dB 

Example: FindthevoltagegainratioA V (ratio)=(VO/VI)fora20dBgainamplifier 

havinga50 Ωinputandoutimpedance. 

A V (dB)=20log10A V (ratio) 

20=20log10A V (ratio) 

20/20=log10A P(ratio) 

10 20/20 = 10 log10(A V (ratio)) 

10=A V (ratio)=(VO/VI) 

• REVIEW: 

• Gainsandlossesmaybeexpressedintermsofaunitlessratio,orintheunitofbels(B) 

ordecibels(dB).Adecibelisliterallyadeci-bel:one-tenthofabel.


• Thebelisfundamentallyaunitforexpressingpowergainorloss. Toconvertapower 

ratiotoeitherbelsordecibels,useoneoftheseequations: 

• A P(Bel) = log A P(ratio) A P(db) = 10 log A P(ratio) 

• Whenusingtheunitofthebelordecibeltoexpressavoltageorcurrentratio,itmustbe 

castintermsofanequivalentpowerratio. Practically,thismeanstheuseofdifferent 

equations,withamultiplicationfactorof2forthelogarithmvaluecorrespondingtoan 

exponentof2forthevoltageorcurrentgainratio: 

• 

A V(Bel) = 2 log A V(ratio) 

A I(Bel) = 2 log A I(ratio) 


A I(dB) = 20 log A I(ratio) 

• Toconvertadecibelgainintoaunitlessratiogain,useoneoftheseequations: 

• 

A V(ratio) = 10 

A V(dB) 

20 

A I(dB) 

20 

AI(ratio) = 10 

A P(ratio) = 10 

A P(dB) 

10 

• Again(amplification)isexpressedasapositivebelordecibelfigure.Aloss(attenuation) 

isexpressedasanegativebelordecibelfigure.Unitygain(nogainorloss;ratio=1)is 

expressedaszerobelsorzerodecibels. 

• Whencalculatingoverallgainforanamplifiersystemcomposedofmultipleamplifier 

stages,individualgainratiosaremultipliedtofindtheoverallgainratio. Belordecibelfiguresforeachamplifierstage,ontheotherhand,areaddedtogethertodetermine 

overallgain. 

1.6 AbsolutedBscales 

Itisalsopossibletousethedecibelasaunitofabsolutepower,inadditiontousingitasan 

expressionofpowergainorloss.Acommonexampleofthisistheuseofdecibelsasameasurementofsoundpressureintensity.Incaseslikethese,themeasurementismadeinreferenceto 

somestandardizedpowerleveldefinedas0dB.Formeasurementsofsoundpressure,0dBis 

looselydefinedasthelowerthresholdofhumanhearing,objectivelyquantifiedas1picowatt 

ofsoundpowerpersquaremeterofarea. 

Asoundmeasuring40dBonthedecibelsoundscalewouldbe10 4 timesgreaterthanthe 

thresholdofhearing.A100dBsoundwouldbe10 10 (tenbillion)timesgreaterthanthethresholdofhearing. 

Becausethehumanearisnotequallysensitivetoallfrequenciesofsound,variationsofthe 

decibelsound-powerscalehavebeendevelopedtorepresentphysiologicallyequivalentsound 

intensitiesatdifferentfrequencies. Somesoundintensityinstrumentswereequippedwith 

filternetworkstogivedisproportionateindicationsacrossthefrequencyscale,theintentof

1.6. ABSOLUTEDBSCALES 15 

whichtobetterrepresenttheeffectsofsoundonthehumanbody.Threefilteredscalesbecame 

commonlyknownasthe“A,”“B,”and“C”weightedscales.Decibelsoundintensityindications 

measuredthroughtheserespectivefilteringnetworksweregiveninunitsofdBA,dBB,and 

dBC.Today,the“A-weightedscale”ismostcommonlyusedforexpressingtheequivalentphysiologicalimpactonthehumanbody,andisespeciallyusefulforratingdangerouslyloudnoise 

sources. 

Anotherstandard-referencedsystemofpowermeasurementintheunitofdecibelshasbeen 

establishedforuseintelecommunicationssystems.ThisiscalledthedBmscale.(Figure1.9) 

Thereferencepoint,0dBm,isdefinedas1milliwattofelectricalpowerdissipatedbya600 Ω 

load.Accordingtothisscale,10dBmisequalto10timesthereferencepower,or10milliwatts; 

20dBmisequalto100timesthereferencepower,or100milliwatts.SomeACvoltmeterscome 

equippedwithadBmrangeorscale(sometimeslabeled“DB”)intendedforuseinmeasuring 

ACsignalpoweracrossa600 Ωload. 0dBmonthisscaleis,ofcourse,elevatedabovezero 

becauseitrepresentssomethinggreaterthan0(actually,itrepresents0.7746voltsacrossa 

600 Ωload,voltagebeingequaltothesquarerootofpowertimesresistance;thesquareroot 

of0.001multipliedby600).Whenviewedonthefaceofananalogmetermovement,thisdBm 

scaleappearscompressedontheleftsideandexpandedontherightinamannernotunlikea 

resistancescale,owingtoitslogarithmicnature. 

Radiofrequencypowermeasurementsforlowlevelsignalsencounteredinradioreceivers 

usedBmmeasurementsreferencedtoa50 Ωload.Signalgeneratorsfortheevaluationofradio 

receiversmayoutputanadjustabledBmratedsignal.Thesignallevelisselectedbyadevice 

calledanattenuator,describedinthenextsection. 

Table: Absolute power levels in dBm (decibel milliwatt) 

Power in 

watts 

1 

0.1 

0.01 

Power in 

milliwatts 

1000 

100 

10 

Power in 

dBm 

30 dB 

20 dB 

10 dB 

0.002 2 

3 dB 

Power in 

milliwatts 

1 

0.1 

0.01 

0.004 4 6 dB 0.001 

0.0001 

Power in 

dBm 

0 dB 

-10 dB 

-20 dB 

-30 dB 

-40 dB 

Figure1.9:AbsolutepowerlevelsindBm(decibelsreferencedto1milliwatt). 

AnadaptationofthedBmscaleforaudiosignalstrengthisusedinstudiorecordingand 

broadcastengineeringforstandardizingvolumelevels,andiscalledtheVUscale.VUmeters 

arefrequentlyseenonelectronicrecordinginstrumentstoindicatewhetherornottherecorded 

signalexceedsthemaximumsignallevellimitofthedevice,wheresignificantdistortionwill


occur. This“volumeindicator”scaleiscalibratedinaccordingtothedBmscale,butdoesnot 

directlyindicatedBmforanysignalotherthansteadysine-wavetones. Theproperunitof 

measurementforaVUmeterisvolumeunits. 

Whenrelativelylargesignalsaredealtwith,andanabsolutedBscalewouldbeusefulfor 

representingsignallevel,specializeddecibelscalesaresometimesusedwithreferencepoints 

greaterthanthe1mWusedindBm. SuchisthecaseforthedBWscale,withareference 

pointof0dBWestablishedat1Watt.AnotherabsolutemeasureofpowercalledthedBkscale 

references0dBkat1kW,or1000Watts. 

• REVIEW: 

• Theunitofthebelordecibelmayalsobeusedtorepresentanabsolutemeasurementof 

powerratherthanjustarelativegainorloss. Forsoundpowermeasurements,0dBis 

definedasastandardizedreferencepointofpowerequalto1picowattpersquaremeter. 

AnotherdBscalesuitedforsoundintensitymeasurementsisnormalizedtothesame 

physiologicaleffectsasa1000Hztone,andiscalledthedBAscale. Inthissystem,0 

dBAisdefinedasanyfrequencysoundhavingthesamephysiologicalequivalenceasa1 

picowatt-per-square-metertoneat1000Hz. 

• AnelectricaldBscalewithanabsolutereferencepointhasbeenmadeforuseintelecommunicationssystems.CalledthedBmscale,itsreferencepointof0dBmisdefinedas1 

milliwattofACsignalpowerdissipatedbya600 Ωload. 

• AVUmeterreadsaudiosignallevelaccordingtothedBmforsine-wavesignals.Because 

itsresponsetosignalsotherthansteadysinewavesisnotthesameastruedBm,itsunit 

ofmeasurementisvolumeunits. 

• dBscaleswithgreaterabsolutereferencepointsthanthedBmscalehavebeeninvented 

forhigh-powersignals.ThedBWscalehasitsreferencepointof0dBWdefinedas1Watt 

ofpower.ThedBkscalesets1kW(1000Watts)asthezero-pointreference. 

1.7 Attenuators 

Attenuatorsarepassivedevices.Itisconvenienttodiscussthemalongwithdecibels.Attenuatorsweakenorattenuatethehighleveloutputofasignalgenerator,forexample,toprovide 

alowerlevelsignalforsomethingliketheantennainputofasensitiveradioreceiver. (Figure1.10)Theattenuatorcouldbebuiltintothesignalgenerator,orbeastand-alonedevice. 

Itcouldprovideafixedoradjustableamountofattenuation. Anattenuatorsectioncanalso 

provideisolationbetweenasourceandatroublesomeload. 

Inthecaseofastand-aloneattenuator,itmustbeplacedinseriesbetweenthesignal 

sourceandtheloadbybreakingopenthesignalpathasshowninFigure1.10. Inaddition, 

itmustmatchboththesourceimpedanceZIandtheloadimpedanceZO,whileprovidinga 

specifiedamountofattenuation. Inthissectionwewillonlyconsiderthespecial,andmost 

common,casewherethesourceandloadimpedancesareequal.Notconsideredinthissection, 

unequalsourceandloadimpedancesmaybematchedbyanattenuatorsection.However,the 

formulationismorecomplex.

1.7. ATTENUATORS 17 

Z I 

Z O 

Attenuator 

Figure1.10: ConstantimpedanceattenuatorismatchedtosourceimpedanceZI andload 

impedanceZO.ForradiofrequencyequipmentZis50 Ω. 

Z I 

T attenuator Π attenuator 

Figure1.11:Tsectionand Πsectionattenuatorsarecommonforms. 

CommonconfigurationsaretheTand ΠnetworksshowninFigure1.11Multipleattenuator 

sectionsmaybecascadedwhenevenweakersignalsareneededasinFigure1.19. 

1.7.1 Decibels 

Voltageratios,asusedinthedesignofattenuatorsareoftenexpressedintermsofdecibels. 

Thevoltageratio(Kbelow)mustbederivedfromtheattenuationindecibels.Powerratiosexpressedasdecibelsareadditive.Forexample,a10dBattenuatorfollowedbya6dBattenuator 

provides16dBofattenuationoverall. 

10dB+6db=16dB 

Changingsoundlevelsareperceptibleroughlyproportionaltothelogarithmofthepower 

ratio(PI/PO). 

soundlevel=log10(PI/PO) 

Achangeof1dBinsoundlevelisbarelyperceptibletoalistener,while2dbisreadily 

perceptible.Anattenuationof3dBcorrespondstocuttingpowerinhalf,whileagainof3db 

correspondstoadoublingofthepowerlevel.Againof-3dBisthesameasanattenuationof 

+3dB,correspondingtohalftheoriginalpowerlevel. 

Thepowerchangeindecibelsintermsofpowerratiois: 

dB=10log10(PI/PO) 

AssumingthattheloadRI atPI isthesameastheloadresistorROatPO(RI =RO),the 

decibelsmaybederivedfromthevoltageratio(VI/VO)orcurrentratio(II/IO): 

Z O


PO=VOIO=VO 2 /R=IO 2 R 

PI=VIII=VI 2 /R=II 2 R 

dB=10log10(PI/PO)=10log10(VI 2 /VO 2 )=20log10(VI/VO) 

dB=10log10(PI/PO)=10log10(II 2 /IO 2 )=20log10(II/IO) 

Thetwomostoftenusedformsofthedecibelequationare: 

dB=10log10(PI/PO) or dB=20log10(VI/VO) 

Wewillusethelatterform,sinceweneedthevoltageratio.Onceagain,thevoltageratio 

formofequationisonlyapplicablewherethetwocorrespondingresistorsareequal. Thatis, 

thesourceandloadresistanceneedtobeequal. 

Example: Powerintoanattenuatoris10Watts,thepoweroutis1Watt. Findthe 

attenuationindB. 

dB=10log10(PI/PO)=10log10(10/1)=10log10(10)=10(1)=10dB 

Example: Findthevoltageattenuationratio(K=(VI/VO))fora10dBattenuator. 

dB=10=20log10(VI/VO) 

10/20=log10(VI/VO) 

10 10/20 = 10 log10(VI/VO) 

3.16=(VI/VO)=A P(ratio) 

Example: Powerintoanattenuatoris100milliwatts,thepoweroutis1milliwatt.Find 

theattenuationindB. 

dB=10log10(PI/PO)=10log10(100/1)=10log10(100)=10(2)=20dB 

Example: Findthevoltageattenuationratio(K=(VI/VO))fora20dBattenuator. 

dB=20=20log10(VI/VO) 

10 20/20 = 10 log10(VI/VO) 

10=(VI/VO)=K


dB = attenuation in decibels 

Z = source/load impedance (resistive) 

K > 1 

K = = 10 dB/20 

R 1 = Z 

R 2 = Z 

V I 

V O 

K-1 

K+1 

2K 

K 2 -1 

R 1 

R 1 

VI VO 

R2 ⇐ Ζ⇒ 

T attenuator 

⇐Ζ⇒ 

Resistors for T-section 

Z = 50 

Attenuation 

dB K=Vi/Vo R1 R2 

1.0 1.12 2.88 433.34 

2.0 1.26 5.73 215.24 

3.0 1.41 8.55 141.93 

4.0 1.58 11.31 104.83 

6.0 2.00 16.61 66.93 

10.0 3.16 25.97 35.14 

20.0 10.00 40.91 10.10 

Figure1.12:FormulasforT-sectionattenuatorresistors,givenK,thevoltageattenuationratio, 

andZI=ZO=50 Ω. 

1.7.2 T-sectionattenuator 

TheTand ΠattenuatorsmustbeconnectedtoaZsourceandZloadimpedance. TheZ- 

(arrows)pointingawayfromtheattenuatorinthefigurebelowindicatethis. TheZ-(arrows) 

pointingtowardtheattenuatorindicatesthattheimpedanceseenlookingintotheattenuator 

withaloadZontheoppositeendisZ,Z=50 Ωforourcase.Thisimpedanceisaconstant(50 

Ω)withrespecttoattenuation–impedancedoesnotchangewhenattenuationischanged. 

ThetableinFigure1.12listsresistorvaluesfortheTand Πattenuatorstomatcha50 Ω 

source/load,asistheusualrequirementinradiofrequencywork. 

Telephoneutilityandotheraudioworkoftenrequiresmatchingto600 Ω. MultiplyallR 

valuesbytheratio(600/50)tocorrectfor600 Ωmatching.Multiplyingby75/50wouldconvert 

tablevaluestomatcha75 Ωsourceandload. 

TheamountofattenuationiscustomarilyspecifiedindB(decibels).Though,weneedthe 

voltage(orcurrent)ratioKtofindtheresistorvaluesfromequations.SeethedB/20termin 

thepowerof10termforcomputingthevoltageratioKfromdB,above. 

TheT(andbelow Π)configurationsaremostcommonlyusedastheyprovidebidirectional 

matching. Thatis,theattenuatorinputandoutputmaybeswappedendforendandstill 

matchthesourceandloadimpedanceswhilesupplyingthesameattenuation. 

DisconnectingthesourceandlookingintotherightatVI,weneedtoseeaseriesparallel 

combinationofR1,R2,R1,andZlookinglikeanequivalentresistanceofZIN,thesameasthe 

source/loadimpedanceZ:(aloadofZisconnectedtotheoutput.) 

ZIN=R1+(R2 ||(R1+Z)) 

Forexample,substitutethe10dBvaluesfromthe50 ΩattenuatortableforR1andR2as 

showninFigure1.13. 

ZIN=25.97+(35.14 ||(25.97+50)) 

ZIN=25.97+(35.14 ||75.97) 

ZIN=25.97+24.03=50


Thisshowsusthatwesee50 Ωlookingrightintotheexampleattenuator(Figure1.13)with 

a50 Ωload. 

Replacingthesourcegenerator,disconnectingloadZatVO,andlookingintotheleft,should 

giveusthesameequationasabovefortheimpedanceatVO,duetosymmetry.Moreover,the 

threeresistorsmustbevalueswhichsupplytherequiredattenuationfrominputtooutput. 

ThisisaccomplishedbytheequationsforR1andR2aboveasappliedtotheT-attenuator 

below. 

Z 

⇐ Ζ⇒ 

=50 

T attenuator 

R 1=26.0 R 1 

V I VO 

R2= 35.1 

⇐ Ζ⇒ 

=50 

10 dB attenuators for matching input/output to Z= 50 Ω. 

Figure1.13:10dBT-sectionattenuatorforinsertionbetweena50 Ωsourceandload. 

1.7.3 PI-sectionattenuator 

ThetableinFigure1.14listsresistorvaluesforthe Πattenuatormatchinga50 Ωsource/load 

atsomecommonattenuationlevels. Theresistorscorrespondingtootherattenuationlevels 

maybecalculatedfromtheequations. 


K > 1 

K = = 10 dB/20 


V R3 I 

VO R 3 = Z 

R 4 = Z 

K 

2K 

K+ 1 

K-1 

2 -1 

VI VO 

R4 R4 ⇐Ζ⇒ ⇐ Ζ⇒ 

Π attenuator 

Z 

Resistors for Π-section 

Z=50.00 

Attenuation 


1.0 1.12 5.77 869.55 

2.0 1.26 11.61 436.21 

3.0 1.41 17.61 292.40 

4.0 1.58 23.85 220.97 

6.0 2.00 37.35 150.48 

10.0 3.16 71.15 96.25 

20.0 10.00 247.50 61.11 

Figure1.14: Formulasfor Π-sectionattenuatorresistors,givenK,thevoltageattenuation 

ratio,andZI=ZO=50 Ω. 

Theaboveapplytothe π-attenuatorbelow.


Z 

R 3=71.2 

VI R4= VO 

96.2 R4 ⇐Ζ⇒ 

=50 

Π attenuator 

⇐Ζ⇒ 

=50 

Figure1.15:10dB Π-sectionattenuatorexampleformatchinga50 Ωsourceandload. 

Whatresistorvalueswouldberequiredforboththe Πattenuatorsfor10dBofattenuation 

matchinga50 Ωsourceandload? 

The10dBcorrespondstoavoltageattenuationratioofK=3.16inthenexttolastlineofthe 

abovetable.Transfertheresistorvaluesinthatlinetotheresistorsontheschematicdiagram 

inFigure1.15. 

1.7.4 L-sectionattenuator 

ThetableinFigure1.16listsresistorvaluesfortheLattenuatorstomatcha50 Ωsource/ 

load.ThetableinFigure1.17listsresistorvaluesforanalternateform.Notethattheresistor 

valuesarenotthesame. 



K > 1 

VI VO K = = 10 dB/20 

R5 = Z 

K-1 

K 

Z 

R6 = 

(K-1) 

R 5 

V I VO 

⇐Ζ⇒ Ζ⇒ 

R 6 

L attenuator 

Resistors for L-section 

Z=,50.00 

Attenuation L 


1.0 1.12 5.44 409.77 

2.0 1.26 10.28 193.11 

3.0 1.41 14.60 121.20 

4.0 1.58 18.45 85.49 

6.0 2.00 24.94 50.24 

10.0 3.16 34.19 23.12 

20.0 10.00 45.00 5.56 

Figure1.16:L-sectionattenuatortablefor50 Ωsourceandloadimpedance. 

TheaboveapplytotheLattenuatorbelow. 

1.7.5 BridgedTattenuator 

ThetableinFigure1.18listsresistorvaluesforthebridgedTattenuatorstomatcha50 Ω 

sourceandload.Thebridged-Tattenuatorisnotoftenused.Whynot? 

Z




K > 1 

K = = 10 dB/20 

VI VO R 7 = Z(K-1) 

R 8 = Z K K-1 

V I 

R 8 

R 7 

V O 

⇐ Ζ⇒ Ζ⇒ 

L attenuator 

Resistors for L-section 

Z=50.00 

Attenuation 


1.0 1.12 6.10 459.77 

2.0 1.26 12.95 243.11 

3.0 1.41 20.63 171.20 

4.0 1.58 29.24 135.49 

6.0 2.00 49.76 100.24 

10.0 3.16 108.11 73.12 

20.0 10.00 450.00 55.56 

Figure1.17:AlternateformL-sectionattenuatortablefor50 Ωsourceandloadimpedance. 



K > 1 

VI VO K = = 10 dB/20 

R6 = 

Z 

(K-1) 

R7 = Z(K-1) 

VI ⇐Ζ⇒ 

R 7 

Ζ Ζ 

R 6 

Bridged T attenuator 

V O 

⇐Ζ⇒ 

Resistors for bridged T 

Z=50.00 

Attenuation 


1.0 1.12 6.10 409.77 

2.0 1.26 12.95 193.11 

3.0 1.41 20.63 121.20 

4.0 1.58 29.24 85.49 

6.0 2.00 49.76 50.24 

10.0 3.16 108.11 23.12 

20.0 10.00 450.00 5.56 

Figure1.18:Formulasandabbreviatedtableforbridged-Tattenuatorsection,Z=50 Ω.


1.7.6 Cascadedsections 

AttenuatorsectionscanbecascadedasinFigure1.19formoreattenuationthanmaybeavailablefromasinglesection.Forexampletwo10dbattenuatorsmaybecascadedtoprovide20 

dBofattenuation,thedBvaluesbeingadditive.ThevoltageattenuationratioKorVI/VOfor 

a10dBattenuatorsectionis3.16.Thevoltageattenuationratioforthetwocascadedsections 

istheproductofthetwoKsor3.16x3.16=10forthetwocascadedsections. 

section 1 section 2 

Figure1.19:Cascadedattenuatorsections:dBattenuationisadditive. 

Variableattenuationcanbeprovidedindiscretestepsbyaswitchedattenuator. TheexampleFigure1.20,showninthe0dBposition,iscapableof0through7dBofattenuationby 

additiveswitchingofnone,oneormoresections. 

S1 S2 S3 

4 dB 2 dB 1 dB 

Figure1.20:Switchedattenuator:attenuationisvariableindiscretesteps. 

Thetypicalmultisectionattenuatorhasmoresectionsthantheabovefigureshows. The 

additionofa3or8dBsectionaboveenablestheunittocoverto10dBandbeyond. Lower 

signallevelsareachievedbytheadditionof10dBand20dBsections,orabinarymultiple16 

dBsection. 

1.7.7 RFattenuators 

Forradiofrequency(RF)work(


metalic conductor 

resistive disc 

resistive rod 

Coaxial T-attenuator for radio frequency work 

Figure1.21:CoaxialT-attenuatorforradiofrequencywork. 

metalic conductor 

resistive rod 

resistive disc 

Coaxial Π-attenuator for radio frequency work 

Figure1.22:Coaxial Π-attenuatorforradiofrequencywork.


RFconnectors,notshown,areattachedtotheendsoftheaboveTand Πattenuators. 

Theconnectorsallowindividualattenuatorstobecascaded,inadditiontoconnectingbetween 

asourceandload. Forexample,a10dBattenuatormaybeplacedbetweenatroublesome 

signalsourceandanexpensivespectrumanalyzerinput. Eventhoughwemaynotneedthe 

attenuation,theexpensivetestequipmentisprotectedfromthesourcebyattenuatingany 

overvoltage. 

Summary:Attenuators 

• Anattenuatorreducesaninputsignaltoalowerlevel. 

• Theamountofattenuationisspecifiedindecibels(dB).Decibelvaluesareadditivefor 

cascadedattenuatorsections. 

• dBfrompowerratio: dB=10log10(PI/PO) 

• dBfromvoltageratio: dB=20log10(VI/VO) 

• Tand Πsectionattenuatorsarethemostcommoncircuitconfigurations. 

Contributors 

Contributorstothischapterarelistedinchronologicalorderoftheircontributions,frommost 

recenttofirst.SeeAppendix2(ContributorList)fordatesandcontactinformation. 

ColinBarnard(November2003):CorrectionregardingAlexanderGrahamBell’scountry 

oforigin(Scotland,nottheUnitedStates).

26 CHAPTER1. AMPLIFIERSANDACTIVEDEVICES

Chapter2 

SOLID-STATEDEVICETHEORY 

Contents 

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 

2.2 Quantumphysics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 

2.3 ValenceandCrystalstructure. . . . . . . . . . . . . . . . . . . . . . . . . . . 41 

2.4 Bandtheoryofsolids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 

2.5 Electronsand“holes” . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 

2.6 TheP-Njunction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 

2.7 Junctiondiodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 

2.8 Bipolarjunctiontransistors . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 

2.9 Junctionfield-effecttransistors. . . . . . . . . . . . . . . . . . . . . . . . . . 65 

2.10 Insulated-gatefield-effecttransistors(MOSFET). . . . . . . . . . . . . . . 70 

2.11 Thyristors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 

2.12 Semiconductormanufacturingtechniques. . . . . . . . . . . . . . . . . . . 75 

2.13 Superconductingdevices.............................. 80 

2.14 Quantumdevices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 

2.15 SemiconductordevicesinSPICE......................... 91 

Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 

2.1 Introduction 

Thischapterwillcoverthephysicsbehindtheoperationofsemiconductordevicesandshow 

howtheseprinciplesareappliedinseveraldifferenttypesofsemiconductordevices. Subsequentchapterswilldealprimarilywiththepracticalaspectsofthesedevicesincircuitsand 

omittheoryasmuchaspossible. 

27

28 CHAPTER2. SOLID-STATEDEVICETHEORY 

2.2 Quantumphysics 

“Ithinkitissafetosaythatnooneunderstandsquantummechanics.” 

PhysicistRichardP.Feynman 

Tosaythattheinventionofsemiconductordeviceswasarevolutionwouldnotbeanexaggeration. 

Notonlywasthisanimpressivetechnologicalaccomplishment,butitpavedthe 

wayfordevelopmentsthatwouldindeliblyaltermodernsociety.Semiconductordevicesmade 

possibleminiaturizedelectronics,includingcomputers,certaintypesofmedicaldiagnosticand 

treatmentequipment,andpopulartelecommunicationdevices,tonameafewapplicationsof 

thistechnology. 

Butbehindthisrevolutionintechnologystandsanevengreaterrevolutioningeneralscience:thefieldofquantumphysics.Withoutthisleapinunderstandingthenaturalworld,thedevelopmentofsemiconductordevices(andmoreadvancedelectronicdevicesstillunderdevelopment)wouldneverhavebeenpossible.Quantumphysicsisanincrediblycomplicatedrealm 

ofscience.Thischapterisbutabriefoverview.WhenscientistsofFeynman’scalibersaythat 

“nooneunderstands[it],”youcanbesureitisacomplexsubject.Withoutabasicunderstandingofquantumphysics,oratleastanunderstandingofthescientificdiscoveriesthatledtoitsformulation,though,itisimpossibletounderstandhowandwhysemiconductorelectronicdevicesfunction.MostintroductoryelectronicstextbooksI’vereadtrytoexplainsemiconductors 

intermsof“classical”physics,resultinginmoreconfusionthancomprehension. 

ManyofushaveseendiagramsofatomsthatlooksomethinglikeFigure2.1. 

e 

e 

e 

N 

P P N 

N P 

P 

N P 

P N N 

e 

e 

e 

e 

P 

N 

= electron 

= proton 

= neutron 

Figure2.1:Rutherfordatom:negativeelectronsorbitasmallpositivenucleus. 

Tinyparticlesofmattercalledprotonsandneutronsmakeupthecenteroftheatom;electronsorbitlikeplanetsaroundastar.Thenucleuscarriesapositiveelectricalcharge,owingto

2.2. QUANTUMPHYSICS 29 

thepresenceofprotons(theneutronshavenoelectricalchargewhatsoever),whiletheatom’s 

balancingnegativechargeresidesintheorbitingelectrons. ThenegativeelectronsareattractedtothepositiveprotonsjustasplanetsaregravitationallyattractedbytheSun,yetthe 

orbitsarestablebecauseoftheelectrons’motion.Weowethispopularmodeloftheatomtothe 

workofErnestRutherford,whoaroundtheyear1911experimentallydeterminedthatatoms’ 

positivechargeswereconcentratedinatiny,densecoreratherthanbeingspreadevenlyabout 

thediameteraswasproposedbyanearlierresearcher,J.J.Thompson. 

Rutherford’sscatteringexperimentinvolvedbombardingathingoldfoilwithpositively 

chargedalphaparticlesasinFigure2.2.YounggraduatestudentsH.GeigerandE.Marsden 

experiencedunexpectedresults. AfewAlphaparticlesweredeflectedatlargeangles. Afew 

Alphaparticleswereback-scattering,recoilingatnearly180 o . Mostoftheparticlespassed 

throughthegoldfoilundeflected,indicatingthatthefoilwasmostlyemptyspace. Thefact 

thatafewalphaparticlesexperiencedlargedeflectionsindicatedthepresenceofaminuscule 

positivelychargednucleus. 

alpha 

particles 

Gold foil 

Figure2.2:Rutherfordscattering:abeamofalphaparticlesisscatteredbyathingoldfoil. 

AlthoughRutherford’satomicmodelaccountedforexperimentaldatabetterthanThompson’s,itstillwasn’tperfect. 

Furtherattemptsatdefiningatomicstructurewereundertaken, 

andtheseeffortshelpedpavethewayforthebizarrediscoveriesofquantumphysics.Todayour 

understandingoftheatomisquiteabitmorecomplex.Nevertheless,despitetherevolutionof 

quantumphysicsanditscontributiontoourunderstandingofatomicstructure,Rutherford’s 

solar-systempictureoftheatomembeddeditselfinthepopularconsciousnesstosuchadegree 

thatitpersistsinsomeareasofstudyevenwheninappropriate. 

Considerthisshortdescriptionofelectronsinanatom,takenfromapopularelectronics 

textbook: 

Orbitingnegativeelectronsarethereforeattractedtowardthepositivenucleus, 

whichleadsustothequestionofwhytheelectronsdonotflyintotheatom’snucleus. 

Theansweristhattheorbitingelectronsremainintheirstableorbitbecauseoftwo 

equalbutoppositeforces. Thecentrifugaloutwardforceexertedontheelectrons 

becauseoftheorbitcounteractstheattractiveinwardforce(centripetal)tryingto 

pulltheelectronstowardthenucleusbecauseoftheunlikecharges.


InkeepingwiththeRutherfordmodel,thisauthorcaststheelectronsassolidchunksof 

matterengagedincircularorbits,theirinwardattractiontotheoppositelychargednucleus 

balancedbytheirmotion. Thereferenceto“centrifugalforce”istechnicallyincorrect(even 

fororbitingplanets),butiseasilyforgivenbecauseofitspopularacceptance:inreality,there 

isnosuchthingasaforcepushinganyorbitingbodyawayfromitscenteroforbit. Itseems 

thatwaybecauseabody’sinertiatendstokeepittravelinginastraightline,andsincean 

orbitisaconstantdeviation(acceleration)fromstraight-linetravel,thereisconstantinertial 

oppositiontowhateverforceisattractingthebodytowardtheorbitcenter(centripetal),beit 

gravity,electrostaticattraction,oreventhetensionofamechanicallink. 

Therealproblemwiththisexplanation,however,istheideaofelectronstravelingincircularorbitsinthefirstplace. 

Itisaverifiablefactthatacceleratingelectricchargesemit 

electromagneticradiation,andthisfactwasknowneveninRutherford’stime.Sinceorbiting 

motionisaformofacceleration(theorbitingobjectinconstantaccelerationawayfromnormal, 

straight-linemotion),electronsinanorbitingstateshouldbethrowingoffradiationlikemud 

fromaspinningtire.Electronsacceleratedaroundcircularpathsinparticleacceleratorscalled 

synchrotronsareknowntodothis,andtheresultiscalledsynchrotronradiation.Ifelectrons 

werelosingenergyinthisway,theirorbitswouldeventuallydecay,resultingincollisionswith 

thepositivelychargednucleus. Nevertheless,thisdoesn’tordinarilyhappenwithinatoms. 

Indeed,electron“orbits”areremarkablystableoverawiderangeofconditions. 

Furthermore,experimentswith“excited”atomsdemonstratedthatelectromagneticenergy 

emittedbyanatomonlyoccursatcertain,definitefrequencies. Atomsthatare“excited”by 

outsideinfluencessuchaslightareknowntoabsorbthatenergyandreturnitaselectromagneticwavesofspecificfrequencies,likeatuningforkthatringsatafixedpitchnomatterhowitisstruck.Whenthelightemittedbyanexcitedatomisdividedintoitsconstituentfrequencies(colors)byaprism,distinctlinesofcolorappearinthespectrum,thepatternofspectrallinesbeinguniquetothatelement.Thisphenomenoniscommonlyusedtoidentifyatomicelements,andevenmeasuretheproportionsofeachelementinacompoundorchemicalmixture. 

AccordingtoRutherford’ssolar-systematomicmodel(regardingelectronsaschunksofmatter 

freetoorbitatanyradius)andthelawsofclassicalphysics,excitedatomsshouldreturnenergyoveravirtuallylimitlessrangeoffrequenciesratherthanaselectfew.Inotherwords,if 

Rutherford’smodelwerecorrect,therewouldbeno“tuningfork”effect,andthelightspectrum 

emittedbyanyatomwouldappearasacontinuousbandofcolorsratherthanasafewdistinct 

lines. 

ApioneeringresearcherbythenameofNielsBohrattemptedtoimproveuponRutherford’smodelafterstudyinginRutherford’slaboratoryforseveralmonthsin1912. 

Tryingto 

harmonizethefindingsofotherphysicists(mostnotably,MaxPlanckandAlbertEinstein), 

Bohrsuggestedthateachelectronhadacertain,specificamountofenergy,andthattheirorbitswerequantizedsuchthateachmayoccupycertainplacesaroundthenucleus,asmarbles 

fixedincirculartracksaroundthenucleusratherthanthefree-rangingsatelliteseachwere 

formerlyimaginedtobe.(Figure2.3)Indeferencetothelawsofelectromagneticsandacceleratingcharges,Bohralludedtothese“orbits”asstationarystatestoescapetheimplicationthat 

theywereinmotion. 

AlthoughBohr’sambitiousattemptatre-framingthestructureoftheatomintermsthat 

agreedclosertoexperimentalresultswasamilestoneinphysics,itwasnotcomplete. His 

mathematicalanalysisproducedbetterpredictionsofexperimentaleventsthananalysesbelongingtopreviousmodels,buttherewerestillsomeunansweredquestionsaboutwhyelec-


P 

O 

Lyman 

series 

N 

M 

Balmer 

series 

Paschen 

series 

Bracket 

series 

n=4 

n=5 

n=6 

n=3 

n=2 (L) 

n=1 (K) 

nucleus 

discharge lamp 

slit 

Hδ Hγ Hβ H α 

4102 A 

4340 

4861 

6563 

Balmer series 

Figure2.3:Bohrhydrogenatom(withorbitsdrawntoscale)onlyallowselectronstoinhabit 

discreteorbitals. Electronsfallingfromn=3,4,5,or6ton=2accountsforBalmerseriesof 

spectrallines. 

tronsshouldbehaveinsuchstrangeways.Theassertionthatelectronsexistedinstationary, 

quantizedstatesaroundthenucleusaccountedforexperimentaldatabetterthanRutherford’s 

model,buthehadnoideawhatwouldforceelectronstomanifestthoseparticularstates.The 

answertothatquestionhadtocomefromanotherphysicist,LouisdeBroglie,aboutadecade 

later. 

DeBroglieproposedthatelectrons,asphotons(particlesoflight)manifestedbothparticlelikeandwave-likeproperties. 

Buildingonthisproposal,hesuggestedthatananalysisof 

orbitingelectronsfromawaveperspectiveratherthanaparticleperspectivemightmakemore 

senseoftheirquantizednature.Indeed,anotherbreakthroughinunderstandingwasreached. 

node 

node 

antinode antinode 

node 

Figure2.4:Stringvibratingatresonantfrequencybetweentwofixedpointsformsstanding 

wave. 

TheatomaccordingtodeBroglieconsistedofelectronsexistingasstandingwaves,aphenomenonwellknowntophysicistsinavarietyofforms. 

Asthepluckedstringofamusical 

instrument(Figure2.4)vibratingataresonantfrequency,with“nodes”and“antinodes”atstablepositionsalongitslength.DeBroglieenvisionedelectronsaroundatomsstandingaswaves 

bentaroundacircleasinFigure2.5. 

Electronsonlycouldexistincertain,definite“orbits”aroundthenucleusbecausethose 

weretheonlydistanceswherethewaveendswouldmatch. Inanyotherradius,thewave


antinode 

node node 

nucleus 

antinode 

node 

node 

antinode 

antinode 

antinode 

(a) (b) 

antinode 

node 

node 

antinode 

node 

nucleus 

node 

antinode 

node 

node 

antinode 

Figure2.5:“Orbiting”electronasstandingwavearoundthenucleus,(a)twocyclesperorbit, 

(b)threecyclesperorbit. 

shoulddestructivelyinterferewithitselfandthusceasetoexist. 

DeBroglie’shypothesisgavebothmathematicalsupportandaconvenientphysicalanalogy 

toaccountforthequantizedstatesofelectronswithinanatom,buthisatomicmodelwasstill 

incomplete.Withinafewyears,though,physicistsWernerHeisenbergandErwinSchrodinger, 

workingindependentlyofeachother,builtupondeBroglie’sconceptofamatter-waveduality 

tocreatemoremathematicallyrigorousmodelsofsubatomicparticles. 

ThistheoreticaladvancefromdeBroglie’sprimitivestandingwavemodeltoHeisenberg’s 

matrixandSchrodinger’sdifferentialequationmodelswasgiventhenamequantummechanics,anditintroducedarathershockingcharacteristictotheworldofsubatomicparticles:the 

traitofprobability,oruncertainty. Accordingtothenewquantumtheory,itwasimpossible 

todeterminetheexactpositionandexactmomentumofaparticleatthesametime. The 

popularexplanationofthis“uncertaintyprinciple”wasthatitwasameasurementerror(i.e. 

byattemptingtopreciselymeasurethepositionofanelectron,youinterferewithitsmomentumandthuscannotknowwhatitwasbeforethepositionmeasurementwastaken,andvice 

versa).Thestartlingimplicationofquantummechanicsisthatparticlesdonotactuallyhave 

precisepositionsandmomenta,butratherbalancethetwoquantitiesinasuchwaythattheir 

combineduncertaintiesneverdiminishbelowacertainminimumvalue. 

Thisformof“uncertainty”relationshipexistsinareasotherthanquantummechanics.As 

discussedinthe“Mixed-FrequencyACSignals”chapterinvolumeIIofthisbookseries,there 

isamutuallyexclusiverelationshipbetweenthecertaintyofawaveform’stime-domaindata 

anditsfrequency-domaindata. Insimpleterms,themorepreciselyweknowitsconstituent 

frequency(ies),thelesspreciselyweknowitsamplitudeintime,andviceversa. Toquote 

myself: 

Awaveformofinfiniteduration(infinitenumberofcycles)canbeanalyzedwith 

absoluteprecision,butthelesscyclesavailabletothecomputerforanalysis,theless 

precisetheanalysis. . . Thefewertimesthatawavecycles,thelesscertainits 

antinode


frequencyis. Takingthisconcepttoitslogicalextreme,ashortpulse–awaveform 

thatdoesn’tevencompleteacycle–actuallyhasnofrequency,butratheractsasan 

infiniterangeoffrequencies.Thisprincipleiscommontoallwave-basedphenomena, 

notjustACvoltagesandcurrents. 

Inordertopreciselydeterminetheamplitudeofavaryingsignal,wemustsampleitover 

averynarrowspanoftime. However,doingthislimitsourviewofthewave’sfrequency. 

Conversely,todetermineawave’sfrequencywithgreatprecision,wemustsampleitover 

manycycles,whichmeansweloseviewofitsamplitudeatanygivenmoment.Thus,wecannot 

simultaneouslyknowtheinstantaneousamplitudeandtheoverallfrequencyofanywavewith 

unlimitedprecision.Strangeryet,thisuncertaintyismuchmorethanobserverimprecision;it 

residesintheverynatureofthewave.Itisnotasthoughitwouldbepossible,giventheproper 

technology,toobtainprecisemeasurementsofbothinstantaneousamplitudeandfrequencyat 

once.Quiteliterally,awavecannothavebothaprecise,instantaneousamplitude,andaprecise 

frequencyatthesametime. 

Theminimumuncertaintyofaparticle’spositionandmomentumexpressedbyHeisenberg 

andSchrodingerhasnothingtodowithlimitationinmeasurement;ratheritisanintrinsic 

propertyoftheparticle’smatter-wavedualnature.Electrons,therefore,donotreallyexistin 

their“orbits”aspreciselydefinedbitsofmatter,orevenaspreciselydefinedwaveshapes,but 

ratheras“clouds”–thetechnicaltermiswavefunction–ofprobabilitydistribution,asifeach 

electronwere“spread”or“smeared”overarangeofpositionsandmomenta. 

Thisradicalviewofelectronsasimprecisecloudsatfirstseemstocontradicttheoriginal 

principleofquantizedelectronstates:thatelectronsexistindiscrete,defined“orbits”around 

atomicnuclei. Itwas,afterall,thisdiscoverythatledtotheformationofquantumtheory 

toexplainit. Howodditseemsthatatheorydevelopedtoexplainthediscretebehaviorof 

electronsendsupdeclaringthatelectronsexistas“clouds”ratherthanasdiscretepiecesof 

matter.However,thequantizedbehaviorofelectronsdoesnotdependonelectronshavingdefinitepositionandmomentumvalues,butratheronotherpropertiescalledquantumnumbers. 

Inessence,quantummechanicsdispenseswithcommonlyheldnotionsofabsolutepositionand 

absolutemomentum,andreplacesthemwithabsolutenotionsofasorthavingnoanaloguein 

commonexperience. 

Eventhoughelectronsareknowntoexistinethereal,“cloud-like”formsofdistributedprobabilityratherthanasdiscretechunksofmatter,those“clouds”haveothercharacteristicsthatarediscrete.Anyelectroninanatomcanbedescribedbyfournumericalmeasures(thepreviouslymentionedquantumnumbers),calledthePrincipal,AngularMomentum,Magnetic, 

andSpinnumbers.Thefollowingisasynopsisofeachofthesenumbers’meanings: 

PrincipalQuantumNumber:Symbolizedbythelettern,thisnumberdescribestheshell 

thatanelectronresidesin. Anelectron“shell”isaregionofspacearoundanatom’snucleus 

thatelectronsareallowedtoexistin,correspondingtothestable“standingwave”patternsof 

deBroglieandBohr. Electronsmay“leap”fromshelltoshell,butcannotexistbetweenthe 

shellregions. 

Theprinciplequantumnumbermustbeapositiveinteger(awholenumber,greaterthan 

orequalto1). Inotherwords,principlequantumnumberforanelectroncannotbe1/2or 

-3.Theseintegervalueswerenotarrivedatarbitrarily,butratherthroughexperimentalevidenceoflightspectra:thedifferingfrequencies(colors)oflightemittedbyexcitedhydrogen 

atomsfollowasequencemathematicallydependentonspecific,integervaluesasillustratedin


Figure2.3. 

Eachshellhasthecapacitytoholdmultipleelectrons.Ananalogyforelectronshellsisthe 

concentricrowsofseatsofanamphitheater.Justasapersonseatedinanamphitheatermust 

choosearowtositin(onecannotsitbetweenrows),electronsmust“choose”aparticularshell 

to“sit”in.Asinamphitheaterrows,theoutermostshellsholdmoreelectronsthantheinner 

shells. Also,electronstendtoseekthelowestavailableshell,aspeopleinanamphitheater 

seektheclosestseattothecenterstage.Thehighertheshellnumber,thegreatertheenergy 

oftheelectronsinit. 

Themaximumnumberofelectronsthatanyshellmayholdisdescribedbytheequation2n 2 , 

where“n”istheprinciplequantumnumber. Thus,thefirstshell(n=1)canhold2electrons; 

thesecondshell(n=2)8electrons,andthethirdshell(n=3)18electrons.(Figure2.6) 

K L M N O P Q 

n = 1 2 3 4 

2n 2 = 2 8 18 32 

observed fill = 2 8 18 32 18 18 2 

Figure2.6: Principalquantumnumbernandmaximumnumberofelectronspershellboth 

predictedby2(n 2 ),andobserved.Orbitalsnottoscale. 

Electronshellsinanatomwereformerlydesignatedbyletterratherthanbynumber.The 

firstshell(n=1)waslabeledK,thesecondshell(n=2)L,thethirdshell(n=3)M,thefourth 

shell(n=4)N,thefifthshell(n=5)O,thesixthshell(n=6)P,andtheseventhshell(n=7)Q. 

AngularMomentumQuantumNumber:Ashell,iscomposedofsubshells. Onemight 

beinclinedtothinkofsubshellsassimplesubdivisionsofshells,aslanesdividingaroad. 

Thesubshellsaremuchstranger. Subshellsareregionsofspacewhereelectron“clouds”are 

allowedtoexist,anddifferentsubshellsactuallyhavedifferentshapes. Thefirstsubshell 

isshapedlikeasphere,(Figure2.7(s))whichmakessensewhenvisualizedasacloudof 

electronssurroundingtheatomicnucleusinthreedimensions.Thesecondsubshell,however, 

resemblesadumbbell,comprisedoftwo“lobes”joinedtogetheratasinglepointneartheatom’s 

center. (Figure2.7(p))Thethirdsubshelltypicallyresemblesasetoffour“lobes”clustered 

aroundtheatom’snucleus. Thesesubshellshapesarereminiscentofgraphicaldepictionsof 

radioantennasignalstrength,withbulbouslobe-shapedregionsextendingfromtheantenna 

invariousdirections.(Figure2.7(d)) 

Validangularmomentumquantumnumbersarepositiveintegerslikeprincipalquantum 

numbers,butalsoincludezero.Thesequantumnumbersforelectronsaresymbolizedbythe 

letterl. Thenumberofsubshellsinashellisequaltotheshell’sprincipalquantumnumber. 

Thus,thefirstshell(n=1)hasonesubshell,numbered0;thesecondshell(n=2)hastwo 

subshells,numbered0and1;thethirdshell(n=3)hasthreesubshells,numbered0,1,and2.


z 

y 

1 of 1 

(s) 

x 

p x shown 

p y, p z similar 

(p) (d x 2 -y 2) 

x 

1 of 3 1 of 5 

d x 2 -y 2 shown 

d xy, d yz, d xz similar 

d z 2 shown 

Figure2.7:Orbitals:(s)Threefoldsymmetry.(p)Shown:px,oneofthreepossibleorientations 

(px,py,pz),abouttheirrespectiveaxes.(d)Shown:dx 2 -y 2 similartodxy,dyz,dxz.Shown:dz 2 . 

Possibled-orbitalorientations:five. 

Anolderconventionforsubshelldescriptionusedlettersratherthannumbers.Inthisnotation,thefirstsubshell(l=0)wasdesignateds,thesecondsubshell(l=1)designatedp,thethird 

subshell(l=2)designatedd,andthefourthsubshell(l=3)designatedf.Theletterscomefrom 

thewordssharp,principal(nottobeconfusedwiththeprincipalquantumnumber,n),diffuse, 

andfundamental.Youwillstillseethisnotationalconventioninmanyperiodictables,usedto 

designatetheelectronconfigurationoftheatoms’outermost,orvalence,shells.(Figure2.8) 

K 

n = 1 

2 8 18 18 1 

electrons 

S L PL 

(d z 2) 

1 of 5 

2 2 2 10 2 10 1 

6 6 6 

l = 0 0,1 0, 1, 2 0,1, 2 0 

2 3 4 5 

n = 1 2 3 4 5 

(a) 

1s 

(b) 

2 2s 2 2p 6 3s 2 3p 6 3d 10 4s 2 4p 6 4d 10 5s 1 

L M N O 

spectroscopic 

notation 

S K 

SMPMDMS N 

PN 

DN SO Figure2.8: (a)BohrrepresentationofSilveratom,(b)SubshellrepresentationofAgwith 

divisionofshellsintosubshells(angularquantumnumberl). Thisdiagramimpliesnothing 

abouttheactualpositionofelectrons,butrepresentsenergylevels. 

MagneticQuantumNumber:Themagneticquantumnumberforanelectronclassifies 

whichorientationitssubshellshapeispointed. The“lobes”forsubshellspointinmultiple 

directions.Thesedifferentorientationsarecalledorbitals.Forthefirstsubshell(s;l=0),which 

resemblesaspherepointinginno“direction”,sothereisonlyoneorbital. Forthesecond 

(p;l=1)subshellineachshell,whichresemblesdumbbellspointinthreepossibledirections.


Thinkofthreedumbbellsintersectingattheorigin,eachorientedalongadifferentaxisina 

three-axiscoordinatespace. 

Validnumericalvaluesforthisquantumnumberconsistofintegersrangingfrom-ltol,and 

aresymbolizedasmlinatomicphysicsandlzinnuclearphysics.Tocalculatethenumberof 

orbitalsinanygivensubshell,doublethesubshellnumberandadd1,(2·l+1).Forexample,the 

firstsubshell(l=0)inanyshellcontainsasingleorbital,numbered0;thesecondsubshell(l=1) 

inanyshellcontainsthreeorbitals,numbered-1,0,and1;thethirdsubshell(l=2)contains 

fiveorbitals,numbered-2,-1,0,1,and2;andsoon. 

Likeprincipalquantumnumbers,themagneticquantumnumberarosedirectlyfromexperimentalevidence:TheZeemaneffect,thedivisionofspectrallinesbyexposinganionized 

gastoamagneticfield,hencethename“magnetic”quantumnumber. 

SpinQuantumNumber: Likethemagneticquantumnumber,thispropertyofatomic 

electronswasdiscoveredthroughexperimentation.Closeobservationofspectrallinesrevealed 

thateachlinewasactuallyapairofveryclosely-spacedlines,andthisso-calledfinestructure 

washypothesizedtoresultfromeachelectron“spinning”onanaxisasifaplanet. Electrons 

withdifferent“spins”wouldgiveoffslightlydifferentfrequenciesoflightwhenexcited. The 

name“spin”wasassignedtothisquantumnumber.Theconceptofaspinningelectronisnow 

obsolete,beingbettersuitedtothe(incorrect)viewofelectronsasdiscretechunksofmatter 

ratherthanas“clouds”;but,thenameremains. 

Spinquantumnumbersaresymbolizedasmsinatomicphysicsandszinnuclearphysics. 

Foreachorbitalineachsubshellineachshell,theremaybetwoelectrons,onewithaspinof 

+1/2andtheotherwithaspinof-1/2. 

ThephysicistWolfgangPaulidevelopedaprincipleexplainingtheorderingofelectrons 

inanatomaccordingtothesequantumnumbers. Hisprinciple,calledthePauliexclusion 

principle,statesthatnotwoelectronsinthesameatommayoccupytheexactsamequantum 

states.Thatis,eachelectroninanatomhasauniquesetofquantumnumbers.Thislimitsthe 

numberofelectronsthatmayoccupyanygivenorbital,subshell,andshell. 

Shownhereistheelectronarrangementforahydrogenatom: 

K shell 

(n = 1) 

subshell 

(l) 

0 0 

orbital 

(m l) 

spin 

(m s) 

Hydrogen 

Atomic number (Z) = 1 

(one proton in nucleus) 

Spectroscopic notation: 1s 1 

1 /2 One electron 

Withoneprotoninthenucleus,ittakesoneelectrontoelectrostaticallybalancetheatom 

(theproton’spositiveelectricchargeexactlybalancedbytheelectron’snegativeelectriccharge). 

Thisoneelectronresidesinthelowestshell(n=1),thefirstsubshell(l=0),intheonlyorbital 

(spatialorientation)ofthatsubshell(ml=0),withaspinvalueof1/2. Acommonmethodof 

describingthisorganizationisbylistingtheelectronsaccordingtotheirshellsandsubshells


inaconventioncalledspectroscopicnotation.Inthisnotation,theshellnumberisshownasan 

integer,thesubshellasaletter(s,p,d,f),andthetotalnumberofelectronsinthesubshell(all 

orbitals,allspins)asasuperscript.Thus,hydrogen,withitsloneelectronresidinginthebase 

level,isdescribedas1s 1 . 

Proceedingtothenextatom(inorderofatomicnumber),wehavetheelementhelium: 

K shell 

(n = 1) 

subshell 

(l) 

0 0 

Spectroscopic notation: 

orbital 

(m l) 

spin 

(m s) 

0 0 - 1 / 2 electron 

1 /2 

Helium 


(two protons in nucleus) 

1s 2 

electron 

Aheliumatomhastwoprotonsinthenucleus,andthisnecessitatestwoelectronstobalancethedouble-positiveelectriccharge.Sincetwoelectrons–onewithspin=1/2andtheother 

withspin=-1/2–fitintooneorbital,theelectronconfigurationofheliumrequiresnoadditional 

subshellsorshellstoholdthesecondelectron. 

However,anatomrequiringthreeormoreelectronswillrequireadditionalsubshellsto 

holdallelectrons,sinceonlytwoelectronswillfitintothelowestshell(n=1).Considerthenext 

atominthesequenceofincreasingatomicnumbers,lithium: 

L shell 

(n = 2) 

K shell 

(n = 1) 

subshell 

(l) 

0 0 

0 0 

Spectroscopic notation: 

orbital 

(m l) 

spin 

(m s) 

0 0 - 1 / 2 electron 

1 /2 

Lithium 


1s 2 2s 1 

1 /2 electron 

electron 

AnatomoflithiumusesafractionoftheLshell’s(n=2)capacity.Thisshellactuallyhasa 

totalcapacityofeightelectrons(maximumshellcapacity=2n 2 electrons).Ifweexaminethe 

organizationoftheatomwithacompletelyfilledLshell,wewillseehowallcombinationsof 

subshells,orbitals,andspinsareoccupiedbyelectrons:


L shell 

(n = 2) 

K shell 

(n = 1) 

subshell 

(l) 

1 

1 

1 

1 

1 

1 

0 0 

orbital 

(m l) 

0 

0 

spin 

(m s) 

1 - 1 / 2 

1 

1 /2 

- 1 / 2 

1 /2 

-1 - 

-1 

1 

/2 

1 / 2 

0 0 - 1 / 2 

1 /2 

0 0 - 

0 0 

1 

/2 

1 / 2 

Neon 


Spectroscopic notation: 1s 2 2s 2 2p 6 

p subshell 

(l = 1) 

6 electrons 

s subshell 

(l = 0) 

2 electrons 

s subshell 

(l = 0) 

2 electrons 

Often,whenthespectroscopicnotationisgivenforanatom,anyshellsthatarecompletely 

filledareomitted,andtheunfilled,orthehighest-levelfilledshell,isdenoted. Forexample, 

theelementneon(showninthepreviousillustration),whichhastwocompletelyfilledshells, 

maybespectroscopicallydescribedsimplyas2p 6 ratherthan1s 2 2s 2 2p 6 . Lithium,withitsK 

shellcompletelyfilledandasolitaryelectronintheLshell,maybedescribedsimplyas2s 1 

ratherthan1s 2 2s 1 . 

Theomissionofcompletelyfilled,lower-levelshellsisnotjustanotationalconvenience.It 

alsoillustratesabasicprincipleofchemistry:thatthechemicalbehaviorofanelementisprimarilydeterminedbyitsunfilledshells.Bothhydrogenandlithiumhaveasingleelectronin 

theiroutermostshells(1s 1 and2s 1 ,respectively),givingthetwoelementssomesimilarproperties.Botharehighlyreactive,andreactiveinmuchthesameway(bondingtosimilarelements 

insimilarmodes).ItmatterslittlethatlithiumhasacompletelyfilledKshellunderneathits 

almost-vacantLshell:theunfilledLshellistheshellthatdeterminesitschemicalbehavior. 

Elementshavingcompletelyfilledoutershellsareclassifiedasnoble,andaredistinguished 

byalmostcompletenon-reactivitywithotherelements.Theseelementsusedtobeclassifiedas 

inert,whenitwasthoughtthatthesewerecompletelyunreactive,butarenowknowntoform 

compoundswithotherelementsunderspecificconditions. 

Sinceelementswithidenticalelectronconfigurationsintheiroutermostshell(s)exhibit 

similarchemicalproperties,DimitriMendeleevorganizedthedifferentelementsinatable 

accordingly.Suchatableisknownasaperiodictableoftheelements,andmoderntablesfollow 

thisgeneralforminFigure2.9.


He 2 

Helium 

4.00260 

1s 2 

Ne 10 

Neon 

20.179 

2p 6 

Ar 18 

Argon 

39.948 

3p 6 

Kr 36 

Krypton 

83.80 

4p 6 

Xe 54 

Xenon 

131.30 

5p 6 

13 VIIIA 

Rn 86 

Radon 

(222) 

K 19 

Potassium 

39.0983 

4s 1 

Ca 20 

Calcium 

4s 2 

Na 11 

Sodium 

3s 1 

Mg 12 

Magnesium 

3s 2 

H 1 

Hydrogen 

1s 1 

Li 3 

Lithium 

6.941 

2s 1 

Be 4 

Beryllium 

2s 2 

Sc 21 

Scandium 

3d 1 4s 2 

Ti 22 

Titanium 

3d 2 4s 2 

V 23 

Vanadium 

50.9415 

3d 3 4s 2 

Cr 24 

Chromium 

3d 5 4s 1 

Mn 25 

Manganese 

3d 5 4s 2 

Fe 26 

Iron 

55.847 

3d 6 4s 2 

Co 27 

Cobalt 

3d 7 4s 2 

Ni 28 

Nickel 

3d 8 4s 2 

Cu 29 

Copper 

63.546 

3d 10 4s 1 

Zn 30 

Zinc 

3d 10 4s 2 

Ga 31 

Gallium 

4p 1 

B 5 

Boron 

10.81 

2p 1 

C 6 

Carbon 

12.011 

2p 2 

N 7 

Nitrogen 

14.0067 

2p 3 

O 8 

Oxygen 

15.9994 

2p 4 

F 9 

Fluorine 

18.9984 

2p 5 

K 19 

Potassium 

39.0983 

4s 1 

Symbol Atomic number 

Name 

Atomic mass 

Electron 

configuration Al 13 

Aluminum 

26.9815 

3p 1 

Si 14 

Silicon 

28.0855 

3p 2 

P 15 

Phosphorus 

30.9738 

3p 3 

S 16 

Sulfur 

32.06 

3p 4 

Cl 17 

Chlorine 

35.453 

3p 5 

Periodic Table of the Elements 

Germanium 

4p 2 

Ge 32 As 33 

Arsenic 

4p 3 

Se 34 

Selenium 

78.96 

4p 4 

Br 35 

Bromine 

79.904 

4p 5 

I 53 

Iodine 

126.905 

5p 5 

37 

Rubidium 

85.4678 

5s 1 

Sr 38 

Strontium 

87.62 

5s 2 

Y 39 

Yttrium 

4d 1 5s 2 

Zr 40 

Zirconium 

91.224 

4d 2 5s 2 

Nb 41 

Niobium 

92.90638 

4d 4 5s 1 

Mo 42 

Molybdenum 

95.94 

4d 5 5s 1 

Tc 43 

Technetium 

(98) 

4d 5 5s 2 

Ru 44 

Ruthenium 

101.07 

4d 7 5s 1 

Rh 45 

Rhodium 

4d 8 5s 1 

Pd 46 

Palladium 

106.42 

4d 10 5s 0 

Ag 47 

Silver 

107.8682 

4d 10 5s 1 

Cd 48 

Cadmium 

112.411 

4d 10 5s 2 

In 49 

Indium 

114.82 

5p 1 

Sn 50 

Tin 

118.710 

5p 2 

Sb 51 

Antimony 

121.75 

5p 3 

Te 52 

Tellurium 

127.60 

5p 4 

Po 84 

Polonium 

(209) 

6p 4 

At 85 

Astatine 

(210) 

6p 5 

Metalloids Nonmetals 

Metals 

Rb 

Cs 55 

Cesium 

132.90543 

6s 1 

Ba 56 

Barium 

137.327 

6s 2 

57 - 71 Hf 72 

Lanthanide Hafnium 

series 178.49 

5d 2 6s 2 

Ta 73 

Tantalum 

180.9479 

5d 3 6s 2 

W 74 

Tungsten 

183.85 

5d 4 6s 2 

Re 75 

Rhenium 

186.207 

5d 5 6s 2 

Os 76 

Osmium 

190.2 

5d 6 6s 2 

Ir 77 

Iridium 

192.22 

5d 7 6s 2 

Pt 78 

Platinum 

195.08 

5d 9 6s 1 

Au 79 

Gold 

196.96654 

5d 10 6s 1 

Hg 80 

Mercury 

200.59 

5d 10 6s 2 

Tl 81 

Thallium 

204.3833 

6p 1 

Pb 82 

Lead 

207.2 

6p 2 

Bi 83 

Bismuth 

208.98037 

6p 3 

1 IA 

1.00794 

2 IIA 

Group new 1 IA Group old 

13 IIIA 14 IVA 15 VA 16 VIA 17 VIIA 

9.012182 

(averaged according to 

occurence on earth) 

22.989768 24.3050 

3 IIIB 4 IVB 5 VB 6 VIB 7 VIIB 8 VIIIB 9 VIIIB 10 VIIIB 11 IB 12 IIB 

40.078 44.955910 47.88 51.9961 54.93805 58.93320 58.69 65.39 69.723 72.61 74.92159 

88.90585 102.90550 

Fr 87 Ra 88 89 - 103 Unq 104 Unp 105 Unh 106 Uns 107 108 109 

Francium Radium Actinide Unnilquadium Unnilpentium Unnilhexium Unnilseptium 

(223) (226) series (261) (262) (263) (262) 

6p 6 

6d 4 7s 2 

6d 3 7s 2 

6d 2 7s 2 

7s 2 

7s 1 

Lu 71 

Lutetium 

174.967 

4f 14 5d 1 6s 2 

Yb 70 

Ytterbium 

173.04 

Tm 69 

Thulium 

168.93421 

Er 68 

Erbium 

167.26 

Ho 67 

Holmium 

164.93032 

Dy 66 

Dysprosium 

162.50 

Tb 65 

Terbium 

158.92534 

Gd 64 

Gadolinium 

157.25 

Eu 63 

Europium 

151.965 

Sm 62 

Samarium 

150.36 

Nd 60 Pm 61 

NeodymiumPromethium 

(145) 

4f 5 6s 2 

Pr 59 

Praseodymium 

140.90765 

Ce 58 

Cerium 

140.115 

4f 1 5d 1 6s 2 

La 57 

Lanthanum 

138.9055 

Lanthanide 

series 

4f 14 6s 2 

4f 13 6s 2 

4f 12 6s 2 

4f 11 6s 2 

4f 10 6s 2 

4f 9 6s 2 

4f 7 5d 1 6s 2 

4f 7 6s 2 

4f 6 6s 2 

144.24 

4f 4 6s 2 

Figure2.9:Periodictableofchemicalelements. 

4f 3 6s 2 

5d 1 6s 2 

Lr 103 

Lawrencium 

(260) 

No 102 

Nobelium 

(259) 

Md 101 

Mendelevium 

(258) 

Fm 100 

Fermium 

(257) 

5f 12 6d 0 7s 2 

Es 99 

Einsteinium 

(252) 

5f 11 6d 0 7s 2 

Cf 98 

Californium 

(251) 

5f 10 6d 0 7s 2 

Bk 97 

Berkelium 

(247) 

5f 9 6d 0 7s 2 

Cm 96 

Curium 

(247) 

5f 7 6d 1 7s 2 

Am 95 

Americium 

(243) 

5f 7 6d 0 7s 2 

Pu 94 

Plutonium 

(244) 

5f 6 6d 0 7s 2 

Np 93 

Neptunium 

(237) 

5f 4 6d 1 7s 2 

U 92 

Uranium 

238.0289 

5f 3 6d 1 7s 2 

Pa 91 

Protactinium 

231.03588 

Th 90 

Thorium 

232.0381 

Ac 89 

Actinium 

(227) 

Actinide 

series 

6d 1 7s 2 

6d 0 7s 2 

5f 13 6d 0 7s 2 

5f 2 6d 1 7s 2 

6d 2 7s 2 

6d 1 7s 2


DmitriMendeleev,aRussianchemist,wasthefirsttodevelopaperiodictableoftheelements.AlthoughMendeleevorganizedhistableaccordingtoatomicmassratherthanatomicnumber,andproducedatablethatwasnotquiteasusefulasmodernperiodictables,hisdevelopmentstandsasanexcellentexampleofscientificproof.Seeingthepatternsofperiodicity(similarchemicalpropertiesaccordingtoatomicmass),Mendeleevhypothesizedthatallelementsshouldfitintothisorderedscheme. 

Whenhediscovered“empty”spotsinthetable, 

hefollowedthelogicoftheexistingorderandhypothesizedtheexistenceofheretoforeundiscoveredelements.Thesubsequentdiscoveryofthoseelementsgrantedscientificlegitimacyto 

Mendeleev’shypothesis,furtheringfuturediscoveries,andleadingtotheformoftheperiodic 

tableweusetoday. 

Thisishowscienceshouldwork:hypothesesfollowedtotheirlogicalconclusions,andaccepted,modified,orrejectedasdeterminedbytheagreementofexperimentaldatatothoseconclusions.Anyfoolmayformulateahypothesisafter-the-facttoexplainexistingexperimentaldata,andmanydo. 

Whatsetsascientifichypothesisapartfromposthocspeculationis 

thepredictionoffutureexperimentaldatayetuncollected,andthepossibilityofdisproofasa 

resultofthatdata.Toboldlyfollowahypothesistoitslogicalconclusion(s)anddaretopredict 

theresultsoffutureexperimentsisnotadogmaticleapoffaith,butratherapublictestofthat 

hypothesis,opentochallengefromanyoneabletoproducecontradictorydata.Inotherwords, 

scientifichypothesesarealways“risky”duetotheclaimtopredicttheresultsofexperiments 

notyetconducted,andarethereforesusceptibletodisproofiftheexperimentsdonotturnout 

aspredicted. Thus,ifahypothesissuccessfullypredictstheresultsofrepeatedexperiments, 

itsfalsehoodisdisproven. 

Quantummechanics,firstasahypothesisandlaterasatheory,hasproventobeextremely 

successfulinpredictingexperimentalresults,hencethehighdegreeofscientificconfidence 

placedinit. Manyscientistshavereasontobelievethatitisanincompletetheory,though, 

asitspredictionsholdtruemoreatmicrophysicalscalesthanatmacroscopicdimensions,but 

neverthelessitisatremendouslyusefultheoryinexplainingandpredictingtheinteractions 

ofparticlesandatoms. 

Asyouhavealreadyseeninthischapter,quantumphysicsisessentialindescribingand 

predictingmanydifferentphenomena. Inthenextsection,wewillseeitssignificanceinthe 

electricalconductivityofsolidsubstances,includingsemiconductors. Simplyput,nothingin 

chemistryorsolid-statephysicsmakessensewithinthepopulartheoreticalframeworkofelectronsexistingasdiscretechunksofmatter,whirlingaroundatomicnucleilikeminiaturesatellites. 

Itiswhenelectronsareviewedas“wavefunctions”existingindefinite,discretestates 

thattheregularandperiodicbehaviorofmattercanbeexplained. 

• REVIEW: 

• Electronsinatomsexistin“clouds”ofdistributedprobability,notasdiscretechunksof 

matterorbitingthenucleusliketinysatellites,ascommonillustrationsofatomsshow. 

• Individualelectronsaroundanatomicnucleusseekunique“states,”describedbyfour 

quantumnumbers: thePrincipalQuantumNumber,knownastheshell;theAngular 

MomentumQuantumNumber,knownasthesubshell;theMagneticQuantumNumber, 

describingtheorbital(subshellorientation);andtheSpinQuantumNumber,orsimply 

spin. Thesestatesarequantized,meaningthatno“in-between”conditionsexistforan 

electronotherthanthosestatesthatfitintothequantumnumberingscheme.

2.3. VALENCEANDCRYSTALSTRUCTURE 41 

• ThePrincipalQuantumNumber(n)describesthebasiclevelorshellthatanelectron 

residesin. Thelargerthisnumber,thegreaterradiustheelectroncloudhasfromthe 

atom’snucleus,andthegreaterthatelectron’senergy. Principalquantumnumbersare 

wholenumbers(positiveintegers). 

• TheAngularMomentumQuantumNumber(l)describestheshapeoftheelectroncloud 

withinaparticularshellorlevel,andisoftenknownasthe“subshell.”Thereareasmany 

subshells(electroncloudshapes)inanygivenshellasthatshell’sprincipalquantum 

number.Angularmomentumquantumnumbersarepositiveintegersbeginningatzero 

andendingatonelessthantheprincipalquantumnumber(n-1). 

• TheMagneticQuantumNumber(ml)describeswhichorientationasubshell(electron 

cloudshape)has. Subshellsmayassumeasmanydifferentorientationsas2-timesthe 

subshellnumber(l)plus1,(2l+1)(E.g.forl=1,ml=-1,0,1)andeachuniqueorientation 

iscalledanorbital.Thesenumbersareintegersrangingfromthenegativevalueofthe 

subshellnumber(l)through0tothepositivevalueofthesubshellnumber. 

• TheSpinQuantumNumber(ms)describesanotherpropertyofanelectron,andmaybe 

avalueof+1/2or-1/2. 

• Pauli’sExclusionPrinciplesaysthatnotwoelectronsinanatommaysharetheexact 

samesetofquantumnumbers.Therefore,nomorethantwoelectronsmayoccupyeach 

orbital(spin=1/2andspin=-1/2),2l+1orbitalsineverysubshell,andnsubshellsinevery 

shell,andnomore. 

• Spectroscopicnotationisaconventionfordenotingtheelectronconfigurationofanatom. 

Shellsareshownaswholenumbers,followedbysubshellletters(s,p,d,f),withsuperscriptednumberstotalingthenumberofelectronsresidingineachrespectivesubshell. 

• Anatom’schemicalbehaviorissolelydeterminedbytheelectronsintheunfilledshells. 

Low-levelshellsthatarecompletelyfilledhavelittleornoeffectonthechemicalbonding 

characteristicsofelements. 

• Elementswithcompletelyfilledelectronshellsarealmostentirelyunreactive,andare 

callednoble(formerlyknownasinert). 

2.3 ValenceandCrystalstructure 

Valence: Theelectronsintheoutermostshell,orvalenceshell,areknownasvalenceelectrons. 

Thesevalenceelectronsareresponsibleforthechemicalpropertiesofthechemical 

elements.Itistheseelectronswhichparticipateinchemicalreactionswithotherelements.An 

oversimplifiedchemistryruleapplicabletosimplereactionsisthatatomstrytoformacompleteoutershellof8electrons(twofortheLshell). 

Atomsmaygiveawayafewelectronsto 

exposeanunderlyingcompleteshell.Atomsmayacceptafewelectronstocompletetheshell. 

Thesetwoprocessesformionsfromatoms.Atomsmayevenshareelectronsamongatomsin 

anattempttocompletetheoutershell. Thisprocessformsmolecularbonds. Thatis,atoms 

associatetoformamolecule.


ForexamplegroupIelements:Li,Na,K,Cu,Ag,andAuhaveasinglevalenceelectron. 

(Figure2.10)Theseelementsallhavesimilarchemicalproperties. Theseatomsreadilygive 

awayoneelectrontoreactwithotherelements. Theabilitytoeasilygiveawayanelectron 

makestheseelementsexcellentconductors. 

Li 

Na 

K 

Cu Ag 

Au 

Figure2.10:PeriodictablegroupIAelements:Li,Na,andK,andgroupIBelements:Cu,Ag, 

andAuhaveoneelectronintheouter,orvalence,shell,whichisreadilydonated.Innershell 

electrons:Forn=1,2,3,4;2n 2 =2,8,18,32. 

GroupVIIAelements:Fl,Cl,Br,andIallhave7electronsintheoutershell. Theseelementsreadilyacceptanelectrontofilluptheoutershellwithafull8electrons.(Figure2.11) 

Iftheseelementsdoacceptanelectron,anegativeionisformedfromtheneutralatom.These 

elementswhichdonotgiveupelectronsareinsulators. 

F Cl 

Br 

Figure2.11: PeriodictablegroupVIIAelements: F,Cl,Br,andIwith7valenceelectrons 

readilyacceptanelectroninreactionswithotherelements. 

Forexample,aClatomacceptsanelectronfromanNaatomtobecomeaCl − ionasshownin 

Figure2.12.Anionisachargedparticleformedfromanatombyeitherdonatingoraccepting 

anelectron.AstheNaatomdonatesanelectron,itbecomesaNa + ion.ThisishowNaandCl 

atomscombinetoformNaCl,tablesalt,whichisactuallyNa + Cl − ,apairofions.TheNa + and 

Cl − carryingoppositecharges,attractoneother. 

SodiumchloridecrystallizesinthecubicstructureshowninFigure2.16.Thismodelisnot 

toscaletoshowthethreedimensionalstructure.TheNa + Cl − ionsareactuallypackedsimilar 

tolayersofstackedmarbles.Theeasilydrawncubiccrystalstructureillustratesthatasolid 

crystalmaycontainchargedparticles. 

GroupVIIIAelements:He,Ne,Ar,Kr,Xeallhave8electronsinthevalenceshell.(Figure 

I


= 

Na Cl Na + 

+ - 

Figure2.12:NeutralSodiumatomdonatesanelectrontoneutralChlorineatomformingNa + 

andCl − ions. 

below)Thatis,thevalenceshelliscompletemeaningtheseelementsneitherdonatenoraccept 

electrons. NordotheyreadilyparticipateinchemicalreactionssincegroupVIIIAelements 

donoteasilycombinewithotherelements.InrecentyearschemistshaveforcedXeandKrto 

formafewcompounds,howeverforthepurposesofourdiscussionthisisnotapplicable.These 

elementsaregoodelectricalinsulatorsandaregasesatroomtemperature. 

He Ne 

Ar 

Kr 

Figure2.13:GroupVIIIAelements:He,Ne,Ar,Kr,Xearelargelyunreactivesincethevalence 

shelliscomplete.. 

GroupIVAelements: C,Si,Ge,having4electronsinthevalenceshellasshowninFigure2.14formcompoundsbysharingelectronswithotherelementswithoutformingions.This 

sharedelectronbondingisknownascovalentbonding. Notethatthecenteratom(andthe 

othersbyextension)hascompleteditsvalenceshellbysharingelectrons.Notethatthefigure 

isa2-drepresentationofbonding,whichisactually3-d. Itisthisgroup,IVA,thatweare 

interestedinforitssemiconductingproperties. 

Crystalstructure:Mostinorganicsubstancesformtheiratoms(orions)intoanordered 

arrayknownasacrystal. Theouterelectroncloudsofatomsinteractinanorderlymanner. 

Evenmetalsarecomposedofcrystalsatthemicroscopiclevel. Ifametalsampleisgiven 

anopticalpolish,thenacidetched,themicroscopicmicrocrystallinestructureshowsasin 

Figure2.15. Itisalsopossibletopurchase,atconsiderableexpense,metallicsinglecrystal 

specimensfromspecializedsuppliers.Polishingandetchingsuchaspecimendisclosesnomicrocrystallinestructure. 

Practicallyallindustrialmetalsarepolycrystalline. Mostmodern 

semiconductors,ontheotherhand,aresinglecrystaldevices.Weareprimarilyinterestedin 

monocrystallinestructures. 

Manymetalsaresoftandeasilydeformedbythevariousmetalworkingtechniques. The 

microcrystalsaredeformedinmetalworking. Also,thevalenceelectronsarefreetomove 

aboutthecrystallattice,andfromcrystaltocrystal. Thevalenceelectronsdonotbelongto 

Cl - 

Xe


C Si 

Ge 

(a) 

(b) 

Figure2.14: (a)GroupIVAelements: C,Si,Gehaving4electronsinthevalenceshell,(b) 

completethevalenceshellbysharingelectronswithotherelements. 

(a) (b) (c) 

Figure2.15:(a)Metalsample,(b)polished,(c)acidetchedtoshowmicrocrystallinestructure. 

anyparticularatom,buttoallatoms. 

TherigidcrystalstructureinFigure2.16iscomposedofaregularrepeatingpatternof 

positiveNaionsandnegativeClions.TheNaandClatomsformNa + andCl − ionsbytransferringanelectronfromNatoCl,withnofreeelectrons.Electronsarenotfreetomoveabout 

thecrystallattice,adifferencecomparedwithametal.Noraretheionsfree.Ionsarefixedin 

placewithinthecrystalstructure.Though,theionsarefreetomoveaboutiftheNaClcrystal 

isdissolvedinwater.However,thecrystalnolongerexists.Theregular,repeatingstructureis 

gone.EvaporationofthewaterdepositstheNa + andCl − ionsintheformofnewcrystalsas 

theoppositelychargedionsattracteachother.Ionicmaterialsformcrystalstructuresdueto 

thestrongelectrostaticattractionoftheoppositelychargedions. 

SemiconductorsinGroup14(formerlypartofGroupIV)formatetrahedralbondingpatternutilizingthesandporbitalelectronsabouttheatom,sharingelectron-pairbondstofouradjacentatoms.(Figure2.18(a)).Group14elementshavefourouterelectrons:twoinasphericals-orbitalandtwoinp-orbitals. 

Oneofthep-orbitalsisunoccupied. Thethreep-orbitals 

hybridizewiththes-orbitaltoformfoursp 3 molecularorbitals.ThesefourelectroncloudsrepeloneanothertoequidistanttetrahedralspacingabouttheSiatom,attractedbythepositive 

nucleusasshowninFigure2.17. 

Everysemiconductoratom,Si,Ge,orC(diamond)ischemicallybondedtofourotheratoms 

bycovalentbonds,sharedelectronbonds. Twoelectronsmayshareanorbitalifeachhave 

oppositespinquantumnumbers. Thus,anunpairedelectronmayshareanorbitalwithan 

electronfromanotheratom. ThiscorrespondstooverlappingFigure2.18(a)oftheelectron


z 

y 

s z 2 

Figure2.16:NaClcrystalhavingacubicstructure. 

x 

+ + 

p x 

Figure2.17:Ones-orbitalandthreep-orbitalelectronshybridize,formingfoursp 3 molecular 

orbitals. 

p y 

Cl - 

Na + 

= 

sp 3


clouds,orbonding.Figure2.18(b)isonefourthofthevolumeofthediamondcrystalstructure 

unitcellshowninFigure2.19attheorigin. Thebondsareparticularlystrongindiamond, 

decreasinginstrengthgoingdowngroupIVtosilicon,andgermanium.Siliconandgermanium 

bothformcrystalswithadiamondstructure. 

(a) 

(b) 

Figure2.18:(a)TetrahedralbondingofSiatom.(b)leadsto1/4ofthecubicunitcell 

Thediamondunitcellisthebasiccrystalbuildingblock. Figure2.19showsfouratoms 

(dark)bondedtofourotherswithinthevolumeofthecell. Thisisequivalenttoplacingone 

ofFigure2.18(b)attheorigininFigure2.19,thenplacingthreemoreonadjacentfacestofill 

thefullcube. Sixatomsfallonthemiddleofeachofthesixcubefaces,showingtwobonds. 

Theothertwobondstoadjacentcubeswereomittedforclarity.Outofeightcubecorners,four 

atomsbondtoanatomwithinthecube. Wherearetheotherfouratomsbonded? Theother 

fourbondtoadjacentcubesofthecrystal.Keepinmindthateventhoughfourcorneratoms 

shownobondsinthecube,allatomswithinthecrystalarebondedinonegiantmolecule. A 

semiconductorcrystalisbuiltupfromcopiesofthisunitcell. 

Thecrystaliseffectivelyonemolecule.Anatomcovalentbondstofourothers,whichinturn 

bondtofourothers,andsoon.Thecrystallatticeisrelativelystiffresistingdeformation.Few 

electronsfreethemselvesforconductionaboutthecrystal.Apropertyofsemiconductorsisthat 

onceanelectronisfreed,apositivelychargedemptyspacedevelopswhichalsocontributesto 

conduction. 

• REVIEW 

• Atomstrytoformacompleteouter,valence,shellof8-electrons(2-electronsfortheinnermostshell).Atomsmaydonateafewelectronstoexposeanunderlyingshellof8,accept 

afewelectronstocompleteashell,orshareelectronstocompleteashell. 

• Atomsoftenformorderedarraysofionsoratomsinarigidstructureknownasacrystal. 

• Aneutralatommayformapositiveionbydonatinganelectron. 

• Aneutralatommayformanegativeionbyacceptinganelectron 

• ThegroupIVAsemiconductors:C,Si,Gecrystallizeintoadiamondstructure.Eachatom 

inthecrystalispartofagiantmolecule,bondingtofourotheratoms.

2.4. BANDTHEORYOFSOLIDS 47 

Face centered atoms 

Atom bonded to 4 others 

Other atoms bonded to 

chain in cube 

Atoms bonded outside of 

cube 

Figure2.19:Si,Ge,andC(diamond)forminterleavedfacecenteredcube. 

• Mostsemiconductordevicesaremanufacturedfromsinglecrystals. 

2.4 Bandtheoryofsolids 

Quantumphysicsdescribesthestatesofelectronsinanatomaccordingtothefour-foldscheme 

ofquantumnumbers. Thequantumnumbersdescribetheallowablestateselectronsmayassumeinanatom. 

Tousetheanalogyofanamphitheater,quantumnumbersdescribehow 

manyrowsandseatsareavailable.Individualelectronsmaybedescribedbythecombination 

ofquantumnumbers,likeaspectatorinanamphitheaterassignedtoaparticularrowand 

seat. 

Likespectatorsinanamphitheatermovingbetweenseatsandrows,electronsmaychange 

theirstatuses,giventhepresenceofavailablespacesforthemtofit,andavailableenergy. 

Sinceshellleveliscloselyrelatedtotheamountofenergythatanelectronpossesses,“leaps” 

betweenshell(andevensubshell)levelsrequirestransfersofenergy.Ifanelectronistomove 

intoahigher-ordershell,itrequiresthatadditionalenergybegiventotheelectronfroman 

externalsource.Usingtheamphitheateranalogy,ittakesanincreaseinenergyforaperson 

tomoveintoahigherrowofseats,becausethatpersonmustclimbtoagreaterheightagainst 

theforceofgravity. Conversely,anelectron“leaping”intoalowershellgivesupsomeofits 

energy,likeapersonjumpingdownintoalowerrowofseats,theexpendedenergymanifesting 

asheatandsound. 

Notall“leaps”areequal.Leapsbetweendifferentshellsrequireasubstantialexchangeof 

energy,butleapsbetweensubshellsorbetweenorbitalsrequirelesserexchanges.


Whenatomscombinetoformsubstances, theoutermostshells, subshells, andorbitals 

merge,providingagreaternumberofavailableenergylevelsforelectronstoassume. When 

largenumbersofatomsareclosetoeachother,theseavailableenergylevelsformanearly 

continuousbandwhereinelectronsmaymoveasillustratedinFigure2.20 

Significant leap required 

for an electron to move 

to the next higher level 

3p 

3s 

Single atom 

Shorter leap 

required 

3p 

3s 

Five atoms 

in close proximity 

Overlap permits 

electrons to freely 

drift between bands 

3p 

Overlap 

3s 

Multitudes of atoms 


Figure2.20:Electronbandoverlapinmetallicelements. 

Itisthewidthofthesebandsandtheirproximitytoexistingelectronsthatdetermines 

howmobilethoseelectronswillbewhenexposedtoanelectricfield. Inmetallicsubstances, 

emptybandsoverlapwithbandscontainingelectrons,meaningthatelectronsofasingleatom 

maymovetowhatwouldnormallybeahigher-levelstatewithlittleornoadditionalenergy 

imparted.Thus,theouterelectronsaresaidtobe“free,”andreadytomoveatthebeckoning 

ofanelectricfield. 

Bandoverlapwillnotoccurinallsubstances,nomatterhowmanyatomsareclosetoeach 

other. Insomesubstances,asubstantialgapremainsbetweenthehighestbandcontaining 

electrons(theso-calledvalenceband)andthenextband,whichisempty(theso-calledconductionband). 

SeeFigure2.21. Asaresult,valenceelectronsare“bound”totheirconstituent 

atomsandcannotbecomemobilewithinthesubstancewithoutasignificantamountofimpartedenergy.Thesesubstancesareelectricalinsulators. 

Materialsthatfallwithinthecategoryofsemiconductorshaveanarrowgapbetweenthe 

valenceandconductionbands. Thus,theamountofenergyrequiredtomotivateavalence 

electronintotheconductionbandwhereitbecomesmobileisquitemodest.(Figure2.22) 

Atlowtemperatures,littlethermalenergyisavailabletopushvalenceelectronsacross 

thisgap,andthesemiconductingmaterialactsmoreasaninsulator.Athighertemperatures, 

though,theambientthermalenergybecomesenoughtoforceelectronsacrossthegap,andthe 

materialwillincreaseconductionofelectricity. 

Itisdifficulttopredicttheconductivepropertiesofasubstancebyexaminingtheelectron 

configurationsofitsconstituentatoms. Althoughthebestmetallicconductorsofelectricity 

(silver,copper,andgold)allhaveouterssubshellswithasingleelectron,therelationship 

betweenconductivityandvalenceelectroncountisnotnecessarilyconsistent:

2.4. BANDTHEORYOFSOLIDS 49 

Significant leap required 

for an electron to enter 

the conduction band and 

travel through the material 

Multitudes of atoms 


Conduction band 

"Energy gap" 

Valence band 

Figure2.21:Electronbandseparationininsulatingsubstances. 

Small leap required 

for an electron to enter 

the conduction band and 

travel through the material 

semiconducting substance 

metalic substance for reference 

(a) 

Conduction band 

"Energy gap" 

Valence band 

(b) 

Insignificant leap 

for electron to 

enter conduction 

band 

Figure2.22:Electronbandseparationinsemiconductingsubstances,(a)multitudesofsemiconductingcloseatomsstillresultsinasignificantbandgap,(b)multitudesofclosemetal 

atomsforreference.


Element 

Silver (Ag) 

Specific resistance 

(ρ) at 20 o Electron 

Celsius configuration 

9.546 Ω⋅cmil/ft 4d 10 5s 1 

Copper (Cu) 10.09 Ω⋅cmil/ft 3d 10 4s 1 

Gold (Au) 13.32 Ω⋅cmil/ft 5d 10 6s 1 

Aluminum (Al) 15.94 Ω⋅cmil/ft 3p 1 

Tungsten (W) 31.76 Ω⋅cmil/ft 5d 4 6s 2 

Element 

Specific resistance 

(ρ) at 20 o Electron 

Celsius configuration 

Molybdenum (Mo) 32.12 Ω⋅cmil/ft 4d 5 5s 1 

Zinc (Zn) 35.49 Ω⋅cmil/ft 3d 10 4s 2 

Nickel (Ni) 41.69 Ω⋅cmil/ft 3d 8 4s 2 

Iron (Fe) 57.81 Ω⋅cmil/ft 3d 6 4s 2 

Platinum (Pt) 63.16 Ω⋅cmil/ft 5d 9 6s 1 

Theelectronbandconfigurationsproducedbycompoundsofdifferentelementsdefieseasy 

associationwiththeelectronconfigurationsofitsconstituentelements. 

• REVIEW: 

• Energyisrequiredtoremoveanelectronfromthevalencebandtoahigherunoccupied 

band,aconductionband.Moreenergyisrequiredtomovebetweenshells,lessbetween 

subshells. 

• Sincethevalenceandconductionbandsoverlapinmetals,littleenergyremovesanelectron.Metalsareexcellentconductors. 

• Thelargegapbetweenthevalenceandconductionbandsofaninsulatorrequireshigh 

energytoremoveanelectron.Thus,insulatorsdonotconduct. 

• Semiconductorshaveasmallnon-overlappinggapbetweenthevalenceandconduction 

bands.Puresemiconductorsareneithergoodinsulatorsnorconductors.Semiconductors 

aresemi-conductive. 

2.5 Electronsand“holes” 

Puresemiconductorsarerelativelygoodinsulatorsascomparedwithmetals,thoughnotnearly 

asgoodasatrueinsulatorlikeglass.Tobeusefulinsemiconductorapplications,theintrinsic 

semiconductor(pureundopedsemiconductor)musthavenomorethanoneimpurityatomin 

10billionsemiconductoratoms. Thisisanalogoustoagrainofsaltimpurityinarailroad 

boxcarofsugar.Impure,ordirtysemiconductorsareconsiderablymoreconductive,thoughnot 

asgoodasmetals.Whymightthisbe?Toanswerthatquestion,wemustlookattheelectron 

structureofsuchmaterialsinFigure2.23. 

Figure2.23(a)showsfourelectronsinthevalenceshellofasemiconductorformingcovalent 

bondstofourotheratoms. Thisisaflattened,easiertodraw,versionofFigure2.19. All 

electronsofanatomaretiedupinfourcovalentbonds,pairsofsharedelectrons.Electronsare 

notfreetomoveaboutthecrystallattice.Thus,intrinsic,pure,semiconductorsarerelatively 

goodinsulatorsascomparedtometals. 

ThermalenergymayoccasionallyfreeanelectronfromthecrystallatticeasinFigure2.23 

(b).Thiselectronisfreeforconductionaboutthecrystallattice.Whentheelectronwasfreed, 

itleftanemptyspotwithapositivechargeinthecrystallatticeknownasahole.Thisholeis 

notfixedtothelattice;but,isfreetomoveabout.Thefreeelectronandholebothcontribute

2.5. ELECTRONSAND“HOLES” 51 

(a) 

hole electron 

(b) 

Figure2.23:(a)Intrinsicsemiconductorisaninsulatorhavingacompleteelectronshell. (b) 

However,thermalenergycancreatefewelectronholepairsresultinginweakconduction. 

toconductionaboutthecrystallattice. Thatis,theelectronisfreeuntilitfallsintoahole. 

Thisiscalledrecombination. Ifanexternalelectricfieldisappliedtothesemiconductor,the 

electronsandholeswillconductinoppositedirections. Increasingtemperaturewillincrease 

thenumberofelectronsandholes,decreasingtheresistance.Thisisoppositeofmetals,where 

resistanceincreaseswithtemperaturebyincreasingthecollisionsofelectronswiththecrystal 

lattice.Thenumberofelectronsandholesinanintrinsicsemiconductorareequal.However, 

bothcarriersdonotnecessarilymovewiththesamevelocitywiththeapplicationofanexternal 

field.Anotherwayofstatingthisisthatthemobilityisnotthesameforelectronsandholes. 

Puresemiconductors,bythemselves,arenotparticularlyuseful.Though,semiconductors 

mustberefinedtoahighlevelofpurityasastartingpointpriortheadditionofspecificimpurities. 

Semiconductormaterialpureto1partin10billion,mayhavespecificimpuritiesadded 

atapproximately1partper10milliontoincreasethenumberofcarriers. Theadditionofa 

desiredimpuritytoasemiconductorisknownasdoping.Dopingincreasestheconductivityof 

asemiconductorsothatitismorecomparabletoametalthananinsulator. 

Itispossibletoincreasethenumberofnegativechargecarrierswithinthesemiconductor 

crystallatticebydopingwithanelectrondonorlikePhosphorus.Electrondonors,alsoknown 

asN-typedopantsincludeelementsfromgroupVAoftheperiodictable:nitrogen,phosphorus, 

arsenic,andantimony.NitrogenandphosphorusareN-typedopantsfordiamond.Phosphorus, 

arsenic,andantimonyareusedwithsilicon. 

ThecrystallatticeinFigure2.24(b)containsatomshavingfourelectronsintheouter 

shell,formingfourcovalentbondstoadjacentatoms. Thisistheanticipatedcrystallattice. 

Theadditionofaphosphorusatomwithfiveelectronsintheoutershellintroducesanextra 

electronintothelatticeascomparedwiththesiliconatom. Thepentavalentimpurityforms 

fourcovalentbondstofoursiliconatomswithfourofthefiveelectrons,fittingintothelattice 

withoneelectronleftover.Notethatthisspareelectronisnotstronglybondedtothelatticeas 

theelectronsofnormalSiatomsare.Itisfreetomoveaboutthecrystallattice,notbeingbound 

tothePhosphoruslatticesite.Sincewehavedopedatonepartphosphorusin10millionsilicon 

atoms,fewfreeelectronswerecreatedcomparedwiththenumeroussiliconatoms.However, 

manyelectronswerecreatedcomparedwiththefewerelectron-holepairsinintrinsicsilicon. 

Applicationofanexternalelectricfieldproducesstrongconductioninthedopedsemiconductor 

intheconductionband(abovethevalenceband). Aheavierdopinglevelproducesstronger


conduction.Thus,apoorlyconductingintrinsicsemiconductorhasbeenconvertedintoagood 

electricalconductor. 

(a) 

P 

Si 

B 

(b) 

Si Si Si Si 

Si Si Si Si 

Si 

Si 

P 

Si Si 

Si Si Si 

electron 

Si 

B 

Si Si 

(c) 

Si Si Si Si 

hole 

hole movement 

electron 

movement 

Figure2.24: (a)OutershellelectronconfigurationofdonorN-typePhosphorus,Silicon(for 

reference),andacceptorP-typeBoron. (b)N-typedonorimpuritycreatesfreeelectron(c)Ptypeacceptorimpuritycreateshole,apositivechargecarrier. 

Itisalsopossibletointroduceanimpuritylackinganelectronascomparedwithsilicon, 

havingthreeelectronsinthevalenceshellascomparedwithfourforsilicon. InFigure2.24 

(c),thisleavesanemptyspotknownasahole,apositivechargecarrier.Theboronatomtries 

tobondtofoursiliconatoms,butonlyhasthreeelectronsinthevalenceband.Inattempting 

toformfourcovalentbondsthethreeelectronsmovearoundtryingtoformfourbonds. This 

makestheholeappeartomove.Furthermore,thetrivalentatommayborrowanelectronfrom 

anadjacent(ormoredistant)siliconatomtoformfourcovalentbonds. However,thisleaves 

thesiliconatomdeficientbyoneelectron.Inotherwords,theholehasmovedtoanadjacent(or 

moredistant)siliconatom.Holesresideinthevalenceband,alevelbelowtheconductionband. 

Dopingwithanelectronacceptor,anatomwhichmayacceptanelectron,createsadeficiencyof 

electrons,thesameasanexcessofholes.Sinceholesarepositivechargecarriers,anelectron 

acceptordopantisalsoknownasaP-typedopant.TheP-typedopantleavesthesemiconductor 

withanexcessofholes,positivechargecarriers. TheP-typeelementsfromgroupIIIAofthe 

periodictableinclude: boron,aluminum,gallium,andindium. BoronisusedasaP-type 

dopantforsiliconanddiamondsemiconductors,whileindiumisusedwithgermanium. 

The“marbleinatube”analogytoelectronconductioninFigure2.25relatesthemovement 

ofholeswiththemovementofelectrons. Themarblerepresentelectronsinaconductor,the 

tube. ThemovementofelectronsfromlefttorightasinawireorN-typesemiconductoris 

explainedbyanelectronenteringthetubeattheleftforcingtheexitofanelectronatthe 

right. ConductionofN-typeelectronsoccursintheconductionband. Comparethatwiththe 

movementofaholeinthevalenceband. 

ForaholetoenterattheleftofFigure2.25(b),anelectronmustberemoved.Whenmoving 

aholelefttoright,theelectronmustbemovedrighttoleft.Thefirstelectronisejectedfrom 

theleftendofthetubesothattheholemaymovetotherightintothetube. Theelectronis 

movingintheoppositedirectionofthepositivehole. Astheholemovesfarthertotheright, 

electronsmustmovelefttoaccommodatethehole. Theholeistheabsenceofanelectronin 

thevalencebandduetoP-typedoping.Ithasalocalizedpositivecharge.Tomovetheholein 

agivendirection,thevalenceelectronsmoveintheoppositedirection. 

ElectronflowinanN-typesemiconductorissimilartoelectronsmovinginametallicwire.

2.5. ELECTRONSAND“HOLES” 53 

(a) 

electron movement 

(b) 

hole movement 

electron movement 

Figure2.25: Marbleinatubeanalogy: (a)Electronsmoverightintheconductionbandas 

electronsentertube.(b)Holemovesrightinthevalencebandaselectronsmoveleft. 

TheN-typedopantatomswillyieldelectronsavailableforconduction. Theseelectrons,due 

tothedopantareknownasmajoritycarriers,fortheyareinthemajorityascomparedtothe 

veryfewthermalholes. IfanelectricfieldisappliedacrosstheN-typesemiconductorbarin 

Figure2.26(a),electronsenterthenegative(left)endofthebar,traversethecrystallattice, 

andexitatrighttothe(+)batteryterminal. 

electron enters electron exits 

(a) N-type 

crystal lattice 

(b) P-type 

Figure2.26:(a)N-typesemiconductorwithelectronsmovinglefttorightthroughthecrystal 

lattice.(b)P-typesemiconductorwithholesmovinglefttoright,whichcorrespondstoelectrons 

movingintheoppositedirection. 

CurrentflowinaP-typesemiconductorisalittlemoredifficulttoexplain. TheP-type 

dopant,anelectronacceptor,yieldslocalizedregionsofpositivechargeknownasholes. The 

majoritycarrierinaP-typesemiconductoristhehole.Whileholesformatthetrivalentdopant 

atomsites,theymaymoveaboutthesemiconductorbar.NotethatthebatteryinFigure2.26 

(b)isreversedfrom(a).ThepositivebatteryterminalisconnectedtotheleftendoftheP-type 

bar.Electronflowisoutofthenegativebatteryterminal,throughtheP-typebar,returningto 

thepositivebatteryterminal.Anelectronleavingthepositive(left)endofthesemiconductor 

barforthepositivebatteryterminalleavesaholeinthesemiconductor,thatmaymovetothe 

right. Holestraversethecrystallatticefromlefttoright. Atthenegativeendofthebaran 

electronfromthebatterycombineswithahole,neutralizingit.Thismakesroomforanother 

holetomoveinatthepositiveendofthebartowardtheright.Keepinmindthatasholesmove 

lefttoright,thatitisactuallyelectronsmovingintheoppositedirectionthatisresponsiblefor 

theapparantholemovement.


TheelementsusedtoproducesemiconductorsaresummarizedinFigure2.27. TheoldestgroupIVAbulksemiconductormaterialgermaniumisonlyusedtoalimitedextenttoday.Siliconbasedsemiconductorsaccountforabout90%ofcommercialproductionofallsemiconductors.Diamondbasedsemiconductorsarearesearchanddevelopmentactivitywithconsiderablepotentialatthistime.Compoundsemiconductorsnotlistedincludesilicongermanium 

(thinlayersonSiwafers),siliconcarbideandIII-Vcompoundssuchasgalliumarsenide.III- 

VIcompoundsemiconductorsinclude:AlN,GaN,InN,AlP,AlAs,AlSb,GaP,GaAs,GaSb,InP, 

InAs,InSb,AlxGa1−xAsandInxGa1−xAs. ColumnsIIandVIofperiodictable,notshownin 

thefigure,alsoformcompoundsemiconductors. 

Elemental semiconductors 

C(diamond), Si, Ge 

B 

P-type dopant for C 

B, Al, Ga, In 

P-type dopant for Si 

Al, Ga, In 

P-type dopant for Ge 

13 IIIA 14 IVA 15 VA 

B 5 

Boron 

10.81 

2p 1 

Al 13 

Aluminum 

26.9815 

3p 1 

Ga 31 Ge 32 As 33 

Gallium Germanium Arsenic 

69.723 72.61 74.92159 

4p 1 

In 49 

Indium 

114.82 

5p 1 

C 6 

Carbon 

12.011 

2p 2 

Si 14 

Silicon 

28.0855 

3p 2 

4p 2 

N 7 

Nitrogen 

14.0067 

2p 3 

P 15 

Phosphorus 

30.9738 

3p 3 

4p 3 

Sb 51 

Antimony 

121.75 

5p 3 

N, P 

N-type dopant for C 

P, As, Sb 

N-type dopant for Si, Ge 

Figure2.27:GroupIIIAP-typedopants,groupIVbasicsemiconductormaterials,andgroup 

VAN-typedopants. 

ThemainreasonfortheinclusionoftheIIIAandVAgroupsinFigure2.27istoshowthe 

dopantsusedwiththegroupIVAsemiconductors.GroupIIIAelementsareacceptors,P-type 

dopants,whichacceptelectronsleavingaholeinthecrystallattice,apositivecarrier.Boron 

istheP-typedopantfordiamond,andthemostcommondopantforsiliconsemiconductors. 

IndiumistheP-typedopantforgermanium. 

GroupVAelementsaredonors,N-typedopants,yieldingafreeelectron. Nitrogenand 

PhosphorusaresuitableN-typedopantsfordiamond. Phosphorusandarsenicarethemost 

commonlyusedN-typedopantsforsilicon;though,antimonycanbeused. 

• REVIEW: 

• Intrinsicsemiconductormaterials,pureto1partin10billion,arepoorconductors. 

• N-typesemiconductorisdopedwithapentavalentimpuritytocreatefreeelectrons.Such 

amaterialisconductive.Theelectronisthemajoritycarrier. 

• P-typesemiconductor,dopedwithatrivalentimpurity,hasanabundanceoffreeholes. 

Thesearepositivechargecarriers. TheP-typematerialisconductive. Theholeisthe 

majoritycarrier.

2.6. THEP-NJUNCTION 55 

• MostsemiconductorsarebasedonelementsfromgroupIVAoftheperiodictable,silicon 

beingthemostprevalent. Germaniumisallbutobsolete. Carbon(diamond)isbeing 

developed. 

• Compoundsemiconductorssuchassiliconcarbide(groupIVA)andgalliumarsenide(group 

III-V)arewidelyused. 

2.6 TheP-Njunction 

IfablockofP-typesemiconductorisplacedincontactwithablockofN-typesemiconductorin 

Figure2.28(a),theresultisofnovalue. Wehavetwoconductiveblocksincontactwitheach 

other,showingnouniqueproperties.Theproblemistwoseparateanddistinctcrystalbodies. 

Thenumberofelectronsisbalancedbythenumberofprotonsinbothblocks. Thus,neither 

blockhasanynetcharge. 

However,asinglesemiconductorcrystalmanufacturedwithP-typematerialatoneendand 

N-typematerialattheotherinFigure2.28(b)hassomeuniqueproperties.TheP-typematerial 

haspositivemajoritychargecarriers,holes,whicharefreetomoveaboutthecrystallattice. 

TheN-typematerialhasmobilenegativemajoritycarriers,electrons. Nearthejunction,the 

N-typematerialelectronsdiffuseacrossthejunction,combiningwithholesinP-typematerial. 

TheregionoftheP-typematerialnearthejunctiontakesonanetnegativechargebecause 

oftheelectronsattracted. SinceelectronsdepartedtheN-typeregion,ittakesonalocalized 

positivecharge.Thethinlayerofthecrystallatticebetweenthesechargeshasbeendepleted 

ofmajoritycarriers,thus,isknownasthedepletionregion.Itbecomesnonconductiveintrinsic 

semiconductormaterial. Ineffect,wehavenearlyaninsulatorseparatingtheconductiveP 

andNdopedregions. 

N 

electron 

(a) 

P 

crystal lattice 

hole 

(b) 

no charge 

separation 

N P 

intrinsic 

charge 

separation 

Figure2.28:(a)BlocksofPandNsemiconductorincontacthavenoexploitableproperties.(b) 

SinglecrystaldopedwithPandNtypeimpuritiesdevelopsapotentialbarrier. 

ThisseparationofchargesatthePNjunctionconstitutesapotentialbarrier.Thispotential 

barriermustbeovercomebyanexternalvoltagesourcetomakethejunctionconduct. The 

formationofthejunctionandpotentialbarrierhappensduringthemanufacturingprocess. 

Themagnitudeofthepotentialbarrierisafunctionofthematerialsusedinmanufacturing. 

SiliconPNjunctionshaveahigherpotentialbarrierthangermaniumjunctions.


InFigure2.29(a)thebatteryisarrangedsothatthenegativeterminalsupplieselectrons 

totheN-typematerial. Theseelectronsdiffusetowardthejunction. Thepositiveterminal 

removeselectronsfromtheP-typesemiconductor,creatingholesthatdiffusetowardthejunction. 

Ifthebatteryvoltageisgreatenoughtoovercomethejunctionpotential(0.6VinSi), 

theN-typeelectronsandP-holescombineannihilatingeachother.Thisfreesupspacewithin 

thelatticeformorecarrierstoflowtowardthejunction.Thus,currentsofN-typeandP-type 

majoritycarriersflowtowardthejunction.Therecombinationatthejunctionallowsabattery 

currenttoflowthroughthePNjunctiondiode.Suchajunctionissaidtobeforwardbiased. 

depletion region 

electrons holes electrons holes 

N P 

N 

P 

(a) Forward (b) Reverse 

Figure2.29: (a)Forwardbatterybiasrepelscarrierstowardjunction,whererecombination 

resultsinbatterycurrent.(b)Reversebatterybiasattractscarrierstowardbatteryterminals, 

awayfromjunction.Depletionregionthicknessincreases.Nosustainedbatterycurrentflows. 

IfthebatterypolarityisreversedasinFigure2.29(b)majoritycarriersareattractedaway 

fromthejunctiontowardthebatteryterminals.ThepositivebatteryterminalattractsN-type 

majoritycarriers,electrons,awayfromthejunction. ThenegativeterminalattractsP-type 

majoritycarriers,holes,awayfromthejunction. Thisincreasesthethicknessofthenonconductingdepletionregion.Thereisnorecombinationofmajoritycarriers;thus,noconduction. 

Thisarrangementofbatterypolarityiscalledreversebias. 

ThediodeschematicsymbolisillustratedinFigure2.30(b)correspondingtothedoped 

semiconductorbarat(a).Thediodeisaunidirectionaldevice.Electroncurrentonlyflowsin 

onedirection,againstthearrow,correspondingtoforwardbias.Thecathode,bar,ofthediode 

symbolcorrespondstoN-typesemiconductor. Theanode,arrow,correspondstotheP-type 

semiconductor. Torememberthisrelationship,Not-pointing(bar)onthesymbolcorresponds 

toN-typesemiconductor.Pointing(arrow)correspondstoP-type. 

IfadiodeisforwardbiasedasinFigure2.30(a),currentwillincreaseslightlyasvoltageis 

increasedfrom0V.Inthecaseofasilicondiodeameasurablecurrentflowswhenthevoltage 

approaches0.6VinFigure2.30(c).Asthevoltageincreasespast0.6V,currentincreasesconsiderablyaftertheknee.Increasingthevoltagewellbeyond0.7Vmayresultinhighenough 

currenttodestroythediode.Theforwardvoltage,VF,isacharacteristicofthesemiconductor: 

0.6to0.7Vforsilicon,0.2Vforgermanium,afewvoltsforLightEmittingDiodes(LED). 

TheforwardcurrentrangesfromafewmAforpointcontactdiodesto100mAforsmallsignal 

diodestotensorthousandsofamperesforpowerdiodes. 

Ifthediodeisreversebiased,onlytheleakagecurrentoftheintrinsicsemiconductorflows. 

ThisisplottedtotheleftoftheorigininFigure2.30(c). Thiscurrentwillonlybeashighas 

1 µAforthemostextremeconditionsforsiliconsmallsignaldiodes. Thiscurrentdoesnot

2.6. THEP-NJUNCTION 57 

(a) 

electrons holes 

N 

N-type 

(not pointing) 

P-type 

(pointing) 

(b) cathode anode 

P 

(c) 

reverse bias 

breakdown 

I 

mA 

µA 

forward 

bias V 

0.7 

Figure2.30: (a)ForwardbiasedPNjunction,(b)Correspondingdiodeschematicsymbol(c) 

SiliconDiodeIvsVcharacteristiccurve. 

increaseappreciablywithincreasingreversebiasuntilthediodebreaksdown.Atbreakdown, 

thecurrentincreasessogreatlythatthediodewillbedestroyedunlessahighseriesresistance 

limitscurrent. Wenormallyselectadiodewithahigherreversevoltageratingthananyappliedvoltagetopreventthis. 

Silicondiodesaretypicallyavailablewithreversebreakdown 

ratingsof50,100,200,400,800Vandhigher. Itispossibletofabricatediodeswithalower 

ratingofafewvoltsforuseasvoltagestandards. 

WepreviouslymentionedthatthereverseleakagecurrentofunderaµAforsilicondiodes 

wasduetoconductionoftheintrinsicsemiconductor.Thisistheleakagethatcanbeexplained 

bytheory. Thermalenergyproducesfewelectronholepairs,whichconductleakagecurrent 

untilrecombination.Inactualpracticethispredictablecurrentisonlypartoftheleakagecurrent.Muchoftheleakagecurrentisduetosurfaceconduction,relatedtothelackofcleanlinessofthesemiconductorsurface.Bothleakagecurrentsincreasewithincreasingtemperature,approachingaµAforsmallsilicondiodes.Forgermanium,theleakagecurrentisordersofmagnitudehigher.Sincegermaniumsemiconductorsarerarelyusedtoday,thisisnotaprobleminpractice. 

• REVIEW: 

• PNjunctionsarefabricatedfromamonocrystallinepieceofsemiconductorwithbotha 

P-typeandN-typeregioninproximityatajunction. 

• ThetransferofelectronsfromtheNsideofthejunctiontoholesannihilatedonthePside 

ofthejunctionproducesabarriervoltage.Thisis0.6to0.7Vinsilicon,andvarieswith 

othersemiconductors. 

• AforwardbiasedPNjunctionconductsacurrentoncethebarriervoltageisovercome. 

Theexternalappliedpotentialforcesmajoritycarrierstowardthejunctionwhererecombinationtakesplace,allowingcurrentflow.


• AreversebiasedPNjunctionconductsalmostnocurrent. Theappliedreversebiasattractsmajoritycarriersawayfromthejunction.Thisincreasesthethicknessofthenonconductingdepletionregion. 

• ReversebiasedPNjunctionsshowatemperaturedependentreverseleakagecurrent. 

ThisislessthanaµAinsmallsilicondiodes. 

2.7 Junctiondiodes 

Thereweresomehistoriccrude,butusablesemiconductorrectifiersbeforehighpuritymaterialswereavailable.FerdinandBrauninventedaleadsulfide,PbS,basedpointcontactrectifier 

in1874. Cuprousoxiderectifierswereusedaspowerrectifiersin1924. Theforwardvoltage 

dropis0.2V.ThelinearcharacteristiccurveperhapsiswhyCu2Owasusedasarectifierfor 

theACscaleonD’Arsonvalbasedmultimeters.Thisdiodeisalsophotosensitive. 

Seleniumoxiderectifierswereusedbeforemodernpowerdioderectifiersbecameavailable. 

TheseandtheCu2Orectifierswerepolycrystallinedevices.Photoelectriccellswereoncemade 

fromSelenium. 

Beforethemodernsemiconductorera,anearlydiodeapplicationwasasaradiofrequency 

detector,whichrecoveredaudiofromaradiosignal.The“semiconductor”wasapolycrystalline 

pieceofthemineralgalena,leadsulfide,PbS.Apointedmetallicwireknownasacatwhisker 

wasbroughtincontactwithaspotonacrystalwithinthepolycrystallinemineral.(Figure2.31) 

Theoperatorlaboredtofinda“sensitive”spotonthegalenabymovingthecatwhiskerabout. 

PresumablytherewerePandN-typespotsrandomlydistributedthroughoutthecrystaldue 

tothevariabilityofuncontrolledimpurities. Lessoftenthemineralironpyrites,foolsgold, 

wasused,aswasthemineralcarborundum,siliconcarbide,SiC,anotherdetector,partofa 

foxholeradio,consistedofasharpenedpencilleadboundtoabentsafetypin,touchingarusty 

blue-bladedisposablerazorblade.Theseallrequiredsearchingforasensitivespot,easilylost 

becauseofvibration. 

ReplacingthemineralwithanN-dopedsemiconductor(Figure2.32(a))makesthewhole 

surfacesensitive,sothatsearchingforasensitivespotwasnolongerrequired.Thisdevicewas 

perfectedbyG.W.Pickardin1906.ThepointedmetalcontactproducedalocalizedP-typeregion 

withinthesemiconductor.Themetalpointwasfixedinplace,andthewholepointcontactdiode 

encapsulatedinacylindricalbodyformechanicalandelectricalstability.(Figure2.32(d))Note 

thatthecathodebarontheschematiccorrespondstothebaronthephysicalpackage. 

SiliconpointcontactdiodesmadeanimportantcontributiontoradarinWorldWarII,detectinggiga-hertzradiofrequencyechosignalsintheradarreceiver.Theconcepttobemade 

clearisthatthepointcontactdiodeprecededthejunctiondiodeandmodernsemiconductors 

byseveraldecades.Eventothisday,thepointcontactdiodeisapracticalmeansofmicrowave 

frequencydetectionbecauseofitslowcapacitance.Germaniumpointcontactdiodeswereonce 

morereadilyavailablethantheyaretoday,beingpreferredforthelower0.2Vforwardvoltage 

insomeapplicationslikeself-poweredcrystalradios.Pointcontactdiodes,thoughsensitiveto 

awidebandwidth,havealowcurrentcapabilitycomparedwithjunctiondiodes. 

Mostdiodestodayaresiliconjunctiondiodes. Thecross-sectioninFigure2.32(b)looksa 

bitmorecomplexthanasimplePNjunction;though,itisstillaPNjunction.Startingatthe 

cathodeconnection,theN + indicatesthisregionisheavilydoped,havingnothingtodowith

2.7. JUNCTIONDIODES 59 

Anode 

P + 

N 

Figure2.31:Crystaldetector 

Anode 

Anode 

Cathode 

(a) (b) (c) (d) 

Cathode 

Cathode 

Figure2.32:Silicondiodecross-section:(a)pointcontactdiode,(b)junctiondiode,(c)schematic 

symbol,(d)smallsignaldiodepackage. 

P + 

N - 

N +


polarity. Thisreducestheseriesresistanceofthediode. TheN − regionislightlydopedas 

indicatedbythe(-).Lightdopingproducesadiodewithahigherreversebreakdownvoltage, 

importantforhighvoltagepowerrectifierdiodes.Lowervoltagediodes,evenlowvoltagepower 

rectifiers,wouldhavelowerforwardlosseswithheavierdoping. Theheaviestlevelofdoping 

producezenerdiodesdesignedforalowreversebreakdownvoltage. However,heavydoping 

increasesthereverseleakagecurrent. TheP + regionattheanodecontactisheavilydoped 

P-typesemiconductor,agoodcontactstrategy.Glassencapsulatedsmallsignaljunctiondiodes 

arecapableof10’sto100’sofmAofcurrent. Plasticorceramicencapsulatedpowerrectifier 

diodeshandleto1000’sofamperesofcurrent. 

• REVIEW: 

• Pointcontactdiodeshavesuperbhighfrequencycharacteristics,usablewellintothemicrowavefrequencies. 

• Junctiondiodesrangeinsizefromsmallsignaldiodestopowerrectifierscapableof1000’s 

ofamperes. 

• Thelevelofdopingnearthejunctiondeterminesthereversebreakdownvoltage. Light 

dopingproducesahighvoltagediode.Heavydopingproducesalowerbreakdownvoltage, 

andincreasesreverseleakagecurrent. Zenerdiodeshavealowerbreakdownvoltage 

becauseofheavydoping. 

2.8 Bipolarjunctiontransistors 

Thebipolarjunctiontransistor(BJT)wasnamedbecauseitsoperationinvolvesconductionby 

twocarriers:electronsandholesinthesamecrystal.Thefirstbipolartransistorwasinvented 

atBellLabsbyWilliamShockley,WalterBrattain,andJohnBardeensolatein1947thatit 

wasnotpublisheduntil1948. Thus,manytextsdifferastothedateofinvention. Brattain 

fabricatedagermaniumpointcontacttransistor,bearingsomeresemblancetoapointcontact 

diode.Withinamonth,Shockleyhadamorepracticaljunctiontransistor,whichwedescribein 

followingparagraphs.TheywereawardedtheNobelPrizeinPhysicsin1956forthetransistor. 

ThebipolarjunctiontransistorshowninFigure2.33(a)isanNPNthreelayersemiconductorsandwichwithanemitterandcollectorattheends,andabaseinbetween.Itisasifathird 

layerwereaddedtoatwolayerdiode. Ifthisweretheonlyrequirement,wewouldhaveno 

morethanapairofback-to-backdiodes.Infact,itisfareasiertobuildapairofback-to-back 

diodes.Thekeytothefabricationofabipolarjunctiontransistoristomakethemiddlelayer, 

thebase,asthinaspossiblewithoutshortingtheoutsidelayers,theemitterandcollector.We 

cannotoveremphasizetheimportanceofthethinbaseregion. 

ThedeviceinFigure2.33(a)hasapairofjunctions,emittertobaseandbasetocollector, 

andtwodepletionregions. 

Itiscustomarytoreversebiasthebase-collectorjunctionofabipolarjunctiontransistor 

asshownin(Figure2.33(b). Notethatthisincreasesthewidthofthedepletionregion. The 

reversebiasvoltagecouldbeafewvoltstotensofvoltsformosttransistors.Thereisnocurrent 

flow,exceptleakagecurrent,inthecollectorcircuit.

2.8. BIPOLARJUNCTIONTRANSISTORS 61 

N +- P - + 

N 

+- - + 

+- - + 

+- - + 

+- - + 

+- - + 

+- - + 

+- - + 

(a) B 

(b) 

N +- P- 

+ 

N 

+- - + 

+- - + 

+- - + 

+- - + 

+- - + 

+- - + 

+- - + 

emitter base collector emitter base collector 

E 

C E 

B 

C 

- + 

- + 

Figure2.33:(a)NPNjunctionbipolartransistor.(b)Applyreversebiastocollectorbasejunction. 

InFigure2.34(a),avoltagesourcehasbeenaddedtotheemitterbasecircuit.Normallywe 

forwardbiastheemitter-basejunction,overcomingthe0.6Vpotentialbarrier.Thisissimilar 

toforwardbiasingajunctiondiode. Thisvoltagesourceneedstoexceed0.6Vformajority 

carriers(electronsforNPN)toflowfromtheemitterintothebasebecomingminoritycarriers 

intheP-typesemiconductor. 

Ifthebaseregionwerethick,asinapairofback-to-backdiodes,allthecurrententering 

thebasewouldflowoutthebaselead. InourNPNtransistorexample,electronsleavingthe 

emitterforthebasewouldcombinewithholesinthebase,makingroomformoreholestobe 

createdatthe(+)batteryterminalonthebaseaselectronsexit. 

However,thebaseismanufacturedthin.Afewmajoritycarriersintheemitter,injectedas 

minoritycarriersintothebase,actuallyrecombine.SeeFigure2.34(b).Fewelectronsinjected 

bytheemitterintothebaseofanNPNtransistorfallintoholes.Also,fewelectronsentering 

thebaseflowdirectlythroughthebasetothepositivebatteryterminal. Mostoftheemitter 

currentofelectronsdiffusesthroughthethinbaseintothecollector.Moreover,modulatingthe 

smallbasecurrentproducesalargerchangeincollectorcurrent.Ifthebasevoltagefallsbelow 

approximately0.6Vforasilicontransistor,thelargeemitter-collectorcurrentceasestoflow. 

InFigure2.35wetakeacloserlookatthecurrentamplificationmechanism.Wehavean 

enlargedviewofanNPNjunctiontransistorwithemphasisonthethinbaseregion.Though 

notshown,weassumethatexternalvoltagesources1)forwardbiastheemitter-basejunction, 

2)reversebiasthebase-collectorjunction.Electrons,majoritycarriers,entertheemitterfrom 

the(-)batteryterminal.Thebasecurrentflowcorrespondstoelectronsleavingthebaseterminalforthe(+)batteryterminal.Thisisbutasmallcurrentcomparedtotheemittercurrent. 

MajoritycarrierswithintheN-typeemitterareelectrons,becomingminoritycarrierswhen 

enteringtheP-typebase.TheseelectronsfacefourpossiblefatesenteringthethinP-typebase. 

AfewatFigure2.35(a)fallintoholesinthebasethatcontributestobasecurrentflowtothe 

(+)batteryterminal. Notshown,holesinthebasemaydiffuseintotheemitterandcombine 

withelectrons,contributingtobaseterminalcurrent. Fewat(b)flowonthroughthebaseto 

the(+)batteryterminalasifthebasewerearesistor.Both(a)and(b)contributetothevery 

smallbasecurrentflow. Basecurrentistypically1%ofemitterorcollectorcurrentforsmall 

signaltransistors. Mostoftheemitterelectronsdiffuserightthroughthethinbase(c)into


N P- 

+ 

N 

- + 

- + 

- + 

- + 

- + 

- + 

- + 

(a) 

- + 

E 

- + 

B 

C 

- + 

- + 

(b) 

N 

P 

- 

- 

- 

+ 

+ 

+ 

+ 

N 

- + 

E C 

- + B 

- + 

- + 

Figure2.34: NPNjunctionbipolartransistorwithreversebiasedcollector-base: (a)Adding 

forwardbiastobase-emitterjunction,resultsin(b)asmallbasecurrentandlargeemitterand 

collectorcurrents. 

holes 

electrons 

- + 

- + depletion 

region 

(c) 

(a) 

(d) 

- 

- 

+ 

+ 

(b) 

depletion 

N 

emitter 

P region 

base 

N 

collector 

Figure2.35: Dispositionofelectronsenteringbase: (a)Lostduetorecombinationwithbase 

holes. (b)Flowsoutbaselead. (c)Mostdiffusefromemitterthroughthinbaseintobasecollectordepletionregion,and(d)arerapidlysweptbythestrongdepletionregionelectricfield 

intothecollector.

2.8. BIPOLARJUNCTIONTRANSISTORS 63 

thebase-collectordepletionregion.Notethepolarityofthedepletionregionsurroundingthe 

electronat(d). Thestrongelectricfieldsweepstheelectronrapidlyintothecollector. The 

strengthofthefieldisproportionaltothecollectorbatteryvoltage. Thus99%oftheemitter 

currentflowsintothecollector.Itiscontrolledbythebasecurrent,whichis1%oftheemitter 

current.Thisisapotentialcurrentgainof99,theratioofIC/IB,alsoknownasbeta, β. 

Thismagic,thediffusionof99%oftheemittercarriersthroughthebase,isonlypossibleif 

thebaseisverythin.Whatwouldbethefateofthebaseminoritycarriersinabase100times 

thicker? Onewouldexpecttherecombinationrate,electronsfallingintoholes,tobemuch 

higher. Perhaps99%,insteadof1%,wouldfallintoholes,nevergettingtothecollector. The 

secondpointtomakeisthatthebasecurrentmaycontrol99%oftheemittercurrent,onlyif 

99%oftheemittercurrentdiffusesintothecollector.Ifitallflowsoutthebase,nocontrolis 

possible. 

Anotherfeatureaccountingforpassing99%oftheelectronsfromemittertocollectoristhat 

realbipolarjunctiontransistorsuseasmallheavilydopedemitter.Thehighconcentrationof 

emitterelectronsforcesmanyelectronstodiffuseintothebase.Thelowerdopingconcentration 

inthebasemeansfewerholesdiffuseintotheemitter,whichwouldincreasethebasecurrent. 

Diffusionofcarriersfromemittertobaseisstronglyfavored. 

Thethinbaseandtheheavilydopedemitterhelpkeeptheemitterefficiencyhigh,99%for 

example.Thiscorrespondsto100%emittercurrentsplittingbetweenthebaseas1%andthe 

collectoras99%.Theemitterefficiencyisknownas α=IC/IE. 

BipolarjunctiontransistorsareavailableasPNPaswellasNPNdevices. Wepresenta 

comparisonofthesetwoinFigure2.36.Thedifferenceisthepolarityofthebaseemitterdiode 

junctions,assignifiedbythedirectionoftheschematicsymbolemitterarrow. Itpointsin 

thesamedirectionastheanodearrowforajunctiondiode,againstelectroncurrentflow.See 

diodejunction,Figure2.30. ThepointofthearrowandbarcorrespondtoP-typeandN-type 

semiconductors,respectively.ForNPNandPNPemitters,thearrowpointsawayandtoward 

thebaserespectively.Thereisnoschematicarrowonthecollector.However,thebase-collector 

junctionisthesamepolarityasthebase-emitterjunctioncomparedtoadiode.Note,wespeak 

ofdiode,notpowersupply,polarity. 

(a) 

N P 

N 

- + 

E 

- + 

B 

- + 

- + 

(b) 

P 

C E 

+ 

- 

N 

+ - B + - 

Figure2.36:CompareNPNtransistorat(a)withthePNPtransistorat(b).Notedirectionof 

emitterarrowandsupplypolarity. 

ThevoltagesourcesforPNPtransistorsarereversedcomparedwithanNPNtransistors 

+ 

C 

- 

P


asshowninFigure2.36.Thebase-emitterjunctionmustbeforwardbiasedinbothcases.The 

baseonaPNPtransistorisbiasednegative(b)comparedwithpositive(a)foranNPN.Inboth 

casesthebase-collectorjunctionisreversebiased.ThePNPcollectorpowersupplyisnegative 

comparedwithpositiveforanNPNtransistor. 

N + 

N - 

P 

Collector 

N + 

Base Emitter 

(a) 

Base 

(b) 

(c) 

Collector 

Emitter 

P+ 

Base 

P substrate 

Emitter Collector 

N + 

N + P base 

N collector epitaxial layer 

buried 

Figure2.37:Bipolarjunctiontransistor:(a)discretedevicecross-section,(b)schematicsymbol, 

(c)integratedcircuitcross-section. 

NotethattheBJTinFigure2.37(a)hasheavydopingintheemitterasindicatedbythe 

N + notation.ThebasehasanormalP-dopantlevel.Thebaseismuchthinnerthanthenotto-scalecross-sectionshows. 

ThecollectorislightlydopedasindicatedbytheN − notation. 

Thecollectorneedstobelightlydopedsothatthecollector-basejunctionwillhaveahigh 

breakdownvoltage.Thistranslatesintoahighallowablecollectorpowersupplyvoltage.Small 

signalsilicontransistorshavea60-80Vbreakdownvoltage.Though,itmayruntohundreds 

ofvoltsforhighvoltagetransistors.Thecollectoralsoneedstobeheavilydopedtominimize 

ohmiclossesifthetransistormusthandlehighcurrent.Thesecontradictingrequirementsare 

metbydopingthecollectormoreheavilyatthemetalliccontactarea. Thecollectornearthe 

baseislightlydopedascomparedwiththeemitter.Theheavydopingintheemittergivesthe 

emitter-basealowapproximate7Vbreakdownvoltageinsmallsignaltransistors.Theheavily 

dopedemittermakestheemitter-basejunctionhavezenerdiodelikecharacteristicsinreverse 

bias. 

TheBJTdie,apieceofaslicedanddicedsemiconductorwafer,ismountedcollectordown 

toametalcaseforpowertransistors. Thatis,themetalcaseiselectricallyconnectedtothe 

collector. Asmallsignaldiemaybeencapsulatedinepoxy. Inpowertransistors,aluminum 

bondingwiresconnectthebaseandemittertopackageleads. Smallsignaltransistordies 

maybemounteddirectlytotheleadwires.Multipletransistorsmaybefabricatedonasingle 

diecalledanintegratedcircuit.Eventhecollectormaybebondedouttoaleadinsteadofthe 

case.Theintegratedcircuitmaycontaininternalwiringofthetransistorsandotherintegrated 

components.TheintegratedBJTshownin(Figure??)ismuchthinnerthanthe“nottoscale” 

drawing.TheP + regionisolatesmultipletransistorsinasingledie.Analuminummetalization 

layer(notshown)interconnectsmultipletransistorsandothercomponents.Theemitterregion 

isheavilydoped,N + comparedtothebaseandcollectortoimproveemitterefficiency. 

DiscretePNPtransistorsarealmostashighqualityastheNPNcounterpart.However,in- 

N +

2.9. JUNCTIONFIELD-EFFECTTRANSISTORS 65 

tegratedPNPtransistorsarenotnearlyagoodastheNPNvarietywithinthesameintegrated 

circuitdie.Thus,integratedcircuitsusetheNPNvarietyasmuchaspossible. 

• REVIEW: 

• Bipolartransistorsconductcurrentusingbothelectronsandholesinthesamedevice. 

• Operationofabipolartransistorasacurrentamplifierrequiresthatthecollector-base 

junctionbereversebiasedandtheemitter-basejunctionbeforwardbiased. 

• Atransistordiffersfromapairofbacktobackdiodesinthatthebase,thecenterlayer,is 

verythin.Thisallowsmajoritycarriersfromtheemittertodiffuseasminoritycarriers 

throughthebaseintothedepletionregionofthebase-collectorjunction,wherethestrong 

electricfieldcollectsthem. 

• Emitterefficiencyisimprovedbyheavierdopingcomparedwiththecollector. Emitter 

efficiency: α=IC/IE,0.99forsmallsignaldevices 

• Currentgainis β=IC/IB,100to300forsmallsignaltransistors. 

2.9 Junctionfield-effecttransistors 

ThefieldeffecttransistorwasproposedbyJuliusLilienfeldinUSpatentsin1926and1933 

(1,900,018). Moreover,Shockley,Brattain,andBardeenwereinvestigatingthefieldeffect 

transistorin1947.Though,theextremedifficultiessidetrackedthemintoinventingthebipolar 

transistorinstead.Shockley’sfieldeffecttransistortheorywaspublishedin1952.However,the 

materialsprocessingtechnologywasnotmatureenoughuntil1960whenJohnAtallaproduced 

aworkingdevice. 

Afieldeffecttransistor(FET)isaunipolardevice,conductingacurrentusingonlyone 

kindofchargecarrier.IfbasedonanN-typeslabofsemiconductor,thecarriersareelectrons. 

Conversely,aP-typebaseddeviceusesonlyholes. 

Atthecircuitlevel,fieldeffecttransistoroperationissimple.Avoltageappliedtothegate, 

inputelement,controlstheresistanceofthechannel,theunipolarregionbetweenthegate 

regions. (Figure2.38)InanN-channeldevice,thisisalightlydopedN-typeslabofsilicon 

withterminalsattheends.Thesourceanddrainterminalsareanalogoustotheemitterand 

collector,respectively,ofaBJT.InanN-channeldevice,aheavyP-typeregiononbothsidesof 

thecenteroftheslabservesasacontrolelectrode,thegate.Thegateisanalogoustothebase 

ofaBJT. 

“Cleanlinessisnexttogodliness”appliestothemanufactureoffieldeffecttransistors. 

Thoughitispossibletomakebipolartransistorsoutsideofacleanroom,itisanecessity 

forfieldeffecttransistors. Eveninsuchanenvironment,manufactureistrickybecauseof 

contaminationcontrolissues. Theunipolarfieldeffecttransistorisconceptuallysimple,but 

difficulttomanufacture.Mosttransistorstodayareametaloxidesemiconductorvariety(later 

section)ofthefieldeffecttransistorcontainedwithinintegratedcircuits. However,discrete 

JFETdevicesareavailable. 

AproperlybiasedN-channeljunctionfieldeffecttransistor(JFET)isshowninFigure2.38. 

Thegateconstitutesadiodejunctiontothesourcetodrainsemiconductorslab. Thegateis


Source 

N 

Gate 

P 

Drain 

N 

+ - Channel 

Figure2.38:Junctionfieldeffecttransistorcross-section. 

reversebiased.Ifavoltage(oranohmmeter)wereappliedbetweenthesourceanddrain,the 

N-typebarwouldconductineitherdirectionbecauseofthedoping.Neithergatenorgatebias 

isrequiredforconduction.Ifagatejunctionisformedasshown,conductioncanbecontrolled 

bythedegreeofreversebias. 

Figure2.39(a)showsthedepletionregionatthegatejunction. Thisisduetodiffusionof 

holesfromtheP-typegateregionintotheN-typechannel,givingthechargeseparationabout 

thejunction,withanon-conductivedepletionregionatthejunction. Thedepletionregion 

extendsmoredeeplyintothechannelsideduetotheheavygatedopingandlightchannel 

doping. 

ThethicknessofthedepletionregioncanbeincreasedFigure2.39(b)byapplyingmoderate 

reversebias. Thisincreasestheresistanceofthesourcetodrainchannelbynarrowingthe 

channel.Increasingthereversebiasat(c)increasesthedepletionregion,decreasesthechannelwidth,andincreasesthechannelresistance. 

IncreasingthereversebiasVGSat(d)will 

pinch-offthechannelcurrent. Thechannelresistancewillbeveryhigh. ThisVGSatwhich 

pinch-offoccursisVP,thepinch-offvoltage. Itistypicallyafewvolts. Insummation,the 

channelresistancecanbecontrolledbythedegreeofreversebiasingonthegate. 

Thesourceanddrainareinterchangeable,andthesourcetodraincurrentmayflowin 

eitherdirectionforlowleveldrainbatteryvoltage(¡0.6V).Thatis,thedrainbatterymay 

bereplacedbyalowvoltageACsource. Forahighdrainpowersupplyvoltage,to10’sof 

voltsforsmallsignaldevices,thepolaritymustbeasindicatedinFigure2.40(a). Thisdrain 

powersupply,notshowninpreviousfigures,distortsthedepletionregion,enlargingitonthe 

drainsideofthegate. ThisisamorecorrectrepresentationforcommonDCdrainsupply 

voltages,fromafewtotensofvolts.AsdrainvoltageVDSincreased,thegatedepletionregion 

expandstowardthedrain. Thisincreasesthelengthofthenarrowchannel,increasingits 

resistancealittle. Wesay”alittle”becauselargeresistancechangesareduetochanging 

gatebias. Figure2.40(b)showstheschematicsymbolforanN-channelfieldeffecttransistor


S 

N 

P-type 

G 

S N 

D 

D 

(b) 

S N 

D 

(a) (c) 

S N 

D 

G G 

Figure2.39: N-channelJFET:(a)Depletionatgatediode. (b)Reversebiasedgatediodeincreasesdepletionregion.(c)Increasingreversebiasenlargesdepletionregion.(d)Increasing 

reversebiaspinches-offtheS-Dchannel. 

comparedtothesiliconcross-sectionat(a). Thegatearrowpointsinthesamedirectionas 

ajunctiondiode. The“pointing”arrowand“non-pointing”barcorrespondtoPandN-type 

semiconductors,respectively. 

S 

electron current 

P-type to G 

N 

G 

(a) (b) 

D 

Figure2.40:N-channelJFETelectroncurrentflowfromsourcetodrainin(a)cross-section,(b) 

schematicsymbol. 

Figure2.40showsalargeelectroncurrentflowfrom(-)batteryterminal,toFETsource, 

outthedrain,returningtothe(+)batteryterminal. Thiscurrentflowmaybecontrolledby 

varyingthegatevoltage. Aloadinserieswiththebatteryseesanamplifiedversionofthe 

changinggatevoltage. 

P-channelfieldeffecttransistorsarealsoavailable. ThechannelismadeofP-typematerial. 

ThegateisaheavilydoppedN-typeregion. Allthevoltagesourcesarereversedinthe 

P-channelcircuit(Figure2.41)ascomparedwiththemorepopularN-channeldevice. Also 

note,thearrowpointsoutofthegateoftheschematicsymbol(b)oftheP-channelfieldeffect 

transistor. 

Asthepositivegatebiasvoltageisincreased,theresistanceoftheP-channelincreases, 

decreasingthecurrentflowinthedraincircuit. 

Discretedevicesaremanufacturedwiththecross-sectionshowninFigure2.42.Thecross- 

S 

G 

G 

D 

(d)


P 

S D 

G 

to G 

N-type 

(a) (b) 

S D 

G 

Figure2.41:P-channelJFET:(a)N-typegate,P-typechannel,reversedvoltagesourcescomparedwithN-channeldevice.(b)Notereversedgatearrowandvoltagesourcesonschematic. 

section,orientedsothatitcorrespondstotheschematicsymbol,isupsidedownwithrespect 

toasemiconductorwafer. Thatis,thegateconnectionsareonthetopofthewafer. The 

gateisheavilydoped,P + ,todiffuseholeswellintothechannelforalargedepletionregion. 

ThesourceanddrainconnectionsinthisN-channeldeviceareheavilydoped,N + tolower 

connectionresistance. However,thechannelsurroundingthegateislightlydopedtoallow 

holesfromthegatetodiffusedeeplyintothechannel.ThatistheN − region. 

P + 

N + 

N - 

N + 

Drain 

Gate Source 

P + 

(a) 

Gate 

(b) 

(c) 

Source 

Drain 

Source 

N 

P substrate 

Gate 

P + 

Drain 

Figure2.42: Junctionfieldeffecttransistor: (a)Discretedevicecross-section,(b)schematic 

symbol,(c)integratedcircuitdevicecross-section. 

AllthreeFETterminalsareavailableonthetopofthediefortheintegratedcircuitversion 

sothatametalizationlayer(notshown)caninterconnectmultiplecomponents.(Figure2.42(c) 

)IntegratedcircuitFET’sareusedinanalogcircuitsforthehighgateinputresistance..The 

N-channelregionunderthegatemustbeverythinsothattheintrinsicregionaboutthegate 

cancontrolandpinch-offthechannel.Thus,gateregionsonbothsidesofthechannelarenot 

necessary. 

Thestaticinductionfieldeffecttransistor(SIT)isashortchanneldevicewithaburiedgate. 

(Figure2.43)Itisapowerdevice,asopposedtoasmallsignaldevice.Thelowgateresistance 

andlowgatetosourcecapacitancemakeforafastswitchingdevice. TheSITiscapableof 

hundredsofampsandthousandsofvolts.And,issaidtobecapableofanincrediblefrequency 

of10gHz.[25]


Gate 

P + 

Cross-section 

Drain 

P + 

N + 

N - 

N + 

P + 

P + 

Junction field-effect transistor 

(static induction type) 

Gate 

Schematic symbol 

Drain 

Source 

Source (a) (b) 

Figure 2.43: Junction field effect transistor (static induction type): (a) Cross-section, (b) 


Gate 

Drain 

Source 

N + 

(a) Source (b) substrate 

Gate 

N - 

Drain 

Figure2.44:Metalsemiconductorfieldeffecttransistor(MESFET):(a)schematicsymbol,(b) 

cross-section. 

N +


TheMetalsemiconductorfieldeffecttransistor(MESFET)issimilartoaJFETexceptthe 

gateisaschottkydiodeinsteadofajunctiondiode. Aschottkydiodeisametalrectifying 

contacttoasemiconductorcomparedwithamorecommonohmiccontact.InFigure2.44the 

sourceanddrainareheavilydoped(N + ). Thechannelislightlydoped(N − ). MESFET’sare 

higherspeedthanJFET’s.TheMESETisadepletionmodedevice,normallyon,likeaJFET. 

Theyareusedasmicrowavepoweramplifiersto30gHz.MESFET’scanbefabricatedfromsilicon,galliumarsenide,indiumphosphide,siliconcarbide,andthediamondallotropeofcarbon. 

• REVIEW: 

• Theunipolarjunctionfieldeffecttransistor(FETorJFET)issocalledbecauseconduction 

inthechannelisduetoonetypeofcarrier 

• TheJFETsource,gate,anddraincorrespondtotheBJT’semitter,base,andcollector, 

respectively. 

• Applicationofreversebiastothegatevariesthechannelresistancebyexpandingthe 

gatediodedepletionregion. 

2.10 Insulated-gatefield-effecttransistors(MOSFET) 

Theinsulated-gatefield-effecttransistor(IGFET),alsoknownasthemetaloxidefieldeffect 

transistor(MOSFET),isaderivativeofthefieldeffecttransistor(FET).Today,mosttransistorsareoftheMOSFETtypeascomponentsofdigitalintegratedcircuits. 

Thoughdiscrete 

BJT’saremorenumerousthandiscreteMOSFET’s.TheMOSFETtransistorcountwithinan 

integratedcircuitmayapproachhundredsofamillion.ThedimensionsofindividualMOSFET 

devicesareunderamicron,decreasingevery18months.MuchlargerMOSFET’sarecapable 

ofswitchingnearly100amperesofcurrentatlowvoltages;somehandlenearly1000Vatlower 

currents. Thesedevicesoccupyagoodfractionofasquarecentimeterofsilicon. MOSFET’s 

findmuchwiderapplicationthanJFET’s.However,MOSFETpowerdevicesarenotaswidely 

usedasbipolarjunctiontransistorsatthistime. 

TheMOSFEThassource,gate,anddrainterminalsliketheFET.However,thegatelead 

doesnotmakeadirectconnectiontothesiliconcomparedwiththecasefortheFET.The 

MOSFETgateisametallicorpolysiliconlayeratopasilicondioxideinsulator.Thegatebears 

aresemblancetoametaloxidesemiconductor(MOS)capacitorinFigure2.45.Whencharged, 

theplatesofthecapacitortakeonthechargepolarityoftherespectivebatteryterminals. 

ThelowerplateisP-typesiliconfromwhichelectronsarerepelledbythenegative(-)battery 

terminaltowardtheoxide,andattractedbythepositive(+)topplate.Thisexcessofelectrons 

neartheoxidecreatesaninverted(excessofelectrons)channelundertheoxide.Thischannel 

isalsoaccompaniedbyadepletionregionisolatingthechannelfromthebulksiliconsubstrate. 

InFigure2.46(a)theMOScapacitorisplacedbetweenapairofN-typediffusionsinaPtypesubstrate.Withnochargeonthecapacitor,nobiasonthegate,theN-typediffusions,the 

sourceanddrain,remainelectricallyisolated. 

Apositivebiasappliedtothegate,chargesthecapacitor(thegate).Thegateatoptheoxide 

takesonapositivechargefromthegatebiasbattery.TheP-typesubstratebelowthegatetakes 

onanegativecharge. Aninversionregionwithanexcessofelectronsformsbelowthegate

2.10. INSULATED-GATEFIELD-EFFECTTRANSISTORS(MOSFET) 71 

P 

oxide 

P 

(a) (b) 

+ 

- 

oxide 

P 

+ + + + + + 

- - - - - - 

depletion 

Figure2.45:N-channelMOScapacitor:(a)nocharge,(b)charged. 

Source Gate Drain 

Ν 

N + N + 

depletion 

(a) (b) 

N + 

P 

- + 

S G D 

inverted channel 

+ + + + + + 

- - - - - - 

depletion 

- 

inverted 

channel 

Figure2.46:N-channelMOSFET(enhancementtype):(a)0Vgatebias,(b)positivegatebias. 

oxide. ThisregionnowconnectsthesourceanddrainN-typeregions,formingacontinuous 

N-regionfromsourcetodrain. Thus,theMOSFET,liketheFETisaunipolardevice. One 

typeofchargecarrierisresponsibleforconduction. ThisexampleisanN-channelMOSFET. 

Conductionofalargecurrentfromsourcetodrainispossiblewithavoltageappliedbetween 

theseconnections. Apracticalcircuitwouldhavealoadinserieswiththedrainbatteryin 

Figure2.46(b). 

TheMOSFETdescribedaboveinFigure2.46isknownasanenhancementmodeMOSFET. 

Thenon-conducting,off,channelisturnedonbyenhancingthechannelbelowthegateby 

applicationofabias.Thisisthemostcommonkindofdevice.TheotherkindofMOSFETwill 

notbedescribedhere. SeetheInsulated-gatefield-effecttransistorchapterforthedepletion 

modedevice. 

TheMOSFET,liketheFET,isavoltagecontrolleddevice. Avoltageinputtothegate 

controlstheflowofcurrentfromsourcetodrain.Thegatedoesnotdrawacontinuouscurrent. 

Though,thegatedrawsasurgeofcurrenttochargethegatecapacitance. 

Thecross-sectionofanN-channeldiscreteMOSFETisshowninFigure2.47(a).Discrete 

devicesareusuallyoptimizedforhighpowerswitching.TheN + indicatesthatthesourceand 

drainareheavilyN-typedoped.Thisminimizesresistivelossesinthehighcurrentpathfrom 

sourcetodrain.TheN − indicateslightdoping.TheP-regionunderthegate,betweensource 

anddraincanbeinvertedbyapplicationofapositivebiasvoltage. Thedopingprofileisa 

cross-section,whichmaybelaidoutinaserpentinepatternonthesilicondie. Thisgreatly 

increasesthearea,andconsequently,thecurrenthandlingability. 

TheMOSFETschematicsymbolinFigure2.47(b)showsa“floating”gate,indicatingno 

N + 

N + 

+


N + 

N - 

Drain 

P 

N + 

(a) Gate Source 

inversion 

= silicon dioxide 

insulator 

Gate 

Drain 

Source 

Figure2.47:N-channelMOSFET(enhancementtype):(a)Cross-section,(b)schematicsymbol. 

directconnectiontothesiliconsubstrate.Thebrokenlinefromsourcetodrainindicatesthat 

thisdeviceisoff,notconducting,withzerobiasonthegate. Anormally“off”MOSFETis 

anenhancementmodedevice. Thechannelmustbeenhancedbyapplicationofabiastothe 

gateforconduction.The“pointing”endofthesubstratearrowcorrespondstoP-typematerial, 

whichpointstowardanN-typechannel,the“non-pointing”end. Thisisthesymbolforan 

N-channelMOSFET.ThearrowpointsintheoppositedirectionforaP-channeldevice(not 

shown).MOSFET’sarefourterminaldevices:source,gate,drain,andsubstrate.Thesubstrate 

isconnectedtothesourceindiscreteMOSFET’s,makingthepackagedpartathreeterminal 

device. MOSFET’s,thatarepartofanintegratedcircuit,havethesubstratecommontoall 

devices,unlesspurposelyisolated.Thiscommonconnectionmaybebondedoutofthediefor 

connectiontoagroundorpowersupplybiasvoltage. 

(a) 

N + 

Gate 

N + 

N - 

Drain 

P P 

N + 

Source 

inversion 

= silicon dioxide 

insulator 

Gate 

(b) 

Drain 

Source 

Figure2.48:N-channel“V-MOS”transistor:(a)Cross-section,(b)schematicsymbol. 

TheV-MOSdevicein(Figure2.48)isanimprovedpowerMOSFETwiththedopingprofile 

arrangedforloweron-statesourcetodrainresistance. VMOStakesitsnamefromtheVshapedgateregion,whichincreasesthecross-sectionalareaofthesource-drainpath. 

This 

(b)

2.11. THYRISTORS 73 

minimizeslossesandallowsswitchingofhigherlevelsofpower. UMOS,avariationusinga 

U-shapedgrove,ismorereproducibleinmanufacture. 

• REVIEW: 

• MOSFET’sareunipoarconductiondevices,conductionwithonetypeofchargecarrier, 

likeaFET,butunlikeaBJT. 

• AMOSFETisavoltagecontrolleddevicelikeaFET.Agatevoltageinputcontrolsthe 

sourcetodraincurrent. 

• TheMOSFETgatedrawsnocontinuouscurrent,exceptleakage.However,aconsiderable 

initialsurgeofcurrentisrequiredtochargethegatecapacitance. 

2.11 Thyristors 

Thyristorsareabroadclassificationofbipolar-conductingsemiconductordeviceshavingfour 

(ormore)alternatingN-P-N-Players. Thyristorsinclude: siliconcontrolledrectifier(SCR), 

TRIAC,gateturnoffswitch(GTO),siliconcontrolledswitch(SCS),ACdiode(DIAC),unijunctiontransistor(UJT),programmableunijunctiontransistor(PUT).OnlytheSCRisexamined 

inthissection;thoughtheGTOismentioned. 

Shockleyproposedthefourlayerdiodethyristorin1950. Itwasnotrealizeduntilyears 

lateratGeneralElectric. SCR’sarenowavailabletohandlepowerlevelsspanningwatts 

tomegawatts. Thesmallestdevices,packagedlikesmall-signaltransistors,switch100’sof 

milliampsatnear100VAC.Thelargestpackageddevicesare172mmindiameter,switching 

5600Ampsat10,000VAC.ThehighestpowerSCR’smayconsistofawholesemiconductor 

waferseveralinchesindiameter(100’sofmm). 

P 

N 

P P 

Gate N Gate 

(a) 

Anode 

N 

Cathode 

(b) 

Anode 

+ 

− 

Cathode 

Figure2.49:Siliconcontrolledrectifier(SCR):(a)dopingprofile,(b)BJTequivalentcircuit. 

ThesiliconcontrolledrectifierisafourlayerdiodewithagateconnectionasinFigure2.49 

(a).Whenturnedon,itconductslikeadiode,foronepolarityofcurrent.Ifnottriggeredon, 

itisnonconducting. Operationisexplainedintermsofthecompoundconnectedtransistor 

equivalentinFigure2.49(b).Apositivetriggersignalisappliedbetweenthegateandcathode


terminals.ThiscausestheNPNequivalenttransistortoconduct.ThecollectoroftheconductingNPNtransistorpullslow,movingthePNPbasetowardsitscollectorvoltage,whichcauses 

thePNPtoconduct.ThecollectoroftheconductingPNPpullshigh,movingtheNPNbasein 

thedirectionofitscollector.Thispositivefeedback(regeneration)reinforcestheNPN’salready 

conductingstate. Moreover,theNPNwillnowconductevenintheabsenceofagatesignal. 

OnceanSCRconducts,itcontinuesforaslongasapositiveanodevoltageispresent.Forthe 

DCbatteryshown,thisisforever. However,SCR’saremostoftenusedwithanalternating 

currentorpulsatingDCsupply.Conductionceaseswiththeexpirationofthepositivehalfof 

thesinewaveattheanode.Moreover,mostpracticalSCRcircuitsdependontheACcyclegoing 

tozerotocutofforcommutatetheSCR. 

Figure2.50(a)showsthedopingprofileofanSCR.Notethatthecathode,whichcorrespondstoanequivalentemitterofanNPNtransistorisheavilydopedasN 

+ indicates. The 

anodeisalsoheavilydoped(P + ). ItistheequivalentemitterofaPNPtransistor. Thetwo 

middlelayers,correspondingtobaseandcollectorregionsoftheequivalenttransistors,are 

lessheavilydoped:N − andP.ThisprofileinhighpowerSCR’smaybespreadacrossawhole 

semiconductorwaferofsubstantialdiameter. 

P + 

P + 

N - 

P 

Anode 

N + 

(a) 

Gate Cathode 

schematic symbols 

Anode 

Gate 

Cathode 

Anode 

Gate 

Cathode 

SCR GTO 

(b) (c) 

Figure2.50:Thyristors:(a)Cross-section,(b)siliconcontrolledrectifier(SCR)symbol,(c)gate 

turn-offthyristor(GTO)symbol. 

TheschematicsymbolsforanSCRandGTOareshowninFigures2.50(b&c).Thebasic 

diodesymbolindicatesthatcathodetoanodeconductionisunidirectionallikeadiode. The 

additionofagateleadindicatescontrolofdiodeconduction. Thegateturnoffswitch(GTO) 

hasbidirectionalarrowsaboutthegatelead,indicatingthattheconductioncanbedisabledby 

anegativepulse,aswellasinitiatedbyapositivepulse. 

InadditiontotheubiquitoussiliconbasedSCR’s,experimentalsiliconcarbidedeviceshave 

beenproduced.Siliconcarbide(SiC)operatesathighertemperatures,andismoreconductive 

ofheatthananymetal,secondtodiamond.Thisshouldallowforeitherphysicallysmalleror 

higherpowercapabledevices. 

• REVIEW: 

• SCR’sarethemostprevalentmemberofthethyristorfourlayerdiodefamily.

2.12. SEMICONDUCTORMANUFACTURINGTECHNIQUES 75 

• ApositivepulseappliedtothegateofanSCRtriggersitintoconduction. Conduction 

continuesevenifthegatepulseisremoved. Conductiononlyceaseswhentheanodeto 

cathodevoltagedropstozero. 

• SCR’saremostoftenusedwithanACsupply(orpulsatingDC)becauseofthecontinuous 

conduction. 

• Agateturnoffswitch(GTO)maybeturnedoffbyapplicationofanegativepulsetothe 

gate. 

• SCR’sswitchmegawattsofpower,upto5600Aand10,000V. 

2.12 Semiconductormanufacturingtechniques 

Themanufactureofonlysiliconbasedsemiconductorsisdescribedinthissection;mostsemiconductorsaresilicon.Siliconisparticularlysuitableforintegratedcircuitsbecauseitreadily 

formsanoxidecoating,usefulinpatterningintegratedcomponentsliketransistors. 

SiliconisthesecondmostcommonelementintheEarth’scrustintheformofsilicondioxide, 

SiO2,otherwiseknownassilicasand. Siliconisfreedfromsilicondioxidebyreductionwith 

carboninanelectricarcfurnace 

SiO2 + C = CO2+ Si 

Suchmetalurgicalgradesiliconissuitableforuseinsiliconsteeltransformerlaminations, 

butnotnearlypureenoughforsemiconductorapplications. ConversiontothechlorideSiCl4 

(orSiHCl3)allowspurificationbyfractionaldistillation.Reductionbyultrapurezincormagnesiumyieldsspongesilicon,requiringfurtherpurification. 

Or,thermaldecompositionona 

hotpolycrystallinesiliconrodheaterbyhydrogenyieldsultrapuresilicon. 

Si + 3HCl = SiHCl3 + H2 

SiHCl3 + H2 = Si + 3HCl2 

Thepolycrystallinesiliconismeltedinafusedsilicacrucibleheatedbyaninductionheated 

graphitesuceptor. Thegraphiteheatermayalternatelybedirectlydrivenbyalowvoltage 

athighcurrent. IntheCzochralskiprocess,thesiliconmeltissolidifiedontoapencilsized 

monocrystalsiliconrodofthedesiredcrystallatticeorientation. (Figure2.51)Therodisrotatedandpulledupwardataratetoencouragethediametertoexpandtoseveralinches.Once 

thisdiameterisattained,thebouleisautomaticallypulledataratetomaintainaconstant 

diametertoalengthofafewfeet. Dopantsmaybeaddedtothecruciblemelttocreate,for 

example,aP-typesemiconductor. Thegrowingapparatusisenclosedwithinaninertatmosphere. 

Thefinishedbouleisgroundtoaprecisefinaldiameter,andtheendstrimmed.Theboule 

isslicedintowafersbyaninsidediameterdiamondsaw. Thewafersaregroundflatand 

polished. ThewaferscouldhaveanN-typeepitaxiallayergrownatopthewaferbythermal 

depositionforhigherquality.Wafersatthisstageofmanufacturearedeliveredbythesilicon 

wafermanufacturertothesemiconductormanufacturer. 

Theprocessingofsemiconductorsinvolvesphotolithography,aprocessformakingmetal 

lithographicprintingplatesbyacidetching. Theelectronicsbasedversionofthisistheprocessingofcopperprintedcircuitboards.ThisisreviewedinFigure2.53asaneasyintroduction 

tothephotolithographyinvolvedinsemiconductorprocessing.


lift rod 

Si boule 

fused silica crucible 

graphite suceptor 

RF induction coil 

Si melt 

Figure2.51:Czochralskimonocrystallinesilicongrowth. 

Si boule 

diamond blade 

driven edge 

cut wafers 

Figure2.52:Siliconbouleisdiamondsawedintowafers.


(a) copper PCB (b) apply photoresist (c) place artwork (d) expose 

(e) remove artwork (f) develop resist (g) etch copper (h) strip resist 

Figure2.53: Processingofcopperprintedcircuitboardsissimilartothephotolithographic 

stepsofsemiconductorprocessing. 

WestartwithacopperfoillaminatedtoanepoxyfiberglassboardinFigure2.53(a). We 

alsoneedpositiveartworkwithblacklinescorrespondingtothecopperwiringlinesandpads 

thataretoremainonthefinishedboard.Positiveartworkisrequiredbecausepositiveacting 

resistisused.Though,negativeresistisavailableforbothcircuitboardsandsemiconductor 

processing. At(b)theliquidpositivephotoresistisappliedtothecopperfaceoftheprinted 

circuitboard(PCB).Itisallowedtodryandmaybebakedinanoven. Theartworkmaybe 

aplasticfilmpositivereproductionoftheoriginalartworkscaledtotherequiredsize. The 

artworkisplacedincontactwiththecircuitboardunderaglassplateat(c). Theboardis 

exposedtoultravioletlight(d)toformalatentimageofsoftenedphotoresist.Theartworkis 

removed(e)andthesoftenedresistwashedawaybyanalkalinesolution(f). Therinsedand 

dried(baked)circuitboardhasahardenedresistimageatopthecopperlinesandpadsthat 

aretoremainafteretching. Theboardisimmersedintheetchant(g)toremovecoppernot 

protectedbyhardenedresist.Theetchedboardisrinsedandtheresistremovedbyasolvent. 

Themajordifferenceinthepatterningofsemiconductorsisthatasilicondioxidelayeratop 

thewafertakestheplaceoftheresistduringthehightemperatureprocessingsteps.Though, 

theresistisrequiredinlowtemperaturewetprocessingtopatternthesilicondioxide. 

AnN-typedopedsiliconwaferinFigure2.54(a)isthestartingmaterialinthemanufacture 

ofsemiconductorjunctions.Asilicondioxidelayer(b)isgrownatopthewaferinthepresence 

ofoxygenorwatervaporathightemperature(over1000 o Cinadiffusionfurnace. Apool 

ofresistisappliedtothecenterofthecooledwafer,thenspuninavacuumchucktoevenly 

distributetheresist.Thebakedonresist(c)hasachromeonglassmaskappliedtothewafer 

at(d).Thismaskcontainsapatternofwindowswhichisexposedtoultravioletlight(e). 

AfterthemaskisremovedinFigure2.54(f),thepositiveresistcanbedeveloped(g)in 

analkalinesolution,openingwindowsintheUVsoftenedresist.Thepurposeoftheresistis 

toprotectthesilicondioxidefromthehydrofluoricacidetch(h),leavingonlyopenwindows 

correspondingtothemaskopenings.Theremainingresist(i)isstrippedfromthewaferbefore 

returningtothediffusionfurnace. ThewaferisexposedtoagaseousP-typedopantathigh 

temperatureinadiffusionfurnace(j). Thedopantonlydiffusesintothesiliconthroughthe 

openingsinthesilicondioxidelayer. EachP-diffusionthroughanopeningproducesaPN


(a) N-type wafer (b) grow SiO 2 (c) apply photoresist (d) place mask 

(e) expose (f) remove mask (g) develop resist (h) HF etch 

(i) strip resist 

BH 3 

(j) P-type diffusion 

Figure2.54:Manufactureofasilicondiodejunction. 

junction.Ifdiodeswerethedesiredproduct,thewaferwouldbediamondscribedandbroken 

intoindividualdiodechips. However,thewholewafermaybeprocessedfurtherintobipolar 

junctiontransistors. 

Toconvertthediodesintotransistors,asmallN-typediffusioninthemiddleoftheexistingP-regionisrequired. 

Repeatingthepreviousstepswithamaskhavingsmalleropenings 

accomplishesthis.ThoughnotshowninFigure2.54(j),anoxidelayerwasprobablyformedin 

thatstepduringtheP-diffusion.TheoxidelayerovertheP-diffusionisshowninFigure2.55 

(k).Positivephotoresistisappliedanddried(l).Thechromeonglassemittermaskisapplied 

(m),andUVexposed(n). Themaskisremoved(o). TheUVsoftenedresistintheemitter 

openingisremovedwithanalkalinesolution(p). Theexposedsilicondioxideisetchedaway 

withhydrofluoricacid(HF)at(q) 

Aftertheunexposedresistisstrippedfromthewafer(r),itisplacedinadiffusionfurnace 

(Figure2.55(s)forhightemperatureprocessing.AnN-typegaseousdopant,suchphosphorus 

oxychloride(POCl)diffusesthroughthesmallemitterwindowintheoxide(s). Thiscreates 

NPNlayerscorrespondingtotheemitter,base,andcollectorofaBJT.Itisimportantthatthe 

N-typeemitternotbedrivenallthewaythroughtheP-typebase,shortingtheemitterand 

collector. Thebaseregionbetweentheemitterandcollectoralsoneedstobethinsothatthe 

transistorhasauseful β. Otherwise,athickbaseregioncouldformapairofdiodesrather 

thanatransistor. At(t)metalizationisshownmakingcontactwiththetransistorregions. 

Thisrequiresarepeatoftheprevioussteps(notshownhere)withamaskforcontactopenings 

throughtheoxide. Anotherrepeatwithanothermaskdefinesthemetalizationpatternatop 

theoxideandcontactingthetransistorregionsthroughtheopenings. 

Themetalizationcouldconnectnumeroustransistorsandothercomponentsintoanintegratedcircuit. 

Though,onlyonetransistorisshown. Thefinishedwaferisdiamondscribed 

andbrokenintoindividualdiesforpackaging.Finegaugealuminumwirebondsthemetalized 

contactsonthedietoaleadframe,whichbringsthecontactsoutofthefinalpackage.


(k) grow SiO 2 (l) apply photoresist (m) place mask (n) expose 

(o) remove mask (p) develop resist (q) HF etch 

POCl 

(s) N-type diffusion 

C B E 

(t) metalization 

(r) strip resist 

Figure2.55: Manufactureofabipolarjunctiontransistor,continuationofManufactureofa 

silicondiodejunction. 

• REVIEW: 

• Mostsemiconductorarebasedonultrapuresiliconbecauseitformsaglassoxideatopthe 

wafer. Thisoxidecanbepatternedwithphotolithography,makingcomplexintegrated 

circuitspossible. 

• SausageshapedsinglecrystalsofsiliconaregrownbytheCzochralskiprocess,Theseare 

diamondsawedintowafers. 

• Thepatterningofsiliconwafersbyphotolithographyissimilartopatterningcopper 

printedcircuitboards.Photoresistisappliedtothewafer,whichisexposedtoUVlight 

throughamask.Theresistisdeveloped,thenthewaferisetched. 

• hydrofluoricacidetchingopenswindowsintheprotectivesilicondioxideatopthewafer. 

• Exposuretogaseousdopantsathightemperatureproducessemiconductorjunctionsas 

definedbytheopeningsinthesilicondioxidelayer. 

• Thephotolithographyisrepeatedformorediffusions,contacts,andmetalization. 

• Themetalizationmayinterconnectmultiplecomponentsintoanintegratedcircuit.


2.13 Superconductingdevices 

Superconductingdevices,thoughnotwidelyused,havesomeuniquecharacteristicsnotavailableinstandardsemiconductordevices.Highsensitivitywithrespecttoamplificationofelectricalsignals,detectionofmagneticfields,anddetectionoflightareprizedapplications.High 

speedswitchingisalsopossible,thoughnotappliedtocomputersatthistime. Conventional 

superconductingdevicesmustbecooledtowithinafewdegreesof0Kelvin(-273 o C).Though, 

workisproceedingatthistimeonhightemperaturesuperconductorbaseddevices,usableat90 

Kandbelow.Thisissignificantbecauseinexpensiveliquidnitrogenmaybeusedforcooling. 

Superconductivity:HeikeOnnesdiscoveredsuperconductivityinmercury(Hg)in1911, 

forwhichhewonaNobelprize. Mostmetalsdecreaseelectricalresistancewithdecreasing 

temperature. Though,mostdonotdecreasetozeroresistanceas0Kelvinisapproached. 

Mercuryisuniqueinthatitsresistanceabruptlydropstozero Ωat4.2K.Superconductors 

loseallresistanceabruptlywhencooledbelowtheircriticaltemperature,TcApropertyof 

superconductivityisnopowerlossinconductors.Currentmayflowinaloopofsuperconducting 

wireforthousandsofyears.Superconductorsincludelead(Pb),aluminum,(Al),tin(Sn)and 

niobium(Nb). 

Cooperpair:Losslessconductioninsuperconductorsisnotbyordinaryelectronflow.Electronflowinnormalconductorsencountersoppositionascollisionswiththerigidionicmetal 

crystallattice. Decreasingvibrationsofthecrystallatticewithdecreasingtemperatureaccountsfordecreasingresistance–uptoapoint.Latticevibrationsceaseatabsolutezero,but 

nottheenergydissipatingcollisionsofelectronswiththelattice.Thus,normalconductorsdo 

notloseallresistanceatabsolutezero. 

Electronsinsuperconductorsformapairofelectronscalledacooperpair,astemperature 

dropsbelowthecriticaltemperatureatwhichsuperconductivitybegins.Thecooperpairexists 

becauseitisatalowerenergylevelthanunpairedelectrons. Theelectronsareattractedto 

eachotherduetotheexchangeofphonons,verylowenergyparticlesrelatedtovibrations.This 

cooperpair,quantummechanicalentity(particleorwave)isnotsubjecttothenormallaws 

ofphysics. Thisentitypropagatesthroughthelatticewithoutencounteringthemetalions 

comprisingthefixedlattice. Thus,itdissipatesnoenergy. Thequantummechanicalnature 

ofthecooperpaironlyallowsittoexchangediscreteamountsofenergy,notcontinuously 

variableamounts.Anabsoluteminimumquantumofenergyisacceptabletothecooperpair. 

Ifthevibrationalenergyofthecrystallatticeisless,(duetothelowtemperature),thecooper 

paircannotacceptit,cannotbescatteredbythelattice.Thus,underthecriticaltemperature, 

thecooperpairsflowunimpededthroughthelattice. 

Josephsonjunctions:BrianJosephsonwonaNobelprizeforhis1962predictionofthe 

Josephesonjunction.AJosephsonjunctionisapairofsuperconductorsbridgedbyathininsulator,asinFigure2.56(a),throughwhichelectronscantunnel.ThefirstJosephsonjunctions 

wereleadsuperconductorsbridgedbyaninsulator. Thesedaysatri-layerofaluminumand 

niobiumispreferred. Electronscantunnelthroughtheinsulatorevenwithzerovoltageappliedacrossthesuperconductors. 

Ifavoltageisappliedacrossthejunction,thecurrentdecreasesandoscillatesatahigh 

frequencyproportionaltovoltage. Therelationshipbetweenappliedvoltageandfrequency 

issoprecisethatthestandardvoltisnowdefinedintermsofJosephsonjunctionoscillation 

frequency.TheJosephsonjunctioncanalsoserveasahyper-sensitivedetectoroflowlevelmagneticfields. 

Itisalsoverysensitivetoelectromagneticradiationfrommicrowavestogamma

2.13. SUPERCONDUCTINGDEVICES 81 

rays. 

lead (Pb) 

lead oxide 

gate 

(a) (b) 

Figure2.56:(a)Josephsonjunction,(b)Josephsontransistor. 

Josephsontransistor:AnelectrodeclosetotheoxideoftheJosephsonjunctioncaninfluencethejunctionbycapacitivecoupling. 

SuchanassemblyinFigure2.56(b)isaJosephson 

transistor. AmajorfeatureoftheJosephsontransistorislowpowerdissipationapplicable 

tohighdensitycircuitry,forexample,computers. Thistransistorisgenerallypartofamore 

complexsuperconductingdevicelikeaSQUIDorRSFQ. 

SQUID:ASuperconductingquantuminterferencedeviceorSQUIDisanassemblyofJosephsonjunctionswithinasuperconductingring.OnlytheDCSQUIDisconsideredinthisdiscussion.Thisdeviceishighlysensitivetolowlevelmagneticfields. 

AconstantcurrentbiasisforcedacrosstheringinparallelwithbothJosephsonjunctions 

inFigure2.57. Thecurrentdividesequallybetweenthetwojunctionsintheabsenceofan 

appliedmagneticfieldandnovoltageisdevelopedacrossacrossthering.[4]Whileanyvalue 

ofMagneticflux(Φ)maybeappliedtotheSQUID,onlyaquantizedvalue(amultipleofthe 

fluxquanta)canflowthroughtheopeninginthesuperconductingring.[2]Iftheappliedfluxis 

notanexactmultipleofthefluxquanta,theexcessfluxiscancelledbyacirculatingcurrent 

aroundtheringwhichproducesafractionalfluxquanta.Thecirculatingcurrentwillflowin 

thatdirectionwhichcancelsanyexcessfluxaboveamultipleofthefluxquanta.Itmayeither 

addto,orsubtractfromtheappliedflux,upto ±(1/2)afluxquanta.Ifthecirculatingcurrent 

flowsclockwise,thecurrentaddstothetopJosephesonjunctionandsubtractsfromthelower 

one.Changingappliedfluxlinearlycausesthecirculatingcurrenttovaryasasinusoid.[3]This 

canbemeasuredasavoltageacrosstheSQUID.Astheappliedmagneticfieldisincreased,a 

voltagepulsemaybecountedforeachincreasebyafluxquanta.[19] 

ASQUIDissaidtobesensitiveto10 −14 Tesla,Itcandetectthemagneticfieldofneural 

currentsinthebrainat10 −13 Tesla. Comparethiswiththe30x10 −6 Teslastrengthofthe 

Earth’smagneticfield. 

Rapidsinglefluxquantum(RSFQ):Ratherthanmimicsiliconsemiconductorcircuits, 

RSFQcircuitsrelyuponnewconcepts: magneticfluxquantizationwithinasuperconductor, 

andmovementofthefluxquantaproducesapicosecondquantizedvoltagepulse.Magneticflux 

canonlyexistwithinasectionofsuperconductorquantizedindiscretemultiples.Thelowest 

fluxquantaallowedisemployed. ThepulsesareswitchedbyJosephsonjunctionsinsteadof 

conventionaltransistors. Thesuperconductorsarebasedonatriplelayerofaluminumand


+ 

- 

I constant 

JJ 

Φ 

JJ 

±∆Ι V 

counter 

Figure2.57:Superconductionquantuminterferencedevice(SQUID):Josephsonjunctionpair 

withinasuperconductingring. AchangeinfluxproducesavoltagevariationacrosstheJJ 

pair. 

niobiumwithacriticaltemperatureof9.5K,cooledto5K. 

RSQF’soperateatover100gHzwithverylittlepowerdissipation.Manufactureissimple 

withexistingphotolithographictechniques. Though,operationrequiresrefrigerationdown 

to5K.Realworldcommercialapplicationsincludeanalog-to-digitalanddigitaltoanalog 

converters,toggleflip-flops,shiftregisters,memory,adders,andmultipliers.[5] 

Hightemperaturesuperconductors:Hightemperaturesuperconductorsarecompounds 

exhibitingsuperconductivityabovetheliquidnitrogenboilingpointof77K.Thisissignificant 

becauseliquidnitrogenisreadilyavailableandinexpensive.Mostconventionalsuperconductorsaremetals;widelyusedhightemperaturesuperconductorsarecuprates,mixedoxidesof 

copper(Cu),forexampleYBa2Cu3O7−x,criticaltemperature,Tc=90K.Alistofothersis 

available.[23]Mostofthedevicesdescribedinthissectionarebeingdevelopedinhightemperaturesuperconductorversionsforlesscriticalapplications. 

Thoughtheydonothavethe 

performanceoftheconventionalmetalsuperconductordevices,theliquidnitrogencoolingis 

moreavailable. 

• REVIEW: 

• Mostmetalsdecreaseresistanceastheyapproachabsolute0;though,theresistancedoes 

notdropto0.Superconductorsexperiencearapiddroptozeroresistanceattheircritical 

temperatureonbeingcooled.TypicallyTciswithin10Kofabsolutezero. 

• ACooperpair,electronpair,aquantummechanicalentity,movesunimpededthroughthe 

metalcrystallattice. 

• ElectronsareabletotunnelthroughaJosephsonjunction,aninsulatinggapacrossa 

pairofsuperconductors. 

• Theadditionofathirdelectrode,orgate,nearthejunctionconstitutesaJosephsontransistor. 

• ASQUID,Superconductionquantuminterferencedevice,isahighlysensitivedetector 

ofmagneticfields.Itcountsquantumunitsofamagneticfieldwithinasuperconducting 

ring. 

• RSFQ,Rapidsinglefluxquantumisahighspeedswitchingdevicebasedonswitching 

themagneticquantaexistingwithingasuperconductingloop.

2.14. QUANTUMDEVICES 83 

• Hightemperaturesuperconductors,Tcaboveliquidnitrogenboilingpoint,mayalsobe 

usedtobuildthesuperconductingdevicesinthissection. 

2.14 Quantumdevices 

Mostintegratedcircuitsaredigital,basedonMOS(CMOS)transistors.Everycoupleofyears 

sincethelate1960’sageometryshrinkhastakenplace,increasingthecircuitdensity–more 

circuitryatlowercostinthesamespace. Asofthiswriting(2006),theMOStransistorgate 

lengthis65-nmforleadingedgeproduction,with45-nmanticipatedwithinayear. At65nmleakagecurrentswerebecomingevident. 

At45-nm,heroicinnovationswererequiredto 

minimizethisleakage. TheendofshrinkageinMOStransistorsisexpectedat20-to30nm. 

Thoughsomethinkthat1-to2-nmisthelimit. Photolithography,orotherlithographic 

techniques,willcontinuetoimprove,providingeversmallergeometry.However,conventional 

MOStransistorsarenotexpectedtobeusableatthesesmallergeometriesbelow20-to30-nm. 

Improvedphotolithographywillhavetobeappliedtootherthantheconventionaltransistors,dimensions(under20-to30-nm). 

TheobjectionalMOSleakagecurrentsaredueto 

quantummechanicaleffects–electrontunnelingthroughgateoxide,andthenarrowchannel. 

Insummary,quantummechanicaleffectsareahindrancetoeversmallerconventionalMOS 

transistors. Thepathtoeversmallergeometrydevicesinvolvesuniqueactivedeviceswhich 

makepracticaluseofquantummechanicalprinciples. Asphysicalgeometrybecomesvery 

small,electronsmaybetreatedasthequantummechanicalequivalent: awave. Devices 

makinguseofquantummechanicalprinciplesinclude: resonanttunnelingdiodes,quantum 

tunnelingtransistors,metalinsulatormetaldiodes,andquantumdottransistors. 

Quantumtunneling: isthepassingofelectronsthroughaninsulatingbarrierwhichis 

thincomparedtothedeBroglie(page31)electronwavelength.Ifthe“electronwave”islarge 

comparedtothebarrier,thereisapossibilitythatthewaveappearsonbothsidesofthebarrier. 

Energy 

Energy 

Clasical view Quantum mechanical view 

Figure2.58:Classicalviewofanelectronsurmountingabarrier,ornot.Quantummechanical 

viewallowsanelectrontotunnelthroughabarrier. Theprobability(green)isrelatedtothe 

barrierthickness.AfterFigure1[22] 

Inclassicalphysics,anelectronmusthavesufficientenergytosurmountabarrier. Otherwise,itrecoilsfromthebarrier. 

(Figure2.58)Quantummechanicsallowsforaprobability 

oftheelectronbeingontheothersideofthebarrier. Iftreatedasawave,theelectronmay 

lookquitelargecomparedtothethicknessofthebarrier.Evenwhentreatedasawave,there 

isonlyasmallprobabilitythatitwillbefoundontheothersideofathickbarrier.Seegreen 

Energy


portionofcurve,Figure2.58.Thinningthebarrierincreasestheprobabilitythattheelectron 

isfoundontheothersideofthebarrier.[22] 

Tunneldiode: Theunqualifiedtermtunneldiodereferstotheesakitunneldiode,an 

earlyquantumdevice.Areversebiaseddiodeformsadepletionregion,aninsulatingregion, 

betweentheconductiveanodeandcathode.Thisdepletionregionisonlythinascomparedto 

theelectronwavelengthwhenheavilydoped–1000timesthedopingofarectifierdiode.With 

properbiasing,quantumtunnelingispossible.See(page144)fordetails. 

RTD,resonanttunnelingdiode:Thisisaquantumdevicenottobeconfusedwiththe 

Esakitunneldiode,(page144),aconventionalheavilydopedbipolarsemiconductor.Electrons 

tunnelthroughtwobarriersseparatedbyawellinflowingsourcetodraininaresonanttunnelingdiode.Tunnelingisalsoknownasquantummechanicaltunneling.Theflowofelectrons 

iscontrolledbydiodebias.Thismatchestheenergylevelsoftheelectronsinthesourcetothe 

quantizedlevelinthewellsothatelectronscantunnelthroughthebarriers.Theenergylevel 

inthewellisquantizedbecausethewellissmall. Whentheenergylevelsareequal,aresonanceoccurs,allowingelectronflowthroughthebarriersasshowninFigure2.59(b).Nobias 

ortoomuchbias,inFigures2.59(a)and(c)respectively,yieldsanenergymismatchbetween 

thesourceandthewell,andnoconduction. 

Energy eV 

1 

0 

GaAs 

AlAs AlAs 

InGaAs 



GaAs 

Energy eV 

1 

0 

barrier barrier 

energy 

level 

source 

10 20 30 40 nm 10 20 30 40 nm 

10 20 30 40 nm 

(a) (b) (c) 

well 

Figure2.59:Resonanttunnelingdiode(RTD):(a)Nobias,sourceandwellenergylevelsnot 

matched,noconduction.(b)Smallbiascausesmatchedenergylevels(resonance);conduction 

results.(c)Furtherbiasmismatchesenergylevels,decreasingconduction. 

AsbiasisincreasedfromzeroacrosstheRTD,thecurrentincreasesandthendecreases, 

correspondingtooff,on,andoffstates. Thismakessimplificationofconventionaltransistor 

circuitspossiblebysubstitutingapairofRTD’sfortwotransistors.Forexample,twoback-tobackRTD’sandatransistorformamemorycell,usingfewercomponents,lessareaandpower 

comparedwithaconventionalcircuit. ThepotentialapplicationofRTD’sistoreducethe 

componentcount,area,andpowerdissipationofconventionaltransistorcircuitsbyreplacing 

some,thoughnotall,transistors.[11]RTD’shavebeenshowntooscillateupto712gHz.[8] 

Double-layertunnelingtransistor:TheDeltt,otherwiseknownastheDouble-layertunnelingtransistorisconstructedofapairofconductivewellsseparatedbyaninsulatororhigh 

bandgapsemiconductor.(Figure2.60)Thewellsaresothinthatelectronsareconfinedtotwo 

dimensions.Theseareknownasquantumwells.Apairofthesequantumwellsareinsulated 

byathinGaAlAs,highbandgap(doesnoteasilyconduct)layer.Electronscantunnelthrough 

theinsulatinglayeriftheelectronsinthetwoquantumwellshavethesamemomentumand 

energy. Thewellsaresothinthattheelectronmaybetreatedasawave–thequantummechanicaldualityofparticlesandwaves. 

Thetopandoptionalbottomcontrolgatesmaybe 

adjustedtoequalizetheenergylevels(resonance)oftheelectronstoallowconductionfrom 

drain 

Energy eV 

1 

0


sourcetodrain.Figure2.60,barrierdiagramredbarsshowunequalenergylevelsinthewells, 

an“off-state”condition.Properbiasingofthegatesequalizestheenergylevelsofelectronsin 

thewells,the“on-state”condition. Thebarswouldbeatthesamelevelintheenergylevel 

diagram. 

well 

barrier 

well 

barrier 

diagram 

bottom quantum well 

contact (drain) 

top gate 

top quantum well 

depletion 

tunneling 

bottom 

depletion gate 

top depletion 

gate 

GaAs 

GaAlAs 

top quantum well 

contact (drain) 

depletion 

insulator 

GaAs 

bottom quantum well 

bottom gate (optional) 

Figure2.60:Double-layertunnelingtransistor(Deltt)iscomposedoftwoelectroncontaining 

wellsseparatedbyanonconductingbarrier. Thegatevoltagesmaybeadjustedsothatthe 

energyandmomentumoftheelectronsinthewellsareequalwhichpermitselectronstotunnel 

throughthenonconductivebarrier. (Theenergylevelsareshownasunequalinthebarrier 

diagram.) 

Ifgatebiasisincreasedbeyondthatrequiredfortunneling,theenergylevelsinthequantumwellsnolongermatch,tunnelingisinhibited,sourcetodraincurrentdecreases.Tosummarize,increasinggatebiasfromzeroresultsinon,off,onconditions. 

Thisallowsapairof 

Deltt’stobestackedinthemannerofaCMOScomplementarypair;though,differentp-andntypetransistorsarenotrequired.Powersupplyvoltageisabout100mV.ExperimentalDeltt’s 

havebeenproducedwhichoperatenear4.2K,77K,and0 o C.Roomtemperatureversionsare 

expected.[11][13][20] 

MIIMdiode:Themetal-insulator-insulator-metal(MIIM)diodeisaquantumtunnelingdevice,notbasedonsemiconductors.See“MIIMdiodesection”Figure2.61.Theinsulatorlayers 

mustbethincomparedtothedeBroglie(page31)electronwavelength,forquantumtunneling 

tobepossible. Fordiodeaction,theremustbeapreferedtunnelingdirection,resultingina 

sharpbendinthediodeforwardcharacteristiccurve.TheMIIMdiodehasasharperforward 

curvethanthemetalinsulatormetal(MIM)diode,notconsideredhere. 

TheenergylevelsofM1andM2areequalin“nobias”Figure2.61. However,(thermal) 

electronscannotflowduetothehighI1andI2barriers.ElectronsinmetalM2haveahigher 

energylevelin“reversebias”Figure2.61,butstillcannotovercometheinsulatorbarrier.As 

“forwardbias”Figure2.61isincreased,aquantumwell,anareawhereelectronsmayexist, 

isformedbetweentheinsulators. ElectronsmaypassthroughinsulatorI1ifM1isbisedat 

thesameenergylevelasthequantumwell.Asimpleexplanationisthatthedistancethrough 

theinsulatorsisshorter. Alongerexplanationisthatasbiasincreases,theprobabilityof 

theelectronwaveoverlappingfromM1tothequantumwellincreases. Foramoredetailed


M 1 

I 1 

I 2 

M 2 

Energy 

M 1 

I 1 I 2 

M 2 

Energy 

quantum 

well 

Distance 

Distance 

Distance 

MIIM diode 

section No bias Forward bias Reverse bias 

Energy 

M1 I2 I1 M2 M1 I1 I2 Figure2.61: Metalinsulatorinsulatormetal(MIIM)diode: Crosssectionofdiode. Energy 

levelsfornobias,forwardbias,andreversebias.AfterFigure1[21]. 

explanationseePhiarCorp.[21] 

MIIMdevicesoperateathigherfrequencies(3.7THz)thanmicrowavetransistors.[16]The 

additionofathirdelectrodetoaMIIMdiodeproducesatransistor. 

Quantumdottransistor: Anisolatedconductormaytakeonacharge, measuredin 

coulombsforlargeobjects. Foranano-scaleisolatedconductorknownasaquantumdot,the 

chargeismeasuredinelectrons. Aquantumdotof1-to3-nmmaytakeonanincremental 

chargeofasingleelectron. Thisisthebasisofthequantumdottransistor,alsoknownasa 

singleelectrontransistor. 

Aquantumdotplacedatopathininsulatoroveranelectronrichsourceisknownasasingle 

electronbox.(Figure2.62(a))Theenergyrequiredtotransferanelectronisrelatedtothesize 

ofthedotandthenumberofelectronsalreadyonthedot. 

Agateelectrodeabovethequantumdotcanadjusttheenergylevelofthedotsothatquantummechanicaltunnelingofanelectron(asawave)fromthesourcethroughtheinsulatoris 

possible.(Figure2.62(b))Thus,asingleelectronmaytunneltothedot. 

gate 

quantum 

dot 

source 

tunnel 

barrier 

--- 

+++ 

(a) (b) (c) 

+++ 

--- 

tunneling 

source drain 

tunnel 

barrier 

Figure2.62:(a)Singleelectronbox,anisolatedquantumdotseparatedfromanelectronsource 

byaninsulator.(b)Positivechargeonthegatepolarizesquantumdot,tunnelinganelectron 

fromthesourcetothedot. (c)Quantumtransistor:channelisreplacedbyquantumdotsurroundedbytunnelingbarrier. 

+ 

Ifthequantumdotissurroundedbyatunnelbarrierandembeddedbetweenthesource 

M 2


anddrainofaconventionalFET,asinFigure2.62(c),thechargeonthedotcanmodulatethe 

flowofelectronsfromsourcetodrain. Asgatevoltageincreases,thesourcetodraincurrent 

increases,uptoapoint. Afurtherincreaseingatevoltagedecreasesdraincurrent. Thisis 

similartothebehavioroftheRTDandDelttresonantdevices.Onlyonekindoftransistoris 

requiredtobuildacomplementarylogicgate.[11] 

Singleelectrontransistor:Ifapairofconductors,superconductors,orsemiconductors 

areseparatedbyapairoftunnelbarriers(insulator),surroundingatinyconductiveisland, 

likeaquantumdot,theflowofasinglecharge(aCooperpairforsuperconductors)maybe 

controlledbyagate.ThisisasingleelectrontransistorsimilartoFigure2.62(c).Increasing 

thepositivechargeonthegate,allowsanelectrontotunneltotheisland.Ifitissufficiently 

small,thelowcapacitancewillcausethedotpotentialtorisesubstantiallyduetothesingle 

electron.Nomoreelectronscantunneltotheislandduetheelectroncharge.Thisisknownat 

thecoulombblockade.Theelectronwhichtunneledtotheisland,cantunneltothedrain. 

Singleelectrontransistorsoperateatnearabsolutezero. Theexceptionisthegraphene 

singleelectrontransistor,havingagrapheneisland.Theyareallexperimentaldevices. 

Graphenetransistor:Graphite,anallotropeofcarbon,doesnothavetherigidinterlockingcrystallinestructureofdiamond. 

Nonetheless,ithasacrystallinestructure–oneatom 

thick,asocalledtwo-dimensionalstructure.Agraphiteisathree-dimensionalcrystal.However,itcleavesintothinsheets. 

Experimenters,takingthistotheextreme,producemicron 

sizedspecksasthinasasingleatomknownasgraphene.(Figure2.63(a))Thesemembranes 

haveuniqueelectronicproperties.Highlyconductive,conductionisbyeitherelectronsorholes, 

withoutdopingofanykind.[12] 

Graphenesheetsmaybecutintotransistorstructuresbylithographictechniques. The 

transistorsbearsomeresemblancetoaMOSFET.Agatecapacitivelycoupledtoagraphene 

channelcontrolsconduction. 

Assilicontransistorsscaletosmallersizes,leakageincreasesalongwithpowerdissipation. 

Andtheygetsmallereverycoupleofyears.Graphenetransistorsdissipatelittlepower.And, 

theyswitchathighspeed.Graphenemightbeareplacementforsiliconsomeday. 

Graphenecanbefashionedintodevicesassmallassixtyatomswide. Graphenequantumdotswithinatransistorthissmallserveassingleelectrontransistors. 

Previoussingle 

electrontransistorsfashionedfromeithersuperconductorsorconventionalsemiconductors 

operatenearabsolutezero. Graphenesingleelectrontransistorsuniquelyfunctionatroom 

temperature.[24] 

Graphenetransistorsarelaboratorycuriositiesatthistime.Iftheyaretogointoproductiontwodecadesfromnow,graphenewafersmustbeproduced. 

Thefirststep,productionof 

graphenebychemicalvapordeposition(CVD)hasbeenaccomplishedonanexperimentalscale. 

Though,nowafersareavailabletodate. 

Carbonnanotubetransistor:Ifa2-Dsheetofgrapheneisrolled,theresulting1-Dstructureisknownasacarbonnanotube.(Figure2.63(b))Thereasontotreatitas1-dimensionalis 

thatitishighlyconductive.Electronstraversethecarbonnanotubewithoutbeingscatteredby 

acrystallattice.Resistanceinnormalmetalsiscausedbyscatteringofelectronsbythemetalliccrystallinelattice. 

Ifelectronsavoidthisscattering,conductionissaidtobebyballistic 

transport. Bothmetallic(acting)andsemiconductingcarbonnanotubeshavebeenproduced. 

[6] 

Fieldeffecttransistorsmaybefashionedfromacarbonnanotubesbydepositingsource 

anddraincontactsontheends,andcapacitivelycouplingagatetothenanotubebetweenthe


(a) (b) 

Figure2.63:(a)Graphene:Asinglesheetofthegraphiteallotropeofcarbon. Theatomsare 

arrangedinahexagonalpatternwithacarbonateachintersection. (b)Carbonnanotube:A 

rolled-upsheetofgraphene. 

contacts. Bothp-andn-typetransistorshavebeenfabricated. Whytheinterestincarbon 

nanotubetransistors? NanotubesemiconductorsareSmaller,faster,lowerpowercompared 

withsilicontransistors.[7] 

Spintronics: Conventionalsemiconductorscontroltheflowofelectroncharge,current. 

Digitalstatesarerepresentedby“on”or“off”flowofcurrent.Assemiconductorsbecomemore 

densewiththemovetosmallergeometry,thepowerthatmustbedissipatedasheatincreases 

tothepointthatitisdifficulttoremove. Electronshavepropertiesotherthanchargesuch 

asspin.Atentativeexplanationofelectronspinistherotationofdistributedelectroncharge 

aboutthespinaxis,analogoustodiurnalrotationoftheEarth.Theloopsofcurrentcreatedby 

chargemovement,formamagneticfield.However,theelectronismorelikeapointchargethan 

adistributedcharge,Thus,therotatingdistributedchargeanalogyisnotacorrectexplanation 

ofspin. Electronspinmayhaveoneoftwostates: upordownwhichmayrepresentdigital 

states.Morepreciselythespin(ms)quantumnumbermaybe ±1/2theangularmomentum(l) 

quantumnumber.[1] 

Controllingelectronspininsteadofchargeflowconsiderablyreducespowerdissipationand 

increasesswitchingspeed. Spintronics,anacronymforSPINTRansportelectrONICS,isnot 

widelyappliedbecauseofthedifficultyofgenerating,controlling,andsensingelectronspin. 

However,highdensity,non-volatilemagneticspinmemoryisinproductionusingmodified 

semiconductorprocesses.Thisisrelatedtothespinvalvemagneticreadheadusedincomputer 

harddiskdrives,notmentionedfurtherhere. 

Asimplemagnetictunneljunction(MTJ)isshowninFigure2.64(a),consistingofapairof 

ferromagnetic,strongmagneticpropertieslikeiron(Fe),layersseparatedbyathininsulator. 

Electronscantunnelthroughasufficientlythininsulatorduetothequantummechanical 

propertiesofelectrons–thewavenatureofelectrons.ThecurrentflowthroughtheMTJisa 

functionofthemagnetization,spinpolarity,oftheferromagneticlayers.Theresistanceofthe 

MTJislowifthemagneticspinofthetoplayerisinthesamedirection(polarity)asthebottom 

layer.Ifthemagneticspinsofthetwolayersoppose,theresistanceishigher.[9] 

Thechangeinresistancecanbeenhancedbytheadditionofanantiferromagnet,material 

havingspinsalignedbutopposing,belowthebottomlayerinFigure2.64(b).Thisbiasmagnet 

pinsthelowerferromagneticlayerspintoasingleunchangingpolarity.Thetoplayermagnetization(spin)maybeflippedtorepresentdatabytheapplicationofanexternalmagneticfield


(a) 

contact 

ferromagnet 

tunneling 

insulator 

ferromagnet 

contact 

antiferromagnet 

contact 

Figure2.64: (a)Magnetictunneljunction(MTJ):Pairofferromagneticlayersseparatedby 

athininsulator. Theresistancevarieswiththemagnetizationpolarityofthetoplayer(b) 

Antiferromagneticbiasmagnetandpinnedbottomferromagneticlayerincreasesresistance 

sensitivitytochangesinpolarityofthetopferromagneticlayer.Adaptedfrom[9]Figure3. 

notshowninthefigure. Thepinnedlayerisnotaffectedbyexternalmagneticfields. Again, 

theMTJresistanceislowestwhenthespinofthetopferromagneticlayeristhesamesenseas 

thebottompinnedferromagneticlayer.[9] 

TheMTJmaybeimprovedfurtherbysplittingthepinnedferromagneticlayerintotwo 

layersseparatedbyabufferlayerinFigure 2.65(a).Thisisolatesthetoplayer.Thebottom 

ferromagneticlayerispinnedbytheantiferromagnetasinthepreviousfigure.Theferromagneticlayeratopthebufferisattractedbythebottomferromagneticlayer. 

Oppositesattract. 

Thus,thespinpolarityoftheadditionallayerisoppositeofthatinthebottomlayerdueto 

attraction.Thebottomandmiddleferromagneticlayersremainfixed.Thetopferromagnetic 

layermaybesettoeitherspinpolaritybyhighcurrentsinproximateconductors(notshown). 

Thisishowdataarestored. Dataarereadoutbythedifferenceincurrentflowthroughthe 

tunneljunction.Resistanceislowestifthelayersonbothsidesoftheinsultinglayerareofthe 

samespin.[9] 

Anarrayofmagnetictunneljunctionsmaybeembeddedinasiliconwaferwithconductors 

connectingthetopandbottomterminalsforreadingdatabitsfromtheMTJ’swithconventionalCMOScircuitry. 

OnesuchMTJisshowninFigure2.65(b)withthereadconductors. 

Notshown,anothercrossedarrayofconductorscarryingheavywritecurrentsswitchthemagneticspinofthetopferromagneticlayertostoredata.Acurrentisappliedtooneofmany“X” 

conductorsanda“Y”conductor. OneMTJinthearrayismagnetizedundertheconductors’ 

cross-over. DataarereadoutbysensingtheMTJcurrentwithconventionalsiliconsemiconductorcircuitry.[10] 

Themainreasonforinterestinmagnetictunneljunctionmemoryisthatitisnonvolatile.It 

doesnotlosedatawhenpowered“off”.Othertypesofnonvolatilememoryarecapableofonly 

limitedstoragecycles. MTJmemoryisalsohigherspeedthanmostsemiconductormemory 

types.Itisnow(2006)acommercialproduct.[18] 

Notacommercialproduct,orevenalaboratorydevice,isthetheoreticalspintransistor 

(b)


pinned layers data 

top contact 

ferromagnet 

tunneling 

insulator 

ferromagnet 

coupling layer 

ferromagnet 

antiferromagnet 

(a) bottom contact 

(b) 

Figure2.65:(a)Splittingthepinnedferromagneticlayerof(b)byabufferlayerimprovesstabilityandisolatesthetopferromagneticunpinnedlayer.Dataarestoredinthetopferromagnetic 

layerbasedonspinpolarity(b)MTJcellembeddedinreadlinesofasemiconductordie–one 

ofmanyMTJ’s.Adaptedfrom[10] 

whichmightonedaymakespinlogicgatespossible.Thespintransistorisaderivativeofthe 

theoreticalspindiode. 

Ithasbeenknownforsometimethatelectronsflowingthroughacobalt-ironferromagnet 

becomespinpolarized. Theferromagnetactsasafilterpassingelectronsofonespinpreferentially.Theseelectronsmayflowintoanadjacentnonmagneticconductor(orsemiconductor) 

retainingthespinpolarizationforashorttime,nano-seconds. Though,spinpolarizedelectronsmaypropagateaconsiderabledistancecomparedwithsemiconductordimensions. 

The 

spinpolarizedelectronsmaybedetectedbyanickel-ironferromagneticlayeradjacenttothe 

semiconductor.[1][15] 

Ithasalsobeenshownthatelectronspinpolarizationoccurswhencircularlypolarizedlight 

illuminatessomesemiconductormaterials.Thus,itshouldbepossibletoinjectspinpolarized 

electronsintoasemiconductordiodeortransistor.Theinterestinspinbasedtransistorsand 

gatesisbecauseofthenon-dissipativenatureofspinpropagation,comparedwithdissipative 

chargeflow. Asconventionalsemiconductorsarescaleddowninsize,powerdissipationincreases. 

Atsomepointthescalingdownwillnolongerbepractical. Researchersarelooking 

forareplacementfortheconventionalchargeflowbasedtransistor.Thatdevicemaybebased 

onspintronics.[14] 

• REVIEW: 

• AsMOSgateoxidethinswitheachgenerationofsmallertransistors,excessivegateleakagecausesunacceptablepowerdissipationandheating.Thelimitofscalingdownconventionalsemiconductorgeometryiswithinsight. 

• Resonanttunnelingdiode(RTD):Quantummechanicaleffects,whichdegradeconven-

2.15. SEMICONDUCTORDEVICESINSPICE 91 

tionalsemiconductors,areemployedintheRTD.Theflowofelectronsthroughasufficientlythininsulator,isbythewavenatureoftheelectron–particlewaveduality. 

The 

RTDfunctionsasanamplifier. 

• Doublelayertunnelingtransistor(Deltt):TheDelttisatransistorversionoftheRTD. 

Gatebiascontrolstheabilityofelectronstotunnelthroughathininsulatorfromone 

quantumwelltoanother(sourcetodrain). 

• Quantumdottransistor:Aquantumdot,capableofholdingacharge,issurroundedbya 

thintunnelbarrierreplacingthegateofaconventionalFET.Thechargeonthequantum 

dotcontrolssourcetodraincurrentflow. 

• Spintronics: Electronshavetwobasicproperties: chargeandspin. Conventionalelectronicdevicescontroltheflowofcharge,dissipatingenergy.Spintronicdevicesmanipulateelectronspin,apropagative,non-dissipativeprocess. 

2.15 SemiconductordevicesinSPICE 

TheSPICE(simulationprogram,integratedcircuitemphesis)electronicsimulationprogram 

providescircuitelementsandmodelsforsemiconductors. TheSPICEelementnamesbegin 

withd,q,j,ormcorrespondtodiode,BJT,JFETandMOSFETelements,respectively.These 

elementsareaccompaniedbycorresponding“models”Thesemodelshaveextensivelistsof 

parametersdescribingthedevice.Though,wedonotlistthemhere.Inthissectionweprovide 

averybrieflistingofsimplespicemodelsforsemiconductors,justenoughtogetstarted.For 

moredetailsonmodelsandanextensivelistofmodelparametersseeKuphaldt. [17]This 

referencealsogivesinstructionsonusingSPICE. 

Diode:Thediodestatementbeginswithadiodeelementnamewhichmustbeginwith“d” 

plusoptionalcharacters. Someexamplediodeelementnamesinclude: d1,d2,dtest,da,db, 

d101,etc.Twonodenumbersspecifytheconnectionoftheanodeandcathode,respectively,to 

othercomponents. Thenodenumbersarefollowedbyamodelname,referringtoa“.model” 

statement. 

Themodelstatementlinebeginswith“.model”,followedbythemodelnamematchingone 

ormorediodestatements. Nextisa“d”indicatingthatadiodeisbeingmodeled. TheremainderofthemodelstatementisalistofoptionaldiodeparametersoftheformParameterName=ParameterValue. 

Noneareshownintheexamplebelow. Foralist,seereference, 

“diodes”.[17] 

General form: d[name] [anode] [cathode] [model] 

.model [modelname] d ( [parmtr1=x] [parmtr2=y] . . .) 

Example: d1 1 2 mod1 

.model mod1 d 

Modelsforspecificdiodepartnumbersareoftenfurnishedbythesemiconductordiodemanufacturer. 

Thesemodelsincludeparameters. Otherwise,theparametersdefaulttosocalled 

“defaultvalues”,asintheexample.


BJT,bipolarjunctiontransistor:TheBJTelementstatementbeginswithanelement 

namewhichmustbeginwith“q”withassociatedcircuitsymboldesignatorcharacters,example:q1,q2,qa,qgood.TheBJTnodenumbers(connections)identifythewiringofthecollector, 

base,emitterrespectively. Amodelnamefollowingthenodenumbersisassociatedwitha 

modelstatement. 

General form: q[name] [collector] [base] [emitter] [model] 

.model [modelname] [npn or pnp] ([parmtr1=x] . . .) 

Example: q1 2 3 0 mod1 

.model mod1 pnp 

Example: q2 7 8 9 q2n090 

.model q2n090 npn ( bf=75 ) 

Themodelstatementbeginswith“.model”,followedbythemodelname,followedbyone 

of“npn”or“pnp”. Theoptionallistofparametersfollows,andmaycontinueforafewlines 

beginningwithlinecontinuationsymbol“+”,plus. Shownaboveistheforward βparameter 

setto75forthehypotheticalq2n090model. Detailedtransistormodelsareoftenavailable 

fromsemiconductormanufacturers. 

FET,fieldeffecttransistorThefieldeffecttransistorelementstatementbeginswithan 

elementnamebeginningwith“j”forJFETassociatedwithsomeuniquecharacters,example: 

j101,j2b,jalpha,etc. Thenodenumbersfollowforthedrain,gateandsourceterminals,respectively.Thenodenumbersdefineconnectivitytoothercircuitcomponents.Finally,amodel 

nameindicatestheJFETmodeltouse. 

General form: j[name] [drain] [gate] [source] [model] 

.model [modelname] [njf or pjf] ( [parmtr1=x] . . .) 

Example: j1 2 3 0 mod1 

.model mod1 pjf 

j3 4 5 0 mod2 

.model mod2 njf ( vto=-4.0 ) 

The“.model”intheJFETmodelstatementisfollowedbythemodelnametoidentifythis 

modeltotheJFETelementstatement(s)usingit.Followingthemodelnameiseitherpjfornjf 

forp-channelorn-channelJFET’srespectively.AlonglistofJFETparametersmayfollow.We 

onlyshowhowtosetVp,pinchoffvoltage,to-4.0Vforann-channelJFETmodel.Otherwise, 

thisvtoparameterdefaultsto-2.5Vor2.5Vforn-channelorp-channeldevices,respectively. 

MOSFET,metaloxidefieldeffecttransistorTheMOSFETelementnamemustbegin 

with“m”,andisthefirstwordintheelementstatement.Followingarethefournodenumbers 

forthedrain,gate,source,andsubstrate,respectively.Nextisthemodelname.Notethatthe 

sourceandsubstratearebothconnectedtothesamenode“0”intheexample.DiscreteMOS- 

FET’sarepackagedasthreeterminaldevices,thesourceandsubstratearethesamephysical 

terminal.IntegratedMOSFET’sarefourterminaldevices;thesubstrateisafourthterminal. 

IntegratedMOSFET’smayhavenumerousdevicessharingthesamesubstrate,separatefrom 

thesources.Though,thesourcesmightstillbeconnectedtothecommonsubstrate. 

General form: m[name] [drain] [gate] [source] [substrate] [model] 

.model [modelname] [nmos or pmos] ( [parmtr1=x] . . . )

BIBLIOGRAPHY 93 

Example: m1 2 3 0 0 mod1 

m5 5 6 0 0 mod4 

.model mod1 pmos 

.model mod4 nmos ( vto=1 ) 

TheMOSFETmodelstatementbeginswith“.model”followedbythemodelnamefollowed 

byeither“pmos”or“nmos”.OptionalMOSFETmodelparametersfollow.Thelistofpossible 

parametersislong.SeeVolume5,“MOSFET”fordetails.[17]MOSFETmanufacturersprovide 

detailedmodels.Otherwise,defaultsareineffect. 

ThebareminimumsemiconductorSPICEinformationisprovidedinthissection.Themodelsshownhereallowsimulationofbasiccircuits. 

Inparticular,thesemodelsdonotaccount 

forhighspeedorhighfrequencyoperation.SimulationsareshownintheVolume5Chapter7, 

“UsingSPICE...”. 

• REVIEW: 

• SemiconductorsmaybecomputersimulatedwithSPICE. 

• SPICEprovideselementstatementsandmodelsforthediode,BJT,JFET,andMOSFET. 

Contributors 



MaciejNoszczyski(December2003):CorrectedspellingofNielsBohr’sname. 

BillHeath(September2002):Pointedouterrorinillustrationofcarbonatom–thenucleus 

wasshownwithsevenprotonsinsteadofsix. 

Bibliography 

[1] DavidD.Awschalom,MichaelE.Flatte,NitinSamarth,“Spintronics”,ScientificAmerican,June2002at 

http://www.sciam.com 

[2] John Bland, “The Fluxoid” in “A Mossbauer Spectroscopy and Magnetometry 

Study of Magnetic Multilayers and Oxides”, Oliver Lodge 

Laboratory, Department of Physics, University of Liverpool, 2002, at 

http://www.cmp.liv.ac.uk/frink/thesis/thesis/node45.html 

[3] John Bland, “Superconducting Quantum Interference Device (SQUID)” in “A Mossbauer 

Spectroscopy and Magnetometry Study of Magnetic Multilayers and Oxides”, 

Oliver Lodge Laboratory, Department of Physics, University of Liverpool, 2002, at 


[4] John Bland, “SQUID Magnetometer” in “A Mossbauer Spectroscopy and 

Magnetometry Study of Magnetic Multilayers and Oxides”, Oliver Lodge


Laboratory, Department of Physics, University of Liverpool, 2002, at 


[5] Darren K. Brock, “RSFQ Technology: Circuits and Systems”, Hypres, Inc., NY, at 

http://www.hypres.com/papers/Brock-RSFQ-CirSys-Rev01.pdf 

[6] MatthewBroersma,“Nanotubesbreaksemiconductingrecord”,CnetNews,December 

19,2003,at http://news.com.com/2100-1006-5129761.html 

[7] “Carbon Nanotube Transistor”, Physics News Graphics, May 13, 1998, at 

http://www.aip.org/mgr/png/html/tubefet.htm 

[8] E. R. Brown, C. D. Parker, “Resonant Tunnel Diodes as Submillimetre-Wave 

Sources”, Philosophical Transactions: Mathematical, Physical and Engineering 

Sciences, Vol. 354, No. 1717, The Current Status of Semiconductor Tunnelling 

Devices (Oct. 15, 1996), pp. 2365-2381 at http://links.jstor.org/ 

sici?sici=1364-503X(19961015)354%3A1717%3C2365%3ARTDASS%3E2.0.CO%3B2-Q 

[9] W. J. Gallagher, S. S. P. Parkin, “Development of the magnetic tunnel junction 

MRAM at IBM: From first junctions to a 16-Mb MRAM demonstrator chip”, 

IBM Research and Development, Spintronics, Volume 50, Number 1, 2006, at 

http://www.research.ibm.com/journal/rd/501/gallagher.html 

[10] “IBM,InfineonDevelopMostAdvancedMRAMTechnologytoDate”,IBMResearch,at 

http://domino.research.ibm.com/comm/pr.nsf/pages/news.20030610 mram.html 

[11] LindaGeppert“QuantumTransistors:towardnanoectronic”,IEEESpectrum,September 

2000,at http://www.ece.osu.edu/˜berger/press/quan0900.pdf 

[12] A.K.Geim1andK.S.Novoselov1,“Theriseofgraphene”,NatureMaterials,6,2007,at 

http://www.nature.com/nmat/journal/v6/n3/full/nmat1849.html 

[13] IlanGreenberg,“TransistorTechnologyTakesaQuantumLeap”,WiredNews,December 

8,1997,at http://www.wired.com/news/technology/0,1282,8994,00.html 

[14] R. Colin Johnson, “Spintronics approach advances toward live chips,” EE Times, 

11/06/2006,at http://www.eetimes.com/showArticle.jhtml?articleID=193500309 

[15] R.ColinJohnson“U.ofDelawareresearchersedgeclosertospintronics,”EETimes, 

07/26/2007,at http://www.eetimes.com/news/design/showArticle.jhtml?articleID=201201400 

[16] R.ColinJohnson,“Canmetal-insulatorelectronicsdoitbetter,sanssemiconductors?” 

http://www.eetimes.com/showArticle.jhtml?articleID=201200024 

[17] Tony R. Kuphaldt, “Lessons in Electricity”, Reference, Vol. 5, Ch 7, 2007 at 

http://www.ibiblio.org/obp/electricCircuits/Ref/spice.html 

[18] Tom Lee, “Is nonvolatile MRAM right for your consumer embedded 

device application? ”, Freescale Semiconductor at 

http://www.acumeninfo.com/subscriber/article/getArticle.jhtml? 

articleId=197006965


[19] HyperPhysics, “SQUID Magnetometer”, HyperPhysics at 

http://hyperphysics.phy-astr.gsu.edu/hbase/solids/squid.html 

[20] Phillip F. Schewe, Ben Stein, “A Quantum Tunneling Transistor”, 

Physics Nessw Update, Number 357, February 4, 1998, at 

http://www.aip.org/pnu/1998/physnews.357.htm 

[21] “WhyMIIM?”,PhiarCorporation,at http://www.phiar.com/whyMIIM.php4 

[22] “What is Quantum Tunneling?”, Phiar Corporation, at 

http://www.phiar.com/whatQuantum.php4 

[23] Oxford University, “Theory, Superconductor Synthesis”, Oxford University, 1996, at 

http://www.chem.ox.ac.uk/vrchemistry/super/theory.htm 

[24] John Walko, “Graphene transistor to rival silicon, say researchers”, EE Times Europe,03/02/2007,at 

http://www.eetimes.com/news/design/showArticle.jhtml? 

articleID=197700700 

[25] Ying-Yu Tzou,“Power Electronics: An Introduction”, Institute 

of Control Engineering, National Chiao Tung University, at 

http://pemclab.cn.nctu.edu.tw/peclub/w3cnotes

96 CHAPTER2. SOLID-STATEDEVICETHEORY

Chapter3 

DIODESANDRECTIFIERS 

Contents 

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 

3.2 Metercheckofadiode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .103 

3.3 Dioderatings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .107 

3.4 Rectifiercircuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .108 

3.5 Peakdetector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .115 

3.6 Clippercircuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .117 

3.7 Clampercircuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .121 

3.8 Voltagemultipliers..................................123 

3.9 Inductorcommutatingcircuits . . . . . . . . . . . . . . . . . . . . . . . . . .130 

3.10 Diodeswitchingcircuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .132 

3.10.1 Logic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .132 

3.10.2 Analogswitch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .134 

3.11 Zenerdiodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .135 

3.12 Special-purposediodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .143 

3.12.1 Schottkydiodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .143 

3.12.2 Tunneldiodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .144 

3.12.3 Light-emittingdiodes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .146 

3.12.4 Laserdiodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .150 

3.12.5 Photodiodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .152 

3.12.6 Solarcells . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .154 

3.12.7 Varicaporvaractordiodes . . . . . . . . . . . . . . . . . . . . . . . . . . .158 

3.12.8 Snapdiode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .159 

3.12.9 PINdiodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .159 

3.12.10IMPATTdiode..................................160 

3.12.11Gunndiode. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .161 

3.12.12Shockleydiode. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .162 

3.12.13Constant-currentdiodes . . . . . . . . . . . . . . . . . . . . . . . . . . . .162 

97

98 CHAPTER3. DIODESANDRECTIFIERS 

3.13 Otherdiodetechnologies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .163 

3.13.1 SiCdiodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .163 

3.13.2 Polymerdiode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .163 

3.14 SPICEmodels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .163 

Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .171 


Adiodeisanelectricaldeviceallowingcurrenttomovethroughitinonedirectionwithfar 

greatereasethanintheother. Themostcommonkindofdiodeinmoderncircuitdesignis 

thesemiconductordiode,althoughotherdiodetechnologiesexist. Semiconductordiodesare 

symbolizedinschematicdiagramssuchasFigure3.1.Theterm“diode”iscustomarilyreserved 

forsmallsignaldevices,I≤1A.Thetermrectifierisusedforpowerdevices,I>1A. 

Figure3.1:Semiconductordiodeschematicsymbol:Arrowsindicatethedirectionofelectron 

currentflow. 

Whenplacedinasimplebattery-lampcircuit,thediodewilleitheralloworpreventcurrent 

throughthelamp,dependingonthepolarityoftheappliedvoltage.(Figure3.2) 

+ 

- + 

(a) (b) 

Figure3.2: Diodeoperation: (a)Currentflowispermitted;thediodeisforwardbiased. (b) 

Currentflowisprohibited;thediodeisreversedbiased. 

Whenthepolarityofthebatteryissuchthatelectronsareallowedtoflowthroughthe 

diode,thediodeissaidtobeforward-biased.Conversely,whenthebatteryis“backward”and 

thediodeblockscurrent,thediodeissaidtobereverse-biased.Adiodemaybethoughtofas 

likeaswitch:“closed”whenforward-biasedand“open”whenreverse-biased. 

Oddlyenough,thedirectionofthediodesymbol’s“arrowhead”pointsagainstthedirection 

ofelectronflow. Thisisbecausethediodesymbolwasinventedbyengineers,whopredominantlyuseconventionalflownotationintheirschematics,showingcurrentasaflowofcharge 

fromthepositive(+)sideofthevoltagesourcetothenegative(-).Thisconventionholdstrue 

forallsemiconductorsymbolspossessing“arrowheads:”thearrowpointsinthepermitteddirectionofconventionalflow,andagainstthepermitteddirectionofelectronflow. 

-

3.1. INTRODUCTION 99 

Hydraulic 

check valve 

+ - 

- + 

(a) Flow permitted (b) Flow prohibited 

Figure3.3: Hydrauliccheckvalveanalogy: (a)Electroncurrentflowpermitted. (b)Current 

flowprohibited. 

Diodebehaviorisanalogoustothebehaviorofahydraulicdevicecalledacheckvalve. A 

checkvalveallowsfluidflowthroughitinonlyonedirectionasinFigure3.3. 

Checkvalvesareessentiallypressure-operateddevices: theyopenandallowflowifthe 

pressureacrossthemisofthecorrect“polarity”toopenthegate(intheanalogyshown,greater 

fluidpressureontherightthanontheleft). Ifthepressureisoftheopposite“polarity,”the 

pressuredifferenceacrossthecheckvalvewillcloseandholdthegatesothatnoflowoccurs. 

Likecheckvalves,diodesareessentially“pressure-”operated(voltage-operated)devices. 

Theessentialdifferencebetweenforward-biasandreverse-biasisthepolarityofthevoltage 

droppedacrossthediode. Let’stakeacloserlookatthesimplebattery-diode-lampcircuit 

shownearlier,thistimeinvestigatingvoltagedropsacrossthevariouscomponentsinFigure3.4. 

+ 

+ 

0.7 V 

V Ω 

A COM 

- 

5.3 V 

A COM 

6 V 6 V 

- + 

(a) (b) 

V Ω 

Figure3.4:Diodecircuitvoltagemeasurements:(a)Forwardbiased.(b)Reversebiased. 

Aforward-biaseddiodeconductscurrentanddropsasmallvoltageacrossit,leavingmost 

ofthebatteryvoltagedroppedacrossthelamp.Ifthebattery’spolarityisreversed,thediode 

becomesreverse-biased,anddropsallofthebattery’svoltageleavingnoneforthelamp.Ifwe 

considerthediodetobeaself-actuatingswitch(closedintheforward-biasmodeandopenin 

thereverse-biasmode),thisbehaviormakessense.Themostsubstantialdifferenceisthatthe 

diodedropsalotmorevoltagewhenconductingthantheaveragemechanicalswitch(0.7volts 

versustensofmillivolts). 

- 

6.0 V 

- 

V Ω 

A COM 

+ 

0.0 V 

V Ω 

A COM


Thisforward-biasvoltagedropexhibitedbythediodeisduetotheactionofthedepletion 

regionformedbytheP-Njunctionundertheinfluenceofanappliedvoltage. Ifnovoltage 

appliedisacrossasemiconductordiode,athindepletionregionexistsaroundtheregionofthe 

P-Njunction,preventingcurrentflow.(Figure3.5(a))Thedepletionregionisalmostdevoidof 

availablechargecarriers,andactsasaninsulator: 

(a) 

(b) 

(c) 

P-type 

material 

N-type 

material 

Depletion region 

Anode Cathode 

Stripe marks cathode 

P-N junction representation 

Schematic symbol 

Real component appearance 

Figure3.5:Dioderepresentations:PN-junctionmodel,schematicsymbol,physicalpart. 

TheschematicsymbolofthediodeisshowninFigure3.5(b)suchthattheanode(pointing 

end)correspondstotheP-typesemiconductorat(a).Thecathodebar,non-pointingend,at(b) 

correspondstotheN-typematerialat(a). Alsonotethatthecathodestripeonthephysical 

part(c)correspondstothecathodeonthesymbol. 

Ifareverse-biasingvoltageisappliedacrosstheP-Njunction,thisdepletionregionexpands,furtherresistinganycurrentthroughit.(Figure3.6) 

- 

P N 

Reverse-biased Depletion region 

Figure3.6:Depletionregionexpandswithreversebias. 

Conversely,ifaforward-biasingvoltageisappliedacrosstheP-Njunction,thedepletion 

regioncollapsesbecomingthinner.Thediodebecomeslessresistivetocurrentthroughit.In 

+


orderforasustainedcurrenttogothroughthediode;though,thedepletionregionmustbe 

fullycollapsedbytheappliedvoltage. Thistakesacertainminimumvoltagetoaccomplish, 

calledtheforwardvoltageasillustratedinFigure3.7. 

0.4 V 0.7 V 

Partial forward-biased Forward-biased 

P N P N 

(a) Depletion region (b) Depletion region fully collapsed 

Figure3.7:Inceasingforwardbiasfrom(a)to(b)decreasesdepletionregionthickness. 

Forsilicondiodes,thetypicalforwardvoltageis0.7volts,nominal.Forgermaniumdiodes, 

theforwardvoltageisonly0.3volts.ThechemicalconstituencyoftheP-Njunctioncomprising 

thediodeaccountsforitsnominalforwardvoltagefigure,whichiswhysiliconandgermanium 

diodeshavesuchdifferentforwardvoltages. Forwardvoltagedropremainsapproximately 

constantforawiderangeofdiodecurrents,meaningthatdiodevoltagedropisnotlikethatofa 

resistororevenanormal(closed)switch.Formostsimplifiedcircuitanalysis,thevoltagedrop 

acrossaconductingdiodemaybeconsideredconstantatthenominalfigureandnotrelatedto 

theamountofcurrent. 

Actually,forwardvoltagedropismorecomplex. Anequationdescribestheexactcurrent 

throughadiode,giventhevoltagedroppedacrossthejunction,thetemperatureofthejunction, 

andseveralphysicalconstants.Itiscommonlyknownasthediodeequation: 

I D = I S (e qV D/NkT - 1) 

Where, 

I D = Diode current in amps 

IS = Saturation current in amps 

e = Euler’s constant (~ 2.718281828) 

q = charge of electron (1.6 x 10 -19 (typically 1 x 10 

coulombs) 

-12 amps) 

V D = Voltage applied across diode in volts 

N = "Nonideality" or "emission" coefficient 

(typically between 1 and 2) 

k = Boltzmann’s constant (1.38 x 10 -23 ) 

T = Junction temperature in Kelvins


ThetermkT/qdescribesthevoltageproducedwithintheP-Njunctionduetotheactionof 

temperature,andiscalledthethermalvoltage,orVtofthejunction. Atroomtemperature, 

thisisabout26millivolts.Knowingthis,andassuminga“nonideality”coefficientof1,wemay 

simplifythediodeequationandre-writeitassuch: 

ID = IS (e VD/0.026 -1) 

Where, 



(typically 1 x 10 


-12 amps) 


Youneednotbefamiliarwiththe“diodeequation”toanalyzesimplediodecircuits. Just 

understandthatthevoltagedroppedacrossacurrent-conductingdiodedoeschangewiththe 

amountofcurrentgoingthroughit,butthatthischangeisfairlysmalloverawiderangeof 

currents.Thisiswhymanytextbookssimplysaythevoltagedropacrossaconducting,semiconductordioderemainsconstantat0.7voltsforsiliconand0.3voltsforgermanium.However, 

somecircuitsintentionallymakeuseoftheP-Njunction’sinherentexponentialcurrent/voltage 

relationshipandthuscanonlybeunderstoodinthecontextofthisequation.Also,sincetemperatureisafactorinthediodeequation,aforward-biasedP-Njunctionmayalsobeusedasa 

temperature-sensingdevice,andthuscanonlybeunderstoodifonehasaconceptualgraspon 

thismathematicalrelationship. 

Areverse-biaseddiodepreventscurrentfromgoingthroughit,duetotheexpandeddepletionregion.Inactuality,averysmallamountofcurrentcananddoesgothroughareversebiaseddiode,calledtheleakagecurrent,butitcanbeignoredformostpurposes. 

Theability 

ofadiodetowithstandreverse-biasvoltagesislimited,asitisforanyinsulator. Iftheappliedreverse-biasvoltagebecomestoogreat,thediodewillexperienceaconditionknownas 

breakdown(Figure3.8),whichisusuallydestructive.Adiode’smaximumreverse-biasvoltage 

ratingisknownasthePeakInverseVoltage,orPIV,andmaybeobtainedfromthemanufacturer. 

Likeforwardvoltage,thePIVratingofadiodevarieswithtemperature,exceptthat 

PIVincreaseswithincreasedtemperatureanddecreasesasthediodebecomescooler–exactly 

oppositethatofforwardvoltage. 

Typically,thePIVratingofageneric“rectifier”diodeisatleast50voltsatroomtemperature.DiodeswithPIVratingsinthemanythousandsofvoltsareavailableformodestprices. 

• REVIEW: 

• Adiodeisanelectricalcomponentactingasaone-wayvalveforcurrent. 

• Whenvoltageisappliedacrossadiodeinsuchawaythatthediodeallowscurrent,the 

diodeissaidtobeforward-biased. 

• Whenvoltageisappliedacrossadiodeinsuchawaythatthediodeprohibitscurrent,the 

diodeissaidtobereverse-biased.

3.2. METERCHECKOFADIODE 103 

reverse-bias 

breakdown! 

forward 

reverse 

I D 

0.7 V 

forward-bias 

VD Figure3.8:Diodecurve:showingkneeat0.7VforwardbiasforSi,andreversebreakdown. 

• Thevoltagedroppedacrossaconducting,forward-biaseddiodeiscalledtheforwardvoltage.Forwardvoltageforadiodevariesonlyslightlyforchangesinforwardcurrentand 

temperature,andisfixedbythechemicalcompositionoftheP-Njunction. 

• Silicondiodeshaveaforwardvoltageofapproximately0.7volts. 

• Germaniumdiodeshaveaforwardvoltageofapproximately0.3volts. 

• Themaximumreverse-biasvoltagethatadiodecanwithstandwithout“breakingdown” 

iscalledthePeakInverseVoltage,orPIVrating. 

3.2 Metercheckofadiode 

Beingabletodeterminethepolarity(cathodeversusanode)andbasicfunctionalityofadiode 

isaveryimportantskillfortheelectronicshobbyistortechniciantohave. Sinceweknow 

thatadiodeisessentiallynothingmorethanaone-wayvalveforelectricity,itmakessense 

weshouldbeabletoverifyitsone-waynatureusingaDC(battery-powered)ohmmeterasin 

Figure3.9.Connectedonewayacrossthediode,themetershouldshowaverylowresistance 

at(a).Connectedtheotherwayacrossthediode,itshouldshowaveryhighresistanceat(b) 

(“OL”onsomedigitalmetermodels). 

Ofcourse,todeterminewhichendofthediodeisthecathodeandwhichistheanode,you 

mustknowwithcertaintywhichtestleadofthemeterispositive(+)andwhichisnegative(-) 

whensettothe“resistance”or“Ω”function.WithmostdigitalmultimetersI’veseen,thered 

leadbecomespositiveandtheblackleadnegativewhensettomeasureresistance,inaccordancewithstandardelectronicscolor-codeconvention.However,thisisnotguaranteedforall 

meters. Manyanalogmultimeters,forexample,actuallymaketheirblackleadspositive(+)


V A 

V 

A 

OFF 

COM 

A 

Anode 

Cathode 

+ 

V A 

V 

- A COM 

(a) (b) 

OFF 

A 

Cathode 

Figure3.9:Determinationofdiodepolarity:(a)Lowresistanceindicatesforwardbias,black 

leadiscathodeandredleadanode(formostmeters)(b)Reversingleadsshowshighresistance 

indicatingreversebias. 

andtheirredleadsnegative(-)whenswitchedtothe“resistance”function,becauseitiseasier 

tomanufactureitthatway! 

Oneproblemwithusinganohmmetertocheckadiodeisthatthereadingsobtainedonly 

havequalitativevalue,notquantitative.Inotherwords,anohmmeteronlytellsyouwhichway 

thediodeconducts;thelow-valueresistanceindicationobtainedwhileconductingisuseless.If 

anohmmetershowsavalueof“1.73ohms”whileforward-biasingadiode,thatfigureof1.73 

Ωdoesn’trepresentanyreal-worldquantityusefultousastechniciansorcircuitdesigners. 

Itneitherrepresentstheforwardvoltagedropnorany“bulk”resistanceinthesemiconductor 

materialofthediodeitself,butratherisafiguredependentuponbothquantitiesandwillvary 

substantiallywiththeparticularohmmeterusedtotakethereading. 

Forthisreason,somedigitalmultimetermanufacturersequiptheirmeterswithaspecial 

“diodecheck”functionwhichdisplaystheactualforwardvoltagedropofthediodeinvolts, 

ratherthana“resistance”figureinohms. Thesemetersworkbyforcingasmallcurrent 

throughthediodeandmeasuringthevoltagedroppedbetweenthetwotestleads.(Figure3.10) 

Theforwardvoltagereadingobtainedwithsuchameterwilltypicallybelessthanthe 

“normal”dropof0.7voltsforsiliconand0.3voltsforgermanium,becausethecurrentprovided 

bythemeterisoftrivialproportions.Ifamultimeterwithdiode-checkfunctionisn’tavailable, 

oryouwouldliketomeasureadiode’sforwardvoltagedropatsomenon-trivialcurrent,the 

circuitofFigure3.11maybeconstructedusingabattery,resistor,andvoltmeter 

Connectingthediodebackwardstothistestingcircuitwillsimplyresultinthevoltmeter 

indicatingthefullvoltageofthebattery. 

Ifthiscircuitweredesignedtoprovideaconstantornearlyconstantcurrentthroughthe 

diodedespitechangesinforwardvoltagedrop,itcouldbeusedasthebasisofatemperaturemeasurementinstrument,thevoltagemeasuredacrossthediodebeinginverselyproportional 

todiodejunctiontemperature.Ofcourse,diodecurrentshouldbekepttoaminimumtoavoid 

self-heating(thediodedissipatingsubstantialamountsofheatenergy),whichwouldinterfere 

withtemperaturemeasurement. 

Bewarethatsomedigitalmultimetersequippedwitha“diodecheck”functionmayoutput 

averylowtestvoltage(lessthan0.3volts)whensettotheregular“resistance”(Ω)function: 

Anode 

+ 

-

3.2. METERCHECKOFADIODE 105 

V A 

V A 

A 

OFF 

COM 

+ 

- 

Anode 

Cathode 

Figure3.10: Meterwitha“Diodecheck”functiondisplaystheforwardvoltagedropof0.548 

voltsinsteadofalowresistance. 

+ 

V 

- 

V 

(a) (b) 

V A 

A 

OFF 

COM 

A 

+ - 

Resistor 

Battery 

Diode 

Figure3.11: Measuringforwardvoltageofadiodewithout“diodecheck”meterfunction: (a) 

Schematicdiagram.(b)Pictorialdiagram. 

+ 

-


toolowtofullycollapsethedepletionregionofaPNjunction. Thephilosophyhereisthat 

the“diodecheck”functionistobeusedfortestingsemiconductordevices,andthe“resistance” 

functionforanythingelse. Byusingaverylowtestvoltagetomeasureresistance,itiseasierforatechniciantomeasuretheresistanceofnon-semiconductorcomponentsconnected 

tosemiconductorcomponents,sincethesemiconductorcomponentjunctionswillnotbecome 

forward-biasedwithsuchlowvoltages. 

Considertheexampleofaresistoranddiodeconnectedinparallel,solderedinplaceon 

aprintedcircuitboard(PCB).Normally,onewouldhavetounsoldertheresistorfromthe 

circuit(disconnectitfromallothercomponents)beforemeasuringitsresistance,otherwiseany 

parallel-connectedcomponentswouldaffectthereadingobtained. Whenusingamultimeter 

whichoutputsaverylowtestvoltagetotheprobesinthe“resistance”functionmode,the 

diode’sPNjunctionwillnothaveenoughvoltageimpressedacrossittobecomeforward-biased, 

andwillonlypassnegligiblecurrent.Consequently,themeter“sees”thediodeasanopen(no 

continuity),andonlyregisterstheresistor’sresistance.(Figure3.12) 

V A 

V A 

A 

OFF 

COM 

k 

R1 

Printed circuit board 

Figure3.12:Ohmmeterequippedwithalowtestvoltage(

3.3. DIODERATINGS 107 

V A 

V A 

A 

OFF 

COM 

M 

Figure3.13:Ohmmeterequippedwithalowtestvoltage,toolowtoforwardbiasdiodes,does 

notseediodes. 

whichisnegative!Theactualpolaritymaynotfollowthecolorsoftheleadsasyoumight 

expect,dependingontheparticulardesignofmeter. 

• Somemultimetersprovidea“diodecheck”functionthatdisplaystheactualforwardvoltageofthediodewhenitsconductingcurrent. 

Suchmeterstypicallyindicateaslightly 

lowerforwardvoltagethanwhatis“nominal”foradiode,duetotheverysmallamount 

ofcurrentusedduringthecheck. 

3.3 Dioderatings 

Inadditiontoforwardvoltagedrop(Vf)andpeakinversevoltage(PIV),therearemanyother 

ratingsofdiodesimportanttocircuitdesignandcomponentselection. Semiconductormanufacturersprovidedetailedspecificationsontheirproducts–diodesincluded–inpublications 

knownasdatasheets. Datasheetsforawidevarietyofsemiconductorcomponentsmaybe 

foundinreferencebooksandontheinternet. Iprefertheinternetasasourceofcomponent 

specificationsbecauseallthedataobtainedfrommanufacturerwebsitesareup-to-date. 

Atypicaldiodedatasheetwillcontainfiguresforthefollowingparameters: 

Maximumrepetitivereversevoltage=VRRM,themaximumamountofvoltagethediode 

canwithstandinreverse-biasmode,inrepeatedpulses.Ideally,thisfigurewouldbeinfinite. 

MaximumDCreversevoltage=VRorVDC,themaximumamountofvoltagethediodecan 

withstandinreverse-biasmodeonacontinualbasis.Ideally,thisfigurewouldbeinfinite. 

Maximumforwardvoltage=VF,usuallyspecifiedatthediode’sratedforwardcurrent.Ideally,thisfigurewouldbezero:thediodeprovidingnooppositionwhatsoevertoforwardcurrent. 

Inreality,theforwardvoltageisdescribedbythe“diodeequation.” 

Maximum(average)forwardcurrent=I F(AV ),themaximumaverageamountofcurrent 

thediodeisabletoconductinforwardbiasmode.Thisisfundamentallyathermallimitation: 

howmuchheatcanthePNjunctionhandle,giventhatdissipationpowerisequaltocurrent(I) 

multipliedbyvoltage(VorE)andforwardvoltageisdependentuponbothcurrentandjunction 

temperature.Ideally,thisfigurewouldbeinfinite.


Maximum(peakorsurge)forwardcurrent=IFSMori f(surge),themaximumpeakamount 

ofcurrentthediodeisabletoconductinforwardbiasmode.Again,thisratingislimitedbythe 

diodejunction’sthermalcapacity,andisusuallymuchhigherthantheaveragecurrentrating 

duetothermalinertia(thefactthatittakesafiniteamountoftimeforthediodetoreach 

maximumtemperatureforagivencurrent).Ideally,thisfigurewouldbeinfinite. 

Maximumtotaldissipation=PD,theamountofpower(inwatts)allowableforthediodeto 

dissipate,giventhedissipation(P=IE)ofdiodecurrentmultipliedbydiodevoltagedrop,and 

alsothedissipation(P=I 2 R)ofdiodecurrentsquaredmultipliedbybulkresistance. Fundamentallylimitedbythediode’sthermalcapacity(abilitytotoleratehightemperatures). 

Operatingjunctiontemperature=TJ,themaximumallowabletemperatureforthediode’s 

PNjunction,usuallygivenindegreesCelsius( o C).Heatisthe“Achilles’heel”ofsemiconductor 

devices:theymustbekeptcooltofunctionproperlyandgivelongservicelife. 

Storagetemperaturerange=TSTG,therangeofallowabletemperaturesforstoringadiode 

(unpowered). Sometimesgiveninconjunctionwithoperatingjunctiontemperature(TJ),becausethemaximumstoragetemperatureandthemaximumoperatingtemperatureratings 

areoftenidentical.Ifanything,though,maximumstoragetemperatureratingwillbegreater 

thanthemaximumoperatingtemperaturerating. 

Thermalresistance=R(Θ),thetemperaturedifferencebetweenjunctionandoutsideair 

(R(Θ)JA)orbetweenjunctionandleads(R(Θ)JL)foragivenpowerdissipation. Expressedin 

unitsofdegreesCelsiusperwatt( o C/W).Ideally,thisfigurewouldbezero,meaningthatthe 

diodepackagewasaperfectthermalconductorandradiator,abletotransferallheatenergy 

fromthejunctiontotheoutsideair(ortotheleads)withnodifferenceintemperatureacross 

thethicknessofthediodepackage.Ahighthermalresistancemeansthatthediodewillbuild 

upexcessivetemperatureatthejunction(whereitscritical)despitebesteffortsatcoolingthe 

outsideofthediode,andthuswilllimititsmaximumpowerdissipation. 

Maximumreversecurrent=IR,theamountofcurrentthroughthediodeinreverse-bias 

operation,withthemaximumratedinversevoltageapplied(VDC).Sometimesreferredtoas 

leakagecurrent. Ideally,thisfigurewouldbezero,asaperfectdiodewouldblockallcurrent 

whenreverse-biased.Inreality,itisverysmallcomparedtothemaximumforwardcurrent. 

Typicaljunctioncapacitance=CJ,thetypicalamountofcapacitanceintrinsictothejunction,duetothedepletionregionactingasadielectricseparatingtheanodeandcathodeconnections.Thisisusuallyaverysmallfigure,measuredintherangeofpicofarads(pF). 

Reverserecoverytime=trr,theamountoftimeittakesforadiodeto“turnoff”whenthe 

voltageacrossitalternatesfromforward-biastoreverse-biaspolarity.Ideally,thisfigurewould 

bezero:thediodehaltingconductionimmediatelyuponpolarityreversal.Foratypicalrectifier 

diode,reverserecoverytimeisintherangeoftensofmicroseconds;fora“fastswitching”diode, 

itmayonlybeafewnanoseconds. 

Mostoftheseparametersvarywithtemperatureorotheroperatingconditions,andsoa 

singlefigurefailstofullydescribeanygivenrating.Therefore,manufacturersprovidegraphs 

ofcomponentratingsplottedagainstothervariables(suchastemperature),sothatthecircuit 

designerhasabetterideaofwhatthedeviceiscapableof. 

3.4 Rectifiercircuits

3.4. RECTIFIERCIRCUITS 109 

Nowwecometothemostpopularapplicationofthediode: rectification. Simplydefined, 

rectificationistheconversionofalternatingcurrent(AC)todirectcurrent(DC).Thisinvolves 

adevicethatonlyallowsone-wayflowofelectrons. Aswehaveseen,thisisexactlywhata 

semiconductordiodedoes. Thesimplestkindofrectifiercircuitisthehalf-waverectifier. It 

onlyallowsonehalfofanACwaveformtopassthroughtotheload.(Figure3.14) 

AC 

voltage 

source 

+ 

- 

Load 

Figure3.14:Half-waverectifiercircuit. 

Formostpowerapplications,half-waverectificationisinsufficientforthetask. Theharmoniccontentoftherectifier’soutputwaveformisverylargeandconsequentlydifficultto 

filter. Furthermore,theACpowersourceonlysuppliespowertotheloadonehalfeveryfull 

cycle,meaningthathalfofitscapacityisunused. Half-waverectificationis,however,avery 

simplewaytoreducepowertoaresistiveload.Sometwo-positionlampdimmerswitchesapplyfullACpowertothelampfilamentfor“full”brightnessandthenhalf-waverectifyitfora 

lesserlightoutput.(Figure3.15) 

AC 

voltage 

source 

Bright 

Dim 

Figure3.15:Half-waverectifierapplication:Twolevellampdimmer. 

Inthe“Dim”switchposition,theincandescentlampreceivesapproximatelyone-halfthe 

poweritwouldnormallyreceiveoperatingonfull-waveAC.Becausethehalf-waverectified 

powerpulsesfarmorerapidlythanthefilamenthastimetoheatupandcooldown,thelamp 

doesnotblink. Instead,itsfilamentmerelyoperatesatalessertemperaturethannormal, 

providinglesslightoutput.Thisprincipleof“pulsing”powerrapidlytoaslow-respondingload 

devicetocontroltheelectricalpowersenttoitiscommonintheworldofindustrialelectronics. 

Sincethecontrollingdevice(thediode,inthiscase)iseitherfullyconductingorfullynonconductingatanygiventime,itdissipateslittleheatenergywhilecontrollingloadpower,making 

thismethodofpowercontrolveryenergy-efficient.Thiscircuitisperhapsthecrudestpossible 

methodofpulsingpowertoaload,butitsufficesasaproof-of-conceptapplication. 

IfweneedtorectifyACpowertoobtainthefulluseofbothhalf-cyclesofthesinewave, 

adifferentrectifiercircuitconfigurationmustbeused. Suchacircuitiscalledafull-wave 

rectifier.Onekindoffull-waverectifier,calledthecenter-tapdesign,usesatransformerwitha 

center-tappedsecondarywindingandtwodiodes,asinFigure3.16.


AC 

voltage 

source 

+ 

- 

Load 

Figure3.16:Full-waverectifier,center-tappeddesign. 

Thiscircuit’soperationiseasilyunderstoodonehalf-cycleatatime.Considerthefirsthalfcycle,whenthesourcevoltagepolarityispositive(+)ontopandnegative(-)onbottom.Atthis 

time,onlythetopdiodeisconducting;thebottomdiodeisblockingcurrent,andtheload“sees” 

thefirsthalfofthesinewave,positiveontopandnegativeonbottom.Onlythetophalfofthe 

transformer’ssecondarywindingcarriescurrentduringthishalf-cycleasinFigure3.17. 

+ 

- 

+ 

- 

Figure3.17: Full-wavecenter-taprectifier: Tophalfofsecondarywindingconductsduring 

positivehalf-cycleofinput,deliveringpositivehalf-cycletoload.. 

Duringthenexthalf-cycle,theACpolarityreverses.Now,theotherdiodeandtheotherhalf 

ofthetransformer’ssecondarywindingcarrycurrentwhiletheportionsofthecircuitformerly 

carryingcurrentduringthelasthalf-cyclesitidle.Theloadstill“sees”halfofasinewave,of 

thesamepolarityasbefore:positiveontopandnegativeonbottom.(Figure3.18) 

- 

+ 

- 

+ 

Figure3.18: Full-wavecenter-taprectifier: Duringnegativeinputhalf-cycle,bottomhalfof 

secondarywindingconducts,deliveringapositivehalf-cycletotheload. 

Onedisadvantageofthisfull-waverectifierdesignisthenecessityofatransformerwitha 

+ 

- 

+ 

-


center-tappedsecondarywinding.Ifthecircuitinquestionisoneofhighpower,thesizeand 

expenseofasuitabletransformerissignificant.Consequently,thecenter-taprectifierdesign 

isonlyseeninlow-powerapplications. 

Thefull-wavecenter-tappedrectifierpolarityattheloadmaybereversedbychangingthe 

directionofthediodes. Furthermore,thereverseddiodescanbeparalleledwithanexisting 

positive-outputrectifier. Theresultisdual-polarityfull-wavecenter-tappedrectifierinFigure3.19. 

Notethattheconnectivityofthediodesthemselvesisthesameconfigurationasa 

bridge. 

AC voltage source 

Loads 

Figure3.19:Dualpolarityfull-wavecentertaprectifier 

Another,morepopularfull-waverectifierdesignexists,anditisbuiltaroundafour-diode 

bridgeconfiguration.Forobviousreasons,thisdesigniscalledafull-wavebridge.(Figure3.20) 

+ 

- 

+ 

AC 

voltage 

source + 

Load 

Figure3.20:Full-wavebridgerectifier. 

Currentdirectionsforthefull-wavebridgerectifiercircuitareasshowninFigure3.21for 

positivehalf-cycleandFigure3.22fornegativehalf-cyclesoftheACsourcewaveform. Note 

thatregardlessofthepolarityoftheinput,thecurrentflowsinthesamedirectionthrough 

theload. Thatis,thenegativehalf-cycleofsourceisapositivehalf-cycleattheload. The 

currentflowisthroughtwodiodesinseriesforbothpolarities. Thus,twodiodedropsofthe 

sourcevoltagearelost(0.7·2=1.4VforSi)inthediodes.Thisisadisadvantagecomparedwith 

afull-wavecenter-tapdesign.Thisdisadvantageisonlyaprobleminverylowvoltagepower 

supplies. 

Rememberingtheproperlayoutofdiodesinafull-wavebridgerectifiercircuitcanoftenbe 

frustratingtothenewstudentofelectronics.I’vefoundthatanalternativerepresentationof 

thiscircuitiseasierbothtorememberandtocomprehend.It’stheexactsamecircuit,except 

alldiodesaredrawninahorizontalattitude,all“pointing”thesamedirection.(Figure3.23) 

- 

-


+ 

- 

Figure3.21:Full-wavebridgerectifier:Electronflowforpositivehalf-cycles. 

- 

+ 

Figure3.22:Full-wavebridgerectifier:Electronflowfornegativehalf=cycles. 

AC 

voltage 

source + 

Load 

Figure3.23:AlternativelayoutstyleforFull-wavebridgerectifier. 

+ 

- 

+ 

- 

-


Oneadvantageofrememberingthislayoutforabridgerectifiercircuitisthatitexpands 

easilyintoapolyphaseversioninFigure3.24. 

3-phase 

AC source 

+ 

Load 

Figure3.24:Three-phasefull-wavebridgerectifiercircuit. 

Eachthree-phaselineconnectsbetweenapairofdiodes:onetoroutepowertothepositive 

(+)sideoftheload,andtheothertoroutepowertothenegative(-)sideoftheload.Polyphase 

systemswithmorethanthreephasesareeasilyaccommodatedintoabridgerectifierscheme. 

Takeforinstancethesix-phasebridgerectifiercircuitinFigure3.25. 

6-phase 

AC source 

Figure3.25:Six-phasefull-wavebridgerectifiercircuit. 

- 

+ 

Load 

WhenpolyphaseACisrectified,thephase-shiftedpulsesoverlapeachothertoproduceaDC 

outputthatismuch“smoother”(haslessACcontent)thanthatproducedbytherectificationof 

single-phaseAC.Thisisadecidedadvantageinhigh-powerrectifiercircuits,wherethesheer 

physicalsizeoffilteringcomponentswouldbeprohibitivebutlow-noiseDCpowermustbe 

obtained.ThediagraminFigure3.26showsthefull-waverectificationofthree-phaseAC. 

Inanycaseofrectification–single-phaseorpolyphase–theamountofACvoltagemixed 

withtherectifier’sDCoutputiscalledripplevoltage.Inmostcases,since“pure”DCisthedesiredgoal,ripplevoltageisundesirable.Ifthepowerlevelsarenottoogreat,filteringnetworks 

maybeemployedtoreducetheamountofrippleintheoutputvoltage. 

-


1 2 3 

TIME 

Resultant DC waveform 

Figure3.26:Three-phaseACand3-phasefull-waverectifieroutput. 

Sometimes,themethodofrectificationisreferredtobycountingthenumberofDC“pulses” 

outputforevery360 o ofelectrical“rotation.”Asingle-phase,half-waverectifiercircuit,then, 

wouldbecalleda1-pulserectifier,becauseitproducesasinglepulseduringthetimeofone 

completecycle(360 o )oftheACwaveform. Asingle-phase,full-waverectifier(regardlessof 

design,center-taporbridge)wouldbecalleda2-pulserectifier,becauseitoutputstwopulses 

ofDCduringoneACcycle’sworthoftime.Athree-phasefull-waverectifierwouldbecalleda 

6-pulseunit. 

Modernelectricalengineeringconventionfurtherdescribesthefunctionofarectifiercircuit 

byusingathree-fieldnotationofphases,ways,andnumberofpulses. Asingle-phase,halfwaverectifiercircuitisgiventhesomewhatcrypticdesignationof1Ph1W1P(1phase,1way, 

1pulse),meaningthattheACsupplyvoltageissingle-phase,thatcurrentoneachphaseof 

theACsupplylinesmovesinonlyonedirection(way),andthatthereisasinglepulseofDC 

producedforevery360 o ofelectricalrotation. Asingle-phase,full-wave,center-taprectifier 

circuitwouldbedesignatedas1Ph1W2Pinthisnotationalsystem:1phase,1wayordirection 

ofcurrentineachwindinghalf,and2pulsesoroutputvoltagepercycle.Asingle-phase,fullwave,bridgerectifierwouldbedesignatedas1Ph2W2P:thesameasforthecenter-tapdesign, 

exceptcurrentcangobothwaysthroughtheAClinesinsteadofjustoneway.Thethree-phase 

bridgerectifiercircuitshownearlierwouldbecalleda3Ph2W6Prectifier. 

Isitpossibletoobtainmorepulsesthantwicethenumberofphasesinarectifiercircuit? 

Theanswertothisquestionisyes:especiallyinpolyphasecircuits.Throughthecreativeuse 

oftransformers,setsoffull-waverectifiersmaybeparalleledinsuchawaythatmorethan 

sixpulsesofDCareproducedforthreephasesofAC.A30 o phaseshiftisintroducedfrom 

primarytosecondaryofathree-phasetransformerwhenthewindingconfigurationsarenot 

ofthesametype. Inotherwords,atransformerconnectedeitherY-∆or ∆-Ywillexhibit 

this30 o phaseshift,whileatransformerconnectedY-Yor ∆-∆willnot. Thisphenomenon 

maybeexploitedbyhavingonetransformerconnectedY-Yfeedabridgerectifier,andhave 

anothertransformerconnectedY-∆feedasecondbridgerectifier,thenparalleltheDCoutputs 

ofbothrectifiers.(Figure3.27)Sincetheripplevoltagewaveformsofthetworectifiers’outputs 

arephase-shifted30 o fromoneanother,theirsuperpositionresultsinlessripplethaneither 

rectifieroutputconsideredseparately:12pulsesper360 o insteadofjustsix:

3.5. PEAKDETECTOR 115 

3-phase 

AC input 

3Ph2W12P rectifier circuit 

Primary 

Secondary 

Secondary 

+ 

DC 

output 

- 

Figure3.27:Polyphaserectifiercircuit:3-phase2-way12-pulse(3Ph2W12P) 

• REVIEW: 

• Rectificationistheconversionofalternatingcurrent(AC)todirectcurrent(DC). 

• Ahalf-waverectifierisacircuitthatallowsonlyonehalf-cycleoftheACvoltagewaveform 

tobeappliedtotheload,resultinginonenon-alternatingpolarityacrossit.Theresulting 

DCdeliveredtotheload“pulsates”significantly. 

• Afull-waverectifierisacircuitthatconvertsbothhalf-cyclesoftheACvoltagewaveform 

toanunbrokenseriesofvoltagepulsesofthesamepolarity.TheresultingDCdelivered 

totheloaddoesn’t“pulsate”asmuch. 

• Polyphasealternatingcurrent,whenrectified,givesamuch“smoother”DCwaveform 

(lessripplevoltage)thanrectifiedsingle-phaseAC. 

3.5 Peakdetector 

ApeakdetectorisaseriesconnectionofadiodeandacapacitoroutputtingaDCvoltageequal 

tothepeakvalueoftheappliedACsignal. ThecircuitisshowninFigure3.28withthecorrespondingSPICEnetlist. 

AnACvoltagesourceappliedtothepeakdetector,chargesthe 

capacitortothepeakoftheinput. Thediodeconductspositive“halfcycles,”chargingthecapacitortothewaveformpeak. 

WhentheinputwaveformfallsbelowtheDC“peak”stored 

onthecapacitor,thediodeisreversebiased,blockingcurrentflowfromcapacitorbacktothe 

source.Thus,thecapacitorretainsthepeakvalueevenasthewaveformdropstozero.Another 

viewofthepeakdetectoristhatitisthesameasahalf-waverectifierwithafiltercapacitor 

addedtotheoutput. 

IttakesafewcyclesforthecapacitortochargetothepeakasinFigure3.29duetothe 

seriesresistance(RC“timeconstant”).Whydoesthecapacitornotchargeallthewayto5V?


1 

1.0kΩ 

5 V p-p 

0 V offset 

1 kHz 

0 

3 

V(2) 

output 

2 

0.1uF 

*SPICE 03441.eps 

C1 2 0 0.1u 

R1 1 3 1.0k 

V1 1 0 SIN(0 5 1k) 

D1 3 2 diode 

.model diode d 

.tran 0.01m 50mm 

.end 

Figure3.28: Peakdetector: Diodeconductsonpositivehalfcycleschargingcapacitortothe 

peakvoltage(lessdiodeforwarddrop). 

Itwouldchargeto5Vifan“idealdiode”wereobtainable. However,thesilicondiodehasa 

forwardvoltagedropof0.7Vwhichsubtractsfromthe5Vpeakoftheinput. 

Figure3.29:Peakdetector:Capacitorchargestopeakwithinafewcycles. 

ThecircuitinFigure3.28couldrepresentaDCpowersupplybasedonahalf-waverectifier. 

TheresistancewouldbeafewOhmsinsteadof1kΩduetoatransformersecondarywinding 

replacingthevoltagesourceandresistor. Alarger“filter”capacitorwouldbeused. Apower 

supplybasedona60Hzsourcewithafilterofafewhundred µFcouldsupplyupto100mA. 

Half-wavesuppliesseldomsupplymoreduetothedifficultyoffilteringahalf-wave. 

Thepeakdetectormaybecombinedwithothercomponentstobuildacrystalradio(page 

424).

3.6. CLIPPERCIRCUITS 117 

3.6 Clippercircuits 

Acircuitwhichremovesthepeakofawaveformisknownasaclipper. Anegativeclipperis 

showninFigure3.30.ThisschematicdiagramwasproducedwithXcircuitschematiccapture 

program.XcircuitproducedtheSPICEnetlistFigure3.30,exceptforthesecond,andnextto 

lastpairoflineswhichwereinsertedwithatexteditor. 

1 2 

0 

5 V p 

0 V offset 

1 kHz 

1.0kΩ 

V(2) 

output 


* A K ModelName 

D1 0 2 diode 

R1 2 1 1.0k 

V1 1 0 SIN(0 5 1k) 


.tran .05m 3m 

.end 

Figure3.30:Clipper:clipsnegativepeakat-0.7V. 

Duringthepositivehalfcycleofthe5Vpeakinput,thediodeisreversedbiased.Thediode 

doesnotconduct. Itisasifthediodewerenotthere. Thepositivehalfcycleisunchanged 

attheoutputV(2)inFigure3.31.Sincetheoutputpositivepeaksactuallyoverlaystheinput 

sinewaveV(1),theinputhasbeenshiftedupwardintheplotforclarity.InNutmeg,theSPICE 

displaymodule,thecommand“plotv(1)+1)”accomplishesthis. 

Figure3.31:V(1)+1isactuallyV(1),a10Vptpsinewave,offsetby1Vfordisplayclarity.V(2) 

outputisclippedat-0.7V,bydiodeD1. 

DuringthenegativehalfcycleofsinewaveinputofFigure3.31,thediodeisforwardbiased,


thatis,conducting.Thenegativehalfcycleofthesinewaveisshortedout.Thenegativehalf 

cycleofV(2)wouldbeclippedat0Vforanidealdiode. Thewaveformisclippedat-0.7V 

duetotheforwardvoltagedropofthesilicondiode.Thespicemodeldefaultsto0.7Vunless 

parametersinthemodelstatementspecifyotherwise.GermaniumorSchottkydiodesclipat 

lowervoltages. 

Closerexaminationofthenegativeclippedpeak(Figure3.31)revealsthatitfollowsthe 

inputforaslightperiodoftimewhilethesinewaveismovingtoward-0.7V.Theclipping 

actionisonlyeffectiveaftertheinputsinewaveexceeds-0.7V.Thediodeisnotconductingfor 

thecompletehalfcycle,though,duringmostofit. 

Theadditionofananti-paralleldiodetotheexistingdiodeinFigure3.30yieldsthesymmetricalclipperinFigure3.32. 

1 2 

0 

5 V p 

0 V offset 

1 kHz 

1.0kΩ 

D2 D1 


D1 0 2 diode 

D2 2 0 diode 

R1 2 1 1.0k 

V1 1 0 SIN(0 5 1k) 


.tran 0.05m 3m 

.end 

Figure3.32: Symmetricalclipper: Anti-paralleldiodesclipbothpositiveandnegativepeak, 

leavinga±0.7Voutput. 

DiodeD1clipsthenegativepeakat-0.7Vasbefore.TheadditionaldiodeD2conductsfor 

positivehalfcyclesofthesinewaveasitexceeds0.7V,theforwarddiodedrop.Theremainder 

ofthevoltagedropsacrosstheseriesresistor. Thus,bothpeaksoftheinputsinewaveare 

clippedinFigure3.33.ThenetlistisinFigure3.32 

ThemostgeneralformofthediodeclipperisshowninFigure3.34.Foranidealdiode,the 

clippingoccursattheleveloftheclippingvoltage,V1andV2. However,thevoltagesources 

havebeenadjustedtoaccountforthe0.7Vforwarddropoftherealsilicondiodes. D1clips 

at1.3V+0.7V=2.0Vwhenthediodebeginstoconduct.D2clipsat-2.3V-0.7V=-3.0VwhenD2 

conducts. 

TheclipperinFigure3.34doesnothavetoclipbothlevels. Toclipatonelevelwithone 

diodeandonevoltagesource,removetheotherdiodeandsource. 

ThenetlistisinFigure3.34. ThewaveformsinFigure3.35showtheclippingofv(1)at 

outputv(2). 

Thereisalsoazenerdiodeclippercircuitinthe“Zenerdiode”section.Azenerdiodereplaces 

boththediodeandtheDCvoltagesource. 

Apracticalapplicationofaclipperistopreventanamplifiedspeechsignalfromoverdriving 

aradiotransmitterinFigure3.36. Overdrivingthetransmittergeneratesspuriousradio 

signalswhichcausesinterferencewithotherstations.Theclipperisaprotectivemeasure. 

Asinewavemaybesquaredupbyoverdrivingaclipper.Anotherclipperapplicationisthe 

protectionofexposedinputsofintegratedcircuits.TheinputoftheICisconnectedtoapairof 

diodesasatnode“2”ofFigure??.Thevoltagesourcesarereplacedbythepowersupplyrails

3.6. CLIPPERCIRCUITS 119 

Figure3.33: DiodeD1clipsat-0.7Vasitconductsduringnegativepeaks. D2conductsfor 

positivepeaks,clippingat0.7V. 

1 2 

0 

V3 

5Vp 0Voffset 1kHz 

1.0 kΩ 

D1 

V2 

D2 

3 

V1 

+ 

− 1.3V 

4 

V2 

+ 

− -2.3V 


V1 3 0 1.3 

V2 4 0 -2.3 

D1 2 3 diode 

D2 4 2 diode 

R1 2 1 1.0k 

V3 1 0 SIN(0 5 1k) 



.end 

Figure3.34:D1clipstheinputsinewaveat2V.D2clipsat-3V.


Figure3.35:D1clipsthesinewaveat2V.D2clipsat-3V. 

preamp 

microphone 

clipper 

transmitter 

Figure3.36:Clipperpreventsoverdrivingradiotransmitterbyvoicepeaks.

3.7. CLAMPERCIRCUITS 121 

oftheIC.Forexample,CMOSIC’suse0Vand+5V.Analogamplifiersmightuse ±12Vforthe 

V1andV2sources. 

• REVIEW 

• AresistoranddiodedrivenbyanACvoltagesourceclipsthesignalobservedacrossthe 

diode. 

• Apairofanti-parallelSidiodesclipsymmetricallyat ±0.7V 

• Thegroundedendofaclipperdiode(s)canbedisconnectedandwiredtoaDCvoltageto 

clipatanarbitrarylevel. 

• Aclippercanserveasaprotectivemeasure,preventingasignalfromexceedingtheclip 

limits. 

3.7 Clampercircuits 

ThecircuitsinFigure3.37areknownasclampersorDCrestorers.Thecorrespondingnetlist 

isinFigure3.38. ThesecircuitsclampapeakofawaveformtoaspecificDClevelcompared 

withacapacitivelycoupledsignalwhichswingsaboutitsaverageDClevel(usually0V).Ifthe 

diodeisremovedfromtheclamper,itdefaultstoasimplecouplingcapacitor–noclamping. 

Whatistheclampvoltage? And,whichpeakgetsclamped? InFigure3.37(a)theclamp 

voltageis0Vignoringdiodedrop,(moreexactly0.7VwithSidiodedrop).InFigure3.38,the 

positivepeakofV(1)isclampedtothe0V(0.7V)clamplevel.Whyisthis?Onthefirstpositive 

halfcycle,thediodeconductschargingthecapacitorleftendto+5V(4.3V).Thisis-5V(-4.3 

V)ontherightendatV(1,4).NotethepolaritymarkedonthecapacitorinFigure3.37(a).The 

rightendofthecapacitoris-5VDC(-4.3V)withrespecttoground.ItalsohasanAC5Vpeak 

sinewavecoupledacrossitfromsourceV(4)tonode1.Thesumofthetwoisa5Vpeaksine 

ridingona-5VDC(-4.3V)level.Thediodeonlyconductsonsuccessivepositiveexcursions 

ofsourceV(4)ifthepeakV(4)exceedsthechargeonthecapacitor. Thisonlyhappensifthe 

chargeonthecapacitordrainedoffduetoaload,notshown. Thechargeonthecapacitoris 

equaltothepositivepeakofV(4)(less0.7diodedrop). TheACridingonthenegativeend, 

rightend,isshifteddown.Thepositivepeakofthewaveformisclampedto0V(0.7V)because 

thediodeconductsonthepositivepeak. 

SupposethepolarityofthediodeisreversedasinFigure3.37(b)?Thediodeconductson 

thenegativepeakofsourceV(4). Thenegativepeakisclampedto0V(-0.7V).SeeV(2)in 

Figure3.38. 

ThemostgeneralrealizationoftheclamperisshowninFigure3.37(c)withthediode 

connectedtoaDCreference.Thecapacitorstillchargesduringthenegativepeakofthesource. 

NotethatthepolaritiesoftheACsourceandtheDCreferenceareseriesaiding. Thus,the 

capacitorchargestothesumtothetwo,10VDC(9.3V).Couplingthe5Vpeaksinewave 

acrossthecapacitoryieldsFigure3.38V(3),thesumofthechargeonthecapacitorandthe 

sinewave. Thenegativepeakappearstobeclampedto5VDC(4.3V),thevalueoftheDC 

clampreference(lessdiodedrop). 

DescribethewaveformiftheDCclampreferenceischangedfrom5Vto10V.Theclamped 

waveformwillshiftup. Thenegativepeakwillbeclampedto10V(9.3). Supposethatthe


1000pF 

4 + - 1 

+ 

- 

5 V peak 

0 V offset 

1 kHz 0 

-4.3 V DC 

1000pF 

4 2 4 1000pF 

3 

- 

- + 

4.3 VDC - 

- + 

+ 0 

+ 

(a) (b) (c) 

0 

9.3 V DC 

Figure3.37:Clampers:(a)Positivepeakclampedto0V.(b)Negativepeakclampedto0V.(c) 

Negativepeakclampedto5V. 

+ −5V 


V1 6 0 5 

D1 6 3 diode 

C1 4 3 1000p 

D2 0 2 diode 

C2 4 2 1000p 

C3 4 1 1000p 

D3 1 0 diode 

V2 4 0 SIN(0 5 1k) 



.end 

Figure3.38: V(4)sourcevoltage5Vpeakusedinallclampers. V(1)clamperoutputfrom 

Figure3.37(a).V(1,4)DCvoltageoncapacitorinFigure(a).V(2)clamperoutputfromFigure 

(b).V(3)clamperoutputfromFigure(c).

3.8. VOLTAGEMULTIPLIERS 123 

amplitudeofthesinewavesourceisincreasedfrom5Vto7V?Thenegativepeakclamplevel 

willremainunchanged.Though,theamplitudeofthesinewaveoutputwillincrease. 

Anapplicationoftheclampercircuitisasa“DCrestorer”in“compositevideo”circuitryin 

bothtelevisiontransmittersandreceivers.AnNTSC(USvideostandard)videosignal“white 

level”correspondstominimum(12.5%)transmittedpower.Thevideo“blacklevel”corresponds 

toahighlevel(75%oftransmitterpower.Thereisa“blackerthanblacklevel”correspondingto 

100%transmittedpowerassignedtosynchronizationsignals.TheNTSCsignalcontainsboth 

videoandsynchronizationpulses. Theproblemwiththecompositevideoisthatitsaverage 

DClevelvarieswiththescene,darkvslight. Thevideoitselfissupposedtovary. However, 

thesyncmustalwayspeakat100%.Topreventthesyncsignalsfromdriftingwithchanging 

scenes,a“DCrestorer”clampsthetopofthesyncpulsestoavoltagecorrespondingto100% 

transmittermodulation.[2] 

• REVIEW: 

• AcapacitivelycoupledsignalalternatesaboutitsaverageDClevel(0V). 

• ThesignaloutofaclamperappearsthehaveonepeakclampedtoaDCvoltage.Example: 

Thenegativepeakisclampedto0VDC,thewaveformappearstobeshiftedupward.The 

polarityofthediodedetermineswhichpeakisclamped. 

• Anapplicationofaclamper,orDCrestorer,isinclampingthesyncpulsesofcomposite 

videotoavoltagecorrespondingto100%oftransmitterpower. 

3.8 Voltagemultipliers 

Avoltagemultiplierisaspecializedrectifiercircuitproducinganoutputwhichistheoretically 

anintegertimestheACpeakinput,forexample,2,3,or4timestheACpeakinput. Thus, 

itispossibletoget200VDCfroma100VpeakACsourceusingadoubler,400VDCfroma 

quadrupler.Anyloadinapracticalcircuitwilllowerthesevoltages. 

AvoltagedoublerapplicationisaDCpowersupplycapableofusingeithera240VACor120 

VACsource.Thesupplyusesaswitchselectedfull-wavebridgetoproduceabout300VDCfrom 

a240VACsource.The120Vpositionoftheswitchrewiresthebridgeasadoublerproducing 

about300VDCfromthe120VAC.Inbothcases,300VDCisproduced.Thisistheinputtoa 

switchingregulatorproducinglowervoltagesforpowering,say,apersonalcomputer. 

Thehalf-wavevoltagedoublerinFigure3.39(a)iscomposedoftwocircuits:aclamperat 

(b)andpeakdetector(half-waverectifier)inFigure3.28,whichisshowninmodifiedformin 

Figure3.39(c).C2hasbeenaddedtoapeakdetector(half-waverectifier). 

ReferringtoFigure3.39(b),C2chargesto5V(4.3Vconsideringthediodedrop)onthe 

negativehalfcycleofACinput.TherightendisgroundedbytheconductingD2.Theleftend 

ischargedatthenegativepeakoftheACinput.Thisistheoperationoftheclamper. 

Duringthepositivehalfcycle,thehalf-waverectifiercomesintoplayatFigure3.39(c). 

DiodeD2isoutofthecircuitsinceitisreversebiased. C2isnowinserieswiththevoltage 

source.NotethepolaritiesofthegeneratorandC2,seriesaiding.Thus,rectifierD1seesatotal 

of10Vatthepeakofthesinewave,5Vfromgeneratorand5VfromC2.D1conductswaveform 

v(1)(Figure3.40),chargingC1tothepeakofthesinewaveridingon5VDC(Figure3.40v(2)).


1000pF 

4 1 

5V p-p 

0V offset 

1kHz 0 

(a) 

C2 D2 

D1 

1000pF 

2 

C1 

- 

+ 

5 V 

- 

+ 

C2 

D2 

+ 

- 

- 

5 V 

5 V 

(b) (c) 

C2 

+ 

D1 C1 

Figure3.39: Half-wavevoltagedoubler(a)iscomposedof(b)aclamperand(c)ahalf-wave 

rectifier. 

Waveformv(2)istheoutputofthedoubler,whichstabilizesat10V(8.6Vwithdiodedrops) 

afterafewcyclesofsinewaveinput. 

10V 

+ 

- 


C1 2 0 1000p 

D1 1 2 diode 

C2 4 1 1000p 

D2 0 1 diode 

V1 4 0 SIN(0 5 1k) 



.end 

Figure3.40: Voltagedoubler: v(4)input. v(1)clamperstage. v(2)half-waverectifierstage, 

whichisthedoubleroutput. 

Thefull-wavevoltagedoubleriscomposedofapairofseriesstackedhalf-waverectifiers. 

(Figure3.41)ThecorrespondingnetlistisinFigure3.41. ThebottomrectifierchargesC1on 

thenegativehalfcycleofinput. ThetoprectifierchargesC2onthepositivehalfcycle. Each 

capacitortakesonachargeof5V(4.3Vconsideringdiodedrop).Theoutputatnode5isthe 

seriestotalofC1+C2or10V(8.6Vwithdiodedrops). 

Notethattheoutputv(5)Figure3.42reachesfullvaluewithinonecycleoftheinputv(2) 

excursion. 

Figure3.43illustratesthederivationofthefull-wavedoublerfromapairofoppositepolarityhalf-waverectifiers(a). 

Thenegativerectifierofthepairisredrawnforclarity(b). Both 

arecombinedat(c)sharingthesameground.At(d)thenegativerectifierisre-wiredtoshare


2 

5Vp-p 0Voffset 1kHz 

D2 

D1 

C2 

C1 

5 

1000pF 

3 

1000pF 

0 


*R1 3 0 100k 

*R2 5 3 100k 

D1 0 2 diode 

D2 2 5 diode 

C1 3 0 1000p 

C2 5 3 1000p 

V1 2 3 SIN(0 5 1k) 



.end 

Figure3.41:Full-wavevoltagedoublerconsistsoftwohalf-waverectifiersoperatingonalternatingpolarities. 

Figure3.42: Full-wavevoltagedoubler: v(2)input,v(3)voltageatmidpoint,v(5)voltageat 

output


onevoltagesourcewiththepositiverectifier.Thisyieldsa±5V(4.3Vwithdiodedrop)power 

supply;though,10Vismeasurablebetweenthetwooutputs. Thegroundreferencepointis 

movedsothat+10Visavailablewithrespecttoground. 

+5V 

-5V 

+5V +5V +5V 

-5V 

(a) (b) (c) (d) (e) 

-5V 

Figure3.43:Full-wavedoubler:(a)Pairofdoublers,(b)redrawn,(c)sharingtheground,(d) 

sharethesamevoltagesource.(e)movethegroundpoint. 

Avoltagetripler(Figure3.44)isbuiltfromacombinationofadoublerandahalfwave 

rectifier(C3,D3).Thehalf-waverectifierproduces5V(4.3V)atnode3.Thedoublerprovides 

another10V(8.4V)betweennodes2and3.foratotalof15V(12.9V)attheoutputnode2 

withrespecttoground.ThenetlistisinFigure3.45. 

1000pF 

4 1 

5Vp-p 0Voffset 1kHz Doubler 3 

(a) 

C2 D2 

D1 

Single stage rectifier 

1000pF 

1000pF 

D3 0 

Figure3.44:Voltagetriplercomposedofdoublerstackedatopasinglestagerectifier. 

NotethatV(3)inFigure3.45risesto5V(4.3V)onthefirstnegativehalfcycle.Inputv(4) 

isshiftedupwardby5V(4.3V)dueto5Vfromthehalf-waverectifier.And5Vmoreatv(1) 

duetotheclamper(C2,D2).D1chargesC1(waveformv(2))tothepeakvalueofv(1). 

AvoltagequadruplerisastackedcombinationoftwodoublersshowninFigure3.46.Each 

doublerprovides10V(8.6V)foraseriestotalatnode2withrespecttogroundof20V(17.2 

V).ThenetlistisinFigure3.47. 

ThewaveformsofthequadruplerareshowninFigure3.47.TwoDCoutputsareavailable: 

v(3),thedoubleroutput,andv(2)thequadrupleroutput. Someoftheintermediatevoltages 

2 

C1 

C3 

-5V 

10V 

5V 

15V 

+10V 

+ 

- 

+5V 

+ 

-



C3 3 0 1000p 

D3 0 4 diode 

C1 2 3 1000p 

D1 1 2 diode 

C2 4 1 1000p 

D2 3 1 diode 

V1 4 3 SIN(0 5 1k) 



.end 

Figure3.45: Voltagetripler: v(3)half-waverectifier,v(4)input+5V,v(1)clamper,v(2)final 

output. 

1000pF 

4 1 

5V p-p 

0V offset 

1kHz 

C2 

doubler 1 

doubler 2 

1000pF 

C22 

D2 

D22 

5 

D11 

D1 

1000pF 

3 

1000pF 

Figure3.46: Voltagequadrupler,composedoftwodoublersstackedinseries,withoutputat 

node2. 

2 

C1 

C11 

0 

10V 

10V 

20V


atclampersillustratethattheinputsinewave(notshown),whichswingsby¡plusminus)¿5V, 

issuccessivelyclampedathigherlevels:atv(5),v(4)andv(1). Strictlyv(4)isnotaclamper 

output.ItissimplytheACvoltagesourceinserieswiththev(3)thedoubleroutput.Nonethe 

less,v(1)isaclampedversionofv(4) 



C22 4 5 1000p 

C11 3 0 1000p 

D11 0 5 diode 

D22 5 3 diode 

C1 2 3 1000p 

D1 1 2 diode 

C2 4 1 1000p 

D2 3 1 diode 

V1 4 3 SIN(0 5 1k) 



.end 

Figure3.47: Voltagequadrupler: DCvoltageavailableatv(3)andv(2). Intermediatewaveforms:Clampers:v(5),v(4),v(1). 

Somenotesonvoltagemultipliersareinorderatthispoint. Thecircuitparametersused 

intheexamples(V=5V1kHz,C=1000pf)donotprovidemuchcurrent,microamps.Furthermore,loadresistorshavebeenomitted.Loadingreducesthevoltagesfromthoseshown.Ifthe 

circuitsaretobedrivenbyakHzsourceatlowvoltage,asintheexamples,thecapacitorsare 

usually0.1to1.0 µFsothatmilliampsofcurrentareavailableattheoutput.Ifthemultipliers 

aredrivenfrom50/60Hz,thecapacitorareafewhundredtoafewthousandmicrofaradsto 

providehundredsofmilliampsofoutputcurrent.Ifdrivenfromlinevoltage,payattentionto 

thepolarityandvoltageratingsofthecapacitors. 

Finally,anydirectlinedrivenpowersupply(notransformer)isdangeroustotheexperimenterandlineoperatedtestequipment.Commercialdirectdrivensuppliesaresafebecausethehazardouscircuitryisinanenclosuretoprotecttheuser.Whenbreadboardingthesecircuitswithelectrolyticcapacitorsofanyvoltage,thecapacitorswillexplodeifthepolarityis 

reversed.Suchcircuitsshouldbepoweredupbehindasafetyshield. 

Avoltagemultiplierofcascadedhalf-wavedoublersofarbitrarylengthisknownasa 

Cockcroft-Walton multiplierasshowninFigure3.48. Thismultiplierisusedwhenahigh 

voltageatlowcurrentisrequired.Theadvantageoveraconventionalsupplyisthatanexpensivehighvoltagetransformerisnotrequired–atleastnotashighastheoutput. 

Thepairofdiodesandcapacitorstotheleftofnodes1and2inFigure3.48constitutea 

half-wavedoubler. Rotatingthediodesby45 o counterclockwise,andthebottomcapacitorby 

90 o makesitlooklikeFigure3.39(a).Fourofthedoublersectionsarecascadedtotherightfor


1000pF 

99 1 

1000pF 

3 

5Vp-p 0Voffset 1kHz 

2 

1000pF 

1000pF 

1000pF 

1000pF 

5 7 

4 6 8 

1000pF 

1000pF 

Figure3.48:Cockcroft-Waltonx8voltagemultiplier;outputatv(8). 

atheoreticalx8multiplicationfactor.Node1hasaclamperwaveform(notshown),asinewave 

shiftedupby1x(5V).Theotheroddnumberednodesaresinewavesclampedtosuccessively 

highervoltages.Node2,theoutputofthefirstdoubler,isa2xDCvoltagev(2)inFigure3.49. 

Successiveevennumberednodeschargetosuccessivelyhighervoltages:v(4),v(6),v(8) 

Figure3.49:Cockcroft-Walton(x8)waveforms.Outputisv(8). 

D1 7 8 diode 

C1 8 6 1000p 

D2 6 7 diode 

C2 5 7 1000p 

D3 5 6 diode 

C3 4 6 1000p 

D4 4 5 diode 

C4 3 5 1000p 

D5 3 4 diode 

C5 2 4 1000p 

D6 2 3 diode 

D7 1 2 diode 

C6 1 3 1000p 

C7 2 0 1000p 

C8 99 1 1000p 

D8 0 1 diode 

V1 99 0 SIN(0 5 

1k) 


.tran 0.01m 50m 

.end 

Withoutdiodedrops,eachdoubleryields2Vinor10V,consideringtwodiodedrops(10- 

1.4)=8.6Visrealistic.Foratotalof4doublersoneexpects4·8.6=34.4Voutof40V.Consulting 

Figure3.49,v(2)isaboutright;however,v(8)is


paredwith5msforpreviouscircuits.Itrequired40msecforthevoltagestorisetoaterminal 

valueforthiscircuit.ThenetlistinFigure3.49hasa“.tran0.010m50m”commandtoextend 

thesimulationtimeto50msec;though,only40msecisplotted. 

TheCockcroft-Waltonmultiplierservesasamoreefficienthighvoltagesourceforphotomultipliertubesrequiringupto2000V.[3]Moreover,thetubehasnumerousdynodes,terminalsrequiringconnectiontothelowervoltage“evennumbered”nodes.Theseriesstringof 

multipliertapsreplacesaheatgeneratingresistivevoltagedividerofpreviousdesigns. 

AnAClineoperatedCockcroft-Waltonmultiplierprovideshighvoltageto“iongenerators” 

forneutralizingelectrostaticchargeandforairpurifiers. 

• REVIEW: 

• AvoltagemultiplierproducesaDCmultiple(2,3,4,etc)oftheACpeakinputvoltage. 

• Themostbasicmultiplierisahalf-wavedoubler. 

• Thefull-wavedoubleisasuperiorcircuitasadoubler. 

• Atriplerisahalf-wavedoublerandaconventionalrectifierstage(peakdetector). 

• Aquadruplerisapairofhalf-wavedoublers 

• Alongstringofhalf-wavedoublersisknownasaCockcroft-Waltonmultiplier. 

3.9 Inductorcommutatingcircuits 

Apopularuseofdiodesisforthemitigationofinductive“kickback:”thepulsesofhighvoltage 

producedwhendirectcurrentthroughaninductorisinterrupted. Take,forexample,this 

simplecircuitinFigure3.50withnoprotectionagainstinductivekickback. 

+ 

− 

+ 

− 

+ 

+ 

− 

− − + 

(a) (b) (c) (d) 

Figure3.50: Inductivekickback: (a)Switchopen. (b)Switchclosed,electroncurrentflows 

frombatterythroughcoilwhichhaspolaritymatchingbattery. Magneticfieldstoresenergy. 

(c)Switchopen,Currentstillflowsincoilduetocollapsingmagneticfield.Notepolaritychange 

oncoil.(d)Coilvoltagevstime. 

Whenthepushbuttonswitchisactuated,currentgoesthroughtheinductor,producing 

amagneticfieldaroundit. Whentheswitchisde-actuated,itscontactsopen,interrupting 

currentthroughtheinductor,andcausingthemagneticfieldtorapidlycollapse.Becausethe 

voltageinducedinacoilofwireisdirectlyproportionaltotherateofchangeovertimeof 

magneticflux(Faraday’sLaw:e=NdΦ/dt),thisrapidcollapseofmagnetismaroundthecoil 

producesahighvoltage“spike”. 

V 

off 

on 

off

3.9. INDUCTORCOMMUTATINGCIRCUITS 131 

Iftheinductorinquestionisanelectromagnetcoil,suchasinasolenoidorrelay(constructedforthepurposeofcreatingaphysicalforceviaitsmagneticfieldwhenenergized),the 

effectofinductive“kickback”servesnousefulpurposeatall. Infact,itisquitedetrimental 

totheswitch,asitcausesexcessivearcingatthecontacts,greatlyreducingtheirservicelife. 

Ofthepracticalmethodsformitigatingthehighvoltagetransientcreatedwhentheswitchis 

opened,nonesosimpleastheso-calledcommutatingdiodeinFigure3.51. 

+ 

- 

+ 

- 

(a) (b) (c) 

Figure3.51: Inductivekickbackwithprotection: (a)Switchopen. (b)Switchclosed,storing 

energyinmagneticfield.(c)Switchopen,inductivekickbackisshortedbydiode. 

Inthiscircuit,thediodeisplacedinparallelwiththecoil,suchthatitwillbereverse-biased 

whenDCvoltageisappliedtothecoilthroughtheswitch. Thus,whenthecoilisenergized, 

thediodeconductsnocurrentinFigure3.51(b). 

However,whentheswitchisopened,thecoil’sinductancerespondstothedecreaseincurrentbyinducingavoltageofreversepolarity,inanefforttomaintaincurrentatthesame 

magnitudeandinthesamedirection.Thissuddenreversalofvoltagepolarityacrossthecoil 

forward-biasesthediode,andthediodeprovidesacurrentpathfortheinductor’scurrent,so 

thatitsstoredenergyisdissipatedslowlyratherthansuddenlyinFigure3.51(c). 

Asaresult,thevoltageinducedinthecoilbyitscollapsingmagneticfieldisquitelow: 

merelytheforwardvoltagedropofthediode,ratherthanhundredsofvoltsasbefore. Thus, 

theswitchcontactsexperienceavoltagedropequaltothebatteryvoltageplusabout0.7volts 

(ifthediodeissilicon)duringthisdischargetime. 

Inelectronicsparlance,commutationreferstothereversalofvoltagepolarityorcurrentdirection.Thus,thepurposeofacommutatingdiodeistoactwhenevervoltagereversespolarity, 

forexample,onaninductorcoilwhencurrentthroughitisinterrupted.Alessformaltermfor 

acommutatingdiodeissnubber,becauseit“snubs”or“squelches”theinductivekickback. 

Anoteworthydisadvantageofthismethodistheextratimeitimpartstothecoil’sdischarge. 

Becausetheinducedvoltageisclampedtoaverylowvalue,itsrateofmagneticfluxchange 

overtimeiscomparativelyslow. RememberthatFaraday’sLawdescribesthemagneticflux 

rate-of-change(dΦ/dt)asbeingproportionaltotheinduced,instantaneousvoltage(eorv).If 

theinstantaneousvoltageislimitedtosomelowfigure,thentherateofchangeofmagnetic 

fluxovertimewilllikewisebelimitedtoalow(slow)figure. 

Ifanelectromagnetcoilis“snubbed”withacommutatingdiode,themagneticfieldwilldissipateatarelativelyslowratecomparedtotheoriginalscenario(nodiode)wherethefield 

disappearedalmostinstantlyuponswitchrelease. Theamountoftimeinquestionwillmost 

likelybelessthanonesecond,butitwillbemeasurablyslowerthanwithoutacommutatingdiodeinplace. 

Thismaybeanintolerableconsequenceifthecoilisusedtoactuatean 

+ 

- 

+ 

- 

+ 

- 

- 

+ 

- 

+


electromechanicalrelay,becausetherelaywillpossessanatural“timedelay”uponcoildeenergization,andanunwanteddelayofevenafractionofasecondmaywreakhavocinsome 

circuits. 

Unfortunately,onecannoteliminatethehigh-voltagetransientofinductivekickbackand 

maintainfastde-magnetizationofthecoil:Faraday’sLawwillnotbeviolated.However,ifslow 

de-magnetizationisunacceptable,acompromisemaybestruckbetweentransientvoltageand 

timebyallowingthecoil’svoltagetorisetosomehigherlevel(butnotsohighaswithouta 

commutatingdiodeinplace).TheschematicinFigure3.52showshowthiscanbedone. 

(a) 

Figure3.52:(a)Commutatingdiodewithseriesresistor.(b)Voltagewaveform.(c)Levelwith 

nodiode.(d)Levelwithdiode,noresistor.(e)Compromiselevelwithdiodeandresistor. 

Aresistorplacedinserieswiththecommutatingdiodeallowsthecoil’sinducedvoltageto 

risetoalevelgreaterthanthediode’sforwardvoltagedrop,thushasteningtheprocessofdemagnetization.This,ofcourse,willplacetheswitchcontactsundergreaterstress,andsothe 

resistormustbesizedtolimitthattransientvoltageatanacceptablemaximumlevel. 

3.10 Diodeswitchingcircuits 

Diodescanperformswitchinganddigitallogicoperations.Forwardandreversebiasswitcha 

diodebetweenthelowandhighimpedancestates,respectively.Thus,itservesasaswitch. 

3.10.1 Logic 

Diodescanperformdigitallogicfunctions:AND,andOR.Diodelogicwasusedinearlydigital 

computers. Itonlyfindslimitedapplicationtoday. Sometimesitisconvenienttofashiona 

singlelogicgatefromafewdiodes. 

AnANDgateisshowninFigure3.53.Logicgateshaveinputsandanoutput(Y)whichis 

afunctionoftheinputs. Theinputstothegatearehigh(logic1),say10V,orlow,0V(logic 

0). Inthefigure,thelogiclevelsaregeneratedbyswitches. Ifaswitchisup,theinputis 

effectivelyhigh(1).Iftheswitchisdown,itconnectsadiodecathodetoground,whichislow 

(0).TheoutputdependsonthecombinationofinputsatAandB.Theinputsandoutputare 

customarilyrecordedina“truthtable”at(c)todescribethelogicofagate. At(a)allinputs 

arehigh(1). Thisisrecordedinthelastlineofthetruthtableat(c). Theoutput,Y,ishigh 

(1)duetotheV + onthetopoftheresistor.Itisunaffectedbyopenswitches.At(b)switchA 

pullsthecathodeoftheconnecteddiodelow,pullingoutputYlow(0.7V).Thisisrecordedin 

V 

(b) 

off 

on 

off 

(d) 

(e) 

(c)

3.10. DIODESWITCHINGCIRCUITS 133 

1 

1 

A 

B 

V + 

V + 

Y=1 Y=0 

0 A 

1 

(a) (b) (c) 

Figure3.53:DiodeANDgate 

B 

A B Y 

0 0 0 

0 1 0 

1 0 0 

1 1 1 

thethirdlineofthetruthtable. Thesecondlineofthetruthtabledescribestheoutputwith 

theswitchesreversedfrom(b).SwitchBpullsthediodeandoutputlow.Thefirstlineofthe 

truthtablerecordestheOutput=0forbothinputlow(0). Thetruthtabledescribesalogical 

ANDfunction.Summary:bothinputsAandBhighyieldsahigh(1)out. 

AtwoinputORgatecomposedofapairofdiodesisshowninFigure??.Ifbothinputsare 

logiclowat(a)assimulatedbybothswitches“downward,”theoutputYispulledlowbythe 

resistor.Thislogiczeroisrecordedinthefirstlineofthetruthtableat(c).Ifoneoftheinputs 

ishighasat(b),ortheotherinputishigh,orbothinputshigh,thediode(s)conduct(s),pulling 

theoutputYhigh.Theseresultsarereorderedinthesecondthroughfourthlinesofthetruth 

table.Summary:anyinput“high”isahighoutatY. 

0 

0 

V + 

A 

B 

Y=0 

1 

0 

V + 

A 

B 

Y=1 

A B Y 

0 0 0 

0 1 1 

1 0 1 

1 1 1 

(a) (b) (c) 

line 

operated 

power 

supply 

backup 

battery 

Figure3.54:ORgate:(a)Firstline,truthtable(TT).(b)ThirdlineTT.(d)LogicalORofpower 

linesupplyandback-upbattery. 

AbackupbatterymaybeOR-wiredwithalineoperatedDCpowersupplyinFigure3.54(d) 

topoweraload,evenduringapowerfailure.WithACpowerpresent,thelinesupplypowers 

theload,assumingthatitisahighervoltagethanthebattery.Intheeventofapowerfailure, 

thelinesupplyvoltagedropsto0V;thebatterypowerstheload.Thediodesmustbeinseries 

withthepowersourcestopreventafailedlinesupplyfromdrainingthebattery,andtoprevent 

itfromoverchargingthebatterywhenlinepowerisavailable.DoesyourPCcomputerretain 

itsBIOSsettingwhenpoweredoff?DoesyourVCR(videocassetterecorder)retaintheclock 

settingafterapowerfailure?(PCYes,oldVCRno,newVCRyes.) 

+ 

(d) 

+ 

+ 

load


3.10.2 Analogswitch 

Diodescanswitchanalogsignals. Areversebiaseddiodeappearstobeanopencircuit. A 

forwardbiaseddiodeisalowresistanceconductor.TheonlyproblemisisolatingtheACsignal 

beingswitchedfromtheDCcontrolsignal. ThecircuitinFigure3.55isaparallelresonant 

network: resonanttuninginductorparalleledbyone(ormore)oftheswitchedresonatorcapacitors.ThisparallelLCresonantcircuitcouldbeapreselectorfilterforaradioreceiver.It 

couldbethefrequencydeterminingnetworkofanoscillator(notshown). Thedigitalcontrol 

linesmaybedrivenbyamicroprocessorinterface. 

switching 

diode 

RFC 

decoupling 

capacitor 

switched 

resonator 

capacitor 

RFC 

digital control 

RFC 

RFC 

+5V 

resonant 

tuning 

inductor 

large value 

DC blocking 

capacitor 

Figure3.55:Diodeswitch:Adigitalcontrolsignal(low)selectsaresonatorcapacitorbyforward 

biasingtheswitchingdiode. 

ThelargevalueDCblockingcapacitorgroundstheresonanttuninginductorforACwhile 

blockingDC.ItwouldhavealowreactancecomparedtotheparallelLCreactances. This 

preventstheanodeDCvoltagefrombeingshortedtogroundbytheresonanttuninginductor. 

Aswitchedresonatorcapacitorisselectedbypullingthecorrespondingdigitalcontrollow.This 

forwardbiasestheswitchingdiode. TheDCcurrentpathisfrom+5VthroughanRFchoke 

(RFC),aswitchingdiode,andanRFCtogroundviathedigitalcontrol.ThepurposeoftheRFC 

atthe+5VistokeepACoutofthe+5Vsupply.TheRFCinserieswiththedigitalcontrolisto 

keepACoutoftheexternalcontrolline.ThedecouplingcapacitorshortsthelittleACleaking 

throughtheRFCtoground,bypassingtheexternaldigitalcontrolline. 

Withallthreedigitalcontrollineshigh(≥+5V),noswitchedresonatorcapacitorsareselectedduetodiodereversebias. 

Pullingoneormorelineslow,selectsoneormoreswitched 

resonatorcapacitors,respectively. Asmorecapacitorsareswitchedinparallelwiththeresonanttuninginductor,theresonantfrequencydecreases. 

Thereversebiaseddiodecapacitancemaybesubstantialcomparedwithveryhighfrequencyorultrahighfrequencycircuits.PINdiodesmaybeusedasswitchesforlowercapacitance.

3.11. ZENERDIODES 135 

3.11 Zenerdiodes 

IfweconnectadiodeandresistorinserieswithaDCvoltagesourcesothatthediodeis 

forward-biased,thevoltagedropacrossthediodewillremainfairlyconstantoverawiderange 

ofpowersupplyvoltagesasinFigure3.56(a). 

Accordingtothe“diodeequation”(page101),thecurrentthroughaforward-biasedPN 

junctionisproportionaltoeraisedtothepoweroftheforwardvoltagedrop.Becausethisisan 

exponentialfunction,currentrisesquiterapidlyformodestincreasesinvoltagedrop.Another 

wayofconsideringthisistosaythatvoltagedroppedacrossaforward-biaseddiodechanges 

littleforlargevariationsindiodecurrent.InthecircuitshowninFigure3.56(a),diodecurrent 

islimitedbythevoltageofthepowersupply,theseriesresistor,andthediode’svoltagedrop, 

whichasweknowdoesn’tvarymuchfrom0.7volts. Ifthepowersupplyvoltageweretobe 

increased,theresistor’svoltagedropwouldincreasealmostthesameamount,andthediode’s 

voltagedropjustalittle. Conversely,adecreaseinpowersupplyvoltagewouldresultinan 

almostequaldecreaseinresistorvoltagedrop,withjustalittledecreaseindiodevoltagedrop. 

Inaword,wecouldsummarizethisbehaviorbysayingthatthediodeisregulatingthevoltage 

dropatapproximately0.7volts. 

Voltageregulationisausefuldiodepropertytoexploit. Supposewewerebuildingsome 

kindofcircuitwhichcouldnottoleratevariationsinpowersupplyvoltage,butneededtobe 

poweredbyachemicalbattery,whosevoltagechangesoveritslifetime.Wecouldformacircuit 

asshownandconnectthecircuitrequiringsteadyvoltageacrossthediode,whereitwould 

receiveanunchanging0.7volts. 

Thiswouldcertainlywork,butmostpracticalcircuitsofanykindrequireapowersupply 

voltageinexcessof0.7voltstoproperlyfunction. Onewaywecouldincreaseourvoltage 

regulationpointwouldbetoconnectmultiplediodesinseries,sothattheirindividualforward 

voltagedropsof0.7voltseachwouldaddtocreatealargertotal.Forinstance,ifwehadten 

diodesinseries,theregulatedvoltagewouldbetentimes0.7,or7voltsinFigure3.56(b). 

≈ 0.7 V 

(a) (b) 

≈ ≈7.0 7.0 V 

Figure3.56:ForwardbiasedSireference:(a)singlediode,0.7V,(b)10-diodesinseries7.0V. 

Solongasthebatteryvoltageneversaggedbelow7volts,therewouldalwaysbeabout7 

voltsdroppedacrosstheten-diode“stack.” 

Iflargerregulatedvoltagesarerequired,wecouldeitherusemorediodesinseries(aninelegantoption,inmyopinion),ortryafundamentallydifferentapproach.Weknowthatdiode 

forwardvoltageisafairlyconstantfigureunderawiderangeofconditions,butsoisreverse 

breakdownvoltage,andbreakdownvoltageistypicallymuch,muchgreaterthanforwardvoltage.Ifwereversedthepolarityofthediodeinoursingle-dioderegulatorcircuitandincreased 

thepowersupplyvoltagetothepointwherethediode“brokedown”(couldnolongerwithstand


thereverse-biasvoltageimpressedacrossit),thediodewouldsimilarlyregulatethevoltageat 

thatbreakdownpoint,notallowingittoincreasefurtherasinFigure3.57(a). 

+ 

≈ 50 V 

150 V ≈ 100 V 

- 

(a) (b) 

Zener diode 

Cathode 

Anode 

Figure3.57:(a)ReversebiasedSismall-signaldiodebreaksdownatabout100V.(b)Symbol 

forZenerdiode. 

Unfortunately,whennormalrectifyingdiodes“breakdown,”theyusuallydosodestructively. 

However,itispossibletobuildaspecialtypeofdiodethatcanhandlebreakdown 

withoutfailingcompletely.Thistypeofdiodeiscalledazenerdiode,anditssymbollookslike 

Figure3.57(b). 

Whenforward-biased,zenerdiodesbehavemuchthesameasstandardrectifyingdiodes: 

theyhaveaforwardvoltagedropwhichfollowsthe“diodeequation”andisabout0.7volts. 

Inreverse-biasmode,theydonotconductuntiltheappliedvoltagereachesorexceedsthesocalledzenervoltage,atwhichpointthediodeisabletoconductsubstantialcurrent,andin 

doingsowilltrytolimitthevoltagedroppedacrossittothatzenervoltagepoint.Solongas 

thepowerdissipatedbythisreversecurrentdoesnotexceedthediode’sthermallimits,the 

diodewillnotbeharmed. 

Zenerdiodesaremanufacturedwithzenervoltagesranginganywherefromafewvoltsto 

hundredsofvolts. Thiszenervoltagechangesslightlywithtemperature,andlikecommon 

carbon-compositionresistorvalues,maybeanywherefrom5percentto10percentinerror 

fromthemanufacturer’sspecifications.However,thisstabilityandaccuracyisgenerallygood 

enoughforthezenerdiodetobeusedasavoltageregulatordeviceincommonpowersupply 

circuitinFigure3.58. 

+ 

- 

≈ 12.6 V 

Figure3.58:Zenerdioderegulatorcircuit,Zenervoltage=12.6V). 

Pleasetakenoteofthezenerdiode’sorientationintheabovecircuit:thediodeisreversebiased,andintentionallyso. 

Ifwehadorientedthediodeinthe“normal”way,soastobe 

forward-biased,itwouldonlydrop0.7volts,justlikearegularrectifyingdiode. Ifwewant 

toexploitthisdiode’sreversebreakdownproperties,wemustoperateitinitsreverse-bias 

mode.Solongasthepowersupplyvoltageremainsabovethezenervoltage(12.6volts,inthis 

example),thevoltagedroppedacrossthezenerdiodewillremainatapproximately12.6volts.


Likeanysemiconductordevice,thezenerdiodeissensitivetotemperature.Excessivetemperaturewilldestroyazenerdiode,andbecauseitbothdropsvoltageandconductscurrent,itproducesitsownheatinaccordancewithJoule’sLaw(P=IE).Therefore,onemustbecarefultodesigntheregulatorcircuitinsuchawaythatthediode’spowerdissipationratingis 

notexceeded.Interestinglyenough,whenzenerdiodesfailduetoexcessivepowerdissipation, 

theyusuallyfailshortedratherthanopen.Adiodefailedinthismannerisreadilydetected:it 

dropsalmostzerovoltagewhenbiasedeitherway,likeapieceofwire. 

Let’sexamineazenerdioderegulatingcircuitmathematically,determiningallvoltages, 

currents,andpowerdissipations.Takingthesameformofcircuitshownearlier,we’llperform 

calculationsassumingazenervoltageof12.6volts,apowersupplyvoltageof45volts,anda 

seriesresistorvalueof1000 Ω(we’llregardthezenervoltagetobeexactly12.6voltssoasto 

avoidhavingtoqualifyallfiguresas“approximate”inFigure3.59(a) 

Ifthezenerdiode’svoltageis12.6voltsandthepowersupply’svoltageis45volts,therewill 

be32.4voltsdroppedacrosstheresistor(45volts-12.6volts=32.4volts).32.4voltsdropped 

across1000 Ωgives32.4mAofcurrentinthecircuit.(Figure3.59(b)) 

45 V 

+ 

- 

1 kΩ 

12.6 V 

45 V 

(a) (b) 

+ 

- 

32.4 V 

1 kΩ 

32.4 mA 

32.4 mA 

12.6 V 

Figure3.59:(a)ZenerVoltageregulatorwith1000 Ωresistor.(b)Calculationofvoltagedrops 

andcurrent. 

Poweriscalculatedbymultiplyingcurrentbyvoltage(P=IE),sowecancalculatepower 

dissipationsforboththeresistorandthezenerdiodequiteeasily: 

P resistor = (32.4 mA)(32.4 V) 

P resistor = 1.0498 W 

P diode = (32.4 mA)(12.6 V) 

P diode = 408.24 mW 

Azenerdiodewithapowerratingof0.5wattwouldbeadequate,aswouldaresistorrated 

for1.5or2wattsofdissipation. 

Ifexcessivepowerdissipationisdetrimental,thenwhynotdesignthecircuitfortheleast 

amountofdissipationpossible? Whynotjustsizetheresistorforaveryhighvalueofresistance,thusseverelylimitingcurrentandkeepingpowerdissipationfiguresverylow?Takethis 

circuit,forexample,witha100kΩresistorinsteadofa1kΩresistor.Notethatboththepower 

supplyvoltageandthediode’szenervoltageinFigure3.60areidenticaltothelastexample:


45 V 

+ 

- 

32.4 V 

100 kΩ 

324 µA 

324 µA 

12.6 V 

Figure3.60:Zenerregulatorwith100kΩresistor. 

Withonly1/100ofthecurrentwehadbefore(324 µAinsteadof32.4mA),bothpower 

dissipationfiguresshouldbe100timessmaller: 

P resistor = (324 µA)(32.4 V) 

P resistor = 10.498 mW 

P diode = (324 µA)(12.6 V) 

P diode = 4.0824 mW 

Seemsideal,doesn’tit? Lesspowerdissipationmeansloweroperatingtemperaturesfor 

boththediodeandtheresistor,andalsolesswastedenergyinthesystem,right? Ahigher 

resistancevaluedoesreducepowerdissipationlevelsinthecircuit,butitunfortunatelyintroducesanotherproblem.Rememberthatthepurposeofaregulatorcircuitistoprovideastable 

voltageforanothercircuit. Inotherwords,we’reeventuallygoingtopowersomethingwith 

12.6volts,andthissomethingwillhaveacurrentdrawofitsown.Considerourfirstregulator 

circuit,thistimewitha500 ΩloadconnectedinparallelwiththezenerdiodeinFigure3.61. 

45 V 

+ 

- 

32.4 V 

1 kΩ 

32.4 mA 

32.4 mA 

7.2 mA 

25.2 mA 

25.2 mA 

12.6 V 

R load 

500 Ω 

Figure3.61:Zenerregulatorwith1000 Ωseriesresistorand500 Ωload. 

If12.6voltsismaintainedacrossa500 Ωload,theloadwilldraw25.2mAofcurrent. In 

orderforthe1kΩseries“dropping”resistortodrop32.4volts(reducingthepowersupply’s 

voltageof45voltsdownto12.6acrossthezener),itstillmustconduct32.4mAofcurrent. 

Thisleaves7.2mAofcurrentthroughthezenerdiode. 

Nowconsiderour“power-saving”regulatorcircuitwiththe100kΩdroppingresistor,deliv-


eringpowertothesame500 Ωload. Whatitissupposedtodoismaintain12.6voltsacross 

theload,justlikethelastcircuit. However,aswewillsee,itcannotaccomplishthistask. 

(Figure3.62) 

45 V 

44.776 V 

100 kΩ 

447.76 µA 

0 µA 

224 mV 

447.76 µA 447.76 µA 

447.76 µA 

R load 

500 Ω 

Figure3.62:Zenernon-regulatorwith100KΩseriesresistorwith500 Ωload.¿ 

Withthelargervalueofdroppingresistorinplace,therewillonlybeabout224mVof 

voltageacrossthe500 Ωload,farlessthantheexpectedvalueof12.6volts!Whyisthis?Ifwe 

actuallyhad12.6voltsacrosstheload,itwoulddraw25.2mAofcurrent,asbefore.Thisload 

currentwouldhavetogothroughtheseriesdroppingresistorasitdidbefore,butwithanew 

(muchlarger!) droppingresistorinplace,thevoltagedroppedacrossthatresistorwith25.2 

mAofcurrentgoingthroughitwouldbe2,520volts!Sinceweobviouslydon’thavethatmuch 

voltagesuppliedbythebattery,thiscannothappen. 

Thesituationiseasiertocomprehendifwetemporarilyremovethezenerdiodefromthe 

circuitandanalyzethebehaviorofthetworesistorsaloneinFigure3.63. 

45 V 

44.776 V 

100 kΩ 

447.76 µA 

447.76 µA 447.76 µA 

447.76 µA 

224 mV 

Figure3.63:Non-regulatorwithZenerremoved. 

R load 

500 Ω 

Boththe100kΩdroppingresistorandthe500 Ωloadresistanceareinserieswitheach 

other,givingatotalcircuitresistanceof100.5kΩ.Withatotalvoltageof45voltsandatotal 

resistanceof100.5kΩ,Ohm’sLaw(I=E/R)tellsusthatthecurrentwillbe447.76 µA.Figuring 

voltagedropsacrossbothresistors(E=IR),wearriveat44.776voltsand224mV,respectively. 

Ifweweretore-installthezenerdiodeatthispoint,itwould“see”224mVacrossitaswell, 

beinginparallelwiththeloadresistance.Thisisfarbelowthezenerbreakdownvoltageofthe 

diodeandsoitwillnot“breakdown”andconductcurrent.Forthatmatter,atthislowvoltage 

thediodewouldn’tconductevenifitwereforward-biased!Thus,thediodeceasestoregulate 

voltage.Atleast12.6voltsmustbedroppedacrossto“activate”it.


Theanalyticaltechniqueofremovingazenerdiodefromacircuitandseeingwhetheror 

notenoughvoltageispresenttomakeitconductisasoundone. Justbecauseazenerdiode 

happenstobeconnectedinacircuitdoesn’tguaranteethatthefullzenervoltagewillalways 

bedroppedacrossit!Rememberthatzenerdiodesworkbylimitingvoltagetosomemaximum 

level;theycannotmakeupforalackofvoltage. 

Insummary,anyzenerdioderegulatingcircuitwillfunctionsolongastheload’sresistance 

isequaltoorgreaterthansomeminimumvalue. Iftheloadresistanceistoolow,itwill 

drawtoomuchcurrent,droppingtoomuchvoltageacrosstheseriesdroppingresistor,leaving 

insufficientvoltageacrossthezenerdiodetomakeitconduct. Whenthezenerdiodestops 

conductingcurrent,itcannolongerregulatevoltage,andtheloadvoltagewillfallbelowthe 

regulationpoint. 

Ourregulatorcircuitwiththe100kΩdroppingresistormustbegoodforsomevalueof 

loadresistance,though. Tofindthisacceptableloadresistancevalue,wecanuseatableto 

calculateresistanceinthetwo-resistorseriescircuit(nodiode),insertingtheknownvaluesof 

totalvoltageanddroppingresistorresistance,andcalculatingforanexpectedloadvoltageof 

12.6volts: 

Rdropping Rload Total 

E 

I 

R 

100 k 

12.6 

45 

Volts 

Amps 

Ohms 

With45voltsoftotalvoltageand12.6voltsacrosstheload,weshouldhave32.4voltsacross 

Rdropping: 

E 

I 

R 

R dropping R load Total 

32.4 

100 k 

12.6 

45 

Volts 

Amps 

Ohms 

With32.4voltsacrossthedroppingresistor,and100kΩworthofresistanceinit,thecurrent 

throughitwillbe324 µA: 


E 

I 

R 

32.4 

324 µ 

100 k 

Ohm’s Law 

I = E 

R 

12.6 

45 

Volts 

Amps 

Ohms


Beingaseriescircuit,thecurrentisequalthroughallcomponentsatanygiventime: 


E 

I 

R 

32.4 

100 k 

12.6 

45 

324 µ 324 µ 324 µ 

Volts 

Amps 

Ohms 

Rule of series circuits: 

ITotal = I1 = I2 = . . . In CalculatingloadresistanceisnowasimplematterofOhm’sLaw(R=E/I),givingus38.889 

kΩ: 


E 

I 

R 

32.4 

100 k 

12.6 

45 

324 µ 324 µ 324 µ 

38.889 k 

Ohm’s Law 

R = E 

I 

Volts 

Amps 

Ohms 

Thus,iftheloadresistanceisexactly38.889kΩ,therewillbe12.6voltsacrossit,diodeor 

nodiode. Anyloadresistancesmallerthan38.889kΩwillresultinaloadvoltagelessthan 

12.6volts,diodeornodiode. Withthediodeinplace,theloadvoltagewillberegulatedtoa 

maximumof12.6voltsforanyloadresistancegreaterthan38.889kΩ. 

Withtheoriginalvalueof1kΩforthedroppingresistor,ourregulatorcircuitwasable 

toadequatelyregulatevoltageevenforaloadresistanceaslowas500 Ω. Whatweseeisa 

tradeoffbetweenpowerdissipationandacceptableloadresistance.Thehigher-valuedropping 

resistorgaveuslesspowerdissipation,attheexpenseofraisingtheacceptableminimumload 

resistancevalue.Ifwewishtoregulatevoltageforlow-valueloadresistances,thecircuitmust 

bepreparedtohandlehigherpowerdissipation. 

Zenerdiodesregulatevoltagebyactingascomplementaryloads,drawingmoreorlesscurrentasnecessarytoensureaconstantvoltagedropacrosstheload. 

Thisisanalogousto 

regulatingthespeedofanautomobilebybrakingratherthanbyvaryingthethrottleposition: 

notonlyisitwasteful,butthebrakesmustbebuilttohandlealltheengine’spowerwhen 

thedrivingconditionsdon’tdemandit.Despitethisfundamentalinefficiencyofdesign,zener 

dioderegulatorcircuitsarewidelyemployedduetotheirsheersimplicity. Inhigh-powerapplicationswheretheinefficiencieswouldbeunacceptable,othervoltage-regulatingtechniques 

areapplied.Buteventhen,smallzener-basedcircuitsareoftenusedtoprovidea“reference” 

voltagetodriveamoreefficientamplifiercircuitcontrollingthemainpower. 

ZenerdiodesaremanufacturedinstandardvoltageratingslistedinTable 3.1.Thetable 

“Commonzenerdiodevoltages”listscommonvoltagesfor0.3Wand1.3Wparts.Thewattage


correspondstodieandpackagesize,andisthepowerthatthediodemaydissipatewithout 

damage. 

Table3.1:Commonzenerdiodevoltages 

0.5W 

2.7V 3.0V 3.3V 3.6V 3.9V 4.3V 4.7V 

5.1V 5.6V 6.2V 6.8V 7.5V 8.2V 9.1V 

10V 11V 12V 13V 15V 16V 18V 

20V 24V 27V 30V 

1.3W 

4.7V 5.1V 5.6V 6.2V 6.8V 7.5V 8.2V 

9.1V 10V 11V 12V 13V 15V 16V 

18V 20V 22V 24V 27V 30V 33V 

36V 39V 43V 47V 51V 56V 62V 

68V 75V 100V 200V 

Zenerdiodeclipper: Aclippingcircuitwhichclipsthepeaksofwaveformatapproximatelythezenervoltageofthediodes. 

ThecircuitofFigure3.64hastwozenersconnected 

seriesopposingtosymmetricallyclipawaveformatnearlytheZenervoltage. Theresistor 

limitscurrentdrawnbythezenerstoasafevalue. 

1 2 

0 

20V p 

0 V offset 

1 kHz 

1.0kΩ 

V(2) 

output 

Figure3.64:Zenerdiodeclipper: 


D1 4 0 diode 

D2 4 2 diode 

R1 2 1 1.0k 

V1 1 0 SIN(0 20 

1k) 


bv=10 

.tran 0.001m 2m 

.end 

Thezenerbreakdownvoltageforthediodesissetat10Vbythediodemodelparameter 

“bv=10”inthespicenetlistinFigure3.64.Thiscausesthezenerstoclipatabout10V.The 

back-to-backdiodesclipbothpeaks.Forapositivehalf-cycle,thetopzenerisreversebiased, 

breakingdownatthezenervoltageof10V.Thelowerzenerdropsapproximately0.7Vsince 

itisforwardbiased. Thus,amoreaccurateclippinglevelis10+0.7=10.7V.Similarnegative 

half-cycleclippingoccursa-10.7V.(Figure3.65)showstheclippinglevelatalittleover ±10V. 

• REVIEW: 

• Zenerdiodesaredesignedtobeoperatedinreverse-biasmode,providingarelativelylow, 

stablebreakdown,orzenervoltageatwhichtheybegintoconductsubstantialreverse

3.12. SPECIAL-PURPOSEDIODES 143 

current. 

Figure3.65:Zenerdiodeclipper:v(1)inputisclippedatwaveformv(2). 

• Azenerdiodemayfunctionasavoltageregulatorbyactingasanaccessoryload,drawing 

morecurrentfromthesourceifthevoltageistoohigh,andlessifitistoolow. 

3.12 Special-purposediodes 

3.12.1 Schottkydiodes 

Schottkydiodesareconstructedofametal-to-NjunctionratherthanaP-Nsemiconductor 

junction.Alsoknownashot-carrierdiodes,Schottkydiodesarecharacterizedbyfastswitching 

times(lowreverse-recoverytime),lowforwardvoltagedrop(typically0.25to0.4voltsfora 

metal-siliconjunction),andlowjunctioncapacitance. 

TheschematicsymbolforaschottkydiodeisshowninFigure3.66. 

Anode 

Cathode 

Figure3.66:Schottkydiodeschematicsymbol. 

Theforwardvoltagedrop(VF),reverse-recoverytime(trr),andjunctioncapacitance(CJ)of 

Schottkydiodesareclosertoidealthantheaverage“rectifying”diode.Thismakesthemwell 

suitedforhigh-frequencyapplications.Unfortunately,though,Schottkydiodestypicallyhave 

lowerforwardcurrent(IF)andreversevoltage(VRRMandVDC)ratingsthanrectifyingdiodes


andarethusunsuitableforapplicationsinvolvingsubstantialamountsofpower.Thoughthey 

areusedinlowvoltageswitchingregulatorpowersupplies. 

Schottkydiodetechnologyfindsbroadapplicationinhigh-speedcomputercircuits,where 

thefastswitchingtimeequatestohighspeedcapability,andthelowforwardvoltagedrop 

equatestolesspowerdissipationwhenconducting. 

Switchingregulatorpowersuppliesoperatingat100’sofkHzcannotuseconventionalsilicondiodesasrectifiersbecauseoftheirslowswitchingspeed. 

Whenthesignalappliedtoa 

diodechangesfromforwardtoreversebias,conductioncontinuesforashorttime,whilecarriersarebeingsweptoutofthedepletionregion.Conductiononlyceasesafterthistr 

reverse 

recoverytimehasexpired.Schottkydiodeshaveashorterreverserecoverytime. 

Regardlessofswitchingspeed,the0.7Vforwardvoltagedropofsilicondiodescausespoor 

efficiencyinlowvoltagesupplies.Thisisnotaproblemin,say,a10Vsupply.Ina1Vsupply 

the0.7Vdropisasubstantialportionoftheoutput.Onesolutionistouseaschottkypower 

diodewhichhasalowerforwarddrop. 

3.12.2 Tunneldiodes 

Tunneldiodesexploitastrangequantumphenomenoncalledresonanttunnelingtoprovidea 

negativeresistanceforward-biascharacteristics.Whenasmallforward-biasvoltageisapplied 

acrossatunneldiode,itbeginstoconductcurrent.(Figure3.67(b))Asthevoltageisincreased, 

thecurrentincreasesandreachesapeakvaluecalledthepeakcurrent(IP). Ifthevoltage 

isincreasedalittlemore,thecurrentactuallybeginstodecreaseuntilitreachesalowpoint 

calledthevalleycurrent(IV). Ifthevoltageisincreasedfurtheryet,thecurrentbeginsto 

increaseagain,thistimewithoutdecreasingintoanother“valley.” Theschematicsymbolfor 

thetunneldiodeshowninFigure3.67(a). 

Tunnel diode 

Anode 

Cathode 

Forward 

current 

I P 

I V 

(a) (b) VP VV Forward voltage (c) 

Figure3.67:Tunneldiode(a)Schematicsymbol.(b)Currentvsvoltageplot(c)Oscillator. 

Theforwardvoltagesnecessarytodriveatunneldiodetoitspeakandvalleycurrentsare 

knownaspeakvoltage(VP)andvalleyvoltage(VV),respectively. Theregiononthegraph 

wherecurrentisdecreasingwhileappliedvoltageisincreasing(betweenVP andVV onthe 

horizontalscale)isknownastheregionofnegativeresistance. 

Tunneldiodes,alsoknownasEsakidiodesinhonoroftheirJapaneseinventorLeoEsaki, 

areabletotransitionbetweenpeakandvalleycurrentlevelsveryquickly,“switching”between 

highandlowstatesofconductionmuchfasterthanevenSchottkydiodes.Tunneldiodecharacteristicsarealsorelativelyunaffectedbychangesintemperature. 

+ 

−


Breakdown voltage (V) 

1000 

100 

10 

1 

10 14 

Ge 

Si 

10 15 

GaAs 

10 16 

GaP 

Doping concentration (cm -3 ) 

tunneling 

Figure3.68:Reversebreakdownvoltageversusdopinglevel.AfterSze[22] 

TunneldiodesareheavilydopedinboththePandNregions,1000timesthelevelina 

rectifier.ThiscanbeseeninFigure3.68.Standarddiodesaretothefarleft,zenerdiodesnear 

totheleft,andtunneldiodestotherightofthedashedline. Theheavydopingproducesan 

unusuallythindepletionregion. Thisproducesanunusuallylowreversebreakdownvoltage 

withhighleakage. Thethindepletionregioncauseshighcapacitance. Toovercomethis,the 

tunneldiodejunctionareamustbetiny. Theforwarddiodecharacteristicconsistsoftworegions:anormalforwarddiodecharacteristicwithcurrentrisingexponentiallybeyondVF,0.3 

VforGe,0.7VforSi.Between0VandVFisanadditional“negativeresistance”characteristic 

peak. Thisisduetoquantummechanicaltunnelinginvolvingthedualparticle-wavenature 

ofelectrons.Thedepletionregionisthinenoughcomparedwiththeequivalentwavelengthof 

theelectronthattheycantunnelthrough.Theydonothavetoovercomethenormalforward 

diodevoltageVF. TheenergyleveloftheconductionbandoftheN-typematerialoverlaps 

thelevelofthevalencebandintheP-typeregion.Withincreasingvoltage,tunnelingbegins; 

thelevelsoverlap;currentincreases,uptoapoint. Ascurrentincreasesfurther,theenergy 

levelsoverlapless;currentdecreaseswithincreasingvoltage.Thisisthe“negativeresistance” 

portionofthecurve. 

Tunneldiodesarenotgoodrectifiers,astheyhaverelativelyhigh“leakage”currentwhen 

reverse-biased.Consequently,theyfindapplicationonlyinspecialcircuitswheretheirunique 

tunneleffecthasvalue. Toexploitthetunneleffect,thesediodesaremaintainedatabias 

voltagesomewherebetweenthepeakandvalleyvoltagelevels,alwaysinaforward-biased 

polarity(anodepositive,andcathodenegative). 

Perhapsthemostcommonapplicationofatunneldiodeisinsimplehigh-frequencyoscillatorcircuitsasinFigure3.67(c),whereitallowsaDCvoltagesourcetocontributepowertoan 

LC“tank”circuit,thediodeconductingwhenthevoltageacrossitreachesthepeak(tunnel) 

levelandeffectivelyinsulatingatallothervoltages. Theresistorsbiasthetunneldiodeata 

10 17 

10 18


fewtenthsofavoltcenteredonthenegativeresistanceportionofthecharacteristiccurve.The 

L-Cresonantcircuitmaybeasectionofwaveguideformicrowaveoperation.Oscillationto5 

GHzispossible. 

Atonetimethetunneldiodewastheonlysolid-statemicrowaveamplifieravailable.Tunnel 

diodeswerepopularstartinginthe1960’s. Theywerelongerlivedthantravelingwavetube 

amplifiers,animportantconsiderationinsatellitetransmitters.Tunneldiodesarealsoresistanttoradiationbecauseoftheheavydoping.Todayvarioustransistorsoperateatmicrowave 

frequencies.Evensmallsignaltunneldiodesareexpensiveanddifficulttofindtoday.Thereis 

oneremainingmanufacturerofgermaniumtunneldiodes,andnoneforsilicondevices.They 

aresometimesusedinmilitaryequipmentbecausetheyareinsensitivetoradiationandlarge 

temperaturechanges. 

Therehasbeensomeresearchinvolvingpossibleintegrationofsilicontunneldiodesinto 

CMOSintegratedcircuits.Theyarethoughttobecapableofswitchingat100GHzindigital 

circuits. Thesolemanufacturerofgermaniumdevicesproducesthemoneatatime. Abatch 

processforsilicontunneldiodesmustbedeveloped,thenintegratedwithconventionalCMOS 

processes.[21] 

TheEsakitunneldiodeshouldnotbeconfusedwiththeresonanttunnelingdiode(page 

84),ofmorecomplexconstructionfromcompoundsemiconductors.TheRTDisamorerecent 

developmentcapableofhigherspeed. 

3.12.3 Light-emittingdiodes 

Diodes,likeallsemiconductordevices,aregovernedbytheprinciplesdescribedinquantum 

physics.Oneoftheseprinciplesistheemissionofspecific-frequencyradiantenergywhenever 

electronsfallfromahigherenergyleveltoalowerenergylevel. Thisisthesameprinciple 

atworkinaneonlamp,thecharacteristicpink-orangeglowofionizedneonduetothespecific 

energytransitionsofitselectronsinthemidstofanelectriccurrent.Theuniquecolorofaneon 

lamp’sglowisduetothefactthatitsneongasinsidethetube,andnotduetotheparticular 

amountofcurrentthroughthetubeorvoltagebetweenthetwoelectrodes. Neongasglows 

pinkish-orangeoverawiderangeofionizingvoltagesandcurrents. Eachchemicalelement 

hasitsown“signature”emissionofradiantenergywhenitselectrons“jump”betweendifferent, 

quantizedenergylevels. Hydrogengas,forexample,glowsredwhenionized;mercuryvapor 

glowsblue.Thisiswhatmakesspectrographicidentificationofelementspossible. 

ElectronsflowingthroughaPNjunctionexperiencesimilartransitionsinenergylevel,and 

emitradiantenergyastheydoso.Thefrequencyofthisradiantenergyisdeterminedbythe 

crystalstructureofthesemiconductormaterial,andtheelementscomprisingit. Somesemiconductorjunctions,composedofspecialchemicalcombinations,emitradiantenergywithin 

thespectrumofvisiblelightastheelectronschangeenergylevels. Simplyput,thesejunctionsglowwhenforwardbiased.Adiodeintentionallydesignedtoglowlikealampiscalleda 

light-emittingdiode,orLED. 

ForwardbiasedsilicondiodesgiveoffheataselectronandholesfromtheN-typeandP-type 

regions,respectively,recombineatthejunction.InaforwardbiasedLED,therecombinationof 

electronsandholesintheactiveregioninFigure3.69(c)yieldsphotons.Thisprocessisknown 

aselectroluminescence.Togiveoffphotons,thepotentialbarrierthroughwhichtheelectrons 

fallmustbehigherthanforasilicondiode.Theforwarddiodedropcanrangetoafewvoltsfor 

somecolorLEDs.


Diodesmadefromacombinationoftheelementsgallium,arsenic,andphosphorus(called 

gallium-arsenide-phosphide)glowbrightred,andaresomeofthemostcommonLEDsmanufactured. 

ByalteringthechemicalconstituencyofthePNjunction,differentcolorsmaybe 

obtained.EarlygenerationsofLEDswerered,green,yellow,orange,andinfra-red,latergenerationsincludedblueandultraviolet,withvioletbeingthelatestcoloraddedtotheselection. 

Othercolorsmaybeobtainedbycombiningtwoormoreprimary-color(red,green,andblue) 

LEDstogetherinthesamepackage,sharingthesameopticallens.Thisallowedformulticolor 

LEDs,suchastricolorLEDs(commerciallyavailableinthe1980’s)usingredandgreen(which 

cancreateyellow)andlaterRGBLEDs(red,green,andblue),whichcovertheentirecolor 

spectrum. 

TheschematicsymbolforanLEDisaregulardiodeshapeinsideofacircle,withtwosmall 

arrowspointingaway(indicatingemittedlight),showninFigure3.69. 

Anode 

long 

Cathode short 

(a) (b) 

flat 

(c) 

+ 

− 

p-type 

active region 

n-type 

substrate 

electron 

hole 

Figure3.69: LED,LightEmittingDiode: (a)schematicsymbol. (b)Flatsideandshortlead 

ofdevicecorrespondtocathode,aswellastheinternalarrangementofthecathode.(c)Cross 

sectionofLeddie. 

Thisnotationofhavingtwosmallarrowspointingawayfromthedeviceiscommontothe 

schematicsymbolsofalllight-emittingsemiconductordevices.Conversely,ifadeviceislightactivated(meaningthatincominglightstimulatesit),thenthesymbolwillhavetwosmall 

arrowspointingtowardit.LEDscansenselight.Theygenerateasmallvoltagewhenexposed 

tolight,muchlikeasolarcellonasmallscale. Thispropertycanbegainfullyappliedina 

varietyoflight-sensingcircuits. 

BecauseLEDsaremadeofdifferentchemicalsubstancesthansilicondiodes,theirforward 

voltagedropswillbedifferent.Typically,LEDshavemuchlargerforwardvoltagedropsthan 

rectifyingdiodes,anywherefromabout1.6voltstoover3volts,dependingonthecolor.Typical 

operatingcurrentforastandard-sizedLEDisaround20mA.WhenoperatinganLEDfrom 

aDCvoltagesourcegreaterthantheLED’sforwardvoltage,aseries-connected“dropping” 

resistormustbeincludedtopreventfullsourcevoltagefromdamagingtheLED.Considerthe 

examplecircuitinFigure3.70(a)usinga6Vsource. 

WiththeLEDdropping1.6volts,therewillbe4.4voltsdroppedacrosstheresistor.Sizing 

theresistorforanLEDcurrentof20mAisassimpleastakingitsvoltagedrop(4.4volts)and 

dividingbycircuitcurrent(20mA),inaccordancewithOhm’sLaw(R=E/I).Thisgivesusa 

figureof220 Ω. Calculatingpowerdissipationforthisresistor,wetakeitsvoltagedropand 

multiplybyitscurrent(P=IE),andendupwith88mW,wellwithintheratingofa1/8watt 

resistor. Higherbatteryvoltageswillrequirelarger-valuedroppingresistors,andpossibly


+ 

− 

6 V 

R dropping 

220 Ω 

Red LED, 

V F = 1.6 V typical 

I F = 20 mA typical 

(a) (b) 

+ 

− 

24 V 

R dropping 

1.12 kΩ 

Figure3.70:SettingLEDcurrentat20ma.(a)fora6Vsource,(b)fora24Vsource. 

higher-powerratingresistorsaswell. ConsidertheexampleinFigure??(b)forasupply 

voltageof24volts: 

Here,thedroppingresistormustbeincreasedtoasizeof1.12kΩtodrop22.4voltsat20 

mAsothattheLEDstillreceivesonly1.6volts. Thisalsomakesforahigherresistorpower 

dissipation:448mW,nearlyone-halfawattofpower!Obviously,aresistorratedfor1/8watt 

powerdissipationoreven1/4wattdissipationwilloverheatifusedhere. 

DroppingresistorvaluesneednotbepreciseforLEDcircuits. Supposeweweretousea 

1kΩresistorinsteadofa1.12kΩresistorinthecircuitshownabove. Theresultwouldbea 

slightlygreatercircuitcurrentandLEDvoltagedrop,resultinginabrighterlightfromthe 

LEDandslightlyreducedservicelife. Adroppingresistorwithtoomuchresistance(say,1.5 

kΩinsteadof1.12kΩ)willresultinlesscircuitcurrent,lessLEDvoltage,andadimmerlight. 

LEDsarequitetolerantofvariationinappliedpower,soyouneednotstriveforperfectionin 

sizingthedroppingresistor. 

MultipleLEDsaresometimesrequired,sayinlighting. IfLEDsareoperatedinparallel, 

eachmusthaveitsowncurrentlimitingresistorasinFigure??(a)toensurecurrentsdividing 

moreequally. However,itismoreefficienttooperateLEDsinseries(Figure3.71(b))witha 

singledroppingresistor.AsthenumberofseriesLEDsincreasestheseriesresistorvaluemust 

decreasetomaintaincurrent,toapoint.ThenumberofLEDsinseries(Vf)cannotexceedthe 

capabilityofthepowersupply.MultipleseriesstringsmaybeemployedasinFigure3.71(c). 

InspiteofequalizingthecurrentsinmultipleLEDs,thebrightnessofthedevicesmaynot 

matchduetovariationsintheindividualparts.Partscanbeselectedforbrightnessmatching 

forcriticalapplications. 

+ 

− 

6 V 

(a) 

220 Ω + 

− 

140 Ω 

6 V 

+ 

− 

(b) (c) 

6 V 

140 Ω 

Figure3.71:MultipleLEDs:(a)Inparallel,(b)inseries,(c)series-parallel


Alsobecauseoftheiruniquechemicalmakeup,LEDshavemuch,muchlowerpeak-inverse 

voltage(PIV)ratingsthanordinaryrectifyingdiodes. AtypicalLEDmightonlyberatedat 

5voltsinreverse-biasmode. Therefore,whenusingalternatingcurrenttopoweranLED, 

connectaprotectiverectifyingdiodeanti-parallelwiththeLEDtopreventreversebreakdown 

everyotherhalf-cycleasinFigure3.72(a). 

(a) 

+ 

− 

24 V 

R dropping 

1.12 kΩ 

rectifying diode 

Red LED, 

V F = 1.6 V typical 

I F = 20 mA typical 

V R = 5 V maximum 

Figure3.72:DrivinganLEDwithAC 

Theanti-paralleldiodeinFigure3.72canbereplacedwithananti-parallelLED.Theresultingpairofanti-parallelLED’silluminateonalternatinghalf-cyclesoftheACsinewave. 

Thisconfigurationdraws20ma,splittingitequallybetweentheLED’sonalternatingAChalf 

cycles.EachLEDonlyreceives10mAduetothissharing.ThesameistrueoftheLEDantiparallelcombinationwitharectifier.TheLEDonlyreceives10ma.If20mAwasrequiredfor 

theLED(s),Theresistorvaluecouldbehalved. 

TheforwardvoltagedropofLED’sisinverselyproportionaltothewavelength(λ).Aswavelengthdecreasesgoingfrominfraredtovisiblecolorstoultraviolet,Vfincreases. 

Whilethis 

trendismostobviousinthevariousdevicesfromasinglemanufacturer,Thevoltagerangefor 

aparticularcolorLEDfromvariousmanufacturersvaries.Thisrangeofvoltagesisshownin 

Table3.2. 

Table3.2:OpticalandelectricalpropertiesofLED’s 

LED λnm(=10 −9 m) Vf(from) Vf(to) 

infrared 940 1.2 1.7 

red 660 1.5 2.4 

orange 602-620 2.1 2.2 

yellow,green 560-595 1.7 2.8 

white,blue,violet - 3 4 

ultraviolet 370 4.2 4.8 

Aslamps,LEDsaresuperiortoincandescentbulbsinmanyways. Firstandforemostis 

efficiency:LEDsoutputfarmorelightpowerperwattofelectricalinputthananincandescent 

lamp. Thisisasignificantadvantageifthecircuitinquestionisbattery-powered,efficiency 

translatingtolongerbatterylife. SecondisthefactthatLEDsarefarmorereliable,having 

amuchgreaterservicelifethanincandescentlamps.ThisisbecauseLEDsare“cold”devices: 

theyoperateatmuchcoolertemperaturesthananincandescentlampwithawhite-hotmetal 

filament,susceptibletobreakagefrommechanicalandthermalshock.Thirdisthehighspeed 

atwhichLEDsmaybeturnedonandoff. Thisadvantageisalsoduetothe“cold”operation


ofLEDs: theydon’thavetoovercomethermalinertiaintransitioningfromofftoonorvice 

versa.Forthisreason,LEDsareusedtotransmitdigital(on/off)informationaspulsesoflight, 

conductedinemptyspaceorthroughfiber-opticcable,atveryhighratesofspeed(millionsof 

pulsespersecond). 

LEDsexcelinmonochromaticlightingapplicationsliketrafficsignalsandautomotivetail 

lights. Incandescentsareabysmalinthisapplicationsincetheyrequirefiltering,decreasing 

efficiency.LEDsdonotrequirefiltering. 

OnemajordisadvantageofusingLEDsassourcesofilluminationistheirmonochromatic 

(single-color)emission. Noonewantstoreadabookunderthelightofared,green,orblue 

LED.However,ifusedincombination,LEDcolorsmaybemixedforamorebroad-spectrum 

glow.AnewbroadspectrumlightsourceisthewhiteLED.Whilesmallwhitepanelindicators 

havebeenavailableformanyyears,illuminationgradedevicesarestillindevelopment. 

Table3.3:Efficiencyoflighting 

Lamptype Efficiencylumen/watt Lifehrs notes 

WhiteLED 35 100,000 costly 

WhiteLED,future 100 100,000 R&Dtarget 

Incandescent 12 1000 inexpensive 

Halogen 15-17 2000 highqualitylight 

Compactfluorescent 50-100 10,000 costeffective 

Sodiumvapor,lp 70-200 20,000 outdoor 

Mercuryvapor 13-48 18,000 outdoor 

AwhiteLEDisablueLEDexcitingaphosphorwhichemitsyellowlight. Theblueplus 

yellowapproximateswhitelight.Thenatureofthephosphordeterminesthecharacteristicsof 

thelight.Aredphosphormaybeaddedtoimprovethequalityoftheyellowplusbluemixture 

attheexpenseofefficiency. Table 3.3compareswhiteilluminationLEDstoexpectedfuture 

devicesandotherconventionallamps. Efficiencyismeasuredinlumensoflightoutputper 

wattofinputpower.Ifthe50lumens/wattdevicecanbeimprovedto100lumens/watt,white 

LEDswillbecomparabletocompactfluorescentlampsinefficiency. 

LEDsingeneralhavebeenamajorsubjectofR&Dsincethe1960’s. Becauseofthisit 

isimpracticaltocoverallgeometries,chemistries,andcharacteristicsthathavebeencreated 

overthedecades. Theearlydeviceswererelativelydimandtookmoderatecurrents. TheefficiencieshavebeenimprovedinlatergenerationstothepointitishazardoustolookcloselyanddirectlyintoanilluminatedLED.Thiscanresultineyedamage,andtheLEDsonlyrequiredaminorincreaseindroppingvoltage(Vf)andcurrent. 

Modernhighintensitydevices 

havereached180lumensusing0.7Amps(82lumens/watt,LuxeonRebelseriescoolwhite), 

andevenhigherintensitymodelscanuseevenhighercurrentswithacorrespondingincrease 

inbrightness.Otherdevelopments,suchasquantumdots,arethesubjectofcurrentresearch, 

soexpecttoseenewthingsforthesedevicesinthefuture 

3.12.4 Laserdiodes 

Thelaserdiodeisafurtherdevelopmentupontheregularlight-emittingdiode,orLED.The 

term“laser”itselfisactuallyanacronym,despitethefactitsoftenwritteninlower-caseletters.


“Laser”standsforLightAmplificationbyStimulatedEmissionofRadiation,andrefersto 

anotherstrangequantumprocesswherebycharacteristiclightemittedbyelectronsfalling 

fromhigh-leveltolow-levelenergystatesinamaterialstimulateotherelectronsinasubstance 

tomakesimilar“jumps,”theresultbeingasynchronizedoutputoflightfromthematerial.This 

synchronizationextendstotheactualphaseoftheemittedlight,sothatalllightwavesemitted 

froma“lasing”materialarenotjustthesamefrequency(color),butalsothesamephaseas 

eachother,sothattheyreinforceoneanotherandareabletotravelinaverytightly-confined, 

nondispersingbeam.Thisiswhylaserlightstayssoremarkablyfocusedoverlongdistances: 

eachandeverylightwavecomingfromthelaserisinstepwitheachother. 

(a) 

(b) 

(c) 

"white" 

light 

source 

monochromatic 

light 

source 

laser 

light 

source 

Figure3.73: (a)Whitelightofmanywavelengths. (b)Mono-chromaticLEDlight,asingle 

wavelength.(c)Phasecoherentlaserlight. 

Incandescentlampsproduce“white”(mixed-frequency,ormixed-color)lightasinFigure3.73 

(a).RegularLEDsproducemonochromaticlight:samefrequency(color),butdifferentphases, 

resultinginsimilarbeamdispersioninFigure3.73(b). LaserLEDsproducecoherentlight: 

lightthatisbothmonochromatic(single-color)andmonophasic(single-phase),resultingin 

precisebeamconfinementasinFigure3.73(c). 

Laserlightfindswideapplicationinthemodernworld:everythingfromsurveying,where 

astraightandnondispersinglightbeamisveryusefulforprecisesightingofmeasurement 

markers,tothereadingandwritingofopticaldisks,whereonlythenarrownessofafocused 

laserbeamisabletoresolvethemicroscopic“pits”inthedisk’ssurfacecomprisingthebinary 

1’sand0’sofdigitalinformation. 

Somelaserdiodesrequirespecialhigh-power“pulsing”circuitstodeliverlargequantitiesof 

voltageandcurrentinshortbursts.Otherlaserdiodesmaybeoperatedcontinuouslyatlower 

power.Inthecontinuouslaser,laseractionoccursonlywithinacertainrangeofdiodecurrent, 

necessitatingsomeformofcurrent-regulatorcircuit.Aslaserdiodesage,theirpowerrequirementsmaychange(morecurrentrequiredforlessoutputpower),butitshouldberemembered 

thatlow-powerlaserdiodes,likeLEDs,arefairlylong-liveddevices,withtypicalservicelives 

inthetensofthousandsofhours.


3.12.5 Photodiodes 

Aphotodiodeisadiodeoptimizedtoproduceanelectroncurrentflowinresponsetoirradiationbyultraviolet,visible,orinfraredlight.Siliconismostoftenusedtofabricatephotodiodes; 

though,germaniumandgalliumarsenidecanbeused. Thejunctionthroughwhichlightentersthesemiconductormustbethinenoughtopassmostofthelightontotheactiveregion 

(depletionregion)wherelightisconvertedtoelectronholepairs. 

InFigure3.74ashallowP-typediffusionintoanN-typewaferproducesaPNjunctionnear 

thesurfaceofthewafer. TheP-typelayerneedstobethintopassasmuchlightaspossible. 

AheavyN+diffusiononthebackofthewafermakescontactwithmetalization. Thetop 

metalizationmaybeafinegridofmetallicfingersonthetopofthewaferforlargecells. In 

smallphotodiodes,thetopcontactmightbeasolebondwirecontactingthebareP-typesilicon 

top. 

+ 

- 

top metal contact 

p diffusion 


n type 

n+ contact region 

bottom metal contact 

Figure3.74:Photodiode:Schematicsymbolandcrosssection. 

Lightenteringthetopofthephotodiodestackfalloffexponentiallyinwithdepthofthe 

silicon. AthintopP-typelayerallowsmostphotonstopassintothedepletionregionwhere 

electron-holepairsareformed.Theelectricfieldacrossthedepletionregionduetothebuiltin 

diodepotentialcauseselectronstobesweptintotheN-layer,holesintotheP-layer. Actually 

electron-holepairsmaybeformedinanyofthesemiconductorregions.However,thoseformed 

inthedepletionregionaremostlikelytobeseparatedintotherespectiveNandP-regions. 

Manyoftheelectron-holepairsformedinthePandN-regionsrecombine. Onlyafewdoso 

inthedepletionregion. Thus,afewelectron-holepairsintheNandP-regions,andmostin 

thedepletionregioncontributetophotocurrent,thatcurrentresultingfromlightfallingonthe 

photodiode. 

Thevoltageoutofaphotodiodemaybeobserved.Operationinthis photovoltaic(PV)mode 

isnotlinearoveralargedynamicrange,thoughitissensitiveandhaslownoiseatfrequencies 

lessthan100kHz.Thepreferredmodeofoperationisoftenphotocurrent(PC)modebecause 

thecurrentislinearlyproportionaltolightfluxoverseveraldecadesofintensity,andhigher 

frequencyresponsecanbeachieved.PCmodeisachievedwithreversebiasorzerobiasonthe 

photodiode.Acurrentamplifier(transimpedanceamplifier)shouldbeusedwithaphotodiode 

+ 

-


inPCmode.LinearityandPCmodeareachievedaslongasthediodedoesnotbecomeforward 

biased. 

Highspeedoperationisoftenrequiredofphotodiodes,asopposedtosolarcells. Speed 

isafunctionofdiodecapacitance,whichcanbeminimizedbydecreasingcellarea. Thus,a 

sensorforahighspeedfiberopticlinkwilluseanareanolargerthannecessary,say1mm 2 . 

Capacitancemayalsobedecreasedbyincreasingthethicknessofthedepletionregion,inthe 

manufacturingprocessorbyincreasingthereversebiasonthediode. 

PINdiodeThep-i-ndiodeorPINdiodeisaphotodiodewithanintrinsiclayerbetween 

thePandN-regionsasinFigure3.75. TheP-Intrinsic-Nstructureincreasesthedistance 

betweenthePandNconductivelayers,decreasingcapacitance,increasingspeed.Thevolume 

ofthephotosensitiveregionalsoincreases,enhancingconversionefficiency. Thebandwidth 

canextendto10’sofgHz. PINphotodiodesarethepreferredforhighsensitivity,andhigh 

speedatmoderatecost. 


p diffusion 

intrinsic region 

(larger depletion 

region) 

n type 



+ 

- 

Figure3.75: PINphotodiode: Theintrinsicregionincreasesthethicknessofthedepletion 

region. 

Avalanchephotodiode:Anavalanchephotodiode(APD)designedtooperateathighreversebiasexhibitsanelectronmultipliereffectanalogoustoaphotomultipliertube.Thereversebiascanrunfrom10’sofvoltstonearly2000V.Thehighlevelofreversebiasacceleratesphotoncreatedelectron-holepairsintheintrinsicregiontoahighenoughvelocitytofreeadditionalcarriersfromcollisionswiththecrystallattice.Thus,manyelectronsperphotonresult. 

ThemotivationfortheAPDistoachieveamplificationwithinthephotodiodetoovercomenoise 

inexternalamplifiers.Thisworkstosomeextent.However,theAPDcreatesnoiseofitsown. 

AthighspeedtheAPDissuperiortoaPINdiodeamplifiercombination,thoughnotforlow 

speedapplications.APD’sareexpensive,roughlythepriceofaphotomultipliertube.So,they 

areonlycompetitivewithPINphotodiodesfornicheapplications. Onesuchapplicationis 

singlephotoncountingasappliedtonuclearphysics.


3.12.6 Solarcells 

Aphotodiodeoptimizedforefficientlydeliveringpowertoaloadisthesolarcell.Itoperatesin 

photovoltaicmode(PV)becauseitisforwardbiasedbythevoltagedevelopedacrosstheload 

resistance. 

Monocrystallinesolarcellsaremanufacturedinaprocesssimilartosemiconductorprocessing.Thisinvolvesgrowingasinglecrystalboulefrommoltenhighpuritysilicon(P-type), 

though,notashighpurityasforsemiconductors.Thebouleisdiamondsawedorwiresawed 

intowafers.Theendsoftheboulemustbediscardedorrecycled,andsiliconislostinthesaw 

kerf.Sincemoderncellsarenearlysquare,siliconislostinsquaringtheboule.Cellsmaybe 

etchedtotexture(roughen)thesurfacetohelptraplightwithinthecell.Considerablesilicon 

islostinproducingthe10or15cmsquarewafers. Thesedays(2007)itiscommonforsolar 

cellmanufacturertopurchasethewafersatthisstagefromasuppliertothesemiconductor 

industry. 

P-typeWafersareloadedback-to-backintofusedsilicaboatsexposingonlytheoutersurface 

totheN-typedopantinthediffusionfurnace.Thediffusionprocessformsathinn-typelayeron 

thetopofthecell.Thediffusionalsoshortstheedgesofthecellfronttoback.Theperiphery 

mustberemovedbyplasmaetchingtounshortthecell. Silverandoraluminumpasteis 

screenedonthebackofthecell,andasilvergridonthefront.Thesearesinteredinafurnace 

forgoodelectricalcontact.(Figure3.76) 

Thecellsarewiredinserieswithmetalribbons. Forcharging12Vbatteries,36cellsat 

approximately0.5Varevacuumlaminatedbetweenglass,andapolymermetalback. The 

glassmayhaveatexturedsurfacetohelptraplight. 


N diffusion 


P type wafer 

bottom metal 

contact 

- 

Figure3.76:SiliconSolarcell 

Theultimatecommercialhighefficiency(21.5%)singlecrystalsiliconsolarcellshaveall 

contactsonthebackofthecell. Theactiveareaofthecellisincreasedbymovingthetop(-) 

contactconductorstothebackofthecell.Thetop(-)contactsarenormallymadetotheN-type 

siliconontopofthecell.InFigure3.77the(-)contactsaremadetoN + diffusionsonthebottom 

interleavedwith(+)contacts. Thetopsurfaceistexturedtoaidintrappinglightwithinthe 

cell..[18] 

Multicyrstallinesiliconcellsstartoutasmoltensiliconcastintoarectangularmold.As 

+


Antireflectrive coating 

Silicon dioxide passivation 

N-type diffusion 

P-type wafer 

N + diffusion 

- contact 

N + P 

diffusion 

+ diffusion 

+ contact 

- contact 

Figure3.77:Highefficiencysolarcellwithallcontactsontheback.AdaptedfromFigure1[18] 

thesiliconcools,itcrystallizesintoafewlarge(mmtocmsized)randomlyorientedcrystals 

insteadofasingleone.Theremainderoftheprocessisthesameasforsinglecrystalcells.The 

finishedcellsshowlinesdividingtheindividualcrystals,asifthecellswerecracked.Thehigh 

efficiencyisnotquiteashighassinglecrystalcellsduetolossesatcrystalgrainboundaries. 

Thecellsurfacecannotberoughenedbyetchingduetotherandomorientationofthecrystals. 

However,anantireflectrivecoatingimprovesefficiency.Thesecellsarecompetitiveforallbut 

spaceapplications. 

Threelayercell:Thehighestefficiencysolarcellisastackofthreecellstunedtoabsorb 

differentportionsofthesolarspectrum.Thoughthreecellscanbestackedatoponeanother, 

amonolithicsinglecrystalstructureof20semiconductorlayersismorecompact. At32% 

efficiency,itisnow(2007)favoredoversiliconforspaceapplication. Thehighcostprevents 

itfromfindingmanyearthboundapplicationsotherthanconcentratorsbasedonlensesor 

mirrors. 

Intensiveresearchhasrecentlyproducedaversionenhancedforterrestrialconcentrators 

at400-1000sunsand40.7%efficiency.ThisrequireseitherabiginexpensiveFresnellensor 

reflectorandasmallareaoftheexpensivesemiconductor. Thiscombinationisthoughttobe 

competitivewithinexpensivesiliconcellsforsolarpowerplants.[9][23] 

Metalorganicchemicalvapordeposition(MOCVD)depositsthelayersatopaP-typegermaniumsubstrate.ThetoplayersofNandP-typegalliumindiumphosphide(GaInP)having 

abandgapof1.85eV,absorbsultravioletandvisiblelight. Thesewavelengthshaveenough 

energytoexceedthebandgap.Longerwavelengths(lowerenergy)donothaveenoughenergy 

tocreateelectron-holepairs,andpassonthroughtothenextlayer.Agalliumarsenidelayers 

havingabandgapof1.42eV,absorbsnearinfraredlight. Finallythegermaniumlayerand 

substrateabsorbfarinfrared.Theseriesofthreecellsproduceavoltagewhichisthesumof 

thevoltagesofthethreecells. Thevoltagedevelopedbyeachmaterialis0.4Vlessthanthe 

bandgapenergylistedinTable3.4. Forexample,forGaInP:1.8eV/e-0.4V=1.4V.Forall 

threethevoltageis1.4V+1.0V+0.3V=2.7V.[4] 

Crystallinesolarcellarrayshavealongusablelife. Manyarraysareguaranteedfor25


Table3.4:Highefficiencytriplelayersolarcell. 

Layer Bandgap Lightabsorbed 

Galliumindiumphosphide 1.8eV UV,visible 

Galliumarsenide 1.4eV nearinfrared 

Germanium 0.7eV farinfrared 

years,andbelievedtobegoodfor40years. Theydonotsufferinitialdegradationcompared 

withamorphoussilicon. 

Bothsingleandmulticrystallinesolarcellsarebasedonsiliconwafers.Thesiliconisboth 

thesubstrateandtheactivedevicelayers. Muchsiliconisconsumed. Thiskindofcellhas 

beenaroundfordecades,andtakesapproximately86%ofthesolarelectricmarket.Forfurther 

informationaboutcrystallinesolarcellsseeHonsberg.[8] 

Amorphoussiliconthinfilmsolarcellsusetinyamountsoftheactiverawmaterial,silicon.Approximatelyhalfthecostofconventionalcrystallinesolarcellsisthesolarcellgrade 

silicon. Thethinfilmdepositionprocessreducesthiscost. Thedownsideisthatefficiencyis 

abouthalfthatofconventionalcrystallinecells.Moreover,efficiencydegradesby15-35%upon 

exposuretosunlight.A7%efficientcellsoonagesto5%efficiency.Thinfilmamorphoussilicon 

cellsworkbetterthancrystallinecellsindimlight.Theyareputtogooduseinsolarpowered 

calculators. 

Non-siliconbasedsolarcellsmakeupabout7%ofthemarket. Thesearethin-filmpolycrystallineproducts.Variouscompoundsemiconductorsarethesubjectofresearchanddevelopment.Somenon-siliconproductsareinproduction.Generally,theefficiencyisbetterthan 

amorphoussilicon,butnotnearlyasgoodascrystallinesilicon. 

Cadmiumtellurideasapolycrystallinethinfilmonmetalorglasscanhaveahigher 

efficiencythanamorphoussiliconthinfilms.Ifdepositedonmetal,thatlayeristhenegative 

contacttothecadmiumtelluridethinfilm.ThetransparentP-typecadmiumsulfideatopthe 

cadmiumtellurideservesasabufferlayer.Thepositivetopcontactistransparent,electrically 

conductivefluorinedopedtinoxide.Theselayersmaybelaiddownonasacrificialfoilinplace 

oftheglassintheprocessinthefollowingpargraph. Thesacrificialfoilisremovedafterthe 

cellismountedtoapermanentsubstrate. 

AprocessfordepositingcadmiumtellurideonglassbeginswiththedepositionofN-type 

transparent,electricallyconducive,tinoxideonaglasssubstrate. ThenextlayerisP-type 

cadmiumtelluride;though,N-typeorintrinsicmaybeused. Thesetwolayersconstitutethe 

NPjunction.AP + (heavyP-type)layerofleadtellurideaidsinestablishingalowresistance 

contact.Ametallayermakesthefinalcontacttotheleadtelluride.Theselayersmaybelaid 

downbyvacuumdeposition,chemicalvapordeposition(CVD),screenprinting,electrodeposition,oratmosphericpressurechemicalvapordeposition(APCVD)inhelium.[10] 

Avariationofcadmiumtellurideismercurycadmiumtelluride. Havinglowerbulkresistanceandlowercontactresistanceimprovesefficiencyovercadmiumtelluride. 

CadmiumIndiumGalliumdiSelenide: Amostpromisingthinfilmsolarcellatthis 

time(2007)ismanufacturedonateninchwiderollofflexiblepolyimide–CadmiumIndium 

GalliumdiSelenide(CIGS).Ithasaspectacularefficiencyof10%.Though,commercialgrade 

crystallinesiliconcellssurpassedthisdecadesago,CIGSshouldbecostcompetitive. The 

depositionprocessesareatalowenoughtemperaturetouseapolyimidepolymerasasubstrate


+ 

glass substrate 

n Tin oxide 

cadmium suflide 

p cadmium telluride 

(phosphorus doped) 

p+ lead telluride 

metal substrate 

metal contact 

Figure3.78:Cadmiumtelluridesolarcellonglassormetal. 

Tin oxide 

Zinc oxide 

Cadmium suflide 

CIGS Cadmium Indium 

Gallium diSelenide 

Molybdenum 

Polyimide substrate 

- 

- 

− 

+ 

top contact 

N-type transparent 

conductor 

buffer layer 

P type 

bottom contact 

Figure3.79:CadmiumIndiumGalliumdiSelenidesolarcell(CIGS)


insteadofmetalorglass. (Figure3.79)TheCIGSismanufacturedinarolltorollprocess, 

whichshoulddrivedowncosts. GIGScellsmayalsobeproducedbyaninherentlylowcost 

electrochemicalprocess.[7] 

• REVIEW: 

• Mostsolarcellsaresiliconsinglecrystalormulticrystalbecauseoftheirgoodefficiency 

andmoderatecost. 

• Lessefficientthinfilmsofvariousamorphousorpolycrystallinematerialscomprisethe 

restofthemarket. 

• Table 3.5comparesselectedsolarcells. 

Solarcelltype 

Table3.5:Solarcellproperties 

Maximum Practical Notes 

effiefficiencyciency Selenium,polycrystalline 0.7% - 1883,CharlesFritts 

Silicon,singlecrystal - 4% 1950’s,firstsiliconsolarcell 

Silicon, single crystal PERL, 25% - solarcars, cost=100xcommer- 

terrestrial,space cialSilicon,singlecrystal,commer- 

24% 

cialterrestrial 

14-17% $5-$10/peakwatt 

Cypress Semiconductor, Sun- 21.5% 

power,siliconsinglecrystal 

19% allcontactsoncellback 

Gallium Indium Phosphide/ - 

Gallium Arsenide/ Germanium,singlecrystal,multilayer 

32% Preferredforspace. 

Advancedterrestrialversionof - 

above. 

40.7% Usesopticalconcentrator. 

Silicon,multicrystalline 18.5% 15.5% - 

Thinfilms, - - - 

Silicon,amorphous 13% 5-7% Degradesinsunlight.Goodindoorsforcalculatorsorcloudy 

outdoors. 

Cadmium telluride, polycrys- 16% 

talline 

- glassormetalsubstrate 

Copper indium arsenide dise- 18% 10% 10 inch flexible polymer web. 

lenide,polycrystalline [17] 

Organicpolymer,100%plastic 4.5% - R&Dproject 

3.12.7 Varicaporvaractordiodes 

Avariablecapacitancediodeisknownasavaricapdiodeorasavaractor.Ifadiodeisreverse 

biased,aninsulatingdepletionregionformsbetweenthetwosemiconductivelayers.Inmany


diodesthewidthofthedepletionregionmaybechangedbyvaryingthereversebias. This 

variesthecapacitance.Thiseffectisaccentuatedinvaricapdiodes.Theschematicsymbolsis 

showninFigure3.80,oneofwhichispackagedascommoncathodedualdiode. 

capacitance 

symbol voltage 

− 

+ 

V control 

varicap diode 

C large C optional 

Figure3.80:Varicapdiode:Capacitancevarieswithreversebias.Thisvariesthefrequencyof 

aresonantnetwork. 

IfavaricapdiodeispartofaresonantcircuitasinFigure3.80,thefrequencymaybe 

variedwithacontrolvoltage,Vcontrol.Alargecapacitance,lowXc,inserieswiththevaricap 

preventsVcontrolfrombeingshortedoutbyinductorL.Aslongastheseriescapacitorislarge, 

ithasminimaleffectonthefrequencyofresonantcircuit. Coptionalmaybeusedtosetthe 

centerresonantfrequency.Vcontrolcanthenvarythefrequencyaboutthispoint.Notethatthe 

requiredactivecircuitrytomaketheresonantnetworkoscillateisnotshown.Foranexample 

ofavaricapdiodetunedAMradioreceiversee“electronicvaricapdiodetuning,”(page428) 

Somevaricapdiodesmaybereferredtoasabrupt,hyperabrupt,orsuperhyperabrupt. 

Theserefertothechangeinjunctioncapacitancewithchangingreversebiasasbeingabrupt 

orhyper-abrupt,orsuperhyperabrupt. Thesediodesofferarelativelylargechangeincapacitance. 

Thisisusefulwhenoscillatorsorfiltersaresweptoveralargefrequencyrange. 

Varyingthebiasofabruptvaricapsovertheratedlimits,changescapacitancebya4:1ratio, 

hyperabruptby10:1,superhyperabruptby20:1. 

Varactordiodesmaybeusedinfrequencymultipliercircuits. See“Practicalanalogsemiconductorcircuits,”Varactormultiplier 

3.12.8 Snapdiode 

Thesnapdiode,alsoknownasthesteprecoverydiodeisdesignedforuseinhighratiofrequencymultipliersupto20gHz.Whenthediodeisforwardbiased,chargeisstoredinthePN 

junction. Thischargeisdrawnoutasthediodeisreversebiased. Thediodelookslikealow 

impedancecurrentsourceduringforwardbias.Whenreversebiasisapplieditstilllookslike 

alowimpedancesourceuntilallthechargeiswithdrawn.Itthen“snaps”toahighimpedance 

statecausingavoltageimpulse,richinharmonics. Anapplicationsisacombgenerator,a 

generatorofmanyharmonics.Moderatepower2xand4xmultipliersareanotherapplication. 

3.12.9 PINdiodes 

APINdiodeisafastlowcapacitanceswitchingdiode.DonotconfuseaPINswitchingdiode 

withaPINphotodiode(page153).APINdiodeismanufacturedlikeasiliconswitchingdiode 

L


withanintrinsicregionaddedbetweenthePNjunctionlayers.Thisyieldsathickerdepletion 

region,theinsulatinglayeratthejunctionofareversebiaseddiode. Thisresultsinlower 

capacitancethanareversebiasedswitchingdiode. 


p+ contact region 

p diffusion 

intrinsic region 

(larger depletion 

region) 

n type 



Figure3.81:Pindiode:Crosssectionalignedwithschematicsymbol. 

PINdiodesareusedinplaceofswitchingdiodesinradiofrequency(RF)applications,for 

example,aT/Rswitch(page431). The1n40071000V,1Ageneralpurposepowerdiodeis 

reportedtobeusableasaPINswitchingdiode.Thehighvoltageratingofthisdiodeisachieved 

bytheinclusionofanintrinsiclayerdividingthePNjunction.Thisintrinsiclayermakesthe 

1n4007aPINdiode.AnotherPINdiodeapplicationisastheantennaswitch(page431)fora 

directionfinderreceiver. 

PINdiodesserveasvariableresistorswhentheforwardbiasisvaried.Onesuchapplication 

isthevoltagevariableattenuator(page431).ThelowcapacitancecharacteristicofPINdiodes, 

extendsthefrequencyflatresponseoftheattenuatortomicrowavefrequencies. 

3.12.10 IMPATTdiode 

¡TheIMPactAvalancheTransitTimediodeisahighpowerradiofrequency(RF)generator 

operatingfrom3to100gHz.IMPATTdiodesarefabricatedfromsilicon,galliumarsenide,or 

siliconcarbide. 

AnIMPATTdiodeisreversebiasedabovethebreakdownvoltage. Thehighdopinglevels 

produceathindepletionregion. Theresultinghighelectricfieldrapidlyacceleratescarriers 

whichfreeothercarriersincollisionswiththecrystallattice. HolesaresweptintotheP+ 

region.ElectronsdrifttowardtheNregions.Thecascadingeffectcreatesanavalanchecurrent 

whichincreasesevenasvoltageacrossthejunctiondecreases. Thepulsesofcurrentlagthe 

voltagepeakacrossthejunction.A“negativeresistance”effectinconjunctionwitharesonant 

circuitproducesoscillationsathighpowerlevels(highforsemiconductors). 

TheresonantcircuitintheschematicdiagramofFigure3.82isthelumpedcircuitequivalentofawaveguidesection,wheretheIMPATTdiodeismounted.DCreversebiasisapplied


+ − 

choke 

resonant circuit 

drift 

avalanche 

Figure3.82:IMPATTdiode:OscillatorcircuitandheavilydopedPandNlayers. 

throughachokewhichkeepsRFfrombeinglostinthebiassupply.Thismaybeasectionof 

waveguideknownasabiasTee.LowpowerRADARtransmittersmayuseanIMPATTdiode 

asapowersource.Theyaretoonoisyforuseinthereceiver.[20] 

3.12.11 Gunndiode 

Diode,gunnGunndiode 

AgunndiodeissolelycomposedofN-typesemiconductor. Assuch,itisnotatruediode. 

Figure3.83showsalightlydopedN−layersurroundedbyheavilydopedN+layers.Avoltage 

appliedacrosstheN-typegalliumarsenidegunndiodecreatesastrongelectricfieldacrossthe 

lightlydopedN − layer. 

+ − 

choke 

resonant circuit 

N + 

N - 

N + 

I 

1 

N - 

N + 

N + 

P + 

threshold 

Figure3.83: Gunndiode: OscillatorcircuitandcrosssectionofonlyN-typesemiconductor 

diode. 

Asvoltageisincreased,conductionincreasesduetoelectronsinalowenergyconduction 

band.Asvoltageisincreasedbeyondthethresholdofapproximately1V,electronsmovefrom 

thelowerconductionbandtothehigherenergyconductionbandwheretheynolongercontributetoconduction.Inotherwords,asvoltageincreases,currentdecreases,anegativeresistancecondition.Theoscillationfrequencyisdeterminedbythetransittimeoftheconduction 

electrons,whichisinverselyrelatedtothethicknessoftheN − layer. 

Thefrequencymaybecontrolledtosomeextentbyembeddingthegunndiodeintoaresonantcircuit.ThelumpedcircuitequivalentshowninFigure3.83isactuallyacoaxialtrans- 

V


missionlineorwaveguide.Galliumarsenidegunndiodesareavailableforoperationfrom10 

to200gHzat5to65mwpower.Gunndiodesmayalsoserveasamplifiers.[19][14] 

3.12.12 Shockleydiode 

TheShockleydiodeisa4-layerthyristorusedtotriggerlargerthyristors. Itonlyconductsin 

onedirectionwhentriggeredbyavoltageexceedingthebreakovervoltage,about20V.See 

“Thyristors,”TheShockleyDiode.Thebidirectionalversioniscalledadiac.See“Thyristors,” 

TheDIAC. 

3.12.13 Constant-currentdiodes 

Aconstant-currentdiode,alsoknownasacurrent-limitingdiode,orcurrent-regulatingdiode, 

doesexactlywhatitsnameimplies:itregulatescurrentthroughittosomemaximumlevel. 

TheconstantcurrentdiodeisatwoterminalversionofaJFET.Ifwetrytoforcemorecurrent 

throughaconstant-currentdiodethanitscurrent-regulationpoint,itsimply“fightsback”by 

droppingmorevoltage.IfweweretobuildthecircuitinFigure3.84(a)andplotdiodecurrent 

againstdiodevoltage,we’dgetagraphthatrisesatfirstandthenlevelsoffatthecurrent 

regulationpointasinFigure3.84(b). 

R dropping 

constant-current 

diode 

I diode 

(a) (b) 

Figure3.84:Constantcurrentdiode:(a)Testcircuit,(b)currentvsvoltagecharacteristic. 

Oneapplicationforaconstant-currentdiodeistoautomaticallylimitcurrentthroughan 

LEDorlaserdiodeoverawiderangeofpowersupplyvoltagesasinFigure??. 

Ofcourse,theconstant-currentdiode’sregulationpointshouldbechosentomatchtheLED 

orlaserdiode’soptimumforwardcurrent.Thisisespeciallyimportantforthelaserdiode,not 

somuchfortheLED,asregularLEDstendtobemoretolerantofforwardcurrentvariations. 

Anotherapplicationisinthechargingofsmallsecondary-cellbatteries,whereaconstant 

chargingcurrentleadstopredictablechargingtimes. Ofcourse,largesecondary-cellbattery 

banksmightalsobenefitfromconstant-currentcharging,butconstant-currentdiodestendto 

beverysmalldevices,limitedtoregulatingcurrentsinthemilliamprange. 

V diode

3.13. OTHERDIODETECHNOLOGIES 163 

3.13 Otherdiodetechnologies 

3.13.1 SiCdiodes 

Diodesmanufacturedfromsiliconcarbidearecapableofhightemperatureoperationto400 o C. 

Thiscouldbeinahightemperatureenvironment: downholeoilwelllogging,gasturbine 

engines,autoengines. Or,operationinamoderateenvironmentathighpowerdissipation. 

NuclearandspaceapplicationsarepromisingasSiCis100timesmoreresistanttoradiation 

comparedwithsilicon. SiCisabetterconductorofheatthananymetal. Thus,SiCisbetter 

thansiliconatconductingawayheat.BreakdownvoltageisseveralkV.SiCpowerdevicesare 

expectedtoreduceelectricalenergylossesinthepowerindustrybyafactorof100. 

3.13.2 Polymerdiode 

Diodesbasedonorganicchemicalshavebeenproducedusinglowtemperatureprocesses.Hole 

richandelectronrichconductivepolymersmaybeinkjetprintedinlayers. MostoftheresearchanddevelopmentisoftheorganicLED(OLED).However,developmentofinexpensiveprintableorganicRFID(radiofrequencyidentification)tagsisongoing.Inthiseffort,apentaceneorganicrectifierhasbeenoperatedat50MHz.Rectificationto800MHzisadevelopmentgoal.Aninexpensivemetalinsulatormetal(MIM)diodeactinglikeaback-to-backzener 

diodeclipperhasbeendelveloped.Also,atunneldiodelikedevicehasbeenfabricated. 

3.14 SPICEmodels 

TheSPICEcircuitsimulationprogramprovidesformodelingdiodesincircuitsimulations. 

Thediodemodelisbasedoncharacterizationofindividualdevicesasdescribedinaproduct 

datasheetandmanufacturingprocesscharacteristicsnotlisted. Someinformationhasbeen 

extractedfroma1N4004datasheetinFigure3.85. 

Thediodestatementbeginswithadiodeelementnamewhichmustbeginwith“d”plus 

optionalcharacters. Examplediodeelementnamesinclude:d1,d2,dtest,da,db,d101. Two 

nodenumbersspecifytheconnectionoftheanodeandcathode,respectively,toothercomponents. 

Thenodenumbersarefollowedbyamodelname,referringtoasubsequent“.model” 

statement. 

Themodelstatementlinebeginswith“.model,” followedbythemodelnamematching 

oneormorediodestatements. Next,a“d”indicatesadiodeisbeingmodeled. TheremainderofthemodelstatementisalistofoptionaldiodeparametersoftheformParameter- 

Name=ParameterValue. NoneareusedinExamplebelow. Example2hassomeparameters 

defined.Foralistofdiodeparameters,seeTable3.6. 

General form: d[name] [anode] [cathode] [modelname] 

.model ([modelname] d [parmtr1=x] [parmtr2=y] . . .) 

Example: d1 1 2 mod1 

.model mod1 d


I F instaneous forward current (I) 

10 

1.0 

0.1 

0.01 

0.925 

0.6 0.8 1.0 1.2 1.4 1.6 

VF instaneous forward voltage (V) 

Max avg rectified current I O (A) 1 

Peak repetitive reverse voltage V RRM (V) 400 

Peak forward surge current IFSM (A) 30 

Total capacitance CT (pF) 15 

C J junction capacitance (pF) 

100 

30 

10 

1 

1 10 

VR reverse voltage (V) 

100 

Forward voltage drop V F (V) 1 

@ I F (A) 1 

Max reverse current I R (µΑ) 5 

Figure3.85:Datasheet1N4004excerpt,after[6]. 

@ V R (V) 400 

Example2: D2 1 2 Da1N4004 

.model Da1N4004 D (IS=18.8n RS=0 BV=400 IBV=5.00u CJO=30 

M=0.333 N=2) 

TheeasiestapproachtotakeforaSPICEmodelisthesameasforadatasheet: consult 

themanufacturer’swebsite.Table3.7liststhemodelparametersforsomeselecteddiodes.A 

fallbackstrategyistobuildaSPICEmodelfromthoseparameterslistedonthedatasheet. 

Athirdstrategy,notconsideredhere,istotakemeasurementsofanactualdevice. Then, 

calculate,compareandadjusttheSPICEparameterstothemeasurements. 

Ifdiodeparametersarenotspecifiedasin“Example”modelabove,theparameterstakeon 

thedefaultvalueslistedinTable3.6andTable3.7. Thesedefaultsmodelintegratedcircuit 

diodes. ThesearecertainlyadequateforpreliminaryworkwithdiscretedevicesFormore 

criticalwork,useSPICEmodelssuppliedbythemanufacturer[5],SPICEvendors,andother 

sources.[16] 

Otherwise,derivesomeoftheparametersfromthedatasheet.Firstselectavalueforspice 

parameterNbetween1and2. Itisrequiredforthediodeequation(n). Massobrio[1]pp9, 

recommends”..n,theemissioncoefficientisusuallyabout2.”InTable3.7,weseethatpower 

rectifiers1N3891(12A),and10A04(10A)bothuseabout2.Thefirstfourinthetablearenot 

relevantbecausetheyareschottky,schottky,germanium,andsiliconsmallsignal,respectively. 

Thesaturationcurrent,IS,isderivedfromthediodeequation,avalueof(VD,ID)onthegraph 

inFigure3.85,andN=2(ninthediodeequation).

3.14. SPICEMODELS 165 

Table3.6:DiodeSPICEparameters 

Symbol Name Parameter Units Default 

IS IS Saturationcurrent(diodeequa- A 

tion) 

1E-14 

RS RS Parsiticresistance(seriesresis- Ω 

tance) 

0 

n N Emissioncoefficient,1to2 - 1 

τD TT Transittime s 0 

CD(0) CJO Zero-biasjunctioncapacitance F 0 

φ0 VJ Junctionpotential V 1 

m M Junctiongradingcoefficient - 0.5 

- - 0.33forlinearlygradedjunc- - 

tion 

- 

- - 0.5forabruptjunction - - 

Eg EG Activationenergy: eV 1.11 

- - Si:1.11 - - 

- - Ge:0.67 - - 

- - Schottky:0.69 - - 

pi XTI IStemperatureexponent - 3.0 

- - pnjunction:3.0 - - 

- - Schottky:2.0 - - 

kf KF Flickernoisecoefficient - 0 

af AF Flickernoiseexponent - 1 

FC FC Forwardbiasdepletioncapaci- - 

tancecoefficient 

0.5 

BV BV Reversebreakdownvoltage V ∞ 

IBV IBV Reversebreakdowncurrent A 1E-3 

Table3.7:SPICEparametersforselecteddiodes;sk=schottkyGe=germanium;elsesilicon. 

Part IS RS N TT CJO M VJ EG XTI BV IBV 

Default 1E-14 0 1 0 0 0.5 1 1.11 3 ∞ 1m 

1N5711sk 315n 2.8 2.03 1.44n 2.00p 0.333 - 0.69 2 70 10u 

1N5712sk 680p 12 1.003 50p 1.0p 0.5 0.6 0.69 2 20 - 

1N34Ge 200p 84m 2.19 144n 4.82p 0.333 0.75 0.67 - 60 15u 

1N4148 35p 64m 1.24 5.0n 4.0p 0.285 0.6 - - 75 - 

1N3891 63n 9.6m 2 110n 114p 0.255 0.6 - - 250 - 

10A0410A 844n 2.06m 2.06 4.32u 277p 0.333 - - - 400 10u 

1N4004 76.9n 42.2m 1.45 4.32u 39.8p 0.333 - - - 400 5u 

1A 

1N4004 

datasheet 

18.8n - 2 - 30p 0.333 - - - 400 5u


ID = IS(e VD/nVT − 1) 

VT = 26 mV at 25 o C n = 2.0 VD = 0.925 V at 1 A from graph 

1 A = IS(e (0.925V )/(2)(26mV ) − 1) 

IS = 18.8E-9 

ThenumericalvaluesofIS=18.8nandN=2areenteredinlastlineofTable3.7forcomparisontothemanufacturersmodelfor1N4004,whichisconsiderablydifferent.RSdefaultsto0 

fornow.Itwillbeestimatedlater.TheimportantDCstaticparametersareN,IS,andRS. 

Rashid[15]suggeststhatTT, τD,thetransittime,beapproximatedfromthereverserecoverystoredchargeQRR,adatasheetparameter(notavailableonourdatasheet)andIF, 

forwardcurrent. 

ID = IS(e VD/nVT − 1) 

τD = QRR/IF 

WetaketheTT=0defaultforlackofQRR.ThoughitwouldbereasonabletotakeTTfora 

similarrectifierlikethe10A04at4.32u. The1N3891TTisnotavalidchoicebecauseitisa 

fastrecoveryrectifier.CJO,thezerobiasjunctioncapacitanceisestimatedfromtheVRvsCJ 

graphinFigure3.85.Thecapacitanceatthenearesttozerovoltageonthegraphis30pFat 

1V.Ifsimulatinghighspeedtransientresponse,asinswitchingregulatorpowersupplies,TT 

andCJOparametersmustbeprovided. 

ThejunctiongradingcoefficientMisrelatedtothedopingprofileofthejunction.Thisisnot 

adatasheetitem.Thedefaultis0.5foranabruptjunction.WeoptforM=0.333corresponding 

toalinearlygradedjunction.ThepowerrectifiersinTable3.7uselowervaluesforMthan0.5. 

WetakethedefaultvaluesforVJandEG.ManymorediodesuseVJ=0.6thanshownin 

Table3.7.Howeverthe10A04rectifierusesthedefault,whichweuseforour1N4004model 

(Da1N4001inTable3.6).UsethedefaultEG=1.11forsilicondiodesandrectifiers.Table3.6 

listsvaluesforschottkyandgermaniumdiodes.TaketheXTI=3,thedefaultIStemperature 

coefficientforsilicondevices.SeeTable3.6forXTIforschottkydiodes. 

Theabbreviateddatasheet,Figure3.85,listsIR=5µA@VR=400V,correspondingto 

IBV=5uandBV=400respectively.The1n4004SPICEparametersderivedfromthedatasheet 

arelistedinthelastlineofTable3.7forcomparisontothemanufacturer’smodellistedabove 

it.BVisonlynecessaryifthesimulationexceedsthereversebreakdownvoltageofthediode, 

asisthecaseforzenerdiodes.IBV,reversebreakdowncurrent,isfrequentlyomitted,butmay 

beenteredifprovidedwithBV. 

Figure3.86showsacircuittocomparethemanufacturersmodel,themodelderivedfrom 

thedatasheet,andthedefaultmodelusingdefaultparameters.Thethreedummy0Vsources 

arenecessaryfordiodecurrentmeasurement.The1Vsourceissweptfrom0to1.4Vin0.2 

mVsteps.See.DCstatementinthenetlistinTable3.8.DI1N4004isthemanufacturer’sdiode 

model,Da1N4004isourderiveddiodemodel.


+ − 1V 

0 

1 

D1 D2 

+ −0V 

Figure3.86:SPICEcircuitforcomparisonofmanufacturermodel(D1),calculateddatasheet 

model(D2),anddefaultmodel(D3). 

Table3.8:SPICEnetlistparameters:(D1)DI1N4004manufacturer’smodel,(D2)Da1N40004 

datasheetderived,(D3)defaultdiodemodel. 

*SPICE circuit from XCircuit v3.20 

D1 1 5 DI1N4004 

V1 5 0 0 

D2 1 3 Da1N4004 

V2 3 0 0 

D3 1 4 Default 

V3 4 0 0 

V4 1 0 1 

.DC V4 0 1400mV 0.2m 

.model Da1N4004 D (IS=18.8n RS=0 BV=400 IBV=5.00u CJO=30 

+M=0.333 N=2.0 TT=0) 

.MODEL DI1N4004 D (IS=76.9n RS=42.0m BV=400 IBV=5.00u CJO=39.8p 

+M=0.333 N=1.45 TT=4.32u) 

.MODEL Default D 

.end 

+ −0V 

D3 

+ −0V


WecomparethethreemodelsinFigure3.87.andtothedatasheetgraphdatainTable3.9. 

VDisthediodevoltageversusthediodecurrentsforthemanufacturer’smodel,ourcalculated 

datasheetmodelandthedefaultdiodemodel. Thelastcolumn“1N4004graph”isfromthe 

datasheetvoltageversuscurrentcurveinFigure3.85whichweattempttomatch.Comparison 

ofthecurrentsforthethreemodeltothelastcolumnshowsthatthedefaultmodelisgoodat 

lowcurrents,themanufacturer’smodelisgoodathighcurrents,andourcalculateddatasheet 

modelisbestofallupto1A.Agreementisalmostperfectat1AbecausetheIScalculationis 

basedondiodevoltageat1A.Ourmodelgrosslyoverstatescurrentabove1A. 

Figure3.87:Firsttrialofmanufacturermodel,calculateddatasheetmodel,anddefaultmodel. 

ThesolutionistoincreaseRSfromthedefaultRS=0. ChangingRSfrom0to8minthe 

datasheetmodelcausesthecurvetointersect10A(notshown)atthesamevoltageasthe 

manufacturer’smodel.IncreasingRSto28.6mshiftsthecurvefurthertotherightasshownin 

Figure3.88.Thishastheeffectofmorecloselymatchingourdatasheetmodeltothedatasheet 

graph(Figure3.85).Table3.10showsthatthecurrent1.224470e+01Aat1.4Vmatchesthe 

graphat12A.However,thecurrentat0.925Vhasdegradedfrom1.096870e+00aboveto 

7.318536e-01. 

Suggestedreaderexercise:decreaseNsothatthecurrentatVD=0.925Visrestoredto1 

A.Thismayincreasethecurrent(12.2A)atVD=1.4VrequiringanincreaseofRStodecrease 

currentto12A. 

Zenerdiode:Therearetwoapproachestomodelingazenerdiode:settheBVparameter 

tothezenervoltageinthemodelstatement,ormodelthezenerwithasubcircuitcontaininga 

diodeclampersettothezenervoltage. Anexampleofthefirstapproachsetsthebreakdown 

voltageBVto15forthe1n446915Vzenerdiodemodel(IBVoptional): 

.model D1N4469 D ( BV=15 IBV=17m )


Table3.9:Comparisonofmanufacturermodel,calculateddatasheetmodel,anddefaultmodel 

to1N4004datasheetgraphofVvsI. 

model model model 

1N4004 

index 

graph 

VD manufacturer datasheet default 

3500 

0.01 

7.000000e-01 1.612924e+00 1.416211e-02 5.674683e-03 

4001 

0.13 

8.002000e-01 3.346832e+00 9.825960e-02 2.731709e-01 

4500 

0.7 

9.000000e-01 5.310740e+00 6.764928e-01 1.294824e+01 

4625 

1.0 

9.250000e-01 5.823654e+00 1.096870e+00 3.404037e+01 

5000 

2.0 

1.000000e-00 7.395953e+00 4.675526e+00 6.185078e+02 

5500 

3.3 

1.100000e+00 9.548779e+00 3.231452e+01 2.954471e+04 

6000 

5.3 

1.200000e+00 1.174489e+01 2.233392e+02 1.411283e+06 

6500 

8.0 

1.300000e+00 1.397087e+01 1.543591e+03 6.741379e+07 

7000 1.400000e+00 1.621861e+01 1.066840e+04 3.220203e+09 12. 

Figure3.88:Secondtrialtoimprovecalculateddatasheetmodelcomparedwithmanufacturer 

modelanddefaultmodel.


Table3.10:ChangingDa1N4004modelstatementRS=0toRS=28.6mdecreasesthecurrentat 

VD=1.4Vto12.2A. 

.model Da1N4004 D (IS=18.8n RS=28.6m BV=400 IBV=5.00u CJO=30 

+M=0.333 N=2.0 TT=0) 

model model 1N4001 

index VD manufacturer datasheet graph 

3505 7.010000e-01 1.628276e+00 1.432463e-02 0.01 

4000 8.000000e-01 3.343072e+00 9.297594e-02 0.13 

4500 9.000000e-01 5.310740e+00 5.102139e-01 0.7 

4625 9.250000e-01 5.823654e+00 7.318536e-01 1.0 

5000 1.000000e-00 7.395953e+00 1.763520e+00 2.0 

5500 1.100000e+00 9.548779e+00 3.848553e+00 3.3 

6000 1.200000e+00 1.174489e+01 6.419621e+00 5.3 

6500 1.300000e+00 1.397087e+01 9.254581e+00 8.0 

7000 1.400000e+00 1.621861e+01 1.224470e+01 12. 

Thesecondapproachmodelsthezenerwithasubcircuit.ClamperD1andVZinFigure?? 

modelsthe15Vreversebreakdownvoltageofa1N4477Azenerdiode.DiodeDRaccountsfor 

theforwardconductionofthezenerinthesubcircuit. 

A 

K 

1 

2 

3 

D1 

+ − 13.7V 

.SUBCKT DI-1N4744A 

1 2 

* Terminals A K 

D1 1 2 DF 

DZ 3 1 DR 

VZ 2 3 13.7 

.MODEL DF D ( 

IS=27.5p RS=0.620 

N=1.10 

+ CJO=78.3p 

VJ=1.00 M=0.330 

TT=50.1n ) 

.MODEL DR D ( 

IS=5.49f RS=0.804 

N=1.77 ) 

.ENDS 

Figure3.89:Zenerdiodesubcircuitusesclamper(D1andVZ)tomodelzener. 

Tunneldiode:Atunneldiodemaybemodeledbyapairoffieldeffecttransistors(JFET) 

inaSPICEsubcircuit.[11]Anoscillatorcircuitisalsoshowninthisreference. 

Gunndiode:AGunndiodemayalsobemodeledbyapairofJFET’s.[12]Thisreference 

showsamicrowaverelaxationoscillator. 

• REVIEW:


• DiodesaredescribedinSPICEbyadiodecomponentstatementreferringto.modelstatement.The.modelstatementcontainsparametersdescribingthediode.Ifparametersare 

notprovided,themodeltakesondefaultvalues. 

• StaticDCparametersincludeN,IS,andRS.Reversebreakdownparameters:BV,IBV. 

• AccuratedynamictimingrequiresTTandCJOparameters 

• Modelsprovidedbythemanufacturerarehighlyrecommended. 

Contributors 



JeredWierzbicki(December2002): Pointedouterrorindiodeequation–Boltzmann’s 

constantshownincorrectly. 

Bibliography 

[1] PaoloAntognetti, GiuseppeMassobrio“SemiconductorDeviceModelingwithSPICE,” 

ISBN0-07-002107-4,1988 

[2] ATCO Newsletter, Volume 14 No. 1, January 1997 at 

http://www.atco.tv/homepage/vol14 1.pdf 

[3] D.A.Brunner,etal,,“ACockcroft-WaltonBasefortheFEU84-3PhotomultiplierTube,” 

DepartmentofPhysics,IndianaUniversity,Bloomington,Indiana47405January1998, 

at http://dustbunny.physics.indiana.edu/˜paul/cwbase/ 

[4] BrentonBurnet,“TheBasicPhysicsandDesignofIII-VMultijunctionSolar,”NREL,at 

photochemistry.epfl.ch/EDEY/NREL.pdf 

[5] DiodesIncorporated http://www.diodes.com/products/spicemodels/index.php 

[6] Diodes Incorporated, “1N4001/L - 1N4007/l, 1.0A rectifier,” at 

http://www.diodes.com/datasheets/ds28002.pdf 

[7] “Solar firm gains $30 million in funding,” EE Times, 07/12/2007 at 

http://www.eetimes.com/news/latest/showArticle.jhtml?articleID=201001129 

[8] Christiana Honsberg, Stuart Bowden, “Photovoltaics CDROM,” at 

http://www.udel.edu/igert/pvcdrom/ 

[9] R. R. King, et. al., “40% efficient metamorphic GaInP/GaInAs/Ge multijunction 

solar cells”, Applied Physics Letters, 90, 183516 (2007) , at 

http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal& 

id=APPLAB000090000018183516000001&idtype=cvips&gifs=yes


[10] KimWMitchell,“Methodofmakingathinfilmcadmiumtelluridesolarcell,”United 

StatesPatent4734381,http://www.freepatentsonline.com/4734381.html 

[11] KarlH.Muller“RF/MicrowaveAnalysis”IntusoftNewsletter#51,November1997,at 

http://www.intusoft.com/nlhtm/nl51.htm 

[12] “A Gunn Diode Relaxation Oscillator,” Intusoft Newsletter #52, February 1998, at 

http://www.intusoft.com/nlhtm/nl52.htm 

[13] OAK Solar., “Technical LED’s LED color chart,” at 

http://www.oksolar.com/led/led color chart.htm 

[14] IanPoole,“SummaryoftheGunnDiode,”at http://www.radio-electronics.com/ 

nfo/data/semicond/gunndiode/gunndiode.php 

[15] MuhammadH.Rashid,“SPICEforPowerElectronicsandElectricPower,”ISBN0-13- 

030420-4,1993 

[16] “SPICE model index,” V2.16 30-Nov-05, at http://homepages.which.net/ 

˜paul.hills/Circuits/Spice/ModelIndex.html 

[17] NeilThomas,“AdvancingCIGSSolarCellManufacturingTechnology,”April6,2007at 

http://www.renewableenergyaccess.com/rea/news/story?id=48033&src=rss 

[18] P.J. Verlinden, Sinton, K. Wickham, R.M. Swanson Crane, “BACKSIDE- 

CONTACT SILICON SOLAR CELLS WITH IMPROVED EFFICIENCY.” at 

http://www.sunpowercorp.com/techpapers/EPSEC97.pdf 

[19] Christian Wolff, “Radar Principles,” Radar components, Gunn diodes at at 

http://www.radartutorial.eu/17.bauteile/bt12.en.htm 

[20] L. Yuan, M. R. Melloch, J. A. Cooper, K. J. Webb,“Silicon Carbide IM- 

PATT Oscillators for High-Power Microwave and Millimeter-Wave Generation,” 

IEEE/Cornell Conference on Advanced Concepts in High Speed 

Semiconductor Devices and Circuits, Ithaca, NY, August 7-9, 2000. at 

http://www.ecn.purdue.edu/WBG/Device Research/IMPATT Diodes/Index.html 

[21] Alan Seabaugh, Zhaoming HU, Qingmin LIU, David Rink, Jinli 

Wang, “Silicon Based Tunnel Diodes and Integrated Circuits,” at 

http://www.nd.edu/˜nano/0a1003QFDpaper v1.pdf 

[22] S.M.Sze,G.Gibbons,“Avalanchebreakdownvoltagesofabruptandlinearlygradedp-n 

junctionsinGe,Si,GaAs,andGaP,”Appl.Phys.Lett.,8,111(1966). 

[23] LisaZyga,“40%efficientsolarcellstobeusedforsolarelectricity”,PhysOrgForum,at 

http://www.physorg.com/news99904887.html

Chapter4 

BIPOLARJUNCTION 

TRANSISTORS 

Contents 

4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .174 

4.2 Thetransistorasaswitch . . . . . . . . . . . . . . . . . . . . . . . . . . . . .176 

4.3 Metercheckofatransistor. . . . . . . . . . . . . . . . . . . . . . . . . . . . .179 

4.4 Activemodeoperation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .183 

4.5 Thecommon-emitteramplifier . . . . . . . . . . . . . . . . . . . . . . . . . .189 

4.6 Thecommon-collectoramplifier . . . . . . . . . . . . . . . . . . . . . . . . .202 

4.7 Thecommon-baseamplifier . . . . . . . . . . . . . . . . . . . . . . . . . . . .210 

4.8 Thecascodeamplifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .218 

4.9 Biasingtechniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .222 

4.10 Biasingcalculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .235 

4.10.1 BaseBias. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .235 

4.10.2 Collector-feedbackbias . . . . . . . . . . . . . . . . . . . . . . . . . . . . .236 

4.10.3 Emitter-bias . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .237 

4.10.4 Voltagedividerbias . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .243 

4.11 Inputandoutputcoupling . . . . . . . . . . . . . . . . . . . . . . . . . . . . .247 

4.12 Feedback . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .256 

4.13 Amplifierimpedances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .263 

4.14 Currentmirrors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .264 

4.15 Transistorratingsandpackages . . . . . . . . . . . . . . . . . . . . . . . . .269 

4.16 BJTquirks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .271 

4.16.1 Nonlinearity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .272 

4.16.2 Temperaturedrift. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .272 

4.16.3 Thermalrunaway . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .274 

4.16.4 Junctioncapacitance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .274 

4.16.5 Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .275 

173

174 CHAPTER4. BIPOLARJUNCTIONTRANSISTORS 

4.16.6 Thermalmismatch(problemwithparallelingtransistors).........275 

4.16.7 Highfrequencyeffects . . . . . . . . . . . . . . . . . . . . . . . . . . . . .277 

Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .278 


Theinventionofthebipolartransistorin1948usheredinarevolutioninelectronics.Technical 

featspreviouslyrequiringrelativelylarge,mechanicallyfragile,power-hungryvacuumtubes 

weresuddenlyachievablewithtiny,mechanicallyrugged,power-thriftyspecksofcrystalline 

silicon.Thisrevolutionmadepossiblethedesignandmanufactureoflightweight,inexpensive 

electronicdevicesthatwenowtakeforgranted.Understandinghowtransistorsfunctionisof 

paramountimportancetoanyoneinterestedinunderstandingmodernelectronics. 

Myintenthereistofocusasexclusivelyaspossibleonthepracticalfunctionandapplication 

ofbipolartransistors,ratherthantoexplorethequantumworldofsemiconductortheory.Discussionsofholesandelectronsarebetterlefttoanotherchapterinmyopinion. 

HereIwant 

toexplorehowtousethesecomponents,notanalyzetheirintimateinternaldetails. Idon’t 

meantodownplaytheimportanceofunderstandingsemiconductorphysics,butsometimes 

anintensefocusonsolid-statephysicsdetractsfromunderstandingthesedevices’functions 

onacomponentlevel. Intakingthisapproach,however,Iassumethatthereaderpossesses 

acertainminimumknowledgeofsemiconductors: thedifferencebetween“P”and“N”doped 

semiconductors,thefunctionalcharacteristicsofaPN(diode)junction,andthemeaningsof 

theterms“reversebiased”and“forwardbiased.”Iftheseconceptsareuncleartoyou,itisbest 

torefertoearlierchaptersinthisbookbeforeproceedingwiththisone. 

Abipolartransistorconsistsofathree-layer“sandwich”ofdoped(extrinsic)semiconductor 

materials,eitherP-N-PinFigure4.1(b)orN-P-Nat(d).Eachlayerformingthetransistorhas 

aspecificname,andeachlayerisprovidedwithawirecontactforconnectiontoacircuit.The 

schematicsymbolsareshowninFigure4.1(a)and(d). 

collector 

base 

emitter 

collector 

base 

P 

N 

P 

collector 

base 

emitter 

collector 

base 

(a) emitter (b) (c) emitter (d) 

Figure4.1:BJTtransistor:(a)PNPschematicsymbol,(b)physicallayout(c)NPNsymbol,(d) 

layout. 

ThefunctionaldifferencebetweenaPNPtransistorandanNPNtransistoristheproper 

biasing(polarity)ofthejunctionswhenoperating.Foranygivenstateofoperation,thecurrent 

directionsandvoltagepolaritiesforeachkindoftransistorareexactlyoppositeeachother. 

N 

P 

N


Bipolartransistorsworkascurrent-controlledcurrentregulators.Inotherwords,transistorsrestricttheamountofcurrentpassedaccordingtoasmaller,controllingcurrent.Themain 

currentthatiscontrolledgoesfromcollectortoemitter,orfromemittertocollector,depending 

onthetypeoftransistoritis(PNPorNPN,respectively).Thesmallcurrentthatcontrolsthe 

maincurrentgoesfrombasetoemitter,orfromemittertobase,onceagaindependingonthe 

kindoftransistoritis(PNPorNPN,respectively).Accordingtothestandardsofsemiconductor 

symbology,thearrowalwayspointsagainstthedirectionofelectronflow.(Figure4.2) 

B 

C 

E 

= small, controlling current = large, controlled current 

Figure4.2:Smallelectronbasecurrentcontrolslargecollectorelectroncurrentflowingagainst 

emitterarrow. 

Bipolartransistorsarecalledbipolarbecausethemainflowofelectronsthroughthemtakes 

placeintwotypesofsemiconductormaterial:PandN,asthemaincurrentgoesfromemitter 

tocollector(orviceversa).Inotherwords,twotypesofchargecarriers–electronsandholes– 

comprisethismaincurrentthroughthetransistor. 

Asyoucansee,thecontrollingcurrentandthecontrolledcurrentalwaysmeshtogether 

throughtheemitterwire,andtheirelectronsalwaysflowagainstthedirectionofthetransistor’sarrow. 

Thisisthefirstandforemostruleintheuseoftransistors:allcurrentsmustbe 

goingintheproperdirectionsforthedevicetoworkasacurrentregulator. Thesmall,controllingcurrentisusuallyreferredtosimplyasthebasecurrentbecauseitistheonlycurrent 

thatgoesthroughthebasewireofthetransistor.Conversely,thelarge,controlledcurrentis 

referredtoasthecollectorcurrentbecauseitistheonlycurrentthatgoesthroughthecollector 

wire. Theemittercurrentisthesumofthebaseandcollectorcurrents,incompliancewith 

Kirchhoff’sCurrentLaw. 

Nocurrentthroughthebaseofthetransistor,shutsitofflikeanopenswitchandprevents 

currentthroughthecollector.Abasecurrent,turnsthetransistoronlikeaclosedswitchand 

allowsaproportionalamountofcurrentthroughthecollector. Collectorcurrentisprimarily 

limitedbythebasecurrent,regardlessoftheamountofvoltageavailabletopushit.Thenext 

sectionwillexploreinmoredetailtheuseofbipolartransistorsasswitchingelements. 

• REVIEW: 

• Bipolartransistorsaresonamedbecausethecontrolledcurrentmustgothroughtwo 

typesofsemiconductormaterial:PandN.Thecurrentconsistsofbothelectronandhole 

B 

C 

E


flow,indifferentpartsofthetransistor. 

• BipolartransistorsconsistofeitheraP-N-PoranN-P-Nsemiconductor“sandwich”structure. 

• ThethreeleadsofabipolartransistorarecalledtheEmitter,Base,andCollector. 

• Transistorsfunctionascurrentregulatorsbyallowingasmallcurrenttocontrolalarger 

current.Theamountofcurrentallowedbetweencollectorandemitterisprimarilydeterminedbytheamountofcurrentmovingbetweenbaseandemitter. 

• Inorderforatransistortoproperlyfunctionasacurrentregulator,thecontrolling(base) 

currentandthecontrolled(collector)currentsmustbegoingintheproperdirections: 

meshingadditivelyattheemitterandgoingagainsttheemitterarrowsymbol. 

4.2 Thetransistorasaswitch 

Becauseatransistor’scollectorcurrentisproportionallylimitedbyitsbasecurrent,itcanbe 

usedasasortofcurrent-controlledswitch. Arelativelysmallflowofelectronssentthrough 

thebaseofthetransistorhastheabilitytoexertcontroloveramuchlargerflowofelectrons 

throughthecollector. 

Supposewehadalampthatwewantedtoturnonandoffwithaswitch. Suchacircuit 

wouldbeextremelysimpleasinFigure4.3(a). 

Forthesakeofillustration,let’sinsertatransistorinplaceoftheswitchtoshowhowitcan 

controltheflowofelectronsthroughthelamp.Rememberthatthecontrolledcurrentthrough 

atransistormustgobetweencollectorandemitter. Sinceitisthecurrentthroughthelamp 

thatwewanttocontrol,wemustpositionthecollectorandemitterofourtransistorwherethe 

twocontactsoftheswitchwere. Wemustalsomakesurethatthelamp’scurrentwillmove 

againstthedirectionoftheemitterarrowsymboltoensurethatthetransistor’sjunctionbias 

willbecorrectasinFigure4.3(b). 

switch 

+ + 

NPN 

transistor 

PNP 

transistor 

(a) (b) (c) 

Figure4.3:(a)mechanicalswitch,(b)NPNtransistorswitch,(c)PNPtransistorswitch. 

APNPtransistorcouldalsohavebeenchosenforthejob.ItsapplicationisshowninFigure4.3(c). 

ThechoicebetweenNPNandPNPisreallyarbitrary. Allthatmattersisthattheproper 

currentdirectionsaremaintainedforthesakeofcorrectjunctionbiasing(electronflowgoing 

againstthetransistorsymbol’sarrow). 

+

4.2. THETRANSISTORASASWITCH 177 

GoingbacktotheNPNtransistorinourexamplecircuit,wearefacedwiththeneedto 

addsomethingmoresothatwecanhavebasecurrent.Withoutaconnectiontothebasewire 

ofthetransistor,basecurrentwillbezero,andthetransistorcannotturnon,resultingina 

lampthatisalwaysoff. RememberthatforanNPNtransistor,basecurrentmustconsistof 

electronsflowingfromemittertobase(againsttheemitterarrowsymbol,justlikethelamp 

current).Perhapsthesimplestthingtodowouldbetoconnectaswitchbetweenthebaseand 

collectorwiresofthetransistorasinFigure4.4(a). 

switch 

(a) (b) 

+ 

switch 

Figure4.4:Transistor:(a)cutoff,lampoff;(b)saturated,lampon. 

IftheswitchisopenasinFigure4.4(a),thebasewireofthetransistorwillbeleft“floating” 

(notconnectedtoanything)andtherewillbenocurrentthroughit.Inthisstate,thetransistor 

issaidtobecutoff.IftheswitchisclosedasinFigure4.4(b),electronswillbeabletoflowfrom 

theemitterthroughtothebaseofthetransistor,throughtheswitch,uptotheleftsideofthe 

lamp,backtothepositivesideofthebattery.Thisbasecurrentwillenableamuchlargerflow 

ofelectronsfromtheemitterthroughtothecollector,thuslightingupthelamp.Inthisstate 

ofmaximumcircuitcurrent,thetransistorissaidtobesaturated. 

Ofcourse,itmayseempointlesstouseatransistorinthiscapacitytocontrolthelamp. 

Afterall,we’restillusingaswitchinthecircuit,aren’twe? Ifwe’restillusingaswitchto 

controlthelamp–ifonlyindirectly–thenwhat’sthepointofhavingatransistortocontrol 

thecurrent?Whynotjustgobacktoouroriginalcircuitandusetheswitchdirectlytocontrol 

thelampcurrent? 

Twopointscanbemadehere,actually.Firstisthefactthatwhenusedinthismanner,the 

switchcontactsneedonlyhandlewhatlittlebasecurrentisnecessarytoturnthetransistoron; 

thetransistoritselfhandlesmostofthelamp’scurrent.Thismaybeanimportantadvantage 

iftheswitchhasalowcurrentrating:asmallswitchmaybeusedtocontrolarelativelyhighcurrentload. 

Moreimportantly,thecurrent-controllingbehaviorofthetransistorenablesus 

tousesomethingcompletelydifferenttoturnthelamponoroff.ConsiderFigure4.5,wherea 

pairofsolarcellsprovides1Vtoovercomethe0.7VBEofthetransistortocausebasecurrent 

flow,whichinturncontrolsthelamp. 

Or,wecoulduseathermocouple(manyconnectedinseries)toprovidethenecessarybase 

currenttoturnthetransistoroninFigure4.6. 

Evenamicrophone(Figure4.7)withenoughvoltageandcurrent(fromanamplifier)output 

couldturnthetransistoron,provideditsoutputisrectifiedfromACtoDCsothattheemitterbasePNjunctionwithinthetransistorwillalwaysbeforward-biased: 

Thepointshouldbequiteapparentbynow: anysufficientsourceofDCcurrentmaybe 

usedtoturnthetransistoron,andthatsourceofcurrentonlyneedbeafractionofthecurrent 

+


solar 

cell 

thermocouple 

Figure4.5:Solarcellservesaslightsensor. 

+ 

- 

source of 

heat 

Figure4.6:Asinglethermocoupleprovideslessthan40mV.Manyinseriescouldproducein 

excessofthe0.7VtransistorVBEtocausebasecurrentflowandconsequentcollectorcurrent 

tothelamp. 

source of 

sound 

microphone 

Figure4.7: AmplifiedmicrophonesignalisrectifiedtoDCtobiasthebaseofthetransistor 

providingalargercollectorcurrent.

4.3. METERCHECKOFATRANSISTOR 179 

neededtoenergizethelamp.Hereweseethetransistorfunctioningnotonlyasaswitch,but 

asatrueamplifier: usingarelativelylow-powersignaltocontrolarelativelylargeamount 

ofpower. Pleasenotethattheactualpowerforlightingupthelampcomesfromthebattery 

totherightoftheschematic.Itisnotasthoughthesmallsignalcurrentfromthesolarcell, 

thermocouple,ormicrophoneisbeingmagicallytransformedintoagreateramountofpower. 

Rather,thosesmallpowersourcesaresimplycontrollingthebattery’spowertolightupthe 

lamp. 

• REVIEW: 

• TransistorsmaybeusedasswitchingelementstocontrolDCpowertoaload. The 

switched(controlled)currentgoesbetweenemitterandcollector;thecontrollingcurrent 

goesbetweenemitterandbase. 

• Whenatransistorhaszerocurrentthroughit,itissaidtobeinastateofcutoff(fully 

nonconducting). 

• Whenatransistorhasmaximumcurrentthroughit,itissaidtobeinastateofsaturation 

(fullyconducting). 

4.3 Metercheckofatransistor 

Bipolartransistorsareconstructedofathree-layersemiconductorsandwich,eitherPNPor 

NPN.Assuch,transistorsregisterastwodiodesconnectedback-to-backwhentestedwitha 

multimeter’sresistanceordiodecheckfunctionasillustratedinFigurebelow.Lowresistance 

readingsonthebasewiththeblacknegative(-)leadscorrespondtoanN-typematerialinthe 

baseofaPNPtransistor. Onthesymbol,theN-typematerialis”pointed”tobythearrowof 

thebase-emitterjunction,whichisthebaseforthisexample.TheP-typeemittercorresponds 

totheotherendofthearrowofthebase-emitterjunction,theemitter. Thecollectorisvery 

similartotheemitter,andisalsoaP-typematerialofthePNjunction. 

V A 

V 

A 

OFF 

COM 

A 

V A 

V 

A 

OFF 

COM 

A 

base 

collector 

emitter 

V A 

V A 

Figure4.8: PNPtransistormetercheck: (a)forwardB-E,B-C,resistanceislow;(b)reverse 

B-E,B-C,resistanceis ∞. 

V 

A 

OFF 

COM 

A 

V 

A 

OFF 

COM 

A 

base 

collector 

emitter


HereI’massumingtheuseofamultimeterwithonlyasinglecontinuityrange(resistance) 

functiontocheckthePNjunctions.Somemultimetersareequippedwithtwoseparatecontinuitycheckfunctions:resistanceand“diodecheck,”eachwithitsownpurpose.Ifyourmeter 

hasadesignated“diodecheck”function,usethatratherthanthe“resistance”range,andthe 

meterwilldisplaytheactualforwardvoltageofthePNjunctionandnotjustwhetherornotit 

conductscurrent. 

Meterreadingswillbeexactlyopposite,ofcourse,foranNPNtransistor,withbothPN 

junctionsfacingtheotherway.Lowresistancereadingswiththered(+)leadonthebaseisthe 

“opposite”conditionfortheNPNtransistor. 

Ifamultimeterwitha“diodecheck”functionisusedinthistest,itwillbefoundthat 

theemitter-basejunctionpossessesaslightlygreaterforwardvoltagedropthanthecollectorbasejunction.Thisforwardvoltagedifferenceisduetothedisparityindopingconcentration 

betweentheemitterandcollectorregionsofthetransistor:theemitterisamuchmoreheavily 

dopedpieceofsemiconductormaterialthanthecollector,causingitsjunctionwiththebaseto 

produceahigherforwardvoltagedrop. 

Knowingthis,itbecomespossibletodeterminewhichwireiswhichonanunmarkedtransistor.Thisisimportantbecausetransistorpackaging,unfortunately,isnotstandardized.All 

bipolartransistorshavethreewires,ofcourse,butthepositionsofthethreewiresontheactual 

physicalpackagearenotarrangedinanyuniversal,standardizedorder. 

Supposeatechnicianfindsabipolartransistorandproceedstomeasurecontinuitywitha 

multimetersetinthe“diodecheck”mode.Measuringbetweenpairsofwiresandrecordingthe 

valuesdisplayedbythemeter,thetechnicianobtainsthedatainFigure4.9. 

1 

2 3 

• Metertouchingwire1(+)and2(-):“OL” 

• Metertouchingwire1(-)and2(+):“OL” 

• Metertouchingwire1(+)and3(-):0.655V 


• Metertouchingwire2(+)and3(-):0.621V 


Figure4.9: Unknownbipolartransistor. Whichterminalsareemitter,base,andcollector? 

Ω-meterreadingsbetweenterminals. 

Theonlycombinationsoftestpointsgivingconductingmeterreadingsarewires1and3 

(redtestleadon1andblacktestleadon3),andwires2and3(redtestleadon2andblacktest 

leadon3). Thesetworeadingsmustindicateforwardbiasingoftheemitter-to-basejunction 

(0.655volts)andthecollector-to-basejunction(0.621volts). 

Nowwelookfortheonewirecommontobothsetsofconductivereadings. Itmustbethe 

baseconnectionofthetransistor,becausethebaseistheonlylayerofthethree-layerdevice 

commontobothsetsofPNjunctions(emitter-baseandcollector-base). Inthisexample,that 

wireisnumber3,beingcommontoboththe1-3andthe2-3testpointcombinations.Inboth


thosesetsofmeterreadings,theblack(-)metertestleadwastouchingwire3,whichtellsus 

thatthebaseofthistransistorismadeofN-typesemiconductormaterial(black=negative). 

Thus,thetransistorisaPNPwithbaseonwire3,emitteronwire1andcollectoronwire2as 

describedinFigure4.10. 

1 

Emitter 

2 3 

Collector Base 

• EandChighR:1(+)and2(-):“OL” 

• CandEhighR:1(-)and2(+):“OL” 

• EandBforward:1(+)and3(-):0.655V 

• EandBreverse:1(-)and3(+):“OL” 

• CandBforward:2(+)and3(-):0.621V 

• CandBreverse:2(-)and3(+):“OL” 

Figure4.10:BJTterminalsidentifiedby Ω-meter. 

Pleasenotethatthebasewireinthisexampleisnotthemiddleleadofthetransistor,asone 

mightexpectfromthethree-layer“sandwich”modelofabipolartransistor.Thisisquiteoften 

thecase,andtendstoconfusenewstudentsofelectronics.Theonlywaytobesurewhichlead 

iswhichisbyametercheck,orbyreferencingthemanufacturer’s“datasheet”documentation 

onthatparticularpartnumberoftransistor. 

Knowingthatabipolartransistorbehavesastwoback-to-backdiodeswhentestedwitha 

conductivitymeterishelpfulforidentifyinganunknowntransistorpurelybymeterreadings. 

Itisalsohelpfulforaquickfunctionalcheckofthetransistor.Ifthetechnicianweretomeasurecontinuityinanymorethantwooranylessthantwoofthesixtestleadcombinations, 

heorshewouldimmediatelyknowthatthetransistorwasdefective(orelsethatitwasn’ta 

bipolartransistorbutrathersomethingelse–adistinctpossibilityifnopartnumberscanbe 

referencedforsureidentification!). However,the“twodiode”modelofthetransistorfailsto 

explainhoworwhyitactsasanamplifyingdevice. 

Tobetterillustratethisparadox,let’sexamineoneofthetransistorswitchcircuitsusingthe 

physicaldiagraminFigure4.11ratherthantheschematicsymboltorepresentthetransistor. 

ThiswaythetwoPNjunctionswillbeeasiertosee. 

Agrey-coloreddiagonalarrowshowsthedirectionofelectronflowthroughtheemitter-base 

junction.Thispartmakessense,sincetheelectronsareflowingfromtheN-typeemittertothe 

P-typebase:thejunctionisobviouslyforward-biased.However,thebase-collectorjunctionis 

anothermatterentirely. Noticehowthegrey-coloredthickarrowispointinginthedirection 

ofelectronflow(up-wards)frombasetocollector.WiththebasemadeofP-typematerialand 

thecollectorofN-typematerial,thisdirectionofelectronflowisclearlybackwardstothedirectionnormallyassociatedwithaPNjunction! 

AnormalPNjunctionwouldn’tpermitthis 

“backward”directionofflow,atleastnotwithoutofferingsignificantopposition. However,a 

saturatedtransistorshowsverylittleoppositiontoelectrons,allthewayfromemittertocollector,asevidencedbythelamp’sillumination!


solar 

cell 

N 

P 

N 

collector 

base 

emitter 

Figure4.11:Asmallbasecurrentflowingintheforwardbiasedbase-emitterjunctionallowsa 

largecurrentflowthroughthereversebiasedbase-collectorjunction. 

Clearlythen,somethingisgoingonherethatdefiesthesimple“two-diode”explanatory 

modelofthebipolartransistor.WhenIwasfirstlearningabouttransistoroperation,Itriedto 

constructmyowntransistorfromtwoback-to-backdiodes,asinFigure4.12. 

solar 

cell 

no light! 

no current! 

Figure4.12:Apairofback-to-backdiodesdon’tactlikeatransistor! 

Mycircuitdidn’twork,andIwasmystified. Howeverusefulthe“twodiode”description 

ofatransistormightbefortestingpurposes,itdoesn’texplainhowatransistorbehavesasa 

controlledswitch. 

Whathappensinatransistoristhis:thereversebiasofthebase-collectorjunctionprevents 

collectorcurrentwhenthetransistorisincutoffmode(thatis,whenthereisnobasecurrent). 

Ifthebase-emitterjunctionisforwardbiasedbythecontrollingsignal,thenormally-blocking 

actionofthebase-collectorjunctionisoverriddenandcurrentispermittedthroughthecollector,despitethefactthatelectronsaregoingthe“wrongway”throughthatPNjunction.This 

actionisdependentonthequantumphysicsofsemiconductorjunctions,andcanonlytake 

placewhenthetwojunctionsareproperlyspacedandthedopingconcentrationsofthethree 

layersareproperlyproportioned. Twodiodeswiredinseriesfailtomeetthesecriteria;the 

topdiodecannever“turnon”whenitisreversedbiased,nomatterhowmuchcurrentgoes 

throughthebottomdiodeinthebasewireloop.See(page??)formoredetails. 

Thatdopingconcentrationsplayacrucialpartinthespecialabilitiesofthetransistoris 

furtherevidencedbythefactthatcollectorandemitterarenotinterchangeable. Ifthetransistorismerelyviewedastwoback-to-backPNjunctions,ormerelyasaplainN-P-NorP-N-Psandwichofmaterials,itmayseemasthougheitherendofthetransistorcouldserveascollec- 

+

4.4. ACTIVEMODEOPERATION 183 

tororemitter.This,however,isnottrue.Ifconnected“backwards”inacircuit,abase-collector 

currentwillfailtocontrolcurrentbetweencollectorandemitter.Despitethefactthatboththe 

emitterandcollectorlayersofabipolartransistorareofthesamedopingtype(eitherNorP), 

collectorandemitteraredefinitelynotidentical! 

Currentthroughtheemitter-basejunctionallowscurrentthroughthereverse-biasedbasecollectorjunction.Theactionofbasecurrentcanbethoughtofas“openingagate”forcurrent 

throughthecollector.Morespecifically,anygivenamountofemitter-to-basecurrentpermitsa 

limitedamountofbase-to-collectorcurrent.Foreveryelectronthatpassesthroughtheemitterbasejunctionandonthroughthebasewire,acertain,numberofelectronspassthroughthe 

base-collectorjunctionandnomore. 

Inthenextsection,thiscurrent-limitingofthetransistorwillbeinvestigatedinmoredetail. 

• REVIEW: 

• Testedwithamultimeterinthe“resistance”or“diodecheck”modes,atransistorbehaves 

liketwoback-to-backPN(diode)junctions. 

• Theemitter-basePNjunctionhasaslightlygreaterforwardvoltagedropthanthecollectorbasePNjunction,becauseofheavierdopingoftheemittersemiconductorlayer. 

• Thereverse-biasedbase-collectorjunctionnormallyblocksanycurrentfromgoingthrough 

thetransistorbetweenemitterandcollector.However,thatjunctionbeginstoconductif 

currentisdrawnthroughthebasewire. Basecurrentmaybethoughtofas“openinga 

gate”foracertain,limitedamountofcurrentthroughthecollector. 

4.4 Activemodeoperation 

Whenatransistorisinthefully-offstate(likeanopenswitch),itissaidtobecutoff. Conversely,whenitisfullyconductivebetweenemitterandcollector(passingasmuchcurrentthroughthecollectorasthecollectorpowersupplyandloadwillallow),itissaidtobesaturated. 

Thesearethetwomodesofoperationexploredthusfarinusingthetransistorasa 

switch. 

However,bipolartransistorsdon’thavetoberestrictedtothesetwoextrememodesofoperation.Aswelearnedintheprevioussection,basecurrent“opensagate”foralimitedamount 

ofcurrentthroughthecollector. Ifthislimitforthecontrolledcurrentisgreaterthanzero 

butlessthanthemaximumallowedbythepowersupplyandloadcircuit,thetransistorwill 

“throttle”thecollectorcurrentinamodesomewherebetweencutoffandsaturation.Thismode 

ofoperationiscalledtheactivemode. 

Anautomotiveanalogyfortransistoroperationisasfollows:cutoffistheconditionofno 

motiveforcegeneratedbythemechanicalpartsofthecartomakeitmove.Incutoffmode,the 

brakeisengaged(zerobasecurrent),preventingmotion(collectorcurrent).Activemodeisthe 

automobilecruisingataconstant,controlledspeed(constant,controlledcollectorcurrent)as 

dictatedbythedriver.Saturationtheautomobiledrivingupasteephillthatpreventsitfrom 

goingasfastasthedriverwishes. Inotherwords,a“saturated”automobileisonewiththe 

acceleratorpedalpushedallthewaydown(basecurrentcallingformorecollectorcurrentthan 

canbeprovidedbythepowersupply/loadcircuit).


Let’ssetupacircuitforSPICEsimulationtodemonstratewhathappenswhenatransistor 

isinitsactivemodeofoperation.(Figure4.13) 

Current 

source 

I 1 

1 

Q 1 

V ammeter 

2 3 

0 V 

0 0 0 

V 1 

bipolar transistor 

simulation 

i1 0 1 dc 20u 

q1 2 1 0 mod1 

vammeter 3 2 dc 0 

v1 3 0 dc 

.model mod1 npn 

.dc v1 0 2 0.05 

.plot dc 

i(vammeter) 

.end 

Figure4.13:Circuitfor“activemode”SPICEsimulation,andnetlist. 

“Q”isthestandardletterdesignationforatransistorinaschematicdiagram,justas“R” 

isforresistorand“C”isforcapacitor. Inthiscircuit,wehaveanNPNtransistorpowered 

byabattery(V1)andcontrolledbycurrentthroughacurrentsource(I1). Acurrentsource 

isadevicethatoutputsaspecificamountofcurrent,generatingasmuchoraslittlevoltage 

acrossitsterminalstoensurethatexactamountofcurrentthroughit. Currentsourcesare 

notoriouslydifficulttofindinnature(unlikevoltagesources,whichbycontrastattemptto 

maintainaconstantvoltage,outputtingasmuchoraslittlecurrentinthefulfillmentofthat 

task),butcanbesimulatedwithasmallcollectionofelectroniccomponents.Asweareabout 

tosee,transistorsthemselvestendtomimictheconstant-currentbehaviorofacurrentsource 

intheirabilitytoregulatecurrentatafixedvalue. 

IntheSPICEsimulation,we’llsetthecurrentsourceataconstantvalueof20 µA,then 

varythevoltagesource(V1)overarangeof0to2voltsandmonitorhowmuchcurrentgoes 

throughit. The“dummy”battery(Vammeter)inFigure4.13withitsoutputof0voltsserves 

merelytoprovideSPICEwithacircuitelementforcurrentmeasurement. 

Theconstantbasecurrentof20 µAsetsacollectorcurrentlimitof2mA,exactly100times 

asmuch. Noticehowflatthecurveisin(Figure4.15)forcollectorcurrentovertherangeof 

batteryvoltagefrom0to2volts. Theonlyexceptiontothisfeaturelessplotisatthevery 

beginning,wherethebatteryincreasesfrom0voltsto0.25volts.There,thecollectorcurrent 

increasesrapidlyfrom0ampstoitslimitof2mA. 

Let’sseewhathappensifwevarythebatteryvoltageoverawiderrange,thistimefrom0 

to50volts.We’llkeepthebasecurrentsteadyat20 µA.(Figure4.15) 

Sameresult!ThecollectorcurrentinFigure4.15holdsabsolutelysteadyat2mA,although 

thebattery(v1)voltagevariesallthewayfrom0to50volts.Itwouldappearfromoursimulationthatcollector-to-emittervoltagehaslittleeffectovercollectorcurrent,exceptatverylow 

levels(justabove0volts). Thetransistorisactingasacurrentregulator,allowingexactly2 

mAthroughthecollectorandnomore.


Figure4.14:ASweepingcollectorvoltage0to2Vwithbasecurrentconstantat20 µAyields 

constant2mAcollectorcurrentinthesaturationregion. 


simulation 

i1 0 1 dc 20u 

q1 2 1 0 mod1 


v1 3 0 dc 


.dc v1 0 50 2 

.plot dc 

i(vammeter) 

.end 

Figure4.15:Sweepingcollectorvoltage0to50Vwithbasecurrentconstantat20 µAyields 

constant2mAcollectorcurrent.


Nowlet’sseewhathappensifweincreasethecontrolling(I1)currentfrom20 µAto75 

µA,onceagainsweepingthebattery(V1)voltagefrom0to50voltsandgraphingthecollector 

currentinFigure4.16. 


simulation 

i1 0 1 dc 75u 

q1 2 1 0 mod1 


v1 3 0 dc 


.dc v1 0 50 2 i1 

15u 75u 15u 

.plot dc 

i(vammeter) 

.end 

Figure4.16:Sweepingcollectorvoltage0to50V(.dcv10502)withbasecurrentconstantat 

75 µAyieldsconstant7.5mAcollectorcurrent.Othercurvesaregeneratedbycurrentsweep 

(i115u75u15u)inDCanalysisstatement(.dcv10502i115u75u15u). 

Notsurprisingly,SPICEgivesusasimilarplot:aflatline,holdingsteadythistimeat7.5 

mA–exactly100timesthebasecurrent–overtherangeofbatteryvoltagesfromjustabove 

0voltsto50volts.Itappearsthatthebasecurrentisthedecidingfactorforcollectorcurrent, 

theV1batteryvoltagebeingirrelevantaslongasitisaboveacertainminimumlevel. 

Thisvoltage/currentrelationshipisentirelydifferentfromwhatwe’reusedtoseeingacross 

aresistor.Witharesistor,currentincreaseslinearlyasthevoltageacrossitincreases.Here, 

withatransistor,currentfromemittertocollectorstayslimitedatafixed,maximumvalueno 

matterhowhighthevoltageacrossemitterandcollectorincreases. 

Oftenitisusefultosuperimposeseveralcollectorcurrent/voltagegraphsfordifferentbase 

currentsonthesamegraphasinFigure4.17.Acollectionofcurveslikethis–onecurveplotted 

foreachdistinctlevelofbasecurrent–foraparticulartransistoriscalledthetransistor’s 

characteristiccurves: 

Eachcurveonthegraphreflectsthecollectorcurrentofthetransistor,plottedoverarange 

ofcollector-to-emittervoltages,foragivenamountofbasecurrent.Sinceatransistortendsto 

actasacurrentregulator,limitingcollectorcurrenttoaproportionsetbythebasecurrent,itis 

usefultoexpressthisproportionasastandardtransistorperformancemeasure. Specifically, 

theratioofcollectorcurrenttobasecurrentisknownastheBetaratio(symbolizedbythe 

Greekletter β):


I collector 

(mA) 

9 

8 

7 

6 

5 

4 

3 

2 

1 

0 

I base = 75 µA 




0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 

E collector-to-emitter 

Figure4.17:Voltagecollectortoemittervscollectorcurrentforvariousbasecurrents. 

β = I collector 

I base 

β is also known as h fe 

Sometimesthe βratioisdesignatedas“hfe,”alabelusedinabranchofmathematicalsemiconductoranalysisknownas“hybridparameters”whichstrivestoachieveprecisepredictions 

oftransistorperformancewithdetailedequations.Hybridparametervariablesaremany,but 

eachislabeledwiththegeneralletter“h”andaspecificsubscript. Thevariable“hfe”isjust 

another(standardized)wayofexpressingtheratioofcollectorcurrenttobasecurrent,andis 

interchangeablewith“β.”The βratioisunitless. 

βforanytransistorisdeterminedbyitsdesign:itcannotbealteredaftermanufacture.Itis 

raretohavetwotransistorsofthesamedesignexactlymatchbecauseofthephysicalvariables 

afecting β.Ifacircuitdesignreliesonequal βratiosbetweenmultipletransistors,“matched 

sets”oftransistorsmaybepurchasedatextracost. However,itisgenerallyconsideredbad 

designpracticetoengineercircuitswithsuchdependencies. 

The βofatransistordoesnotremainstableforalloperatingconditions. Foranactual 

transistor,the βratiomayvarybyafactorofover3withinitsoperatingcurrentlimits. For 

example,atransistorwithadvertised βof50mayactuallytestwithIc/Ibratiosaslowas30 

andashighas100,dependingontheamountofcollectorcurrent,thetransistor’stemperature, 

andfrequencyofamplifiedsignal,amongotherfactors.Fortutorialpurposesitisadequateto 

assumeaconstant βforanygiventransistor;realizethatreallifeisnotthatsimple! 

Sometimesitishelpfulforcomprehensionto“model”complexelectroniccomponentswitha 

collectionofsimpler,better-understoodcomponents.ThemodelinFigure4.18isusedinmany 

(V)


introductoryelectronicstexts. 

B 

C 

E 

NPN 

diode-rheostat 

model 

Figure4.18:Elementarydioderesistortransistormodel. 

Thismodelcaststhetransistorasacombinationofdiodeandrheostat(variableresistor). 

Currentthroughthebase-emitterdiodecontrolstheresistanceofthecollector-emitterrheostat(asimpliedbythedashedlineconnectingthetwocomponents),thuscontrollingcollector 

current. AnNPNtransistorismodeledinthefigureshown,butaPNPtransistorwouldbe 

onlyslightlydifferent(onlythebase-emitterdiodewouldbereversed).Thismodelsucceedsin 

illustratingthebasicconceptoftransistoramplification:howthebasecurrentsignalcanexert 

controloverthecollectorcurrent.However,Idon’tlikethismodelbecauseitmiscommunicates 

thenotionofasetamountofcollector-emitterresistanceforagivenamountofbasecurrent. 

Ifthisweretrue,thetransistorwouldn’tregulatecollectorcurrentatalllikethecharacteristiccurvesshow. 

Insteadofthecollectorcurrentcurvesflatteningoutaftertheirbriefriseas 

thecollector-emittervoltageincreases,thecollectorcurrentwouldbedirectlyproportionalto 

collector-emittervoltage,risingsteadilyinastraightlineonthegraph. 

Abettertransistormodel,oftenseeninmoreadvancedtextbooks,isshowninFigure4.19. 

B 

C 

E 

B 

B 

NPN 

diode-current source 

model 

Figure4.19:Currentsourcemodeloftransistor. 

Itcaststhetransistorasacombinationofdiodeandcurrentsource,theoutputofthecurrentsourcebeingsetatamultiple(βratio)ofthebasecurrent.Thismodelisfarmoreaccurate 

C 

E 

C 

E

4.5. THECOMMON-EMITTERAMPLIFIER 189 

indepictingthetrueinput/outputcharacteristicsofatransistor:basecurrentestablishesacertainamountofcollectorcurrent,ratherthanacertainamountofcollector-emitterresistance 

asthefirstmodelimplies. Also,thismodelisfavoredwhenperformingnetworkanalysison 

transistorcircuits,thecurrentsourcebeingawell-understoodtheoreticalcomponent.Unfortunately,usingacurrentsourcetomodelthetransistor’scurrent-controllingbehaviorcanbe 

misleading:innowaywillthetransistoreveractasasourceofelectricalenergy.Thecurrent 

sourcedoesnotmodelthefactthatitssourceofenergyisaexternalpowersupply,similarto 

anamplifier. 

• REVIEW: 

• Atransistorissaidtobeinitsactivemodeifitisoperatingsomewherebetweenfullyon 

(saturated)andfullyoff(cutoff). 

• Basecurrentregulatescollectorcurrent. Byregulate,wemeanthatnomorecollector 

currentcanexistthanwhatisallowedbythebasecurrent. 

• Theratiobetweencollectorcurrentandbasecurrentiscalled“Beta”(β)or“hfe”. 

• βratiosaredifferentforeverytransistor,and 

• βchangesfordifferentoperatingconditions. 

4.5 Thecommon-emitteramplifier 

Atthebeginningofthischapterwesawhowtransistorscouldbeusedasswitches,operatingin 

eithertheir“saturation”or“cutoff”modes.Inthelastsectionwesawhowtransistorsbehave 

withintheir“active”modes,betweenthefarlimitsofsaturationandcutoff.Becausetransistors 

areabletocontrolcurrentinananalog(infinitelydivisible)fashion,theyfinduseasamplifiers 

foranalogsignals. 

Oneofthesimplertransistoramplifiercircuitstostudypreviouslyillustratedthetransistor’sswitchingability.(Figure4.20) 

solar 

cell 

Figure4.20:NPNtransistorasasimpleswitch. 

Itiscalledthecommon-emitterconfigurationbecause(ignoringthepowersupplybattery) 

boththesignalsourceandtheloadsharetheemitterleadasacommonconnectionpointshown 

inFigure4.21.Thisisnottheonlywayinwhichatransistormaybeusedasanamplifier,as 

wewillseeinlatersectionsofthischapter.


solar 

cell 

V in 

B 

E 

V out 

C Load 

Figure4.21:Common-emitteramplifier:Theinputandoutputsignalsbothshareaconnection 

totheemitter. 

Before,asmallsolarcellcurrentsaturatedatransistor,illuminatingalamp.Knowingnow 

thattransistorsareableto“throttle”theircollectorcurrentsaccordingtotheamountofbase 

currentsuppliedbyaninputsignalsource,weshouldseethatthebrightnessofthelampin 

thiscircuitiscontrollablebythesolarcell’slightexposure. Whenthereisjustalittlelight 

shoneonthesolarcell,thelampwillglowdimly.Thelamp’sbrightnesswillsteadilyincrease 

asmorelightfallsonthesolarcell. 

Supposethatwewereinterestedinusingthesolarcellasalightintensityinstrument.We 

wanttomeasuretheintensityofincidentlightwiththesolarcellbyusingitsoutputcurrent 

todriveametermovement. Itispossibletodirectlyconnectametermovementtoasolar 

cell(Figure4.22)forthispurpose.Infact,thesimplestlight-exposuremetersforphotography 

workaredesignedlikethis. 

solar 

cell 

+ - 

Figure4.22:Highintensitylightdirectlydriveslightmeter. 

Althoughthisapproachmightworkformoderatelightintensitymeasurements,itwould 

notworkaswellforlowlightintensitymeasurements.Becausethesolarcellhastosupplythe 

metermovement’spowerneeds,thesystemisnecessarilylimitedinitssensitivity.Supposing 

thatourneedhereistomeasureverylow-levellightintensities,wearepressedtofindanother 

solution. 

Perhapsthemostdirectsolutiontothismeasurementproblemistouseatransistor(Figure4.23)toamplifythesolarcell’scurrentsothatmoremeterdeflectionmaybeobtainedfor 

lessincidentlight. 

Currentthroughthemetermovementinthiscircuitwillbe βtimesthesolarcellcurrent. 

Withatransistor βof100,thisrepresentsasubstantialincreaseinmeasurementsensitivity. 

Itisprudenttopointoutthattheadditionalpowertomovethemeterneedlecomesfromthe 

batteryonthefarrightofthecircuit,notthesolarcellitself.Allthesolarcell’scurrentdoes


solar 

cell 

+ 

- 

Figure4.23:Cellcurrentmustbeamplifiedforlowintensitylight. 

iscontrolbatterycurrenttothemetertoprovideagreatermeterreadingthanthesolarcell 

couldprovideunaided. 

Becausethetransistorisacurrent-regulatingdevice,andbecausemetermovementindicationsarebasedonthecurrentthroughthemovementcoil,meterindicationinthiscircuit 

shoulddependonlyonthecurrentfromthesolarcell,notontheamountofvoltageprovidedby 

thebattery.Thismeanstheaccuracyofthecircuitwillbeindependentofbatterycondition,a 

significantfeature!Allthatisrequiredofthebatteryisacertainminimumvoltageandcurrent 

outputabilitytodrivethemeterfull-scale. 

Anotherwayinwhichthecommon-emitterconfigurationmaybeusedistoproducean 

outputvoltagederivedfromtheinputsignal,ratherthanaspecificoutputcurrent.Let’sreplace 

themetermovementwithaplainresistorandmeasurevoltagebetweencollectorandemitter 

inFigure4.24 

solar 

cell 

+ 

- 

- 

R 

V output 

Figure4.24:Commonemitteramplifierdevelopsvoltageoutputduetocurrentthroughload 

resistor. 

Withthesolarcelldarkened(nocurrent),thetransistorwillbeincutoffmodeandbehave 

asanopenswitchbetweencollectorandemitter. Thiswillproducemaximumvoltagedrop 

betweencollectorandemitterformaximumVoutput,equaltothefullvoltageofthebattery. 

Atfullpower(maximumlightexposure),thesolarcellwilldrivethetransistorintosaturationmode,makingitbehavelikeaclosedswitchbetweencollectorandemitter.Theresult 

willbeminimumvoltagedropbetweencollectorandemitter,oralmostzerooutputvoltage. 

Inactuality,asaturatedtransistorcanneverachievezerovoltagedropbetweencollectorand 

emitterbecauseofthetwoPNjunctionsthroughwhichcollectorcurrentmusttravel. However,this“collector-emittersaturationvoltage”willbefairlylow,aroundseveraltenthsofa 

+ 

+ 

- 

+ 

-


volt,dependingonthespecifictransistorused. 

Forlightexposurelevelssomewherebetweenzeroandmaximumsolarcelloutput,thetransistorwillbeinitsactivemode,andtheoutputvoltagewillbesomewherebetweenzeroand 

fullbatteryvoltage.Animportantqualitytonotehereaboutthecommon-emitterconfiguration 

isthattheoutputvoltageisinverselyproportionaltotheinputsignalstrength. Thatis,the 

outputvoltagedecreasesastheinputsignalincreases. Forthisreason,thecommon-emitter 

amplifierconfigurationisreferredtoasaninvertingamplifier. 

AquickSPICEsimulation(Figure4.26)ofthecircuitinFigure4.25willverifyourqualitativeconclusionsaboutthisamplifiercircuit. 

I 1 

1 

0 

2 

0 

Q 1 

R 

5 kΩ 

V output 

V 1 

3 

+ 

15 V 

- 

0 

*common-emitter 

amplifier 

i1 0 1 dc 

q1 2 1 0 mod1 

r 3 2 5000 

v1 3 0 dc 15 


.dc i1 0 50u 2u 

.plot dc v(2,0) 

.end 

Figure4.25:CommonemitterschematicwithnodenumbersandcorrespondingSPICEnetlist. 

Figure4.26:Commonemitter:collectorvoltageoutputvsbasecurrentinput. 

AtthebeginningofthesimulationinFigure4.26wherethecurrentsource(solarcell)is 

outputtingzerocurrent,thetransistorisincutoffmodeandthefull15voltsfromthebattery


isshownattheamplifieroutput(betweennodes2and0).Asthesolarcell’scurrentbeginsto 

increase,theoutputvoltageproportionallydecreases,untilthetransistorreachessaturation 

at30 µAofbasecurrent(3mAofcollectorcurrent). Noticehowtheoutputvoltagetraceon 

thegraphisperfectlylinear(1voltstepsfrom15voltsto1volt)untilthepointofsaturation, 

whereitneverquitereacheszero. Thisistheeffectmentionedearlier,whereasaturated 

transistorcanneverachieveexactlyzerovoltagedropbetweencollectorandemitterdueto 

internaljunctioneffects. Whatwedoseeisasharpoutputvoltagedecreasefrom1voltto 

0.2261voltsastheinputcurrentincreasesfrom28 µAto30 µA,andthenacontinuingdecrease 

inoutputvoltagefromthenon(albeitinprogressivelysmallersteps). Thelowesttheoutput 

voltageevergetsinthissimulationis0.1299volts,asymptoticallyapproachingzero. 

Sofar,we’veseenthetransistorusedasanamplifierforDCsignals.Inthesolarcelllight 

meterexample,wewereinterestedinamplifyingtheDCoutputofthesolarcelltodrivea 

DCmetermovement,ortoproduceaDCoutputvoltage. However,thisisnottheonlyway 

inwhichatransistormaybeemployedasanamplifier.OftenanACamplifierforamplifying 

alternatingcurrentandvoltagesignalsisdesired.Onecommonapplicationofthisisinaudio 

electronics(radios,televisions,andpublic-addresssystems).Earlier,wesawanexampleofthe 

audiooutputofatuningforkactivatingatransistorswitch. (Figure4.27)Let’sseeifwecan 

modifythatcircuittosendpowertoaspeakerratherthantoalampinFigure4.28. 

source of 

sound 

microphone 

Figure4.27:Transistorswitchactivatedbyaudio. 

Intheoriginalcircuit,afull-wavebridgerectifierwasusedtoconvertthemicrophone’sAC 

outputsignalintoaDCvoltagetodrivetheinputofthetransistor.Allwecaredaboutherewas 

turningthelamponwithasoundsignalfromthemicrophone,andthisarrangementsufficed 

forthatpurpose. ButnowwewanttoactuallyreproducetheACsignalanddriveaspeaker. 

Thismeanswecannotrectifythemicrophone’soutputanymore,becauseweneedundistorted 

ACsignaltodrivethetransistor!Let’sremovethebridgerectifierandreplacethelampwitha 

speaker: 

SincethemicrophonemayproducevoltagesexceedingtheforwardvoltagedropofthebaseemitterPN(diode)junction,I’veplacedaresistorinserieswiththemicrophone.Let’ssimulate 

thecircuitinFigure4.29withSPICE.Thenetlistisincludedin(Figure4.30) 

Thesimulationplots(Figure4.30)boththeinputvoltage(anACsignalof1.5voltpeak 

amplitudeand2000Hzfrequency)andthecurrentthroughthe15voltbattery,whichisthe 

sameasthecurrentthroughthespeaker.WhatweseehereisafullACsinewavealternating 

inbothpositiveandnegativedirections,andahalf-waveoutputcurrentwaveformthatonly


source of 

sound 

microphone 

speaker 

Figure4.28:Commonemitteramplifierdrivesspeakerwithaudiofrequencysignal. 

V input 

1.5 V 

2 kHz 

1 

R 1 

1 kΩ 

2 

3 8 Ω 4 

Q 1 

speaker 

V 1 

0 0 0 

15 V 

Figure4.29:SPICEversionofcommonemitteraudioamplifier. 

common-emitter 

amplifier 

vinput 1 0 sin (0 

1.5 2000 0 0) 

r1 1 2 1k 

q1 3 2 0 mod1 

rspkr 3 4 8 

v1 4 0 dc 15 


.tran 0.02m 0.74m 

.plot tran v(1,0) 

i(v1) 

.end 

Figure4.30:SignalclippedatcollectorduetolackofDCbasebias.


pulsesinonedirection. Ifwewereactuallydrivingaspeakerwiththiswaveform,thesound 

producedwouldbehorriblydistorted. 

What’swrongwiththecircuit?Whywon’titfaithfullyreproducetheentireACwaveform 

fromthemicrophone?Theanswertothisquestionisfoundbycloseinspectionofthetransistor 

diodecurrentsourcemodelinFigure4.31. 

B 

C 

E 

B 

NPN 

diode-current source 

model 

Figure4.31:Themodelshowsthatbasecurrentflowinondirection. 

Collectorcurrentiscontrolled,orregulated,throughtheconstant-currentmechanismaccordingtothepacesetbythecurrentthroughthebase-emitterdiode.Notethatbothcurrent 

pathsthroughthetransistoraremonodirectional:onewayonly!Despiteourintenttousethe 

transistortoamplifyanACsignal,itisessentiallyaDCdevice,capableofhandlingcurrents 

inasingledirection.WemayapplyanACvoltageinputsignalbetweenthebaseandemitter, 

butelectronscannotflowinthatcircuitduringthepartofthecyclethatreverse-biasesthe 

base-emitterdiodejunction. Therefore,thetransistorwillremainincutoffmodethroughout 

thatportionofthecycle. Itwill“turnon”initsactivemodeonlywhentheinputvoltageis 

ofthecorrectpolaritytoforward-biasthebase-emitterdiode,andonlywhenthatvoltageis 

sufficientlyhightoovercomethediode’sforwardvoltagedrop. Rememberthatbipolartransistorsarecurrent-controlleddevices:theyregulatecollectorcurrentbasedontheexistenceof 

base-to-emittercurrent,notbase-to-emittervoltage. 

Theonlywaywecangetthetransistortoreproducetheentirewaveformascurrentthrough 

thespeakeristokeepthetransistorinitsactivemodetheentiretime.Thismeanswemust 

maintaincurrentthroughthebaseduringtheentireinputwaveformcycle.Consequently,the 

base-emitterdiodejunctionmustbekeptforward-biasedatalltimes. Fortunately,thiscan 

beaccomplishedwithaDCbiasvoltageaddedtotheinputsignal.Byconnectingasufficient 

DCvoltageinserieswiththeACsignalsource,forward-biascanbemaintainedatallpoints 

throughoutthewavecycle.(Figure4.32) 

Withthebiasvoltagesourceof2.3voltsinplace,thetransistorremainsinitsactivemode 

throughouttheentirecycleofthewave,faithfullyreproducingthewaveformatthespeaker. 

(Figure4.33)Noticethattheinputvoltage(measuredbetweennodes1and0)fluctuatesbetweenabout0.8voltsand3.8volts,apeak-to-peakvoltageof3voltsjustasexpected(source 

voltage=1.5voltspeak). Theoutput(speaker)currentvariesbetweenzeroandalmost300 

mA,180 o outofphasewiththeinput(microphone)signal. 

TheillustrationinFigure4.34isanotherviewofthesamecircuit,thistimewithafew 

C 

E


V input 

1.5 V 

2 kHz 

1 

5 

R 1 

1 kΩ 

+ - 

V bias 

2.3 V 

2 

Q 1 

speaker 

3 8 Ω 4 

0 

Figure4.32:Vbiaskeepstransistorintheactiveregion. 

V 1 

0 

15 V 

Figure4.33:UndistortedoutputcurrentI(v(1)duetoVbias 


amplifier 


1.5 2000 0 0) 

vbias 5 0 dc 2.3 

r1 1 2 1k 

q1 3 2 0 mod1 

rspkr 3 4 8 

v1 4 0 dc 15 


.tran 0.02m 0.78m 


i(v1) 

.end


oscilloscopes(“scopemeters”)connectedatcrucialpointstodisplayallthepertinentsignals. 

V input 

1.5 V 

2 kHz 

R 1 

1 kΩ 

+ - 

V bias 

Q 1 

speaker 

8 Ω 

V 1 

15 V 

Figure4.34:Inputisbiasedupwardatbase.Outputisinverted. 

Theneedforbiasingatransistoramplifiercircuittoobtainfullwaveformreproductionis 

animportantconsideration.Aseparatesectionofthischapterwillbedevotedentirelytothe 

subjectbiasingandbiasingtechniques.Fornow,itisenoughtounderstandthatbiasingmay 

benecessaryforpropervoltageandcurrentoutputfromtheamplifier. 

Nowthatwehaveafunctioningamplifiercircuit,wecaninvestigateitsvoltage,current, 

andpowergains. ThegenerictransistorusedintheseSPICEanalyseshasaβof100,as 

indicatedbytheshorttransistorstatisticsprintoutincludedinthetextoutputinTable 4.1 

(thesestatisticswerecutfromthelasttwoanalysesforbrevity’ssake). 

type npn 

is 1.00E-16 

bf 100.000 

nf 1.000 

br 1.000 

nr 1.000 

Table4.1:BJTSPICEmodelparameters. 

βislistedundertheabbreviation“bf,”whichactuallystandsfor“beta,forward”. Ifwe 

wantedtoinsertourown βratioforananalysis,wecouldhavedonesoonthe .modellineof 

theSPICEnetlist. 

Since βistheratioofcollectorcurrenttobasecurrent,andwehaveourloadconnectedin 

serieswiththecollectorterminalofthetransistorandoursourceconnectedinserieswiththe 

base,theratioofoutputcurrenttoinputcurrentisequaltobeta.Thus,ourcurrentgainfor 

thisexampleamplifieris100,or40dB. 

Voltagegainisalittlemorecomplicatedtofigurethancurrentgainforthiscircuit. As 

always,voltagegainisdefinedastheratioofoutputvoltagedividedbyinputvoltage.Inorder 

toexperimentallydeterminethis,wemodifyourlastSPICEanalysistoplotoutputvoltage 

ratherthanoutputcurrentsowehavetwovoltageplotstocompareinFigure4.35. 

+



amplifier 


1.5 2000 0 0) 


r1 1 2 1k 

q1 3 2 0 mod1 

rspkr 3 4 8 

v1 4 0 dc 15 


.tran 0.02m 0.78m 


v(3) 

.end 

Figure4.35:V(3),theoutputvoltageacrossrspkr,comparedtotheinput. 

Plottedonthesamescale(from0to4volts),weseethattheoutputwaveforminFigure4.35 

Tobehonest,thislowvoltagegainisnotcharacteristictoallcommon-emitteramplifiers. 

Itisaconsequenceofthegreatdisparitybetweentheinputandloadresistances. Ourinput 

resistance(R1)hereis1000 Ω,whiletheload(speaker)isonly8Ω.Becausethecurrentgain 

ofthisamplifierisdeterminedsolelybythe βofthetransistor,andbecausethat βfigure 

isfixed,thecurrentgainforthisamplifierwon’tchangewithvariationsineitherofthese 

resistances. However,voltagegainisdependentontheseresistances. Ifwealtertheload 

resistance,makingitalargervalue,itwilldropaproportionatelygreatervoltageforitsrange 

ofloadcurrents,resultinginalargeroutputwaveform.Let’stryanothersimulation,onlythis 

timewitha30 ΩinFigure4.36loadinsteadofan8Ωload. 

ThistimetheoutputvoltagewaveforminFigure4.36issignificantlygreaterinamplitude 

thantheinputwaveform.Lookingclosely,wecanseethattheoutputwaveformcrestsbetween 

0andabout9volts:approximately3timestheamplitudeoftheinputvoltage. 

Wecandoanothercomputeranalysisofthiscircuit,thistimeinstructingSPICEtoanalyze 

itfromanACpointofview,givinguspeakvoltagefiguresforinputandoutputinsteadofa 

time-basedplotofthewaveforms.(Table4.2) 

Peakvoltagemeasurementsofinputandoutputshowaninputof1.5voltsandanoutput 

of4.418volts.Thisgivesusavoltagegainratioof2.9453(4.418V/1.5V),or9.3827dB.


Figure4.36:Increasingrspkrto30 Ωincreasestheoutputvoltage. 


amplifier 


1.5 2000 0 0) 


r1 1 2 1k 

q1 3 2 0 mod1 

rspkr 3 4 30 

v1 4 0 dc 15 


.tran 0.02m 0.78m 


v(3) 

.end 

Table4.2:SPICEnetlistforprintingACinputandoutputvoltages. 

common-emitter amplifier 

vinput 1 5 ac 1.5 


r1 1 2 1k 

q1 3 2 0 mod1 

rspkr 3 4 30 

v1 4 0 dc 15 


.ac lin 1 2000 2000 

.print ac v(1,0) v(4,3) 

.end 

freq v(1) v(4,3) 

2.000E+03 1.500E+00 4.418E+00


A V = V out 

V in 

A V = 

4.418 V 

1.5 V 

A V = 2.9453 


A V(dB) = 20 log 2.9453 

A V(dB) = 9.3827 dB 

Becausethecurrentgainofthecommon-emitteramplifierisfixedby β,andsincetheinputandoutputvoltageswillbeequaltotheinputandoutputcurrentsmultipliedbytheir 

respectiveresistors,wecanderiveanequationforapproximatevoltagegain: 

A V = β R out 

R in 

A V = (100) 30 Ω 

1000 Ω 

A V = 3 


A V(dB) = 20 log 3 

A V(dB) = 9.5424 dB 

Asyoucansee,thepredictedresultsforvoltagegainarequiteclosetothesimulatedresults. 

Withperfectlylineartransistorbehavior,thetwosetsoffigureswouldexactlymatch.SPICE 

doesareasonablejobofaccountingforthemany“quirks”ofbipolartransistorfunctioninits 

analysis,hencetheslightmismatchinvoltagegainbasedonSPICE’soutput. 

Thesevoltagegainsremainthesameregardlessofwherewemeasureoutputvoltagein 

thecircuit: acrosscollectorandemitter,oracrosstheseriesloadresistoraswedidinthe 

lastanalysis. Theamountofoutputvoltagechangeforanygivenamountofinputvoltage 

willremainthesame. ConsiderthetwofollowingSPICEanalysesasproofofthis. Thefirst 

simulationinFigure4.37istime-based,toprovideaplotofinputandoutputvoltages. You 

willnoticethatthetwosignalsare180 o outofphasewitheachother.Thesecondsimulation 

inTable4.3isanACanalysis,toprovidesimple,peakvoltagereadingsforinputandoutput. 

Westillhaveapeakoutputvoltageof4.418voltswithapeakinputvoltageof1.5volts.The 

onlydifferencefromthelastsetofsimulationsisthephaseoftheoutputvoltage. 

Sofar,theexamplecircuitsshowninthissectionhaveallusedNPNtransistors.PNPtran-



amplifier 


1.5 2000 0 0) 


r1 1 2 1k 

q1 3 2 0 mod1 

rspkr 3 4 30 

v1 4 0 dc 15 


.tran 0.02m 0.74m 


v(3,0) 

.end 

Figure4.37:Common-emitteramplifiershowsavoltagegainwithRspkr=30Ω 

Table4.3:SPICEnetlistforACanalysis 


vinput 1 5 ac 1.5 


r1 1 2 1k 

q1 3 2 0 mod1 

rspkr 3 4 30 

v1 4 0 dc 15 


.ac lin 1 2000 2000 

.print ac v(1,0) v(3,0) 

.end 

freq v(1) v(3) 

2.000E+03 1.500E+00 4.418E+00


sistorsarejustasvalidtouseasNPNinanyamplifierconfiguration,aslongastheproper 

polarityandcurrentdirectionsaremaintained,andthecommon-emitteramplifierisnoexception. 

TheoutputinvertionandgainofaPNPtransistoramplifierarethesameasitsNPN 

counterpart,justthebatterypolaritiesaredifferent.(Figure4.38) 

• REVIEW: 

V input 

- 

V bias 

Figure4.38:PNPversionofcommonemitteramplifier. 

• Common-emittertransistoramplifiersareso-calledbecausetheinputandoutputvoltage 

pointssharetheemitterleadofthetransistorincommonwitheachother,notconsidering 

anypowersupplies. 

• TransistorsareessentiallyDCdevices:theycannotdirectlyhandlevoltagesorcurrents 

thatreversedirection. TomakethemworkforamplifyingACsignals,theinputsignal 

mustbeoffsetwithaDCvoltagetokeepthetransistorinitsactivemodethroughoutthe 

entirecycleofthewave.Thisiscalledbiasing. 

• Iftheoutputvoltageismeasuredbetweenemitterandcollectoronacommon-emitter 

amplifier,itwillbe180 o outofphasewiththeinputvoltagewaveform.Thus,thecommonemitteramplifieriscalledaninvertingamplifiercircuit. 

• Thecurrentgainofacommon-emittertransistoramplifierwiththeloadconnectedin 

serieswiththecollectorisequalto β. Thevoltagegainofacommon-emittertransistor 

amplifierisapproximatelygivenhere: 

• 

A V = β R out 

R in 

• Where“Rout”istheresistorconnectedinserieswiththecollectorand“Rin”istheresistor 

connectedinserieswiththebase. 

4.6 Thecommon-collectoramplifier 

Ournexttransistorconfigurationtostudyisabitsimplerforgaincalculations. Calledthe 

common-collectorconfiguration,itsschematicdiagramisshowninFigure4.39. 

+ 

- 

+

4.6. THECOMMON-COLLECTORAMPLIFIER 203 

V in 

+ 

- 

V out 

R load 

Figure4.39:Commoncollectoramplifierhascollectorcommontobothinputandoutput. 

Itiscalledthecommon-collectorconfigurationbecause(ignoringthepowersupplybattery) 

boththesignalsourceandtheloadsharethecollectorleadasacommonconnectionpointas 

inFigure4.40. 

V in 

B 

V out 

Figure4.40:Commoncollector:Inputisappliedtobaseandcollector.Outputisfromemittercollectorcircuit. 

Itshouldbeapparentthattheloadresistorinthecommon-collectoramplifiercircuitreceivesboththebaseandcollectorcurrents,beingplacedinserieswiththeemitter.Sincethe 

emitterleadofatransistoristheonehandlingthemostcurrent(thesumofbaseandcollector 

currents,sincebaseandcollectorcurrentsalwaysmeshtogethertoformtheemittercurrent), 

itwouldbereasonabletopresumethatthisamplifierwillhaveaverylargecurrentgain.This 

presumptionisindeedcorrect:thecurrentgainforacommon-collectoramplifierisquitelarge, 

largerthananyothertransistoramplifierconfiguration.However,thisisnotnecessarilywhat 

setsitapartfromotheramplifierdesigns. 

Let’sproceedimmediatelytoaSPICEanalysisofthisamplifiercircuit,andyouwillbeable 

toimmediatelyseewhatisuniqueaboutthisamplifier. ThecircuitisinFigure4.41. The 

netlistisinFigure4.42. 

Unlikethecommon-emitteramplifierfromtheprevioussection,thecommon-collectorproducesanoutputvoltageindirectratherthaninverseproportiontotherisinginputvoltage. 

SeeFigure4.42.Astheinputvoltageincreases,sodoestheoutputvoltage.Moreover,aclose 

examinationrevealsthattheoutputvoltageisnearlyidenticaltotheinputvoltage,lagging 

C 

E 

R load 

+ 

-


V in 

1 

1 

2 

3 

Q 1 

R load 

5 kΩ 

V 1 

0 0 0 

2 

15 V 

Figure4.41:CommoncollectoramplifierforSPICE. 

common-collector 

amplifier 

vin 1 0 

q1 2 1 3 mod1 

v1 2 0 dc 15 

rload 3 0 5k 


.dc vin 0 5 0.2 


.end 

Figure4.42:Commoncollector:Outputequalsinputlessa0.7VVBEdrop.


behindbyabout0.7volts. 

Thisistheuniquequalityofthecommon-collectoramplifier: anoutputvoltagethatis 

nearlyequaltotheinputvoltage. Examinedfromtheperspectiveofoutputvoltagechange 

foragivenamountofinputvoltagechange,thisamplifierhasavoltagegainofalmostexactly 

unity(1),or0dB.Thisholdstruefortransistorsofany βvalue,andforloadresistorsofany 

resistancevalue. 

Itissimpletounderstandwhytheoutputvoltageofacommon-collectoramplifierisalways 

nearlyequaltotheinputvoltage.ReferringtothediodecurrentsourcetransistormodelinFigure4.43,weseethatthebasecurrentmustgothroughthebase-emitterPNjunction,which 

isequivalenttoanormalrectifyingdiode. Ifthisjunctionisforward-biased(thetransistor 

conductingcurrentineitheritsactiveorsaturatedmodes),itwillhaveavoltagedropofapproximately0.7volts,assumingsiliconconstruction.This0.7voltdropislargelyirrespective 

oftheactualmagnitudeofbasecurrent;thus,wecanregarditasbeingconstant: 

V in 

B 

+ 

0.7 V 

- 

Figure4.43:Emitterfollower:Emittervoltagefollowsbasevoltage(lessa0.7VVBEdrop.) 

Giventhevoltagepolaritiesacrossthebase-emitterPNjunctionandtheloadresistor,we 

seethatthesemustaddtogethertoequaltheinputvoltage,inaccordancewithKirchhoff’s 

VoltageLaw.Inotherwords,theloadvoltagewillalwaysbeabout0.7voltslessthantheinput 

voltageforallconditionswherethetransistorisconducting. Cutoffoccursatinputvoltages 

below0.7volts,andsaturationatinputvoltagesinexcessofbattery(supply)voltageplus0.7 

volts. 

Becauseofthisbehavior,thecommon-collectoramplifiercircuitisalsoknownasthevoltagefolloweroremitter-followeramplifier,becausetheemitterloadvoltagesfollowtheinputso 

closely. 

Applyingthecommon-collectorcircuittotheamplificationofACsignalsrequiresthesame 

input“biasing”usedinthecommon-emittercircuit: aDCvoltagemustbeaddedtotheAC 

inputsignaltokeepthetransistorinitsactivemodeduringtheentirecycle. Whenthisis 

done,theresultisthenon-invertingamplifierinFigure4.44. 

TheresultsoftheSPICEsimulationinFigure4.45showthattheoutputfollowstheinput. 

Theoutputisthesamepeak-to-peakamplitudeastheinput.Though,theDClevelisshifted 

C 

E 

+ 

- 

R load


V in 

1 

4 

1.5 V 

2 kHz 

1 

+ - 

V bias 

2.3 V 

downwardbyoneVBEdiodedrop. 

2 

3 

0 

Q 1 

R load 

5 kΩ 

V 1 

2 

0 

15 V 

common-collector 

amplifier 

vin 1 4 sin(0 1.5 

2000 0 0) 


q1 2 1 3 mod1 

v1 2 0 dc 15 

rload 3 0 5k 


.tran .02m .78m 


v(3,0) 

.end 

Figure4.44:Commoncollector(emitter-follower)amplifier. 

Figure4.45:Commoncollector(emitter-follower):OutputV3followsinputV1lessa0.7VVBE 

drop. 

Here’sanotherviewofthecircuit(Figure4.46)withoscilloscopesconnectedtoseveral 

pointsofinterest. 

Sincethisamplifierconfigurationdoesn’tprovideanyvoltagegain(infact,inpracticeit 

actuallyhasavoltagegainofslightlylessthan1),itsonlyamplifyingfactoriscurrent. The 

common-emitteramplifierconfigurationexaminedintheprevioussectionhadacurrentgain 

equaltothe βofthetransistor,beingthattheinputcurrentwentthroughthebaseandthe


V in 

1.5 V 

2 kHz 

+ - 

R load 

5 kΩ 

V 1 

15 V 

Figure4.46:Commoncollectornon-invertingvoltagegainis1. 

output(load)currentwentthroughthecollector,and βbydefinitionistheratiobetweenthe 

collectorandbasecurrents.Inthecommon-collectorconfiguration,though,theloadissituated 

inserieswiththeemitter,andthusitscurrentisequaltotheemittercurrent.Withtheemitter 

carryingcollectorcurrentandbasecurrent,theloadinthistypeofamplifierhasallthecurrent 

ofthecollectorrunningthroughitplustheinputcurrentofthebase.Thisyieldsacurrentgain 

of βplus1: 

A I = I emitter 

I base 

A I = 

Icollector+ Ibase Ibase AI = Icollector + 1 

Ibase A I = β + 1 

Onceagain,PNPtransistorsarejustasvalidtouseinthecommon-collectorconfiguration 

asNPNtransistors. Thegaincalculationsareallthesame,asisthenon-invertingofthe 

amplifiedsignal. Theonlydifferenceisinvoltagepolaritiesandcurrentdirectionsshownin 

Figure4.47. 

Apopularapplicationofthecommon-collectoramplifierisforregulatedDCpowersupplies, 

whereanunregulated(varying)sourceofDCvoltageisclippedataspecifiedleveltosupply 

regulated(steady)voltagetoaload. Ofcourse,zenerdiodesalreadyprovidethisfunctionof 

voltageregulationshowninFigure4.48. 

However,whenusedinthisdirectfashion,theamountofcurrentthatmaybesuppliedto 

theloadisusuallyquitelimited. Inessence,thiscircuitregulatesvoltageacrosstheloadby 

keepingcurrentthroughtheseriesresistoratahighenoughleveltodropalltheexcesspower 

sourcevoltageacrossit,thezenerdiodedrawingmoreorlesscurrentasnecessarytokeepthe 

voltageacrossitselfsteady.Forhigh-currentloads,aplainzenerdiodevoltageregulatorwould 

havetoshuntaheavycurrentthroughthediodetobeeffectiveatregulatingloadvoltagein 

theeventoflargeloadresistanceorvoltagesourcechanges. 

+ 

-


V in 

- 

+ 

R load 

Figure4.47:PNPversionofthecommon-collectoramplifier. 

Unregulated 

DC voltage 

source 

R 

Zener 

diode 

R load 

Figure4.48:Zenerdiodevoltageregulator. 

- 

+ 

Regulated voltage 

across load 

Onepopularwaytoincreasethecurrent-handlingabilityofaregulatorcircuitlikethisis 

touseacommon-collectortransistortoamplifycurrenttotheload,sothatthezenerdiode 

circuitonlyhastohandletheamountofcurrentnecessarytodrivethebaseofthetransistor. 

(Figure4.49) 

Unregulated 

DC voltage 

source 

R 

Zener 

diode 

R load 

Figure4.49:Commoncollectorapplication:voltageregulator. 

There’sreallyonlyonecaveattothisapproach:theloadvoltagewillbeapproximately0.7 

voltslessthanthezenerdiodevoltage,duetothetransistor’s0.7voltbase-emitterdrop.Since 

this0.7voltdifferenceisfairlyconstantoverawiderangeofloadcurrents,azenerdiodewith


a0.7volthigherratingcanbechosenfortheapplication. 

Sometimesthehighcurrentgainofasingle-transistor,common-collectorconfigurationisn’t 

enoughforaparticularapplication.Ifthisisthecase,multipletransistorsmaybestagedtogetherinapopularconfigurationknownasaDarlingtonpair,justanextensionofthecommoncollectorconceptshowninFigure4.50. 

B 

Figure4.50:AnNPNdarlingtonpair. 

Darlingtonpairsessentiallyplaceonetransistorasthecommon-collectorloadforanother 

transistor,thusmultiplyingtheirindividualcurrentgains. Basecurrentthroughtheupperlefttransistorisamplifiedthroughthattransistor’semitter,whichisdirectlyconnectedtothe 

baseofthelower-righttransistor,wherethecurrentisagainamplified. Theoverallcurrent 

gainisasfollows: 

Darlington pair current gain 

A I = (β 1 + 1)(β 2 + 1) 

Where, 

β 1 = Beta of first transistor 

β 2 = Beta of second transistor 

Voltagegainisstillnearlyequalto1iftheentireassemblyisconnectedtoaloadincommoncollectorfashion,althoughtheloadvoltagewillbeafull1.4voltslessthantheinputvoltage 


Darlingtonpairsmaybepurchasedasdiscreteunits(twotransistorsinthesamepackage), 

ormaybebuiltupfromapairofindividualtransistors.Ofcourse,ifevenmorecurrentgain 

isdesiredthanwhatmaybeobtainedwithapair,Darlingtontripletorquadrupletassemblies 

maybeconstructed. 

• REVIEW: 

• Common-collectortransistoramplifiersareso-calledbecausetheinputandoutputvoltagepointssharethecollectorleadofthetransistorincommonwitheachother,notcon- 

C 

E


V in 

+ 

- 

+ - 

0.7 V + - 

0.7 V 

R load 

V out = V in - 1.4 

Figure4.51:Darlingtonpairbasedcommon-collectoramplifierlosestwoVBEdiodedrops. 

sideringanypowersupplies. 

V out 

• Thecommon-collectoramplifierisalsoknownasanemitter-follower. 

• Theoutputvoltageonacommon-collectoramplifierwillbeinphasewiththeinputvoltage,makingthecommon-collectoranon-invertingamplifiercircuit. 

• Thecurrentgainofacommon-collectoramplifierisequalto βplus1.Thevoltagegainis 

approximatelyequalto1(inpractice,justalittlebitless). 

• ADarlingtonpairisapairoftransistors“piggybacked”ononeanothersothattheemitter 

ofonefeedscurrenttothebaseoftheotherincommon-collectorform. Theresultisan 

overallcurrentgainequaltotheproduct(multiplication)oftheirindividualcommoncollectorcurrentgains(βplus1). 

4.7 Thecommon-baseamplifier 

Thefinaltransistoramplifierconfiguration(Figure4.52)weneedtostudyisthecommon-base. 

Thisconfigurationismorecomplexthantheothertwo,andislesscommonduetoitsstrange 

operatingcharacteristics. 

Itiscalledthecommon-baseconfigurationbecause(DCpowersourceaside),thesignal 

sourceandtheloadsharethebaseofthetransistorasacommonconnectionpointshownin 

Figure4.53. 

Perhapsthemoststrikingcharacteristicofthisconfigurationisthattheinputsignalsource 

mustcarrythefullemittercurrentofthetransistor,asindicatedbytheheavyarrowsinthe 

firstillustration. Asweknow,theemittercurrentisgreaterthananyothercurrentinthe 

transistor,beingthesumofbaseandcollectorcurrents. Inthelasttwoamplifierconfigurations,thesignalsourcewasconnectedtothebaseleadofthetransistor,thushandlingtheleast 

currentpossible.

4.7. THECOMMON-BASEAMPLIFIER 211 

− 

V in 

+ 

− 

+ 

R load 

Figure4.52:Common-baseamplifier 

− 

E 

V in 

+ 

B 

C 

− 

Figure4.53:Common-baseamplifier:Inputbetweenemitterandbase,outputbetweencollectorandbase. 

Becausetheinputcurrentexceedsallothercurrentsinthecircuit,includingtheoutput 

current,thecurrentgainofthisamplifierisactuallylessthan1(noticehowRloadisconnected 

tothecollector,thuscarryingslightlylesscurrentthanthesignalsource). Inotherwords, 

itattenuatescurrentratherthanamplifyingit. Withcommon-emitterandcommon-collector 

amplifierconfigurations,thetransistorparametermostcloselyassociatedwithgainwas β. 

Inthecommon-basecircuit,wefollowanotherbasictransistorparameter:theratiobetween 

collectorcurrentandemittercurrent,whichisafractionalwayslessthan1. Thisfractional 

valueforanytransistoriscalledthealpharatio,or αratio. 

Sinceitobviouslycan’tboostsignalcurrent,itonlyseemsreasonabletoexpectittoboost 

signalvoltage.ASPICEsimulationofthecircuitinFigure4.54willvindicatethatassumption. 

2 

1 

− 

R 1 

100Ω 

V in 

+ 

Q 1 

0 

− 

+ 

V 1 

15 V 

+ 

R load 

4 

3 

R load 

V out 

5.0kΩ 

Figure4.54:Common-basecircuitforDCSPICEanalysis. 

NoticeinFigure4.55thattheoutputvoltagegoesfrompracticallynothing(cutoff)to15.75 

volts(saturation)withtheinputvoltagebeingsweptoverarangeof0.6voltsto1.2volts.In 

fact,theoutputvoltageplotdoesn’tshowariseuntilabout0.7voltsattheinput,andcutsoff


Figure4.55:Common-baseamplifierDCtransferfunction. 

common-base 

amplifier 

vin 0 1 

r1 1 2 100 

q1 4 0 2 mod1 

v1 3 0 dc 15 

rload 3 4 5k 


.dc vin 0.6 1.2 

.02 


.end 

(flattens)atabout1.12voltsinput.Thisrepresentsaratherlargevoltagegainwithanoutput 

voltagespanof15.75voltsandaninputvoltagespanofonly0.42volts:againratioof37.5, 

or31.48dB.Noticealsohowtheoutputvoltage(measuredacrossRload)actuallyexceedsthe 

powersupply(15volts)atsaturation,duetotheseries-aidingeffectoftheinputvoltagesource. 

AsecondsetofSPICEanalyses(circuitinFigure4.56)withanACsignalsource(andDC 

biasvoltage)tellsthesamestory:ahighvoltagegain 

R 1 

100Ω 

2 

1 

− 

V bias 

V in 

0.12 Vp-p 0Voffset 2kHz 

5 

+ 

Q 1 

0.95 V 

0 

− 

R load 

5.0kΩ 

V 1 

15 V 

+ 

4 

3 

V out 

Figure4.56:Common-basecircuitforSPICEACanalysis. 

Asyoucansee,theinputandoutputwaveformsinFigure4.57areinphasewitheachother. 

Thistellsusthatthecommon-baseamplifierisnon-inverting. 

TheACSPICEanalysisinTable4.4atasinglefrequencyof2kHzprovidesinputand 

outputvoltagesforgaincalculation.


Figure4.57: 

common-base 

amplifier 

vin 5 2 sin (0 

0.12 2000 0 0) 

vbias 0 1 dc 0.95 

r1 2 1 100 

q1 4 0 5 mod1 

v1 3 0 dc 15 

rload 3 4 5k 


.tran 0.02m 0.78m 


v(4) 

.end 

Table4.4:Common-baseACanalysisat2kHz–netlistfollowedbyoutput. 

common-base amplifier 

vin 5 2 ac 0.1 sin 

vbias 0 1 dc 0.95 

r1 2 1 100 

q1 4 0 5 mod1 

v1 3 0 dc 15 

rload 3 4 5k 


.ac dec 1 2000 2000 

.print ac vm(5,2) vm(4,3) 

.end 

frequency mag(v(5,2)) mag(v(4,3)) 

-------------------------------------------- 

0.000000e+00 1.000000e-01 4.273864e+00


Voltagefiguresfromthesecondanalysis(Table4.4)showavoltagegainof42.74(4.274V/ 

0.1V),or32.617dB: 

A V = V out 

V in 

A V = 

4.274 V 

0.10 V 

AV = 42.74 


A V(dB) = 20 log 42.74 

A V(dB) = 32.62 dB 

Here’sanotherviewofthecircuitinFigure4.58,summarizingthephaserelationsandDC 

offsetsofvarioussignalsinthecircuitjustsimulated. 

− 

V bias 

V in 

+ 

Q 1 

− 

R load 

V 1 

Figure4.58:PhaserelationshipsandoffsetsforNPNcommonbaseamplifier. 

...andforaPNPtransistor:Figure4.59. 

Predictingvoltagegainforthecommon-baseamplifierconfigurationisquitedifficult,and 

involvesapproximationsoftransistorbehaviorthataredifficulttomeasuredirectly.Unlikethe 

otheramplifierconfigurations,wherevoltagegainwaseithersetbytheratiooftworesistors 

(common-emitter),orfixedatanunchangeablevalue(common-collector),thevoltagegainof 

thecommon-baseamplifierdependslargelyontheamountofDCbiasontheinputsignal.As 

itturnsout,theinternaltransistorresistancebetweenemitterandbaseplaysamajorrolein 

determiningvoltagegain,andthisresistancechangeswithdifferentlevelsofcurrentthrough 

theemitter. 

Whilethisphenomenonisdifficulttoexplain,itisrathereasytodemonstratethroughthe 

useofcomputersimulation. WhatI’mgoingtodohereisrunseveralSPICEsimulationson 

acommon-baseamplifiercircuit(Figure4.56),changingtheDCbiasvoltageslightly(vbias 

inFigure4.60)whilekeepingtheACsignalamplitudeandallothercircuitparametersconstant. 

Asthevoltagegainchangesfromonesimulationtoanother,differentoutputvoltage 

+


V in 

V bias 

+ − 

Q 1 

R load 

V 1 

+ − 

Figure4.59:PhaserelationshipsandoffsetsforPNPcommonbaseamplifier. 

amplitudeswillbenoted. 

Althoughtheseanalyseswillallbeconductedinthe“transferfunction”mode,eachwas 

first“proofed”inthetransientanalysismode(voltageplottedovertime)toensurethatthe 

entirewavewasbeingfaithfullyreproducedandnot“clipped”duetoimproperbiasing. See 

”*.tran0.02m0.78m”inFigure4.60,the“commentedout”transientanalysisstatement.Gain 

calculationscannotbebasedonwaveformsthataredistorted.SPICEcancalculatethesmall 

signalDCgainforuswiththe“.tfv(4)vin”statement.Theoutputisv(4)andtheinputasvin. 

Atthecommandline,spice-bfilename.cirproducesaprintedoutputduetothe.tfstatement: 

transferfunction,outputimpedance,andinputimpedance. Theabbreviatedoutput 

listingisfromrunswithvbiasat0.85,0.90,0.95,1.00VasrecordedinTable 4.5. 

AtrendshouldbeevidentinTable 4.5. WithincreasesinDCbiasvoltage,voltagegain 

(transferfunction)increasesaswell. Wecanseethatthevoltagegainisincreasingbecause 

eachsubsequentsimulation(vbias=0.85,0.8753,0.90,0.95,1.00V)producesgreatergain 

(transferfunction=37.6,39.440.8,42.7,44.0),respectively. Thechangesarelargelydueto 

minusculevariationsinbiasvoltage. 

ThelastthreelinesofTable ??(right)showtheI(v1)/Iincurrentgainof0.99. (Thelast 

twolineslookinvalid.) Thismakessensefor β=100; α= β/(β+1), α=0.99=100/(100-1). The 

combinationoflowcurrentgain(alwayslessthan1)andsomewhatunpredictablevoltagegain 

conspireagainstthecommon-basedesign,relegatingittofewpracticalapplications. 

Thosefewapplicationsincluderadiofrequencyamplifiers.Thegroundedbasehelpsshield 

theinputattheemitterfromthecollectoroutput,preventinginstabilityinRFamplifiers.The 

commonbaseconfigurationisusableathigherfrequenciesthancommonemitterorcommon 

collector. See“ClassCcommon-base750mWRFpoweramplifier”(page431). Foramore 

elaboratecircuitsee“ClassAcommon-basesmall-signalhighgainamplifier”(page431). 

• REVIEW: 

• Common-basetransistoramplifiersareso-calledbecausetheinputandoutputvoltage 

pointssharethebaseleadofthetransistorincommonwitheachother,notconsidering 

anypowersupplies. 

• Thecurrentgainofacommon-baseamplifierisalwayslessthan1.Thevoltagegainisa 

functionofinputandoutputresistances,andalsotheinternalresistanceoftheemitter-


common-base amp 

vbias=0.85V 

vin 5 2 sin (0 0.12 2000 

0 0) 

vbias 0 1 dc 0.85 

r1 2 1 100 

q1 4 0 5 mod1 

v1 3 0 dc 15 

rload 3 4 5k 


*.tran 0.02m 0.78m 

.tf v(4) vin 

.end 

common-base amp current gain 

Iin 55 5 0A 

vin 55 2 sin (0 0.12 2000 0 

0) 

vbias 0 1 dc 0.8753 

r1 2 1 100 

q1 4 0 5 mod1 

v1 3 0 dc 15 

rload 3 4 5k 


*.tran 0.02m 0.78m 

.tf I(v1) Iin 

.end 

Transfer function 

information: 

transfer function = 

9.900990e-01 

iin input impedance = 

9.900923e+11 

v1 output impedance = 

1.000000e+20 

Figure4.60: SPICEnetlist: Common-base,transferfunction(voltagegain)forvariousDC 

biasvoltages. SPICEnetlist: Common-baseampcurrentgain;Note.tfv(4)vinstatement. 

TransferfunctionforDCcurrentgainI(vin)/Iin;Note.tfI(vin)Iinstatement.


Table4.5:SPICEoutput:Common-basetransferfunction. 

Circuit: common-base amp vbias=0.85V 

transfer function = 3.756565e+01 

output impedance at v(4) = 5.000000e+03 

vin#input impedance = 1.317825e+02 

Circuit: common-base amp vbias=0.8753V Ic=1 mA 

Transfer function information: 















vin#input impedance = 1.124822e+02


basejunction,whichissubjecttochangewithvariationsinDCbiasvoltage. Sufficeto 

saythatthevoltagegainofacommon-baseamplifiercanbeveryhigh. 

• Theratioofatransistor’scollectorcurrenttoemittercurrentiscalled α.The αvaluefor 

anytransistorisalwayslessthanunity,orinotherwords,lessthan1. 

4.8 Thecascodeamplifier 

WhiletheC-B(common-base)amplifierisknownforwiderbandwidththantheC-E(commonemitter)configuration,thelowinputimpedance(10sof 

Ω)ofC-Bisalimitationformany 

applications.ThesolutionistoprecedetheC-BstagebyalowgainC-Estagewhichhasmoderatelyhighinputimpedance(kΩs).SeeFigure4.61.Thestagesareinacascodeconfiguration, 

stackedinseries,asopposedtocascadedforastandardamplifierchain. See“Capacitorcoupledthreestagecommon-emitteramplifier”(page253)foracascadeexample. 

Thecascode 

amplifierconfigurationhasbothwidebandwidthandamoderatelyhighinputimpedance. 

Vi 

R L 

Vo 

Vi 

R L 

Vo 

Common 

base 

Vi 

Common 

emitter 

Common-base Common-emitter Cascode 

Figure4.61:Thecascodeamplifieriscombinedcommon-emitterandcommon-base.Thisisan 

ACcircuitequivalentwithbatteriesandcapacitorsreplacedbyshortcircuits. 

ThekeytounderstandingthewidebandwidthofthecascodeconfigurationistheMiller 

effect.The(page277)isthemultiplicationofthebandwidthrobbingcollector-basecapacitance 

byvoltagegainAv.ThisC-BcapacitanceissmallerthantheE-Bcapacitance.Thus,onewould 

thinkthattheC-Bcapacitancewouldhavelittleeffect.However,intheC-Econfiguration,the 

collectoroutputsignalisoutofphasewiththeinputatthebase. Thecollectorsignalcapacitivelycoupledbackopposesthebasesignal. 

Moreover,thecollectorfeedbackis(1-Av)times 

largerthanthebasesignal.Thus,thesmallC-Bcapacitanceappears(1-Av)timeslargerthan 

itsactualvalue.Thiscapacitivegainreducingfeedbackincreaseswithfrequency,reducingthe 

highfrequencyresponseofaC-Eamplifier. 

TheapproximatevoltagegainoftheC-EamplifierinFigure4.62is-RL/REE.Theemitter 

currentissetto1.0mAbybiasing.REE=26mV/IE=26mV/1.0ma=26 Ω.Thus,Av=-RL/REE= 

-4700/26=-181.Thepn2222datasheetlistCcbo=8pF.[5]ThemillercapacitanceisCcbo(1-Av). 

GainAv=-181,negativesinceitisinvertinggain.Cmiller=Ccbo(1-Av)=8pF(1-(-181)=1456pF 

R L 

Vo

4.8. THECASCODEAMPLIFIER 219 

Acommon-baseconfigurationisnotsubjecttotheMillereffectbecausethegroundedbase 

shieldsthecollectorsignalfrombeingfedbacktotheemitterinput.Thus,aC-Bamplifierhas 

betterhighfrequencyresponse. Tohaveamoderatelyhighinputimpedance,theC-Estage 

isstilldesirable. Thekeyistoreducethegain(toabout1)oftheC-Estagewhichreduces 

theMillereffectC-Bfeedbackto1·CCBO.ThetotalC-Bfeedbackisthefeedbackcapacitance 

1·CCBplustheactualcapacitanceCCBforatotalof2·CCBO.Thisisaconsiderablereduction 

from181·CCBO.Themillercapacitanceforagainof-2C-EstageisCmiller=Ccbo(1-Av)=Cmiller 

=Ccbo(1-(-1))=Ccbo·2. 

Thewaytoreducethecommon-emittergainistoreducetheloadresistance.Thegainofa 

C-EamplifierisapproximatelyRC/RE. TheinternalemitterresistanceREEat1mAemitter 

currentis26Ω.Fordetailsonthe26Ω,see“DerivationofREE”,see(page241).Thecollector 

loadRCistheresistanceoftheemitteroftheC-BstageloadingtheC-Estage,26Ωagain.CE 

gainamplifiergainisapproximatelyAv=RC/RE=26/26=1. ThisMillercapacitanceisCmiller 

=Ccbo(1-Av)=8pF(1-(-1)=16pF.WenowhaveamoderatelyhighinputimpedanceC-Estage 

withoutsufferingtheMillereffect,butnoC-EdBvoltagegain. TheC-Bstageprovidesa 

highvoltagegain,AV =-181. Currentgainofcascodeis βoftheC-Estage,1fortheC-B, β 

overall. Thus,thecascodehasmoderatelyhighinputimpedanceoftheC-E,goodgain,and 

goodbandwidthoftheC-B. 

1 

R3 

80kΩ 

2 

V4 

+ 

− 11.5 V 

C2 

10n F 

V3 

C3 

10n F 

4 5 

0.1 V R5 

p-p 

0V 80 kΩ 

offset 

1kHz 

1.5V 

6 

+ − 

V6 

Cascode 

3 

Q2 

Α 

R4 

4.7 kΩ 

9 

V5 

+ 

Q3 − 

VCC 20 V 

V3 

10 nF 

4 

C1 

15 

R1 

4.7 kΩ 

R2 

80 kΩ 

1.5 V 

16 

+ − 

V2 

13 

Q1 

V1 

19 

Common-base 

Figure4.62:SPICE:Cascodeandcommon-baseforcomparison. 

+ − 10 V 

TheSPICEversionofbothacascodeamplifier,andforcomparison,acommon-emitteramplifierisshowninFigure4.62. 

ThenetlistisinTable4.6. TheACsourceV3drivesboth 

amplifiersvianode4.Thebiasresistorsforthiscircuitarecalculatedinanexampleproblem 

(page246). 

ThewaveformsinFigure4.63showtheoperationofthecascodestage. Theinputsignal 

isdisplayedmultipliedby10sothatitmaybeshownwiththeoutputs. Notethatboththe 

Cascode,Common-emitter,andVa(intermediatepoint)outputsareinvertedfromtheinput. 

BoththeCascodeandCommonemitterhavelargeamplitudeoutputs.TheVapointhasaDC 

levelofabout10V,abouthalfwaybetween20Vandground.Thesignalislargerthancanbe 

accountedforbyaC-Egainof1,Itisthreetimeslargerthanexpected. 

Figure4.64showsthefrequencyresponsetoboththecascodeandcommon-emitterampli-


Figure4.63:SPICEwaveforms.NotethatInputismultipliedby10forvisibility. 

Figure4.64:Cascodevscommon-emitterbanwidth.

4.8. THECASCODEAMPLIFIER 221 

Table4.6:SPICEnetlistforprintingACinputandoutputvoltages. 

*SPICE circuit from XCircuit v3.20 

V1 19 0 10 

Q1 13 15 0 q2n2222 

Q2 3 2 A q2n2222 

R1 19 13 4.7k 

V2 16 0 1.5 

C1 4 15 10n 

R2 15 16 80k 

Q3 A 5 0 q2n2222 

V3 4 6 SIN(0 0.1 1k) ac 1 

R3 1 2 80k 

R4 3 9 4.7k 

C2 2 0 10n 

C3 4 5 10n 

R5 5 6 80k 

V4 1 0 11.5 

V5 9 0 20 

V6 6 0 1.5 

.model q2n2222 npn (is=19f bf=150 

+ vaf=100 ikf=0.18 ise=50p ne=2.5 br=7.5 

+ var=6.4 ikr=12m isc=8.7p nc=1.2 rb=50 

+ re=0.4 rc=0.3 cje=26p tf=0.5n 

+ cjc=11p tr=7n xtb=1.5 kf=0.032f af=1) 

.tran 1u 5m 

.AC DEC 10 1k 100Meg 

.end


fiers.TheSPICEstatementsresponsiblefortheACanalysis,extractedfromthelisting: 

V3 4 6 SIN(0 0.1 1k) ac 1 

.AC DEC 10 1k 100Meg 

Notethe“ac1”isnecessaryattheendoftheV3statement. Thecascodehasmarginally 

bettermid-bandgain.However,weareprimarilylookingforthebandwidthmeasuredatthe 

-3dBpoints,downfromthemidbandgainforeachamplifier.Thisisshownbytheverticalsolid 

linesinFigure4.64.Itisalsopossibletoprintthedataofinterestfromnutmegtothescreen, 

theSPICEgraphicalviewer(command,firstline): 

nutmeg 6 -> print frequency db(vm(3)) db(vm(13)) 

Index frequency db(vm(3)) db(vm(13)) 

22 0.158MHz 47.54 45.41 

33 1.995MHz 46.95 42.06 

37 5.012MHz 44.63 36.17 

Index22givesthemidbanddBgainforCascodevm(3)=47.5dBandCommon-emittervm(13)=45.4dB. 

Outofmanyprintedlines,Index33wastheclosesttobeing3dBdownfrom45.4dBat42.0dB 

fortheCommon-emittercircuit.ThecorrespondingIndex33frequencyisapproximately2Mhz, 

thecommon-emitterbandwidth. Index37vm(3)=44.6dbisapproximately3dbdownfrom 

47.5db. ThecorrespondingIndex37frequencyis5Mhz,thecascodebandwidth. Thus,the 

cascodeamplifierhasawiderbandwidth.Wearenotconcernedwiththelowfrequencydegradationofgain.Itisduetothecapacitors,whichcouldberemediedwithlargerones.The5MHzbandwithofourcascodeexample,whilebetterthanthecommon-emitterexample,isnotexemplaryforanRF(radiofrequency)amplifier. 

ApairofRFormicrowave 

transistorswithlowerinterelectrodecapacitancesshouldbeusedforhigherbandwidth. BeforetheinventionoftheRFdualgateMOSFET,theBJTcascodeamplifiercouldhavebeen 

foundinUHF(ultrahighfrequency)TVtuners. 

• REVIEW 

• Acascodeamplifierconsistsofacommon-emitterstageloadedbytheemitterofacommonbasestage. 

• TheheavilyloadedC-Estagehasalowgainof1,overcomingtheMillereffect 

• Acascodeamplifierhasahighgain,moderatelyhighinputimpedance,ahighoutput 

impedance,andahighbandwidth. 

4.9 Biasingtechniques 

Inthecommon-emittersectionofthischapter,wesawaSPICEanalysiswheretheoutput 

waveformresembledahalf-waverectifiedshape:onlyhalfoftheinputwaveformwasreproduced,withtheotherhalfbeingcompletelycutoff. 

Sinceourpurposeatthattimewasto 

reproducetheentirewaveshape,thisconstitutedaproblem.Thesolutiontothisproblemwas 

toaddasmallbiasvoltagetotheamplifierinputsothatthetransistorstayedinactivemode 

throughouttheentirewavecycle.Thisadditionwascalledabiasvoltage.

4.9. BIASINGTECHNIQUES 223 

Ahalf-waveoutputisnotproblematicforsomeapplications.Infact,someapplicationsmay 

necessitatethisverykindofamplification. Becauseitispossibletooperateanamplifierin 

modesotherthanfull-wavereproductionandspecificapplicationsrequiredifferentrangesof 

reproduction,itisusefultodescribethedegreetowhichanamplifierreproducestheinput 

waveformbydesignatingitaccordingtoclass. Amplifierclassoperationiscategorizedwith 

alphabeticalletters:A,B,C,andAB. 

ForClassAoperation,theentireinputwaveformisfaithfullyreproduced.AlthoughIdidn’t 

introducethisconceptbackinthecommon-emittersection,thisiswhatwewerehopingtoattaininoursimulations. 

ClassAoperationcanonlybeobtainedwhenthetransistorspends 

itsentiretimeintheactivemode,neverreachingeithercutofforsaturation.Toachievethis, 

sufficientDCbiasvoltageisusuallysetatthelevelnecessarytodrivethetransistorexactly 

halfwaybetweencutoffandsaturation. Thisway,theACinputsignalwillbeperfectly“centered”betweentheamplifier’shighandlowsignallimitlevels. 

V input 

V bias 

+ 

- 

Class A 

Amplifier 

Figure4.65:ClassA:Theamplifieroutputisafaithfulreproductionoftheinput. 

ClassBoperationiswhatwehadthefirsttimeanACsignalwasappliedtothecommonemitteramplifierwithnoDCbiasvoltage. 

Thetransistorspenthalfitstimeinactivemode 

andtheotherhalfincutoffwiththeinputvoltagetoolow(orevenofthewrongpolarity!) to 

forward-biasitsbase-emitterjunction. 

V input 

Class B 

Amplifier 

Little or no DC bias voltage 

Figure4.66:ClassB:Biasissuchthathalf(180 o )ofthewaveformisreproduced. 

Byitself,anamplifieroperatinginclassBmodeisnotveryuseful.Inmostcircumstances, 

theseveredistortionintroducedintothewaveshapebyeliminatinghalfofitwouldbeunacceptable.However,classBoperationisausefulmodeofbiasingiftwoamplifiersareoperated


asapush-pullpair,eachamplifierhandlingonlyhalfofthewaveformatatime: 

Input components 

omitted for simplicity 

Q 1 

Q 2 

V output 

+ 

− 

Power 

supply 

Figure4.67: ClassBpushpullamplifier: Eachtransistorreproduceshalfofthewaveform. 

Combiningthehalvesproducesafaithfulreproductionofthewholewave. 

TransistorQ1“pushes”(drivestheoutputvoltageinapositivedirectionwithrespectto 

ground),whiletransistorQ2“pulls”theoutputvoltage(inanegativedirection,toward0volts 

withrespecttoground). Individually,eachofthesetransistorsisoperatinginclassBmode, 

activeonlyforone-halfoftheinputwaveformcycle.Together,however,bothfunctionasateam 

toproduceanoutputwaveformidenticalinshapetotheinputwaveform. 

AdecidedadvantageoftheclassB(push-pull)amplifierdesignovertheclassAdesignis 

greateroutputpowercapability.WithaclassAdesign,thetransistordissipatesconsiderable 

energyintheformofheatbecauseitneverstopsconductingcurrent.Atallpointsinthewave 

cycleitisintheactive(conducting)mode,conductingsubstantialcurrentanddroppingsubstantialvoltage.Thereissubstantialpowerdissipatedbythetransistorthroughoutthecycle. 

InaclassBdesign,eachtransistorspendshalfthetimeincutoffmode,whereitdissipates 

zeropower(zerocurrent=zeropowerdissipation).Thisgiveseachtransistoratimeto“rest” 

andcoolwhiletheothertransistorcarriestheburdenoftheload.ClassAamplifiersaresimplerindesign,buttendtobelimitedtolow-powersignalapplicationsforthesimplereasonof 

transistorheatdissipation. 

AnotherclassofamplifieroperationknownasclassAB,issomewherebetweenclassA 

andclassB:thetransistorspendsmorethan50%butlessthan100%ofthetimeconducting 

current. 

Iftheinputsignalbiasforanamplifierisslightlynegative(oppositeofthebiaspolarity 

forclassAoperation),theoutputwaveformwillbefurther“clipped”thanitwaswithclassB 

biasing,resultinginanoperationwherethetransistorspendsmostofthetimeincutoffmode: 

Atfirst,thisschememayseemutterlypointless.Afterall,howusefulcouldanamplifierbe 

ifitclipsthewaveformasbadlyasthis?Iftheoutputisuseddirectlywithnoconditioningof 

anykind,itwouldindeedbeofquestionableutility. However,withtheapplicationofatank


V input 

V bias 

- 

+ 

Class C 

Amplifier 

Figure4.68:ClassC:Conductionisforlessthanahalfcycle(


Input 

Output 

Figure4.70:ClassDamplifier:Inputsignalandunfilteredoutput. 

theoutputsquarewavepulse. IftherecanbeanygoalstatedoftheclassDdesign,itisto 

avoidactive-modetransistoroperation. SincetheoutputtransistorofaclassDamplifieris 

neverintheactivemode,onlycutofforsaturated,therewillbelittleheatenergydissipated 

byit.Thisresultsinveryhighpowerefficiencyfortheamplifier.Ofcourse,thedisadvantage 

ofthisstrategyistheoverwhelmingpresenceofharmonicsontheoutput. Fortunately,since 

theseharmonicfrequenciesaretypicallymuchgreaterthanthefrequencyoftheinputsignal, 

thesecanbefilteredoutbyalow-passfilterwithrelativeease,resultinginanoutputmore 

closelyresemblingtheoriginalinputsignalwaveform. ClassDtechnologyistypicallyseen 

whereextremelyhighpowerlevelsandrelativelylowfrequenciesareencountered,suchas 

inindustrialinverters(devicesconvertingDCintoACpowertorunmotorsandotherlarge 

devices)andhigh-performanceaudioamplifiers. 

Atermyouwilllikelycomeacrossinyourstudiesofelectronicsissomethingcalledquiescent,whichisamodifierdesignatingthezeroinputconditionofacircuit.Quiescentcurrent, 

forexample,istheamountofcurrentinacircuitwithzeroinputsignalvoltageapplied.Bias 

voltageinatransistorcircuitforcesthetransistortooperateatadifferentlevelofcollector 

currentwithzeroinputsignalvoltagethanitwouldwithoutthatbiasvoltage.Therefore,the 

amountofbiasinanamplifiercircuitdeterminesitsquiescentvalues. 

InaclassAamplifier,thequiescentcurrentshouldbeexactlyhalfofitssaturationvalue 

(halfwaybetweensaturationandcutoff,cutoffbydefinitionbeingzero). ClassBandclassC 

amplifiershavequiescentcurrentvaluesofzero,sincethesearesupposedtobecutoffwithno 

signalapplied.ClassABamplifiershaveverylowquiescentcurrentvalues,justabovecutoff. 

Toillustratethisgraphically,a“loadline”issometimesplottedoveratransistor’scharacteristic 

curvestoillustrateitsrangeofoperationwhileconnectedtoaloadresistanceofspecificvalue 


Aloadlineisaplotofcollector-to-emittervoltageoverarangeofcollectorcurrents.Atthe 

lower-rightcorneroftheloadline,voltageisatmaximumandcurrentisatzero,representing 

aconditionofcutoff.Attheupper-leftcorneroftheline,voltageisatzerowhilecurrentisata 

maximum,representingaconditionofsaturation.Dotsmarkingwheretheloadlineintersects 

thevarioustransistorcurvesrepresentrealisticoperatingconditionsforthosebasecurrents


saturation 

I collector 

0 





"Load line" 


V supply 

cutoff 

Figure4.71: ExampleloadlinedrawnovertransistorcharacteristiccurvesfromVsupply to 

saturationcurrent. 

given. 

Quiescentoperatingconditionsmaybeshownonthisgraphintheformofasingledotalong 

theloadline.ForaclassAamplifier,thequiescentpointwillbeinthemiddleoftheloadline 

asin(Figure4.72. 

I collector 

0 






Quiescent point 

for class A 

operation 

V supply 

Figure4.72:Quiescentpoint(dot)forclassA. 

Inthisillustration,thequiescentpointhappenstofallonthecurverepresentingabase 

currentof40 µA.Ifweweretochangetheloadresistanceinthiscircuittoagreatervalue,it 

wouldaffecttheslopeoftheloadline,sinceagreaterloadresistancewouldlimitthemaximum 

collectorcurrentatsaturation,butwouldnotchangethecollector-emittervoltageatcutoff. 

Graphically,theresultisaloadlinewithadifferentupper-leftpointandthesamelower-right


pointasin(Figure4.73) 

I collector 

The nonhorizontal 

portion of 

the curve 

represents 

transistor 

saturation 

0 






V supply 

Figure4.73:Loadlineresultingfromincreasedloadresistance. 

Notehowthenewloadlinedoesn’tinterceptthe75 µAcurvealongitsflatportionasbefore. 

Thisisveryimportanttorealizebecausethenon-horizontalportionofacharacteristiccurve 

representsaconditionofsaturation. Havingtheloadlineinterceptthe75 µAcurveoutside 

ofthecurve’shorizontalrangemeansthattheamplifierwillbesaturatedatthatamountof 

basecurrent. Increasingtheloadresistorvalueiswhatcausedtheloadlinetointerceptthe 

75 µAcurveatthisnewpoint,anditindicatesthatsaturationwilloccuratalesservalueof 

basecurrentthanbefore. 

Withtheold,lower-valueloadresistorinthecircuit,abasecurrentof75 µAwouldyield 

aproportionalcollectorcurrent(basecurrentmultipliedby β). Inthefirstloadlinegraph,a 

basecurrentof75 µAgaveacollectorcurrentalmosttwicewhatwasobtainedat40 µA,asthe 

βratiowouldpredict.However,collectorcurrentincreasesmarginallybetweenbasecurrents 

75 µAand40 µA,becausethetransistorbeginstolosesufficientcollector-emittervoltageto 

continuetoregulatecollectorcurrent. 

Tomaintainlinear(no-distortion)operation,transistoramplifiersshouldn’tbeoperatedat 

pointswherethetransistorwillsaturate;thatis,wheretheloadlinewillnotpotentiallyfall 

onthehorizontalportionofacollectorcurrentcurve. We’dhavetoaddafewmorecurvesto 

thegraphinFigure4.74beforewecouldtelljusthowfarwecould“push”thistransistorwith 

increasedbasecurrentsbeforeitsaturates. 

Itappearsinthisgraphthatthehighest-currentpointontheloadlinefallingonthe 

straightportionofacurveisthepointonthe50 µAcurve.Thisnewpointshouldbeconsidered 

themaximumallowableinputsignallevelforclassAoperation.AlsoforclassAoperation,the 

biasshouldbesetsothatthequiescentpointishalfwaybetweenthisnewmaximumpointand 

cutoffshowninFigure4.75. 

NowthatweknowalittlemoreabouttheconsequencesofdifferentDCbiasvoltagelevels, 

itistimetoinvestigatepracticalbiasingtechniques. Sofar,I’veshownasmallDCvoltage 

source(battery)connectedinserieswiththeACinputsignaltobiastheamplifierforwhatever 

desiredclassofoperation. Inreallife,theconnectionofaprecisely-calibratedbatterytothe


I collector 

0 








V supply 

Figure4.74:Morebasecurrentcurvesshowssaturationdetail. 

I collector 

0 








New quiescent point 

V supply 

Figure4.75:Newquiescentpointavoidssaturationregion.


inputofanamplifierissimplynotpractical.Evenifitwerepossibletocustomizeabatteryto 

producejusttherightamountofvoltageforanygivenbiasrequirement,thatbatterywould 

notremainatitsmanufacturedvoltageindefinitely.Onceitstartedtodischargeanditsoutput 

voltagedrooped,theamplifierwouldbegintodrifttowardclassBoperation. 

Takethiscircuit,illustratedinthecommon-emittersectionforaSPICEsimulation,for 

instance,inFigure4.76. 

V input 

1.5 V 

2 kHz 

1 

5 

R 1 

1 kΩ 

+ - 

V bias 

2.3 V 

2 

Q 1 

speaker 

3 8 Ω 4 

0 

V 1 

Figure4.76:Impracticalbasebatterybias. 

0 

15 V 

That2.3volt“Vbias”batterywouldnotbepracticaltoincludeinarealamplifiercircuit.A 

farmorepracticalmethodofobtainingbiasvoltageforthisamplifierwouldbetodevelopthe 

necessary2.3voltsusingavoltagedividernetworkconnectedacrossthe15voltbattery.After 

all,the15voltbatteryisalreadytherebynecessity,andvoltagedividercircuitsareeasyto 

designandbuild.Let’sseehowthismightlookinFigure4.77. 

V input 

1.5 V 

2 kHz 

1 

0 

R 2 

R 3 

4 

0 

R 1 

1 kΩ 

V bias 

2 

Q 1 

speaker 

3 8 Ω 4 

Figure4.77:Voltagedividerbias. 

IfwechooseapairofresistorvaluesforR2andR3thatwillproduce2.3voltsacrossR3from 

atotalof15volts(suchas8466 ΩforR2and1533 ΩforR3),weshouldhaveourdesiredvalue 

of2.3voltsbetweenbaseandemitterforbiasingwithnosignalinput. Theonlyproblemis, 

thiscircuitconfigurationplacestheACinputsignalsourcedirectlyinparallelwithR3ofour 

0 

V 1 

0 

15 V


voltagedivider.Thisisnotacceptable,astheACsourcewilltendtooverpoweranyDCvoltage 

droppedacrossR3.Parallelcomponentsmusthavethesamevoltage,soifanACvoltagesource 

isdirectlyconnectedacrossoneresistorofaDCvoltagedivider,theACsourcewill“win”and 

therewillbenoDCbiasvoltageaddedtothesignal. 

Onewaytomakethisschemework,althoughitmaynotbeobviouswhyitwillwork,is 

toplaceacouplingcapacitorbetweentheACvoltagesourceandthevoltagedividerasin 

Figure4.78. 

V input 

1.5 V 

2 kHz 

1 

0 

C 

5 

R 2 

R 3 

4 

0 

8.466 kΩ 

5 

R 1 

1 kΩ 

1.533 kΩ 

2 

Q 1 

speaker 

3 8 Ω 4 

Figure4.78:Couplingcapacitorpreventsvoltagedividerbiasfromflowingintosignalgenerator. 

Thecapacitorformsahigh-passfilterbetweentheACsourceandtheDCvoltagedivider, 

passingalmostalloftheACsignalvoltageontothetransistorwhileblockingallDCvoltage 

frombeingshortedthroughtheACsignalsource. Thismakesmuchmoresenseifyouunderstandthesuperpositiontheoremandhowitworks.Accordingtosuperposition,anylinear, 

bilateralcircuitcanbeanalyzedinapiecemealfashionbyonlyconsideringonepowersource 

atatime,thenalgebraicallyaddingtheeffectsofallpowersourcestofindthefinalresult. 

IfweweretoseparatethecapacitorandR2−−R3voltagedividercircuitfromtherestofthe 

amplifier,itmightbeeasiertounderstandhowthissuperpositionofACandDCwouldwork. 

WithonlytheACsignalsourceineffect,andacapacitorwithanarbitrarilylowimpedance 

atsignalfrequency,almostalltheACvoltageappearsacrossR3: 

WithonlytheDCsourceineffect,thecapacitorappearstobeanopencircuit,andthus 

neitheritnortheshortedACsignalsourcewillhaveanyeffectontheoperationoftheR2−−R3 

voltagedividerinFigure4.80. 

CombiningthesetwoseparateanalysesinFigure4.81,wegetasuperpositionof(almost) 

1.5voltsACand2.3voltsDC,readytobeconnectedtothebaseofthetransistor. 

Enoughtalk–itsabouttimeforaSPICEsimulationofthewholeamplifiercircuitin 

Figure4.82. Wewilluseacapacitorvalueof100 µFtoobtainanarbitrarilylow(0.796 Ω) 

impedanceat2000Hz: 

NotethesubstantialdistortionintheoutputwaveforminFigure4.82. Thesinewaveis 

beingclippedduringmostoftheinputsignal’snegativehalf-cycle.Thistellsusthetransistor 

isenteringintocutoffmodewhenitshouldn’t(I’massumingagoalofclassAoperationas 

before). Whyisthis? Thisnewbiasingtechniqueshouldgiveusexactlythesameamountof 

DCbiasvoltageasbefore,right? 

0 

V 1 

0 

15 V


V input 

1.5 V 

2 kHz 

R 2 

R 3 

8.466 

kΩ 

1.533 

kΩ 

≈ 1.5 V 

2 kHz 

Figure4.79: Duetothecouplingcapacitor’sverylowimpedanceatthesignalfrequency,it 

behavesmuchlikeapieceofwire,thuscanbeomittedforthisstepinsuperpositionanalysis. 

R 2 

R 3 

8.466 

kΩ 

1.533 

kΩ 

2.3 V 

Figure4.80:ThecapacitorappearstobeanopencircuitasfarattheDCanalysisisconcerned 

V input 

1.5 V 

2 kHz 

C 

R 2 

R 3 

8.466 

kΩ 

1.533 

kΩ 

V 1 

Figure4.81:CombinedACandDCcircuit. 

V 1 

15 V 

15 V


Figure4.82:SPICEsimulationofvoltagedividerbias. 

voltage divider 

biasing 


1.5 2000 0 0) 

c1 1 5 100u 

r1 5 2 1k 

r2 4 5 8466 

r3 5 0 1533 

q1 3 2 0 mod1 

rspkr 3 4 8 

v1 4 0 dc 15 


.tran 0.02m 0.78m 


i(v1) 

.end 

WiththecapacitorandR2−−R3resistornetworkunloaded,itwillprovideexactly2.3volts 

worthofDCbias. However,onceweconnectthisnetworktothetransistor,itisnolonger 

unloaded. Currentdrawnthroughthebaseofthetransistorwillloadthevoltagedivider, 

thusreducingtheDCbiasvoltageavailableforthetransistor.Usingthediodecurrentsource 

transistormodelinFigure4.83toillustrate,thebiasproblembecomesevident. 

V input 

C 

R 2 

R 3 

I R3 + I bias 

I R3 

R 1 

I bias 

I R3 

Q 1 

speaker 

Figure4.83:Diodetransistormodelshowsloadingofvoltagedivider. 

Avoltagedivider’soutputdependsnotonlyonthesizeofitsconstituentresistors,butalso 

onhowmuchcurrentisbeingdividedawayfromitthroughaload. Thebase-emitterPN 

junctionofthetransistorisaloadthatdecreasestheDCvoltagedroppedacrossR3,duetothe 

factthatthebiascurrentjoinswithR3’scurrenttogothroughR2,upsettingthedividerratio 

formerlysetbytheresistancevaluesofR2andR3.ToobtainaDCbiasvoltageof2.3volts,the 

V 1


valuesofR2and/orR3mustbeadjustedtocompensatefortheeffectofbasecurrentloading. 

ToincreasetheDCvoltagedroppedacrossR3,lowerthevalueofR2,raisethevalueofR3,or 

both. 

Figure4.84:NodistortionoftheoutputafteradjustingR2andR3. 

voltage divider 

biasing 


1.5 2000 0 0) 

c1 1 5 100u 

r1 5 2 1k 

r2 4 5 6k

4.10. BIASINGCALCULATIONS 235 

afewcyclesaftereach“kick”fromtheamplifier.Becausethetransistorisnotconducting 

mostofthetime,powerefficienciesarehighforaclassCamplifier. 

• ClassDoperationrequiresanadvancedcircuitdesign,andfunctionsontheprincipleof 

representinginstantaneousinputsignalamplitudebythedutycycleofahigh-frequency 

squarewave.Theoutputtransistor(s)neveroperateinactivemode,onlycutoffandsaturation.Littleheatenergydissipatedmakesenergyefficiencyhigh. 

• DCbiasvoltageontheinputsignal,necessaryforcertainclassesofoperation(especially 

classAandclassC),maybeobtainedthroughtheuseofavoltagedividerandcoupling 

capacitorratherthanabatteryconnectedinserieswiththeACsignalsource. 

4.10 Biasingcalculations 

Althoughtransistorswitchingcircuitsoperatewithoutbias,itisunusualforanalogcircuitsto 

operatewithoutbias.Oneofthefewexamplesis“TROne,onetransistorradio”(page425)with 

anamplifiedAM(amplitudemodulation)detector.Notethelackofabiasresistoratthebasein 

thatcircuit.Inthissectionwelookatafewbasicbiascircuitswhichcansetaselectedemitter 

currentIE.GivenadesiredemittercurrentIE,whatvaluesofbiasresistorsarerequired,RB, 

RE,etc? 

4.10.1 BaseBias 

Thesimplestbiasingappliesabase-biasresistorbetweenthebaseandabasebatteryVBB. 

ItisconvenienttousetheexistingVCCsupplyinsteadofanewbiassupply. Anexampleof 

anaudioamplifierstageusingbase-biasingis“Crystalradiowithonetransistor...”(page 

425). Notetheresistorfromthebasetothebatteryterminal. Asimilarcircuitisshownin 

Figure4.85. 

WriteaKVL(Krichhoff’svoltagelaw)equationabouttheloopcontainingthebattery,RB, 

andtheVBEdiodedroponthetransistorinFigure4.85. NotethatweuseVBBforthebase 

supply,eventhoughitisactuallyVCC. If βislargewecanmaketheapproximationthatIC 

=IE.ForsilicontransistorsVBE ∼ =0.7V. 

+ 

_ 

V BE= 

0.7V 

R B 

+ _ 

R C 

V CC 

+ 

_ 

V BB -I ΒR B - V BE = 0 

V BB - V BE = I BR B 

I B = 

V BB - V BE 

R B 

I E = (β+1)Ι Β ≈ βI B 

I E = 

V BB - V BE 

R B/β 

Figure4.85:Base-bias 

(KVL) 

(IE base-bias)


Siliconsmallsignaltransistorstypicallyhaveaβintherangeof100-300.Assumingthat 

wehaveaβ=100transistor,whatvalueofbase-biasresistorisrequiredtoyieldanemitter 

currentof1mA? 

SolvingtheIEbase-biasequationforRB andsubstituting β,VBB,VBE,andIE yields 

930kΩ.Thecloseststandardvalueis910kΩ. 

β = 100 VBB = 10V IC ≈ IE = 1ma 

R B = 

V BB - V BE 

I E /β 

10 - 0.7 

= 1mA/100 = 930k 

Whatistheemittercurrentwitha910kΩresistor? Whatistheemittercurrentifwe 

randomlygetaβ=300transistor? 

β = 100 VBB = 10V RB = 910k VBE = 0.7V 

IE = 

VBB - VBE RB/β = 

10 - 0.7 

910k / 100 

= 1.02mA 

β = 300 

IE = 

10 - 0.7 

910k / 300 

= 3.07mA 

Theemittercurrentislittlechangedinusingthestandardvalue910kΩresistor.However, 

withachangein βfrom100to300,theemittercurrenthastripled.Thisisnotacceptablein 

apoweramplifierifweexpectthecollectorvoltagetoswingfromnearVCCtonearground. 

However,forlowlevelsignalsfrommicro-voltstoaaboutavolt,thebiaspointcanbecentered 

foraβofsquarerootof(100·300)=173.Thebiaspointwillstilldriftbyaconsiderableamount 

.However,lowlevelsignalswillnotbeclipped. 

Base-biasbyitsselfisnotsuitableforhighemittercurrents,asusedinpoweramplifiers. 

Thebase-biasedemittercurrentisnottemperaturestable. Thermalrunawayistheresult 

ofhighemittercurrentcausingatemperatureincreasewhichcausesanincreaseinemitter 

current,whichfurtherincreasestemperature. 

4.10.2 Collector-feedbackbias 

VariationsinbiasduetotemperatureandbetamaybereducedbymovingtheVBBendofthe 

base-biasresistortothecollectorasinFigure4.86.Iftheemittercurrentweretoincrease,the 

voltagedropacrossRCincreases,decreasingVC,decreasingIBfedbacktothebase.This,in 

turn,decreasestheemittercurrent,correctingtheoriginalincrease. 

WriteaKVLequationabouttheloopcontainingthebattery,RC,RB,andtheVBEdrop. 

SubstituteIC ∼ =IEandIB ∼ =IE/β.SolvingforIEyieldstheIECFB-biasequation.SolvingforIB 

yieldstheIBCFB-biasequation. 

Findtherequiredcollectorfeedbackbiasresistorforanemittercurrentof1mA,a4.7K 

collectorloadresistor,andatransistorwith β=100.FindthecollectorvoltageVC.Itshouldbe 

approximatelymidwaybetweenVCCandground.


R B 

+ 

_ 

V BE= 

0.7V 

+ _ 

+ 

_ 

R C 

VC VCC + 

_ 

IC = βIB IC ≈ IE IE ≈ βIB VCC - ICRC - IBRB - VBE = 0 

VCC - IERC - (IE/β)RB - VBE = 0 

VCC - VBE = IERC + (IE/β)RB VCC - VBE = IE((RB/β) + RC) VCC - VBE IE = 

RB/β + RC R B = β 

V CC - V BE 

I E 

- R C 

Figure4.86:Collector-feedbackbias. 

β = 100 VCC = 10V IC ≈ IE = 1ma RC = 4.7k 

VCC - VBE = 10 - 0.7 

RB = β - R 100 -4.7k 

C 

1mA 

I E 

V C = V CC - I CR C = 10 - (1mA)⋅(4.7k) = 5.3V 

= 460k 

(KVL) 

(IE CFB-bias) 

(RB CFB-bias) 

Thecloseststandardvaluetothe460kcollectorfeedbackbiasresistoris470k. Findthe 

emittercurrentIEwiththe470Kresistor. Recalculatetheemittercurrentforatransistor 

with β=100and β=300. 

β = 100 VCC = 10V RC = 4.7k RB = 470k 

I E = 

V CC - V BE 

R B/β + R C 

β = 300 

VCC - VBE IE = 

RB/β + RC 10 - 0.7 

= = 0.989mA 

470k/100 + 4.7k 

10 - 0.7 

= = 1.48mA 

470k/300 + 4.7k 

Weseethatasbetachangesfrom100to300,theemittercurrentincreasesfrom0.989mA 

to1.48mA.Thisisanimprovementoverthepreviousbase-biascircuitwhichhadanincrease 

from1.02mAto3.07mA.Collectorfeedbackbiasistwiceasstableasbase-biaswithrespectto 

betavariation. 

4.10.3 Emitter-bias 

InsertingaresistorREintheemittercircuitasinFigure4.87causesdegeneration,alsoknown 

asnegativefeedback.ThisopposesachangeinemittercurrentIEduetotemperaturechanges, 

resistortolerances,betavariation,orpowersupplytolerance.Typicaltolerancesareasfollows: 

resistor—5%,beta—100-300,powersupply—5%.Whymighttheemitterresistorstabilizea


changeincurrent? ThepolarityofthevoltagedropacrossREisduetothecollectorbattery 

VCC. Theendoftheresistorclosesttothe(-)batteryterminalis(-),theendclosesttothe 

(+)terminalit(+). Notethatthe(-)endofREisconnectedviaVBBbatteryandRBtothe 

base.AnyincreaseincurrentflowthroughREwillincreasethemagnitudeofnegativevoltage 

appliedtothebasecircuit,decreasingthebasecurrent,decreasingtheemittercurrent.This 

decreasingemittercurrentpartiallycompensatestheoriginalincrease. 

_ 

+ 

R B 

V BB 

+ 

_ 

+ 

_ 

R C 

V BE= 

0.7V 

+ 

_ 

R E 

V CC 

KVL loop 

+ 

_ 

VBB -IΒRB - VBE - IERE = 0 

IE = (b+1)IB ≈ βIB VBB -(IΕ/β)RB - VBE - IERE = 0 

VBB - VBE = IE( (RB/β) + RE ) 

IE = 

VBB - VBE RB/β + RE RB/β + RE = 

VBB - VBE R B = β 

V BB - V BE 

I E 

I E 

Figure4.87:Emitter-bias 

- R E 

(IE emitter-bias) 

(RB emitter-bias) 

Notethatbase-biasbatteryVBBisusedinsteadofVCCtobiasthebaseinFigure4.87. 

Laterwewillshowthattheemitter-biasismoreeffectivewithalowerbasebiasbattery. 

Meanwhile,wewritetheKVLequationfortheloopthroughthebase-emittercircuit,payingattentiontothepolaritiesonthecomponents.WesubstituteIB 

∼ =IE/βandsolveforemitter 

currentIE.ThisequationcanbesolvedforRB,equation:RBemitter-bias,Figure4.87. 

Beforeapplyingtheequations:RBemitter-biasandIEemitter-bias,Figure4.87,weneed 

tochoosevaluesforRCandRE. RCisrelatedtothecollectorsupplyVCCandthedesired 

collectorcurrentICwhichweassumeisapproximatelytheemittercurrentIE.Normallythe 

biaspointforVCissettohalfofVCC. Though,itcouldbesethighertocompensateforthe 

voltagedropacrosstheemitterresistorRE. Thecollectorcurrentiswhateverwerequireor 

choose.Itcouldrangefrommicro-AmpstoAmpsdependingontheapplicationandtransistor 

rating.WechooseIC=1mA,typicalofasmall-signaltransistorcircuit.Wecalculateavalue 

forRCandchooseaclosestandardvalue.Anemitterresistorwhichis10-50%ofthecollector 

loadresistorusuallyworkswell. 

V C = V CC/2 = 10/2 = 5V 

R C = Vc/I C = 5/1mA = 5k (4.7k standard value) 

R E = 0.10R C = 0.10(4.7K) = 470Ω


Ourfirstexamplesetsthebase-biassupplytohighatVBB=VCC=10Vtoshowwhyalower 

voltageisdesirable.Determinetherequiredvalueofbase-biasresistorRB.Chooseastandard 

valueresistor.Calculatetheemittercurrentfor β=100and β=300.Comparethestabilization 

ofthecurrenttopriorbiascircuits. 

β= 100 IE ≈ IC=1ma Vcc=V BB=10V RE=470Ω R B = β 

V BB - V BE 

I E 

- R E 

10 - 0.7 

= 100 - 470 = 883k 

0.001 

An883kresistorwascalculatedforRB,an870kchosen.At β=100,IEis1.01mA. 

β= 100 R B = 870k 

VBB - VBE 10 - 0.7 

IE = = 

= 1.01mA 

RB/β + RE 870K/100 + 470 

β= 300 

VBB - VBE 10 - 0.7 

IE = = 

= 2.76mA 

RB/β + RE 870K/300 + 470 

For β=300theemittercurrentsareshowninTable4.7. 

Table4.7:Emittercurrentcomparisonfor β=100, β=300. 

Biascircuit IC β=100 IC β=300 

base-bias 1.02mA 3.07mA 

collectorfeedbackbias 0.989mA 1.48mA 

emitter-bias,VBB=10V 1.01mA 2.76mA 

Table4.7showsthatforVBB=10V,emitter-biasdoesnotdoaverygoodjobofstabilizing 

theemittercurrent.Theemitter-biasexampleisbetterthanthepreviousbase-biasexample, 

but,notbymuch.ThekeytoeffectiveemitterbiasisloweringthebasesupplyVBBnearerto 

theamountofemitterbias. 

HowmuchemitterbiasdoweHave? Rounding,thatisemittercurrenttimesemitterresistor: 

IERE=(1mA)(470)=0.47V.Inaddition,weneedtoovercometheVBE=0.7V.Thus, 

weneedaVBB >(0.47+0.7)Vor >1.17V.Ifemittercurrentdeviates,thisnumberwillchange 

comparedwiththefixedbasesupplyVBB,causingacorrectiontobasecurrentIBandemitter 

currentIE.AgoodvalueforVB >1.17Vis2V. 

β= 100 IE ≈ IC=1ma Vcc=10V VBB=2V RE=470Ω R B = β 

V BB - V BE 

I E 

- R E 

2 - 0.7 

= 100 - 470 = 83k 

0.001 

Thecalculatedbaseresistorof83kismuchlowerthantheprevious883k.Wechoose82k 

fromthelistofstandardvalues.Theemittercurrentswiththe82kRBfor β=100and β=300 

are:


β= 100 R B = 82k 

I E = 

β= 300 

I E = 

V BB - V BE 

R B/β + R E 

V BB - V BE 

R B/β + R E 

2 - 0.7 

= 

82K/100 + 470 

2 - 0.7 

= 

82K/300 + 470 

= 1.01mA 

= 1.75mA 

Comparingtheemittercurrentsforemitter-biaswithVBB=2Vat β=100and β=300to 

thepreviousbiascircuitexamplesinTable4.8,weseeconsiderableimprovementat1.75mA, 

though,notasgoodasthe1.48mAofcollectorfeedback. 







Howcanweimprovetheperformanceofemitter-bias?Eitherincreasetheemitterresistor 

RBordecreasethebase-biassupplyVBBorboth.Asanexample,wedoubletheemitterresistor 

totheneareststandardvalueof910Ω. 

β= 100 IE ≈ IC=1ma Vcc=10V VBB=2V RE=910Ω R B = β 

V BB - V BE 

I E 

- R E 

= 100 

2 - 0.7 

- 910 = 39k 

0.001 

ThecalculatedRB=39kisastandardvalueresistor.NoneedtorecalculateIEfor β=100. 

For β=300,itis: 

β= 300 R B = 39k 

VBB - VBE 2 - 0.7 

IE = = 

= 1.25mA 

RB/β + RE 39K/300 + 910 

Theperformanceoftheemitter-biascircuitwitha910¡Onega¿emitterresistorismuch 

improved.SeeTable 4.9. 

Asanexercise,reworktheemitter-biasexamplewiththebaseresistorrevertedbackto 

470Ω,andthebase-biassupplyreducedto1.5V. 

β= 100 IE ≈ IC=1ma Vcc=10V VBB=1.5V RE=470Ω R B = β 

V BB - V BE 

I E 

- R E 

= 100 

1.5 - 0.7 

- 470 = 33k 

0.001







emitter-bias,VBB=2V,RB=470 1.01mA 1.75mA 


The33kbaseresistorisastandardvalue,emittercurrentat β=100isOK.Theemitter 

currentat β=300is: 

VBB - VBE 1.5 - 0.7 

IE = = 

= 1.38mA 

RB/β + RE 33K/300 + 470 

Table 4.10belowcomparestheexerciseresults1mAand1.38mAtothepreviousexamples. 








emitter-bias,VBB=1.5V,RB=470 1.00mA 1.38mA 

Theemitter-biasequationshavebeenrepeatedinFigure4.88withtheinternalemitter 

resistanceincludedforbetteraccuracy. Theinternalemitterresistanceistheresistancein 

theemittercircuitcontainedwithinthetransistorpackage. ThisinternalresistanceREEis 

significantwhenthe(external)emitterresistorREissmall,orevenzero.Thevalueofinternal 

resistanceREisafunctionofemittercurrentIE,Table4.11. 

Table4.11:DerivationofREE 

REE = KT/IEm 

where: 

K=1.38×10 −23 watt-sec/ o C, Boltzman’s constant 

T= temperature in Kelvins ∼ =300. 

IE = emitter current 

m = varies from 1 to 2 for Silicon 

REE ∼ = 0.026V/IE = 26mV/IE 

Forreferencethe26mVapproximationislistedasequationREEinFigure4.88. 

Themoreaccurateemitter-biasequationsinFigure4.88maybederivedbywritingaKVL 

equation. Alternatively, startwithequationsIEemitter-biasandRB emitter-biasinFigure4.87,substitutingREwithREE+RE.TheresultisequationsIEEBandRBEB,respectively


R B 

_ 

+ 

+ _ + 

V BE= 

0.7V 

+ 

_ V BB 

R C 

R EE_ 

R E 

V CC 

+ 

_ 

VBB -IΒRB - VBE - IEREE - IERE= 0 

IE = (β+1)IB ≈ βIB VBB-(IE/ β)RB-V BE-I EREE-I ERE=0 VBB-V BE=(IE(RB / β) + IEREE + IERE) IE = 

VBB - VBE RB/β + REE + RE RB/β + REE + RE = 

VBB - VBE R B = β 

V BB - V BE 

I E 

R EE = 26mV/I E 

I E 

- R EE -R E 

(KVL) 

(IE EB) 

(RB EB) 

(REE) 

Figure4.88:Emitter-biasequationswithinternalemitterresistanceREEincluded.. 

inFigure4.88. 

RedotheRBcalculationinthepreviousexample(page239)withtheinclusionofREEand 

comparetheresults. 

β=100 IE ≈ IC=1ma Vcc=10V VBB= 2V RE=470Ω R E E = 26mV/1mA = 26Ω 

R B = β 

Vcc-V BE 

I E 

-R EE -R E 

= 100 

2.0 - 0.7 

0.001 

- 26 - 470 

=80.4k 

TheinclusionofREEinthecalculationresultsinalowervalueofthebaseresistorRBa 

showninTable4.12.Itfallsbelowthestandardvalue82kresistorinsteadofaboveit. 

Table4.12:EffectofinclusionofREEoncalculatedRB 

REE? REEValue 

WithoutREE 83k 

WithREE 80.4k 

BypassCapacitorforRE 

Oneproblemwithemitterbiasisthataconsiderablepartoftheoutputsignalisdropped 

acrosstheemitterresistorRE(Figure4.89).Thisvoltagedropacrosstheemitterresistorisin 

serieswiththebaseandofoppositepolaritycomparedwiththeinputsignal.(Thisissimilarto 

acommoncollectorconfigurationhaving


DCemittercurrentstillexperiencesdegenerationintheemitterresistor,thus,stabilizingthe 

DCcurrent. 

C coupling 

R in 

V in 

+ 

_ 

R B 

R E 

R C 

V CC 

+ 

_ 

C coupling 

R in 

V in 

+ 

_ 

R B 

33k 

R E 

470 

R C 

4.7k 

C bypass 

Figure4.89:CbypassisrequiredtopreventACgainreduction. 

Whatvalueshouldthebypasscapacitorbe? Thatdependsonthelowestfrequencytobe 

amplified.ForradiofrequenciesCbpasswouldbesmall.Foranaudioamplifierextendingdown 

to20Hzitwillbelarge.A“ruleofthumb”forthebypasscapacitoristhatthereactanceshould 

be1/10oftheemitterresistanceorless.Thecapacitorshouldbedesignedtoaccommodatethe 

lowestfrequencybeingamplified.Thecapacitorforanaudioamplifiercovering20Hzto20kHz 

wouldbe: 

XC = 

1 

2πfC 

C = 

1 

2πfXC 

C = 

1 

2π20(470/10) 

= 169µF 

NotethattheinternalemitterresistanceREEisnotbypassedbythebypasscapacitor. 

4.10.4 Voltagedividerbias 

Stableemitterbiasrequiresalowvoltagebasebiassupply,Figure4.90.Thealternativetoa 

basesupplyVBBisavoltagedividerbasedonthecollectorsupplyVCC. 

Thedesigntechniqueistofirstworkoutanemitter-biasdesign,ThenconvertittothevoltagedividerbiasconfigurationbyusingThevenin’sTheorem.[4]ThestepsareshowngraphicallyinFigure4.91. 

Drawthevoltagedividerwithoutassigningvalues. Breakthedivider 

loosefromthebase.(Thebaseofthetransistoristheload.)ApplyThevenin’sTheoremtoyield 

asingleTheveninequivalentresistanceRthandvoltagesourceVth. 

TheTheveninequivalentresistanceistheresistancefromloadpoint(arrow)withthebattery(VCC)reducedto0(ground). 

Inotherwords,R1||R2.TheTheveninequivalentvoltageis 

theopencircuitvoltage(loadremoved).Thiscalculationisbythevoltagedividerratiomethod. 

V CC 

+ 

_


R B 

_ 

+ 

+ 

+ _ + 

V BE= 

0.7V 

_ V BB 

R C 

R EE 

_ 

R E 

V CC 

+ 

_ 

+ 

_ 

R1 

+ 

R2 

_ 

+ _ + 

V BE= 

0.7V 

R C 

R EE_ 

R E 

V CC 

Emitter-bias Voltage divider bias 

Figure4.90:VoltageDividerbiasreplacesbasebatterywithvoltagedivider. 

R1 

+ 

R2 

- 

+ _ + 

V BE= 

0.7V 

R C 

R EE_ 

R E 

V CC 

+ 

_ 

+ 

_ 

V CC 

+ 

_ 

R1 

+ 

R2 

_ 

Vth 

Vth 

Figure4.91:Thevenin’sTheoremconvertsvoltagedividertosinglesupplyVthandresistance 

Rth. 

+ 

_ 

+ 

_ 

Rth 

+ 

_


R1isobtainedbyeliminatingR2fromthepairofequationsforRthandVth.Theequationof 

R1isintermsofknownquantitiesRth,Vth,Vcc.NotethatRthisRB,thebiasresistorfrom 

theemitter-biasdesign.TheequationforR2isintermsofR1andRth. 

Rth = R1 || R2 Vth = V CC 

1 1 1 

= + 

Rth R1 R2 

1 R2+R1 

= = 

Rth R1⋅R2 

R1 = 

Rth 

f 

V CC 

1 

R1 

= Rth 

Vth 

R2+R1 

R2 

f = 

R2 

R1 +R2 

Vth R2 

= 

R1 +R2 

V CC 

= 

1 

R1 

⋅ 

1 

f 

1 

R2 

= 

1 1 

- 

Rth R1 

Convertthispreviousemitter-biasexampletovoltagedividerbias. 

V BB 

R B 

33k 

+ 

_ 

R E 

R C 

V CC 

10V 

470 

+ 

_ 

R1 

R2 

? 

? 

R E 

R C 

V CC 

10V 

470 

Figure4.92:Emitter-biasexampleconvertedtovoltagedividerbias. 

Thesevalueswerepreviouslyselectedorcalculatedforanemitter-biasexample 

β= 100 IE ≈ IC=1ma Vcc=10V VBB=1.5V RE=470Ω R B = β 

V BB - V BE 

I E 

- R E 

= 100 

1.5 - 0.7 

- 470 = 33k 

0.001 

SubstitutingVCC,VBB,RByieldsR1andR2forthevoltagedividerbiasconfiguration. 

+ 

_


V BB = Vth = 1.5V 

R B = Rth = 33k 

R1 

R1 

VCC = Rth 

Vth 

= 33k 

10 

= 220k 

1.5 

1 

R2 

1 

R2 

= 

= 

R2 = 38.8k 

1 1 

- 

Rth R1 

1 1 

- 

33k 220k 

R1isastandardvalueof220K.ThecloseststandardvalueforR2correspondingto38.8kis 

39k.ThisdoesnotchangeIEenoughforustocalculateit. 

Problem:CalculatethebiasresistorsforthecascodeamplifierinFigure4.93.VB2isthe 

biasvoltageforthecommonemitterstage. VB1isafairlyhighvoltageat11.5becausewe 

wantthecommon-basestagetoholdtheemitterat11.5-0.7=10.8V,about11V.(Itwillbe10V 

afteraccountingforthevoltagedropacrossRB1.)Thatis,thecommon-basestageistheload, 

substituteforaresistor,forthecommon-emitterstage’scollector. Wedesirea1mAemitter 

current. 

+ 

Vi 

R B1 

V B1 

R B2 

+ 

V B2 

Q1 

Q2 

A 

Cascode 

Vo 

+ 

R L 

V CC 

V CC = 20V I E = 1mA β = 100 V A = 10V 

V BB1 = 11.5V 

I E = 

R B1 = 

R B2 = 

V BB - V BE 

R B/β 

V BB - V BE 

I E/β 

V BB2 - V BE 

I E /β 

V BB2 = 1.5V 

(IE base-bias) 

(V BB1 - V A) - V BE 

I E/β 

Figure4.93:Biasforacascodeamplifier. 

= 

(1.5) - 0.7 

= = 80k 

1mA/100 

R L = 4.7k 

(11.5-10) - 0.7 

= = 80k 

1mA/100 

Problem:Convertthebasebiasresistorsforthecascodeamplifiertovoltagedividerbias 

resistorsdrivenbytheVCCof20V.

4.11. INPUTANDOUTPUTCOUPLING 247 

R BB1 = 80k V CC = Vth = 20V 

V BB1 = 11.5V 

V BB = Vth = 11.5V 

R B = Rth = 80k 

R1 

R1 

1 

R2 

1 

R2 

VCC = Rth 

Vth 

= 80k 

20 

= 139.1k 

11.5 

= 

= 

R2 = 210k 

1 1 

- 

Rth R1 

1 1 

- 

80k 139.1k 

R BB2 = 80k 

V BB2 = 1.5V 

V BB = Vth = 1.5V 

R B = Rth = 80k 

R3 

R3 

1 

R4 

1 

R4 

VCC = Rth 

Vth 

= 80k 

20 

= 1.067Meg 

1.5 

= 

= 

R4 = 86.5k 

1 1 

- 

Rth R3 

1 1 

- 

80k 1067k 

Thefinalcircuitdiagramisshowninthe“PracticalAnalogCircuits”chapter,“ClassA 

cascodeamplifier...”(page431). 

• REVIEW: 

• SeeFigure4.94. 

• Selectbiascircuitconfiguration 

• SelectRCandIEfortheintendedapplication.ThevaluesforRCandIEshouldnormally 

setcollectorvoltageVCto1/2ofVCC. 

• CalculatebaseresistorRBtoachievedesiredemittercurrent. 

• RecalculateemittercurrentIEforstandardvalueresistorsifnecessary. 

• Forvoltagedividerbias,performemitter-biascalculationsfirst,thendetermineR1and 

R2. 

• ForACamplifiers,abypasscapacitorinparallelwithREimprovesACgain.SetXC≤0.10RE 

forlowestfrequency. 

4.11 Inputandoutputcoupling 

ToovercomethechallengeofcreatingnecessaryDCbiasvoltageforanamplifier’sinputsignal 

withoutresortingtotheinsertionofabatteryinserieswiththeACsignalsource,weuseda 

voltagedividerconnectedacrosstheDCpowersource.Tomakethisworkinconjunctionwith 

anACinputsignal,we“coupled”thesignalsourcetothedividerthroughacapacitor,which 

actedasahigh-passfilter. Withthatfilteringinplace,thelowimpedanceoftheACsignal 

sourcecouldn’t“shortout”theDCvoltagedroppedacrossthebottomresistorofthevoltage 

divider.Asimplesolution,butnotwithoutanydisadvantages.


+ 

RC VCC + 

RC VCC R1 

R C 

_ 

R C 

R B 

_ 

R B 

V C 

R2 

V BB + 

R B 

+ 

V CC 

R E 

+ 

V CC 

R E 

_ 

_ 

_ 

V BB = Vth 

VBB - VBE RB/β + RE I E = 

VCC - VBE RB/β + RC I E = 

VBB - VBE RB/β I E = 

RB = Rth 

VCC R1 = Rth 

Vth 

1 1 1 

= - 

R2 Rth R1 

RE ⇐ RE + REE to include REE - R C 

VCC - VBE IE R B = β 

VBB - VBE IE/β R B = 

R EE = 26mv/I E 

Figure4.94:Biasingequationssummary. 

- R E 

VBB - VBE IE R B = β 

Voltage divider bias 

Emitter-bias 

Collector feedback bias 

Base-bias


Mostobviousisthefactthatusingahigh-passfiltercapacitortocouplethesignalsource 

totheamplifiermeansthattheamplifiercanonlyamplifyACsignals. Asteady,DCvoltage 

appliedtotheinputwouldbeblockedbythecouplingcapacitorjustasmuchasthevoltage 

dividerbiasvoltageisblockedfromtheinputsource.Furthermore,sincecapacitivereactance 

isfrequency-dependent,lower-frequencyACsignalswillnotbeamplifiedasmuchashigherfrequencysignals.Non-sinusoidalsignalswilltendtobedistorted,asthecapacitorresponds 

differentlytoeachofthesignal’sconstituentharmonics.Anextremeexampleofthiswouldbe 

alow-frequencysquare-wavesignalinFigure4.95. 

V input 

C 

R 2 

R 3 

Figure4.95:Capacitivelycoupledlowfrequencysquare-waveshowsdistortion. 

Incidentally,thissameproblemoccurswhenoscilloscopeinputsaresettothe“ACcoupling”modeasinFigure4.97.Inthismode,acouplingcapacitorisinsertedinserieswiththe 

measuredvoltagesignaltoeliminateanyverticaloffsetofthedisplayedwaveformduetoDC 

voltagecombinedwiththesignal. ThisworksfinewhentheACcomponentofthemeasured 

signalisofafairlyhighfrequency,andthecapacitorofferslittleimpedancetothesignal. 

However,ifthesignalisofalowfrequency,orcontainsconsiderablelevelsofharmonicsover 

awidefrequencyrange,theoscilloscope’sdisplayofthewaveformwillnotbeaccurate. (Figure4.97)Lowfrequencysignalsmaybeviewedbysettingtheoscilloscopeto“DCcoupling”in 

Figure4.96. 

Inapplicationswherethelimitationsofcapacitivecoupling(Figure4.95)wouldbeintolerable,anothersolutionmaybeused:directcoupling.Directcouplingavoidstheuseofcapacitors 

oranyotherfrequency-dependentcouplingcomponentinfavorofresistors. Adirect-coupled 

amplifiercircuitisshowninFigure4.98. 

Withnocapacitortofiltertheinputsignal,thisformofcouplingexhibitsnofrequency 

dependence. DCandACsignalsalikewillbeamplifiedbythetransistorwiththesamegain 

(thetransistoritselfmaytendtoamplifysomefrequenciesbetterthanothers,butthatis 

anothersubjectentirely!). 

IfdirectcouplingworksforDCaswellasforACsignals,thenwhyusecapacitivecoupling 

foranyapplication? OnereasonmightbetoavoidanyunwantedDCbiasvoltagenaturally 

presentinthesignaltobeamplified. SomeACsignalsmaybesuperimposedonanuncontrolledDCvoltagerightfromthesource,andanuncontrolledDCvoltagewouldmakereliable 

transistorbiasingimpossible. Thehigh-passfilteringofferedbyacouplingcapacitorwould 

V 1


40.00 

coarse 

Hz 

fine 

FUNCTION GENERATOR 

1 10 100 1k 10k 100k 1M 

DC 

output 

OSCILLOSCOPE 

vertical 

V/div 

trigger 

timebase 

s/div 

Y 

DC GND AC 

X 

DC GND AC 

Figure4.96: WithDCcoupling,theoscilloscopeproperlyindicatestheshapeofthesquare 

wavecomingfromthesignalgenerator. 

workwellheretoavoidbiasingproblems. 

Anotherreasontousecapacitivecouplingratherthandirectisitsrelativelackofsignal 

attenuation.Directcouplingthrougharesistorhasthedisadvantageofdiminishing,orattenuating,theinputsignalsothatonlyafractionofitreachesthebaseofthetransistor.Inmany 

applications,someattenuationisnecessaryanywaytopreventsignallevelsfrom“overdriving” 

thetransistorintocutoffandsaturation,soanyattenuationinherenttothecouplingnetwork 

isusefulanyway.However,someapplicationsrequirethattherebenosignallossfromtheinputconnectiontothetransistor’sbaseformaximumvoltagegain,andadirectcouplingscheme 

withavoltagedividerforbiassimplywon’tsuffice. 

Sofar,we’vediscussedacoupleofmethodsforcouplinganinputsignaltoanamplifier,but 

haven’taddressedtheissueofcouplinganamplifier’soutputtoaload. Theexamplecircuit 

usedtoillustrateinputcouplingwillservewelltoillustratetheissuesinvolvedwithoutput 

coupling. 

Inourexamplecircuit,theloadisaspeaker.Mostspeakersareelectromagneticindesign: 

thatis,theyusetheforcegeneratedbyanlightweightelectromagnetcoilsuspendedwithina 

strongpermanent-magnetfieldtomoveathinpaperorplasticcone,producingvibrationsin 

theairwhichourearsinterpretassound. Anappliedvoltageofonepolaritymovesthecone 

outward,whileavoltageoftheoppositepolaritywillmovetheconeinward.Toexploitcone’s 

fullfreedomofmotion,thespeakermustreceivetrue(unbiased)ACvoltage.DCbiasappliedto 

thespeakercoiloffsetstheconefromitsnaturalcenterposition,andthislimitstheback-andforthmotionitcansustainfromtheappliedACvoltagewithoutovertraveling. 

However,our 

examplecircuit(Figure4.98)appliesavaryingvoltageofonlyonepolarityacrossthespeaker,


40.00 

coarse 

Hz 

fine 

FUNCTION GENERATOR 

1 10 100 1k 10k 100k 1M 

DC 

output 

OSCILLOSCOPE 

vertical 

V/div 

trigger 

timebase 

s/div 

Y 

DC GND AC 

X 

DC GND AC 

Figure4.97:Lowfrequency:WithACcoupling,thehigh-passfilteringofthecouplingcapacitor 

distortsthesquarewave’sshapesothatwhatisseenisnotanaccuraterepresentationofthe 

realsignal. 

V input 

1 

0 

R input 

R 2 

R 3 

4 

0 

2 

3 4 

speaker 

Figure4.98:Directcoupledamplifier:directcouplingtospeaker. 

Q1 

0 

V 1 

0


becausethespeakerisconnectedinserieswiththetransistorwhichcanonlyconductcurrent 

oneway.Thiswouldbeunacceptableforanyhigh-poweraudioamplifier. 

SomehowweneedtoisolatethespeakerfromtheDCbiasofthecollectorcurrentsothat 

itonlyreceivesACvoltage. Onewaytoachievethisgoalistocouplethetransistorcollector 

circuittothespeakerthroughatransformerinFigure4.99) 

V input 

R 

R 

R 

Q1 

speaker 

Figure4.99:TransformercouplingisolatesDCfromtheload(speaker). 

Voltageinducedinthesecondary(speaker-side)ofthetransformerwillbestrictlydueto 

variationsincollectorcurrent,becausethemutualinductanceofatransformeronlyworkson 

changesinwindingcurrent.Inotherwords,onlytheACportionofthecollectorcurrentsignal 

willbecoupledtothesecondarysideforpoweringthespeaker. Thespeakerwill“see”true 

alternatingcurrentatitsterminals,withoutanyDCbias. 

Transformeroutputcouplingworks,andhastheaddedbenefitofbeingabletoprovide 

impedancematchingbetweenthetransistorcircuitandthespeakercoilwithcustomwinding 

ratios. However,transformerstendtobelargeandheavy,especiallyforhigh-powerapplications. 

Also,itisdifficulttoengineeratransformertohandlesignalsoverawiderangeof 

frequencies,whichisalmostalwaysrequiredforaudioapplications. Tomakemattersworse, 

DCcurrentthroughtheprimarywindingaddstothemagnetizationofthecoreinonepolarity 

only,whichtendstomakethetransformercoresaturatemoreeasilyinoneACpolaritycycle 

thantheother. Thisproblemisreminiscentofhavingthespeakerdirectlyconnectedinserieswiththetransistor:aDCbiascurrenttendstolimithowmuchoutputsignalamplitude 

thesystemcanhandlewithoutdistortion.Generally,though,atransformercanbedesignedto 

handlealotmoreDCbiascurrentthanaspeakerwithoutrunningintotrouble,sotransformer 

couplingisstillaviablesolutioninmostcases.SeethecouplingtransformerbetweenQ4and 

thespeaker,(page425)asanexampleoftransformercoupling. 

AnothermethodtoisolatethespeakerfromDCbiasintheoutputsignalistoalterthe 

circuitabitanduseacouplingcapacitorinamannersimilartocouplingtheinputsignal 

(Figure4.100)totheamplifier. 

ThiscircuitinFigure4.100resemblesthemoreconventionalformofcommon-emitteramplifier,withthetransistorcollectorconnectedtothebatterythrougharesistor.Thecapacitor 

actsasahigh-passfilter,passingmostoftheACvoltagetothespeakerwhileblockingall 

DCvoltage.Again,thevalueofthiscouplingcapacitorischosensothatitsimpedanceatthe 

V 1


V input 

R 

R 

R 

R 

Q1 

C 

speaker 

Figure4.100:CapacitorcouplingisolatesDCfromtheload. 

expectedsignalfrequencywillbearbitrarilylow. 

TheblockingofDCvoltagefromanamplifier’soutput,beitviaatransformeroracapacitor, 

isusefulnotonlyincouplinganamplifiertoaload,butalsoincouplingoneamplifiertoanother 

amplifier.“Staged”amplifiersareoftenusedtoachievehigherpowergainsthanwhatwould 

bepossibleusingasingletransistorasinFigure4.101. 

V input 

First stage Second stage Third stage 

V 1 

V output 

Figure4.101:Capacitorcoupledthreestagecommon-emitteramplifier. 

Whileitispossibletodirectlycoupleeachstagetothenext(viaaresistorratherthana 

capacitor),thismakesthewholeamplifierverysensitivetovariationsintheDCbiasvoltageof 

thefirststage,sincethatDCvoltagewillbeamplifiedalongwiththeACsignaluntilthelast 

stage.Inotherwords,thebiasingofthefirststagewillaffectthebiasingofthesecondstage, 

andsoon.However,ifthestagesarecapacitivelycoupledshownintheaboveillustration,the 

biasingofonestagehasnoeffectonthebiasingofthenext,becauseDCvoltageisblockedfrom 

passingontothenextstage. 

Transformercouplingbetweenamplifierstagesisalsoapossibility,butlessoftenseendue 

tosomeoftheproblemsinherenttotransformersmentionedpreviously.Onenotableexception 

tothisruleisinradio-frequencyamplifiers(Figure4.102)withsmallcouplingtransformers, 

havingaircores(makingthemimmunetosaturationeffects),thatarepartofaresonantcircuit 

toblockunwantedharmonicfrequenciesfrompassingontosubsequentstages. Theuseof


resonantcircuitsassumesthatthesignalfrequencyremainsconstant,whichistypicalofradio 

circuitry. Also,the“flywheel”effectofLCtankcircuitsallowsforclassCoperationforhigh 

efficiency. 

V input 

First stage Second stage Third stage 

V output 

Figure4.102:ThreestagetunedRFamplifierillustratestransformercoupling. 

NotethetransformercouplingbetweentransistorsQ1,Q2,Q3,andQ4,(page425). The 

threeintermediatefrequency(IF)transformerswithinthedashedboxescoupletheIFsignal 

fromcollectortobaseoffollowingtransistorIFamplifiers.Theintermediatefreqencyampliers 

areRFamplifiers,though,atadifferentfrequencythantheantennaRFinput. 

Havingsaidallthis,itmustbementionedthatitispossibletousedirectcouplingwithina 

multi-stagetransistoramplifiercircuit.IncaseswheretheamplifierisexpectedtohandleDC 

signals,thisistheonlyalternative. 

Thetrendofelectronicstomorewidespreaduseofintegratedcircuitshasencouragedthe 

useofdirectcouplingovertransformerorcapacitorcoupling. Theonlyeasilymanufactured 

integratedcircuitcomponentisthetransistor.Moderatequalityresistorscanalsobeproduced. 

Though,transistorsarefavored. Integratedcapacitorstoonlyafew10’sofpFarepossible. 

Largecapacitorsarenotintegrable.Ifnecessary,thesecanbeexternalcomponents.Thesame 

istrueoftransformers. Sinceintegratedtransistorsareinexpensive,asmanytransistorsas 

possiblearesubstitutedfortheoffendingcapacitorsandtransformers.Asmuchdirectcoupled 

gainaspossibleisdesignedintoICsbetweentheexternalcouplingcomponents.Whileexternal 

capacitorsandtransformersareused,theseareevenbeingdesignedoutifpossible.Theresult 

isthatamodernICradio(See“ICradio”,(page428))looksnothingliketheoriginal4-transistor 

radio(page425). 

Evendiscretetransistorsareinexpensivecomparedwithtransformers.Bulkyaudiotransformerscanbereplacedbytransistors. 

Forexample,acommon-collector(emitterfollower) 

configurationcanimpedancematchalowoutputimpedancelikeaspeaker.Itisalsopossible 

toreplacelargecouplingcapacitorswithtransistorcircuitry. 

Westillliketoillustratetextswithtransformercoupledaudioamplifiers. Thecircuits 

aresimple. Thecomponentcountislow. And,thesearegoodintroductorycircuits—easyto 

understand. 

ThecircuitinFigure4.103(a)isasimplifiedtransformercoupledpush-pullaudioamplifier. 

Inpush-pull,pairoftransistorsalternatelyamplifythepositiveandnegativeportionsofthe 

inputsignal. Neithertransistornortheotherconductsfornosignalinput. Apositiveinput


signalwillbepositiveatthetopofthetransformersecondarycausingthetoptransistorto 

conduct.Anegativeinputwillyieldapositivesignalatthebottomofthesecondary,drivingthe 

bottomtransistorintoconduction. Thusthetransistorsamplifyalternatehalvesofasignal. 

Asdrawn,neithertransistorinFigure4.103(a)willconductforaninputbelow0.7Vpeak. 

Apracticalcircuitconnectsthesecondarycentertaptoa0.7V(orgreater)resistordivider 

insteadofgroundtobiasbothtransistorfortrueclassB. 

input 

+Vcc 

input 

(a) (b) 

Figure4.103:(a)Transformercoupledpush-pullamplifier.(b)Directcoupledcomplementarypairamplifierreplacestransformerswithtransistors. 

ThecircuitinFigure4.103(b)isthemodernversionwhichreplacesthetransformerfunctionswithtransistors. 

TransistorsQ1andQ2arecommonemitteramplifiers,invertingthe 

signalwithgainfrombasetocollector.TransistorsQ3andQ4areknownasacomplementary 

pairbecausetheseNPNandPNPtransistorsamplifyalternatehalves(positiveandnegative,respectively)ofthewaveform. 

Theparallelconnectionthebasesallowsphasesplitting 

withoutaninputtransformerat(a). ThespeakeristheemitterloadforQ3andQ4. Parallel 

connectionoftheemittersoftheNPNandPNPtransistorseliminatesthecenter-tappedoutputtransformerat(a)Thelowoutputimpedanceoftheemitterfollowerservestomatchthe 

low8Ωimpedanceofthespeakertotheprecedingcommonemitterstage.Thus,inexpensive 

transistorsreplacetransformers.Forthecompletecircuitsee“Directcoupledcomplementary 

symmetry3waudioamplifier,”(page423) 

• REVIEW: 

• Capacitivecouplingactslikeahigh-passfilterontheinputofanamplifier. Thistends 

tomaketheamplifier’svoltagegaindecreaseatlowersignalfrequencies. CapacitivecoupledamplifiersareallbutunresponsivetoDCinputsignals. 

• Directcouplingwithaseriesresistorinsteadofaseriescapacitoravoidstheproblemof 

frequency-dependentgain,buthasthedisadvantageofreducingamplifiergainforall 

signalfrequenciesbyattenuatingtheinputsignal. 

R 3 

R 4 

R 1 

R 5 

Q 1 

Q 2 

R 2 

Q 3 

Q 4 

+Vcc


• Transformersandcapacitorsmaybeusedtocoupletheoutputofanamplifiertoaload, 

toeliminateDCvoltagefromgettingtotheload. 

• Multi-stageamplifiersoftenmakeuseofcapacitivecouplingbetweenstagestoeliminate 

problemswiththebiasfromonestageaffectingthebiasofanother. 

4.12 Feedback 

Ifsomepercentageofanamplifier’soutputsignalisconnectedtotheinput,sothattheamplifieramplifiespartofitsownoutputsignal,wehavewhatisknownasfeedback. 

Feedback 

comesintwovarieties:positive(alsocalledregenerative),andnegative(alsocalleddegenerative).Positivefeedbackreinforcesthedirectionofanamplifier’soutputvoltagechange,while 

negativefeedbackdoesjusttheopposite. 

Afamiliarexampleoffeedbackhappensinpublic-address(“PA”)systemswheresomeone 

holdsthemicrophonetooclosetoaspeaker:ahigh-pitched“whine”or“howl”ensues,because 

theaudioamplifiersystemisdetectingandamplifyingitsownnoise. Specifically,thisisan 

exampleofpositiveorregenerativefeedback,asanysounddetectedbythemicrophoneisamplifiedandturnedintoaloudersoundbythespeaker,whichisthendetectedbythemicrophone 

again,andsoon. . . theresultbeinganoiseofsteadilyincreasingvolumeuntilthesystem 

becomes“saturated”andcannotproduceanymorevolume. 

Onemightwonderwhatpossiblebenefitfeedbackistoanamplifiercircuit,givensuchan 

annoyingexampleasPAsystem“howl.”Ifweintroducepositive,orregenerative,feedbackinto 

anamplifiercircuit,ithasthetendencyofcreatingandsustainingoscillations,thefrequency 

ofwhichdeterminedbythevaluesofcomponentshandlingthefeedbacksignalfromoutputto 

input. ThisisonewaytomakeanoscillatorcircuittoproduceACfromaDCpowersupply. 

Oscillatorsareveryusefulcircuits,andsofeedbackhasadefinite,practicalapplicationforus. 

See“Phaseshiftoscillator”(page423)forapracticalapplicationofpositivefeedback. 

Negativefeedback,ontheotherhand,hasa“dampening”effectonanamplifier: ifthe 

outputsignalhappenstoincreaseinmagnitude,thefeedbacksignalintroducesadecreasing 

influenceintotheinputoftheamplifier,thusopposingthechangeinoutputsignal. While 

positivefeedbackdrivesanamplifiercircuittowardapointofinstability(oscillations),negative 

feedbackdrivesittheoppositedirection:towardapointofstability. 

Anamplifiercircuitequippedwithsomeamountofnegativefeedbackisnotonlymore 

stable,butitdistortstheinputwaveformlessandisgenerallycapableofamplifyingawider 

rangeoffrequencies.Thetradeofffortheseadvantages(therejusthastobeadisadvantageto 

negativefeedback,right?)isdecreasedgain.Ifaportionofanamplifier’soutputsignalis“fed 

back”totheinputtoopposeanychangesintheoutput,itwillrequireagreaterinputsignal 

amplitudetodrivetheamplifier’soutputtothesameamplitudeasbefore.Thisconstitutesa 

decreasedgain.However,theadvantagesofstability,lowerdistortion,andgreaterbandwidth 

areworththetradeoffinreducedgainformanyapplications. 

Let’sexamineasimpleamplifiercircuitandseehowwemightintroducenegativefeedback 

intoit,startingwithFigure4.104. 

Theamplifierconfigurationshownhereisacommon-emitter,witharesistorbiasnetwork 

formedbyR1andR2. ThecapacitorcouplesVinputtotheamplifiersothatthesignalsource 

doesn’thaveaDCvoltageimposedonitbytheR1/R2dividernetwork. ResistorR3serves

4.12. FEEDBACK 257 

V input 

R 1 

R 2 

R 3 

R load 

V output 

Figure4.104:Common-emitteramplifierwithoutfeedback. 

thepurposeofcontrollingvoltagegain.Wecouldomititformaximumvoltagegain,butsince 

baseresistorslikethisarecommonincommon-emitteramplifiercircuits,we’llkeepitinthis 

schematic. 

Likeallcommon-emitteramplifiers,thisoneinvertstheinputsignalasitisamplified.In 

otherwords,apositive-goinginputvoltagecausestheoutputvoltagetodecrease,ormove 

towardnegative,andviceversa.TheoscilloscopewaveformsareshowninFigure4.105. 

V input 

R 1 

R 2 

R 3 

R load 

Figure4.105:Common-emitteramplifier,nofeedback,withreferencewaveformsforcomparison. 

Becausetheoutputisaninverted,ormirror-image,reproductionoftheinputsignal,any 

connectionbetweentheoutput(collector)wireandtheinput(base)wireofthetransistorin 

Figure4.106willresultinnegativefeedback. 

TheresistancesofR1,R2,R3,andRfeedbackfunctiontogetherasasignal-mixingnetwork 

sothatthevoltageseenatthebaseofthetransistor(withrespecttoground)isaweighted 

averageoftheinputvoltageandthefeedbackvoltage,resultinginsignalofreducedamplitude 

+ 

- 

+ 

−


V input 

R 1 

R 2 

R 3 

R feedback 

R load 

Figure4.106:Negativefeedback,collectorfeedback,decreasestheoutputsignal. 

goingintothetransistor. So,theamplifiercircuitinFigure4.106willhavereducedvoltage 

gain,butimprovedlinearity(reduceddistortion)andincreasedbandwidth. 

Aresistorconnectingcollectortobaseisnottheonlywaytointroducenegativefeedback 

intothisamplifiercircuit,though.Anothermethod,althoughmoredifficulttounderstandat 

first,involvestheplacementofaresistorbetweenthetransistor’semitterterminalandcircuit 

groundinFigure4.107. 

V input 

R 1 

R 2 

R 3 

R load 

R feedback 

Figure4.107: Emitterfeedback: Adifferentmethodofintroducingnegativefeedbackintoa 

circuit. 

Thisnewfeedbackresistordropsvoltageproportionaltotheemittercurrentthroughthe 

transistor,anditdoessoinsuchawayastoopposetheinputsignal’sinfluenceonthebaseemitterjunctionofthetransistor.Let’stakeacloserlookattheemitter-basejunctionandsee 

whatdifferencethisnewresistormakesinFigure4.108. 

WithnofeedbackresistorconnectingtheemittertogroundinFigure4.108(a),whatever 

levelofinputsignal(Vinput)makesitthroughthecouplingcapacitorandR1/R2/R3resistor 

+ 

- 

+ 

-


networkwillbeimpresseddirectlyacrossthebase-emitterjunctionasthetransistor’sinput 

voltage(VB−E). Inotherwords,withnofeedbackresistor,VB−EequalsVinput. Therefore,if 

Vinputincreasesby100mV,thenVB−Eincreasesby100mV:achangeinoneisthesameasa 

changeintheother,sincethetwovoltagesareequaltoeachother. 

Nowlet’sconsidertheeffectsofinsertingaresistor(Rfeedback)betweenthetransistor’s 

emitterleadandgroundinFigure4.108(b). 

V input 

(a) 

+ 

- 

I base 

V B-E 

+ 

- 

I collector 

I emitter 

V input 

(b) 

+ 

- 

I base 

V B-E 

+ 

- 

I collector 

I emitter 

+ 

Rfeedback - 

V feedback 

Figure4.108:(a)Nofeedbackvs(b)emitterfeedback.Awaveformatthecollectorisinverted 

withrespecttothebase.At(b)theemitterwaveformisin-phase(emitterfollower)withbase, 

outofphasewithcollector. Therefore,theemittersignalsubtractsfromthecollectoroutput 

signal. 

NotehowthevoltagedroppedacrossRfeedback addswithVB−E toequalVinput. With 

RfeedbackintheVinput −−VB−Eloop,VB−EwillnolongerbeequaltoVinput. Weknowthat 

Rfeedbackwilldropavoltageproportionaltoemittercurrent,whichisinturncontrolledbythe 

basecurrent,whichisinturncontrolledbythevoltagedroppedacrossthebase-emitterjunctionofthetransistor(VB−E).Thus,ifVinputweretoincreaseinapositivedirection,itwould 

increaseVB−E,causingmorebasecurrent,causingmorecollector(load)current,causingmore 

emittercurrent,andcausingmorefeedbackvoltagetobedroppedacrossRfeedback. Thisincreaseofvoltagedropacrossthefeedbackresistor,though,subtractsfromVinputtoreducethe 

VB−E,sothattheactualvoltageincreaseforVB−Ewillbelessthanthevoltageincreaseof 

Vinput.Nolongerwilla100mVincreaseinVinputresultinafull100mVincreaseforVB−E, 

becausethetwovoltagesarenotequaltoeachother. 

Consequently,theinputvoltagehaslesscontroloverthetransistorthanbefore,andthe 

voltagegainfortheamplifierisreduced:justwhatweexpectedfromnegativefeedback. 

Inpracticalcommon-emittercircuits,negativefeedbackisn’tjustaluxury;itsanecessity 

forstableoperation.Inaperfectworld,wecouldbuildandoperateacommon-emittertransistoramplifierwithnonegativefeedback,andhavethefullamplitudeofVinputimpressedacross 

thetransistor’sbase-emitterjunction.Thiswouldgiveusalargevoltagegain.Unfortunately, 

though,therelationshipbetweenbase-emittervoltageandbase-emittercurrentchangeswith 

temperature,aspredictedbythe“diodeequation.” Asthetransistorheatsup,therewillbe 

lessofaforwardvoltagedropacrossthebase-emitterjunctionforanygivencurrent. This 

causesaproblemforus,astheR1/R2voltagedividernetworkisdesignedtoprovidethecorrect 

quiescentcurrentthroughthebaseofthetransistorsothatitwilloperateinwhateverclass


ofoperationwedesire(inthisexample,I’veshowntheamplifierworkinginclass-Amode).If 

thetransistor’svoltage/currentrelationshipchangeswithtemperature,theamountofDCbias 

voltagenecessaryforthedesiredclassofoperationwillchange. Ahottransistorwilldraw 

morebiascurrentforthesameamountofbiasvoltage,makingitheatupevenmore,drawing 

evenmorebiascurrent.Theresult,ifunchecked,iscalledthermalrunaway. 

Common-collectoramplifiers,(Figure4.109)however,donotsufferfromthermalrunaway. 

Whyisthis?Theanswerhaseverythingtodowithnegativefeedback. 

V input 

R 1 

R 2 

R 3 

R load 

Figure4.109:Commoncollector(emitterfollower)amplifier. 

Notethatthecommon-collectoramplifier(Figure4.109)hasitsloadresistorplacedinexactlythesamespotaswehadtheRfeedbackresistorinthelastcircuitinFigure4.108(b):betweenemitterandground.Thismeansthattheonlyvoltageimpressedacrossthetransistor’sbase-emitterjunctionisthedifferencebetweenVinputandVoutput,resultinginaverylowvoltagegain(usuallycloseto1foracommon-collectoramplifier).Thermalrunawayisimpossibleforthisamplifier:ifbasecurrenthappenstoincreaseduetotransistorheating,emitter 

currentwilllikewiseincrease,droppingmorevoltageacrosstheload,whichinturnsubtracts 

fromVinputtoreducetheamountofvoltagedroppedbetweenbaseandemitter.Inotherwords, 

thenegativefeedbackaffordedbyplacementoftheloadresistormakestheproblemofthermal 

runawayself-correcting.Inexchangeforagreatlyreducedvoltagegain,wegetsuperbstability 

andimmunityfromthermalrunaway. 

Byaddinga“feedback”resistorbetweenemitterandgroundinacommon-emitteramplifier, 

wemaketheamplifierbehavealittlelesslikean“ideal”common-emitterandalittlemorelike 

acommon-collector. Thefeedbackresistorvalueistypicallyquiteabitlessthantheload, 

minimizingtheamountofnegativefeedbackandkeepingthevoltagegainfairlyhigh. 

Anotherbenefitofnegativefeedback,seenclearlyinthecommon-collectorcircuit,isthat 

ittendstomakethevoltagegainoftheamplifierlessdependentonthecharacteristicsofthe 

transistor. Notethatinacommon-collectoramplifier,voltagegainisnearlyequaltounity 

(1),regardlessofthetransistor’s β. Thismeans,amongotherthings,thatwecouldreplace 

thetransistorinacommon-collectoramplifierwithonehavingadifferent βandnotseeany 

significantchangesinvoltagegain.Inacommon-emittercircuit,thevoltagegainishighlydependenton 

β.Ifweweretoreplacethetransistorinacommon-emittercircuitwithanotherof 

+ 

-


differing β,thevoltagegainfortheamplifierwouldchangesignificantly.Inacommon-emitter 

amplifierequippedwithnegativefeedback,thevoltagegainwillstillbedependentupontransistor 

βtosomedegree,butnotasmuchasbefore,makingthecircuitmorepredictabledespite 

variationsintransistor β. 

Thefactthatwehavetointroducenegativefeedbackintoacommon-emitteramplifierto 

avoidthermalrunawayisanunsatisfyingsolution. Isitpossibetoavoidthermalrunaway 

withouthavingtosuppresstheamplifier’sinherentlyhighvoltagegain?Abest-of-both-worlds 

solutiontothisdilemmaisavailabletousifwecloselyexaminetheproblem:thevoltagegain 

thatwehavetominimizeinordertoavoidthermalrunawayistheDCvoltagegain,nottheAC 

voltagegain.Afterall,itisn’ttheACinputsignalthatfuelsthermalrunaway:itstheDCbias 

voltagerequiredforacertainclassofoperation:thatquiescentDCsignalthatweuseto“trick” 

thetransistor(fundamentallyaDCdevice)intoamplifyinganACsignal.WecansuppressDC 

voltagegaininacommon-emitteramplifiercircuitwithoutsuppressingACvoltagegainifwe 

figureoutawaytomakethenegativefeedbackonlyfunctionwithDC.Thatis,ifweonlyfeed 

backaninvertedDCsignalfromoutputtoinput,butnotaninvertedACsignal. 

TheRfeedbackemitterresistorprovidesnegativefeedbackbydroppingavoltageproportional 

toloadcurrent.Inotherwords,negativefeedbackisaccomplishedbyinsertinganimpedance 

intotheemittercurrentpath.IfwewanttofeedbackDCbutnotAC,weneedanimpedance 

thatishighforDCbutlowforAC.WhatkindofcircuitpresentsahighimpedancetoDCbut 

alowimpedancetoAC?Ahigh-passfilter,ofcourse! 

ByconnectingacapacitorinparallelwiththefeedbackresistorinFigure4.110,wecreate 

theverysituationweneed:apathfromemittertogroundthatiseasierforACthanitisfor 

DC. 

V input 

R 1 

R 2 

R 3 

R load 

R feedback Cbypass 

Figure4.110:HighACvoltagegainreestablishedbyaddingCbypassinparallelwithRfeedback 

Thenewcapacitor“bypasses”ACfromthetransistor’semittertoground,sothatnoappreciableACvoltagewillbedroppedfromemittertogroundto“feedback”totheinputandsuppressvoltagegain.Directcurrent,ontheotherhand,cannotgothroughthebypasscapacitor,andsomusttravelthroughthefeedbackresistor,droppingaDCvoltagebetweenemitterandgroundwhichlowerstheDCvoltagegainandstabilizestheamplifier’sDCresponse,preventingthermalrunaway. 

Becausewewantthereactanceofthiscapacitor(XC)tobeaslow 

+ 

-


aspossible,Cbypassshouldbesizedrelativelylarge.Becausethepolarityacrossthiscapacitor 

willneverchange,itissafetouseapolarized(electrolytic)capacitorforthetask. 

Anotherapproachtotheproblemofnegativefeedbackreducingvoltagegainistousemultistageamplifiersratherthansingle-transistoramplifiers. 

Iftheattenuatedgainofasingle 

transistorisinsufficientforthetaskathand,wecanusemorethanonetransistortomake 

upforthereductioncausedbyfeedback. Anexamplecircuitshowingnegativefeedbackina 

three-stagecommon-emitteramplifierisFigure4.111. 

V input 

R in 

R feedback 

V output 

Figure4.111: Feedbackaroundan“odd”numberofdirectcoupledstagesproducenegative 

feedback. 

Thefeedbackpathfromthefinaloutputtotheinputisthroughasingleresistor,Rfeedback. 

Sinceeachstageisacommon-emitteramplifier(thusinverting),theoddnumberofstages 

frominputtooutputwillinverttheoutputsignal;thefeedbackwillbenegative(degenerative). 

Relativelylargeamountsoffeedbackmaybeusedwithoutsacrificingvoltagegain,becausethe 

threeamplifierstagesprovidemuchgaintobeginwith. 

Atfirst,thisdesignphilosophymayseeminelegantandperhapsevencounter-productive. 

Isn’tthisarathercrudewaytoovercomethelossingainincurredthroughtheuseofnegative 

feedback,tosimplyrecovergainbyaddingstageafterstage? Whatisthepointofcreatinga 

hugevoltagegainusingthreetransistorstagesifwe’rejustgoingtoattenuateallthatgain 

anywaywithnegativefeedback?Thepoint,thoughperhapsnotapparentatfirst,isincreased 

predictabilityandstabilityfromthecircuitasawhole. Ifthethreetransistorstagesaredesignedtoprovideanarbitrarilyhighvoltagegain(inthetensofthousands,orgreater)withno 

feedback,itwillbefoundthattheadditionofnegativefeedbackcausestheoverallvoltagegain 

tobecomelessdependentoftheindividualstagegains,andapproximatelyequaltothesimple 

ratioRfeedback/Rin.Themorevoltagegainthecircuithas(withoutfeedback),themoreclosely 

thevoltagegainwillapproximateRfeedback/Rinoncefeedbackisestablished. Inotherwords, 

voltagegaininthiscircuitisfixedbythevaluesoftworesistors,andnothingmore. 

Thisisanadvantageformass-productionofelectroniccircuitry:ifamplifiersofpredictable 

gainmaybeconstructedusingtransistorsofwidelyvaried βvalues,iteasestheselectionand 

replacementofcomponents. Italsomeanstheamplifier’sgainvarieslittlewithchangesin 

temperature. Thisprincipleofstablegaincontrolthroughahigh-gainamplifier“tamed”by 

negativefeedbackiselevatedalmosttoanartforminelectroniccircuitscalledoperational 

+ 

-

4.13. AMPLIFIERIMPEDANCES 263 

amplifiers,orop-amps.Youmayreadmuchmoreaboutthesecircuitsinalaterchapterofthis 

book! 

• REVIEW: 

• Feedbackisthecouplingofanamplifier’soutputtoitsinput. 

• Positive,orregenerativefeedbackhasthetendencyofmakinganamplifiercircuitunstable,sothatitproducesoscillations(AC).Thefrequencyoftheseoscillationsislargely 

determinedbythecomponentsinthefeedbacknetwork. 

• Negative,ordegenerativefeedbackhasthetendencyofmakinganamplifiercircuitmore 

stable,sothatitsoutputchangeslessforagiveninputsignalthanwithoutfeedback. 

Thisreducesthegainoftheamplifier,buthastheadvantageofdecreasingdistortionand 

increasingbandwidth(therangeoffrequenciestheamplifiercanhandle). 

• Negativefeedbackmaybeintroducedintoacommon-emittercircuitbycouplingcollector 

tobase,orbyinsertingaresistorbetweenemitterandground. 

• Anemitter-to-ground“feedback”resistorisusuallyfoundincommon-emittercircuitsas 

apreventativemeasureagainstthermalrunaway. 

• Negativefeedbackalsohastheadvantageofmakingamplifiervoltagegainmoredependentonresistorvaluesandlessdependentonthetransistor’scharacteristics. 

• Common-collectoramplifiershavemuchnegativefeedback,duetotheplacementofthe 

loadresistorbetweenemitterandground.Thisfeedbackaccountsfortheextremelystablevoltagegainoftheamplifier,aswellasitsimmunityagainstthermalrunaway. 

• Voltagegainforacommon-emittercircuitmaybere-establishedwithoutsacrificingimmunitytothermalrunaway,byconnectingabypasscapacitorinparallelwiththeemitter 

“feedbackresistor.” 

• Ifthevoltagegainofanamplifierisarbitrarilyhigh(tensofthousands,orgreater),and 

negativefeedbackisusedtoreducethegaintoreasonablelevels,itwillbefoundthat 

thegainwillapproximatelyequalRfeedback/Rin. Changesintransistor βorotherinternalcomponentvalueswillhavelittleeffectonvoltagegainwithfeedbackinoperation, 

resultinginanamplifierthatisstableandeasytodesign. 

4.13 Amplifierimpedances 

InputimpedancevariesconsiderablywiththecircuitconfigurationshowninFigure4.112.It 

alsovarieswithbiasing.Notconsideredhere,theinputimpedanceiscomplexandvarieswith 

frequency. Forthecommon-emitterandcommon-collectoritisbaseresistancetimes β. The 

baseresistancecanbebothinternalandexternaltothetransistor.Forthecommon-collector: 

Rin = βRE 

Itisabitmorecomplicatedforthecommon-emittercircuit.Weneedtoknowtheinternal 

emitterresistanceREE.Thisisgivenby:


REE = KT/IEm 

where: 

K=1.38×10 −23 watt-sec/ o C, Boltzman’s constant 

T= temperature in Kelvins ∼ =300. 

IE = emitter current 

m = varies from 1 to 2 for Silicon 

RE ∼ = 0.026V/IE = 26mV/IE 

Thus,forthecommon-emittercircuitRinis 

Rin = βREE/IE 

Asanexampletheinputresistanceofa, β=100,CEconfigurationbiasedat1mAis: 

REE = 26mV/1mA = 0.26Ω 

Rin = βREE = 100(26) = 2600Ω 

Moreover,amoreaccurateRinforthecommon-collectorshouldhaveincludedRe’ 

Rin = β(RE + REE) 

Thisequation(above)isalsoapplicabletoacommon-emitterconfigurationwithanemitter 

resistor. 

Inputimpedanceforthecommon-baseconfigurationisRin=REE. 

Thehighinputimpedanceofthecommon-collectorconfigurationmatcheshighimpedance 

sources. Acrystalorceramicmicrophoneisonesuchhighimpedancesource. ThecommonbasearrangementissometimesusedinRF(radiofrequency)circuitstomatchalowimpedance 

source,forexample,a50 Ωcoaxialcablefeed.Formoderateimpedancesources,thecommonemitterisagoodmatch.Anexampleisadynamicmicrophone. 

TheoutputimpedancesofthethreebasicconfigurationsarelistedinFigure4.112. The 

moderateoutputimpedanceofthecommon-emitterconfigurationhelpsmakeitapopular 

choiceforgeneraluse. TheLowoutputimpedanceofthecommon-collectorisputtogood 

useinimpedancematching,forexample,tranformerlessmatchingtoa4Ohmspeaker.There 

donotappeartobeanysimpleformulasfortheoutputimpedances.However,R.VictorJones 

developsexpressionsforoutputresistance.[3] 

• REVIEW: 

• SeeFigure4.112. 

4.14 Currentmirrors 

Anoften-usedcircuitapplyingthebipolarjunctiontransistoristheso-calledcurrentmirror, 

whichservesasasimplecurrentregulator,supplyingnearlyconstantcurrenttoaloadovera 

widerangeofloadresistances. 

Weknowthatinatransistoroperatinginitsactivemode,collectorcurrentisequaltobase 

currentmultipliedbytheratio β. Wealsoknowthattheratiobetweencollectorcurrentand 

emittercurrentiscalled α.Becausecollectorcurrentisequaltobasecurrentmultipliedby β, 

andemittercurrentisthesumofthebaseandcollectorcurrents, αshouldbemathematically 

derivablefrom β.Ifyoudothealgebra,you’llfindthat α=β/(β+1)foranytransistor. 

We’veseenalreadyhowmaintainingaconstantbasecurrentthroughanactivetransistor 

resultsintheregulationofcollectorcurrent,accordingtothe βratio.Well,the αratioworks

4.14. CURRENTMIRRORS 265 

Basic circuit 

Voltage gain 

Current gain 

Power gain 

Phase inversion 


impedance 

Output 

impedance 

Common emitter Common collector Common base 

high 

high 

high 

Vo 

less than unity 

yes no no 

moderate ≈ 1 k 

moderate ≈ 50 k 

high 

moderate 

less than unity 

moderate 

highest ≈ 300 k low ≈ 50 Ω 

low ≈ 300 Ω 

Vo 

+ - - + + - - + 

- 

Vo 

+ - + 

high, same as CE 

highest ≈ 1 Meg 

Cascode 

+ 

+ 

high, same as CB 

high, same as CE 

highest 

yes 

same as CE, ≈ 1 k 

Vo 

+ 

same as CB, ≈ 1 Meg 

Figure4.112:Amplifiercharacteristics,adaptedfromGETransistorManual,Figure1.21.[2] 

similarly:ifemittercurrentisheldconstant,collectorcurrentwillremainatastable,regulated 

valuesolongasthetransistorhasenoughcollector-to-emittervoltagedroptomaintainitin 

itsactivemode. Therefore,ifwehaveawayofholdingemittercurrentconstantthrougha 

transistor,thetransistorwillworktoregulatecollectorcurrentataconstantvalue. 

Rememberthatthebase-emitterjunctionofaBJTisnothingmorethanaPNjunction,just 

likeadiode,andthatthe“diodeequation”specifieshowmuchcurrentwillgothroughaPN 

junctiongivenforwardvoltagedropandjunctiontemperature: 

I D = I S (e qV D/NkT - 1) 

Where, 




q = charge of electron (1.6 x 10 -19 (typically 1 x 10 

coulombs) 

-12 amps) 


N = "Nonideality" or "emission" coefficient 

(typically between 1 and 2) 

k = Boltzmann’s constant (1.38 x 10 -23 ) 

T = Junction temperature in Kelvins 

Ifbothjunctionvoltageandtemperatureareheldconstant,thenthePNjunctioncurrent 

willbeconstant. Followingthisrationale,ifweweretoholdthebase-emittervoltageofa


transistorconstant,thenitsemittercurrentwillbeconstant,givenaconstanttemperature. 

(Figure4.113) 

V base 

(constant) 

I collector 

(constant) 

(constant) 

Ibase I emitter 

(constant) 

R load 

β (constant) 

α (constant) 

Figure4.113:ConstantVBEgivesconstantIB,constantIE,andconstantIC. 

Thisconstantemittercurrent,multipliedbyaconstant αratio,givesaconstantcollector 

currentthroughRload,ifenoughbatteryvoltageisavailabletokeepthetransistorinitsactive 

modeforanychangeinRload’sresistance. 

Tomaintainaconstantvoltageacrossthetransistor’sbase-emitterjunctionuseaforwardbiaseddiodetoestablishaconstantvoltageofapproximately0.7volts,andconnectitinparallel 

withthebase-emitterjunctionasinFigure4.114. 

0.7 V 

(constant) 

R bias 

I collector 

(constant) 

(constant) 

Ibase I diode 

(constant) 

R load 

β (constant) 

α (constant) 

I emitter 

(constant) 

Figure4.114:Diodejunction0.7Vmaintainsconstantbasevoltage,andconstantbasecurrent. 

Thevoltagedroppedacrossthediodeprobablywon’tbe0.7voltsexactly.Theexactamount 

offorwardvoltagedroppedacrossitdependsonthecurrentthroughthediode,andthediode’s 

temperature,allinaccordancewiththediodeequation.Ifdiodecurrentisincreased(say,by 

reducingtheresistanceofRbias),itsvoltagedropwillincreaseslightly,increasingthevoltage 

dropacrossthetransistor’sbase-emitterjunction,whichwillincreasetheemittercurrentby 

thesameproportion,assumingthediode’sPNjunctionandthetransistor’sbase-emitterjunctionarewell-matchedtoeachother. 

Inotherwords,transistoremittercurrentwillclosely

4.14. CURRENTMIRRORS 267 

equaldiodecurrentatanygiventime.IfyouchangethediodecurrentbychangingtheresistancevalueofRbias,thenthetransistor’semittercurrentwillfollowsuit,becausetheemitter 

currentisdescribedbythesameequationasthediode’s,andbothPNjunctionsexperiencethe 

samevoltagedrop. 

Remember,thetransistor’scollectorcurrentisalmostequaltoitsemittercurrent,asthe 

αratioofatypicaltransistorisalmostunity(1). Ifwehavecontroloverthetransistor’s 

emittercurrentbysettingdiodecurrentwithasimpleresistoradjustment,thenwelikewise 

havecontroloverthetransistor’scollectorcurrent.Inotherwords,collectorcurrentmimics,or 

mirrors,diodecurrent. 

CurrentthroughresistorRloadisthereforeafunctionofcurrentsetbythebiasresistor,the 

twobeingnearlyequal.Thisisthefunctionofthecurrentmirrorcircuit:toregulatecurrent 

throughtheloadresistorbyconvenientlyadjustingthevalueofRbias. Currentthroughthe 

diodeisdescribedbyasimpleequation:powersupplyvoltageminusdiodevoltage(almosta 

constantvalue),dividedbytheresistanceofRbias. 

TobettermatchthecharacteristicsofthetwoPNjunctions(thediodejunctionandthe 

transistorbase-emitterjunction),atransistormaybeusedinplaceofaregulardiode,asin 

Figure4.115(a). 

R bias 

R load 

(a) current sinking 

+ 

− R load 

R bias 

(b) current-sourcing 

Figure4.115:Currentmirrorcircuits. 

Becausetemperatureisafactorinthe“diodeequation,”andwewantthetwoPNjunctions 

tobehaveidenticallyunderalloperatingconditions,weshouldmaintainthetwotransistorsat 

exactlythesametemperature.Thisiseasilydoneusingdiscretecomponentsbygluingthetwo 

transistorcasesback-to-back.Ifthetransistorsaremanufacturedtogetheronasinglechipof 

silicon(asaso-calledintegratedcircuit,orIC),thedesignersshouldlocatethetwotransistors 

closetooneanothertofacilitateheattransferbetweenthem. 

ThecurrentmirrorcircuitshownwithtwoNPNtransistorsinFigure4.115(a)issometimes 

calledacurrent-sinkingtype,becausetheregulatingtransistorconductscurrenttotheload 

fromground(“sinking”current),ratherthanfromthepositivesideofthebattery(“sourcing” 

current). Ifwewishtohaveagroundedload,andacurrentsourcingmirrorcircuit,wemay 

usePNPtransistorslikeFigure4.115(b). 

WhileresistorscanbemanufacturedinICs,itiseasiertofabricatetransistors.ICdesigners 

avoidsomeresistorsbyreplacingloadresistorswithcurrentsources.Acircuitlikeanoperationalamplifierbuiltfromdiscretecomponentswillhaveafewtransistorsandmanyresistors. 

+ 

−


Anintegratedcircuitversionwillhavemanytransistorsandafewresistors.InFigure4.116 

Onevoltagereference,Q1,drivesmultiplecurrentsources:Q2,Q3,andQ4.IfQ2andQ3are 

equalareatransistorstheloadcurrentsIloadwillbeequal.Ifweneeda2·Iload,parallelQ2and 

Q3.Betteryetfabricateonetransistor,sayQ3withtwicetheareaofQ2.CurrentI3willthen 

betwiceI2.Inotherwords,loadcurrentscaleswithtransistorarea. 

R bias 

R load 

I load 

Q1 Q2 Q3 Q4 

Figure4.116:Multiplecurrentmirrorsmaybeslavedfromasingle(Q1-Rbias)voltagesource. 

Notethatitiscustomarytodrawthebasevoltagelinerightthroughthetransistorsymbols 

formultiplecurrentmirrors! OrinthecaseofQ4inFigure4.116,twocurrentsourcesare 

associatedwithasingletransistorsymbol. Theloadresistorsaredrawnalmostinvisibleto 

emphasizethefactthatthesedonotexistinmostcases.Theloadisoftenanother(multiple) 

transistorcircuit,sayapairofemittersofadifferentialamplifier,forexampleQ3andQ4in 

”Asimpleoperationalamplifier”(page410). Often,thecollectorloadofatransistorisnota 

resistorbutacurrentmirror. ForexamplethecollectorloadofQ4collector(page410)isa 

currentmirror(Q2). 

ForanexampleofacurrentmirrorwithmultiplecollectoroutputsseeQ13inthemodel741 

op-amp(page410).TheQ13currentmirroroutputssubstituteforresistorsascollectorloads 

forQ15andQ17.Weseefromtheseexamplesthatcurrentmirrorsarepreferredasloadsover 

resistorsinintegratedcircuitry. 

• REVIEW: 

• Acurrentmirrorisatransistorcircuitthatregulatescurrentthroughaloadresistance, 

theregulationpointbeingsetbyasimpleresistoradjustment. 

• Transistorsinacurrentmirrorcircuitmustbemaintainedatthesametemperaturefor 

preciseoperation.Whenusingdiscretetransistors,youmaygluetheircasestogetherto 

dothis. 

• Currentmirrorcircuitsmaybefoundintwobasicvarieties:thecurrentsinkingconfiguration,wheretheregulatingtransistorconnectstheloadtoground;andthecurrent 

sourcingconfiguration,wheretheregulatingtransistorconnectstheloadtothepositive 

terminaloftheDCpowersupply. 

I load 

+ 

−

4.15. TRANSISTORRATINGSANDPACKAGES 269 

4.15 Transistorratingsandpackages 

Likeallelectricalandelectroniccomponents,transistorsarelimitedintheamountsofvoltageandcurrenteachonecanhandlewithoutsustainingdamage.Sincetransistorsaremore 

complexthansomeoftheothercomponentsyou’reusedtoseeingatthispoint,thesetendto 

havemorekindsofratings.Whatfollowsisanitemizeddescriptionofsometypicaltransistor 

ratings. 

Powerdissipation:Whenatransistorconductscurrentbetweencollectorandemitter,italso 

dropsvoltagebetweenthosetwopoints.Atanygiventime,thepowerdissipatedbyatransistorisequaltotheproduct(multiplication)ofcollectorcurrentandcollector-emittervoltage.Justlikeresistors,transistorsareratedforhowmanywattseachcansafelydissipatewithoutsustainingdamage. 

Hightemperatureisthemortalenemyofallsemiconductordevices, 

andbipolartransistorstendtobemoresusceptibletothermaldamagethanmost.Powerratingsarealwaysreferencedtothetemperatureofambient(surrounding)air.Whentransistors 

aretobeusedinhotterenvironments(>25o,theirpowerratingsmustbederatedtoavoida 

shortenedservicelife. 

Reversevoltages: Aswithdiodes, bipolartransistorsareratedformaximumallowable 

reverse-biasvoltageacrosstheirPNjunctions. ThisincludesvoltageratingsfortheemitterbasejunctionVEB,collector-basejunctionVCB,andalsofromcollectortoemitterVCE. 

VEB,themaximumreversevoltagefromemittertobaseisapproximately7Vforsome 

smallsignaltransistors. SomecircuitdesignersusediscreteBJTsas7Vzenerdiodeswith 

aseriescurrentlimitingresistor. Transistorinputstoanalogintegratedcircuitsalsohavea 

VEBrating,whichifexceededwillcausedamage,nozeneringoftheinputsisallowed. 

Theratingformaximumcollector-emittervoltageVCEcanbethoughtofasthemaximum 

voltageitcanwithstandwhileinfull-cutoffmode(nobasecurrent).Thisratingisofparticular 

importancewhenusingabipolartransistorasaswitch.Atypicalvalueforasmallsignaltransistoris60to80V.Inpowertransistors,thiscouldrangeto1000V,forexample,ahorizontal 

deflectiontransistorinacathoderaytubedisplay. 

Collectorcurrent:AmaximumvalueforcollectorcurrentICwillbegivenbythemanufacturerinamps.Typicalvaluesforsmallsignaltransistorsare10sto100sofmA,10sofAfor 

powertransistors. Understandthatthismaximumfigureassumesasaturatedstate(minimumcollector-emittervoltagedrop).Ifthetransistorisnotsaturated,andinfactisdropping 

substantialvoltagebetweencollectorandemitter,themaximumpowerdissipationratingwill 

probablybeexceededbeforethemaximumcollectorcurrentrating.Justsomethingtokeepin 

mindwhendesigningatransistorcircuit! 

Saturationvoltages:Ideally,asaturatedtransistoractsasaclosedswitchcontactbetween 

collectorandemitter,droppingzerovoltageatfullcollectorcurrent. Inrealitythisisnever 

true.Manufacturerswillspecifythemaximumvoltagedropofatransistoratsaturation,both 

betweenthecollectorandemitter,andalsobetweenbaseandemitter(forwardvoltagedrop 

ofthatPNjunction). Collector-emittervoltagedropatsaturationisgenerallyexpectedtobe 

0.3voltsorless,butthisfigureisofcoursedependentonthespecifictypeoftransistor. Low 

voltagetransistors,lowVCE,showlowersaturationvoltages. Thesaturationvoltageisalso 

lowerforhigherbasedrivecurrent. 

Base-emitterforwardvoltagedrop,kVBE,issimilartothatofanequivalentdiode, ∼ =0.7V, 

whichshouldcomeasnosurprise. 

Beta:Theratioofcollectorcurrenttobasecurrent, βisthefundamentalparameterchar-


acterizingtheamplifyingabilityofabipolartransistor. βisusuallyassumedtobeaconstant 

figureincircuitcalculations,butunfortunatelythisisfarfromtrueinpractice. Assuch, 

manufacturersprovideasetof β(or“hfe”)figuresforagiventransistoroverawiderangeof 

operatingconditions,usuallyintheformofmaximum/minimum/typicalratings. Itmaysurpriseyoutoseejusthowwidely 

βcanbeexpectedtovarywithinnormaloperatinglimits.One 

popularsmall-signaltransistor,the2N3903,isadvertisedashavingaβrangingfrom15to 

150dependingontheamountofcollectorcurrent.Generally, βishighestformediumcollector 

currents,decreasingforverylowandveryhighcollectorcurrents.hfeissmallsignalACgain; 

hFEislargeACsignalgainorDCgain. 

Alpha:theratioofcollectorcurrenttoemittercurrent, α=IC/IE. αmaybederivedfrom 

β,being α=β/(β+1). 

Bipolartransistorscomeinawidevarietyofphysicalpackages. Packagetypeisprimarilydependentupontherequiredpowerdissipationofthetransistor,muchlikeresistors:the 

greaterthemaximumpowerdissipation,thelargerthedevicehastobetostaycool. Figure4.117showsseveralstandardizedpackagetypesforthree-terminalsemiconductordevices, 

anyofwhichmaybeusedtohouseabipolartransistor.Therearemanyothersemiconductor 

devicesotherthanbipolartransistorswhichhavethreeconnectionpoints.Notethatthepinoutsofplastictransistorscanvarywithinasinglepackagetype,e.g.TO-92inFigure4.117.It 

isimpossibletopositivelyidentifyathree-terminalsemiconductordevicewithoutreferencing 

thepartnumberprintedonit,orsubjectingittoasetofelectricaltests. 

TO-3 

case, Collector 

E 

B 

16.89 

30.15 

39.37 

5.8 

TO-39 

9.4 

5.3 

E Β C 

E Β C 

TO-18 

6.6 

10.7 

Β C E 

B C E 

TO-3 (300 w) TO-220 (150 w) (TO-247 250 w) 

15.5 

5.2 

5.3 

E Β C 

E C Β 

TO-92 

Figure4.117:Transistorpackages,dimensionsinmm. 

SmallplastictransistorpackagesliketheTO-92candissipateafewhundredmilliwatts. 

Themetalcans,TO-18andTO-39candissipatemorepower,severalhundredmilliwatts.Plas- 

16 

21

4.16. BJTQUIRKS 271 

ticpowertransistorpackagesliketheTO-220andTO-247dissipatewellover100watts,approachingthedissipationoftheallmetalTO-3.ThedissipationratingslistedinFigure4.117arethemaximumeverencounteredbytheauthorforhighpowereddevices.Mostpowertransistorsareratedathalforlessthanthelistedwattage.Consultspecificdevicedatasheetsfor 

actualratings.ThesemiconductordieintheTO-220andTO-247plasticpackagesismounted 

toaheatconductivemetalslugwhichtransfersheatfromthebackofthepackagetoametal 

heatsink,notshown. Athincoatingofthermallyconductivegreaseisappliedtothemetal 

beforemountingthetransistortotheheatsink.SincetheTO-220andTO-247slugs,andthe 

TO-3caseareconnectedtothecollector,itissometimesnecessarytoelectricallyisolatethese 

fromagroundedheatsinkbyaninterposedmicaorpolymerwasher.Thedatasheetratingsfor 

thepowerpackagesareonlyvalidwhenmountedtoaheatsink.Withoutaheatsink,aTO-220 

dissipatesapproximately1wattsafelyinfreeair. 

Datasheetmaximumpowerdisipationratingsaredifficulttoacheiveinpractice.Themaximumpowerdissipationisbasedonaheatsinkmaintainingthetransistorcaseatnomorethan 

25 o C.Thisisdifficultwithanaircooledheatsink.Theallowablepowerdissipationdecreases 

withincreasingtemperature. Thisisknownasderating. Manypowerdevicedatasheetsincludeadissipationversuscasetermperauregraph. 

• REVIEW: 

• Powerdissipation:maximumallowablepowerdissipationonasustainedbasis. 

• Reversevoltages:maximumallowableVCE,VCB,VEB. 

• Collectorcurrent:themaximumallowablecollectorcurrent. 

• SaturationvoltageistheVCEvoltagedropinasaturated(fullyconducting)transistor. 

• Beta: β=IC/IB 

• Alpha: α=IC/IE α= β/(β+1) 

• TransistorPackagesareamajorfactorinpowerdissipation. Largerpackagesdissipate 

morepower. 

4.16 BJTquirks 

Anidealtransistorwouldshow0%distortioninamplifyingasignal. Itsgainwouldextend 

toallfrequencies.Itwouldcontrolhundredsofamperesofcurrent,athundredsofdegreesC. 

Inpractice,availabledevicesshowdistortion. Amplificationislimitedatthehighfrequency 

endofthespectrum.Realpartsonlyhandletensofampereswithprecautions.Caremustbe 

takenwhenparallelingtransistorsforhighercurrent.Operationatelevatedtemperaturescan 

destroytransistorsifprecautionsarenottaken.


Figure4.118:Distortioninlargesignalcommon-emitteramplifier. 

4.16.1 Nonlinearity 

TheclassAcommon-emitteramplifier(similartoFigure4.34)isdrivenalmosttoclippingin 

Figure4.118.Notethatthepositivepeakisflatterthanthenegativepeaks.Thisdistortionis 

unacceptableinmanyapplicationslikehigh-fidelityaudio. 

Smallsignalamplifiersarerelativelylinearbecausetheyuseasmalllinearsectionofthe 

transistorcharacteristics.Largesignalamplifiersarenot100%linearbecausetransistorcharacteristicslike 

βarenotconstant,butvarywithcollectorcurrent. βishighatlowcollector 

current,andlowatverylowcurrentorhighcurrent.Though,weprimarilyencounterdecreasing 

βwithincreasingcollectorcurrent. 

TheSPICElistinginTable4.119illustrateshowtoquantifytheamountofdistortion.The 

”.fourier2000v(2)”commandtellsSPICEtopermafourieranalysisat2000Hzontheoutput 

v(2). Atthecommandline”spice-bcircuitname.cir”producestheFourieranalysisoutputin 

Table4.119.ItshowsTHD(totalharmonicdistortion)ofover10%,andthecontributionofthe 

individualharmonics. 

Apartialsolutiontothisdistortionistodecreasethecollectorcurrentoroperatetheamplifieroverasmallerportionoftheloadline.Theultimatesolutionistoapplynegativefeedback. 

See(page256). 

4.16.2 Temperaturedrift 

TemperatureaffectstheACandDCcharacteristicsoftransistors. Thetwoaspectstothis 

problemareenvironmentaltemperaturevariationandself-heating. Someapplications,like 

militaryandautomotive,requireoperationoveranextendedtemperaturerange.Circuitsina 

benignenvironmentaresubjecttoself-heating,inparticularhighpowercircuits.



Vbias 4 0 0.74 

Vsig 5 4 sin (0 125m 2000 0 0) 

rbias 6 5 2k 

q1 2 6 0 q2n2222 

r 3 2 1000 

v1 3 0 dc 10 

.model q2n2222 npn (is=19f bf=150 

+ vaf=100 ikf=0.18 ise=50p ne=2.5 

br=7.5 

+ var=6.4 ikr=12m isc=8.7p nc=1.2 

rb=50 

+ re=0.4 rc=0.3 cje=26p tf=0.5n 

+ cjc=11p tr=7n xtb=1.5 kf=0.032f 

af=1) 

.fourier 2000 v(2) 

.tran 0.02m 0.74m 

.end 

spice -b ce.cir 

Fourier analysis 

v(2): 

THD: 10.4688 

Har Freq Norm 

Mag 

--- ---- 

--------- 

0 0 0 

1 2000 1 

2 4000 

0.0979929 

3 6000 

0.0365461 

4 8000 

0.00438709 

5 10000 

0.00115878 

6 12000 

0.00089388 

7 14000 

0.00021169 

8 16000 

3.8158e-05 

9 18000 

3.3726e-05 

Figure4.119:SPICEnetlist:fortransientandfourieranalyses.Fourieranalysisshows10% 

totalharmonicdistortion(THD).


LeakagecurrentICOand βincreasewithtemperature.TheDC βhFEincreasesexponentially.TheAC 

βhfeincreases,butnotasrapidly.Itdoublesovertherangeof-55 o to85 o C.As 

temperatureincreases,theincreaseinhfewillyieldalargercommon-emitteroutput,which 

couldbeclippedinextremecases.TheincreaseinhFEshiftsthebiaspoint,possiblyclipping 

onepeak. Theshiftinbiaspointisamplifiedinmulti-stagedirect-coupledamplifiers. The 

solutionissomeformofnegativefeedbacktostabilizethebiaspoint.ThisalsostabilizesAC 

gain. 

IncreasingtemperatureinFigure4.120(a)willdecreaseVBEfromthenominal0.7Vfor 

silicontransistors.DecreasingVBEincreasescollectorcurrentinacommon-emitteramplifier, 

furthershiftingthebiaspoint.ThecureforshiftingVBEisapairoftransistorsconfiguredas 

adifferentialamplifier.IfbothtransistorsinFigure4.120(b)areatthesametemperature,the 

VBEwilltrackwithchangingtemperatureandcancel. 

+ 

VBE +Vcc 

- 

+ 

VBE - 

-Vee 

(a) (b) 

+Vcc 

-Vee 

+ 

- V BE 

Figure4.120:(a)singleendedCEamplifiervs(b)differentialamplifierwithVBEcancellation. 

Themaximumrecommendedjunctiontemperatureforsilicondevicesisfrequently125 o C. 

Though,thisshouldbederatedforhigherreliability.Transistoractionceasesbeyond150 o C. 

Siliconcarbideanddiamondtransistorswilloperateconsiderablyhigher. 

4.16.3 Thermalrunaway 

Theproblemwithincreasingtemperaturecausingincreasingcollectorcurrentisthatmorecurrentincreasethepowerdissipatedbythetransistorwhich,inturn,increasesitstemperature. 

Thisself-reinforcingcycleisknownasthermalrunaway,whichmaydestroythetransistor. 

Again,thesolutionisabiasschemewithsomeformofnegativefeedbacktostabilizethebias 

point. 

4.16.4 Junctioncapacitance 

Capacitanceexistsbetweentheterminalsofatransistor.Thecollector-basecapacitanceCCB 

andemitter-basecapacitanceCEBdecreasethegainofacommonemittercircuitathigher 

frequencies.


Inacommonemitteramplifier,thecapacitivefeedbackfromcollectortobaseeffectively 

multipliesCCBby β.Theamountofnegativegain-reducingfeedbackisrelatedtobothcurrent 

gain,andamountofcollector-basecapacitance.ThisisknownastheMillereffect,(page277). 

4.16.5 Noise 

Theultimatesensitivityofsmallsignalamplifiersislimitedbynoiseduetorandomvariations 

incurrentflow.Thetwomajorsourcesofnoiseintransistorsareshotnoiseduetocurrentflow 

ofcarriersinthebaseandthermalnoise.Thesourceofthermalnoiseisdeviceresistanceand 

increaseswithtemperature: 

V n = 4kTRB n 

where 

k = boltzman’s conatant (1.38•10 −23 watt-sec/K) 

T = resistor tempeature in kelvins 

R = resistance in Ohms 

B n = noise bandwidth in Hz 

Noiseinatransistoramplifierisdefinedintermsofexcessnoisegeneratedbytheamplifier, 

notthatnoiseamplifiedfrominputtooutput,butthatgeneratedwithintheamplifier.Thisis 

determinedbymeasuringthesignaltonoiseratio(S/N)attheamplifierinputandoutput.The 

ACvoltageoutputofanamplifierwithasmallsignalinputcorrespondstoS+N,signalplus 

noise.TheACvoltagewithnosignalincorrespondstonoiseN.ThenoisefigureFisdefinedin 

termsofS/Nofamplifierinputandoutput: 

F = (S/N) i 

(S/N) o 

F dB = 10 log F 

ThenoisefigureFforRF(radiofrequency)transistorsisusuallylistedontransistordata 

sheetsindecibels,FdB. AgoodVHF(veryhighfrequency,30MHzto300Mhz)noisefigure 

is


Noise figure F (decibels) 

1/f noise 

-10 dB/decade 

f Ln 

shot noise and 

thermal noise 

white noise region 

f Hn 

20 dB/decade 

Log Frequency 

Figure4.121:SmallsignaltransistornoisefigurevsFrequency.AfterThiele,Figure11.147[1] 

Incorrect 

+V +V 

Correct 

Figure4.122:Transistorsparalleledforincreasedpowerrequireemitterballastresistors


Itisnotpracticaltoselectidenticaltransistors.The βforsmallsignaltransistorstypically 

hasarangeof100-300,powertransistors:20-50.Ifeachonecouldbematched,onestillmight 

runhotterthantheotherduetoenvironmentalconditions.Thehottertransistordrawsmore 

currentresultinginthermalrunaway.Thesolutionwhenparallelingbipolartransistorsisto 

insertemitterresistorsknownasballastresistorsoflessthananohm.Ifthehottertransistor 

drawsmorecurrent,thevoltagedropacrosstheballastresistorincreases—negativefeedback. 

Thisdecreasesthecurrent. Mountingalltransistorsonthesameheatsinkhelpsequalize 

currenttoo. 

4.16.7 Highfrequencyeffects 

Theperformanceofatransistoramplifierisrelativelyconstant,uptoapoint,asshownbythe 

smallsignalcommon-emittercurrentgainwithincreasingfrequencyinFigure4.123.Beyond 

thatpointtheperformanceofatransistordegradesasfrequencyincreases. 

Betacutofffrequency,fTisthefrequencyatwhichcommon-emittersmallsignalcurrent 

gain(hfe)fallstounity. (Figure4.123)Apracticalamplifiermusthaveagain >1. Thus,a 

transistorcannotbeusedinapracticalamplifieratfT.Amoreusablelimitforatransistoris 

0.1·fT. 

h fe 

100 

10 

1 

log f 

Figure4.123:Common-emittersmallsignalcurrentgain(hfe)vsfrequency. 

SomeRFsiliconbipolartransistorsareusableasamplifersuptoafewGHz. Silicongermaniumdevicesextendtheupperrangeto10GHz. 

Alphacutofffrequency,falphaisthefrequencyatwhichthe αfallsto0.707oflowfrequency 

α,0 α=0.707α0.Alphacutoffandbetacutoffarenearlyequal:falpha ∼ =fTBetacutofffT 

isthepreferredfigureofmeritofhighfrequencyperformance. 

fmaxisthehighestfrequencyofoscillationpossibleunderthemostfavorableconditionsof 

biasandimpedancematching.Itisthefrequencyatwhichthepowergainisunity.Allofthe 

outputisfedbacktotheinputtosustainoscillations. fmaxisanupperlimitforfrequencyof 

operationofatransistorasanactivedevice.Though,apracticalamplifierwouldnotbeusable 

atfmax. 

Millereffect:Thehighfrequencylimitforatransistorisrelatedtothejunctioncapacitances.ForexampleaPN2222AhasaninputcapacitanceCobo=9pFandanoutputcapacitance 

f T


Cibo=25pFfromC-BandE-Brespectively. [5]AlthoughtheC-Ecapacitanceof25pFseems 

large,itislessofafactorthantheC-B(9pF)capacitance.becauseoftheMillereffect,theC-B 

capacitancehasaneffectonthebaseequivalenttobetatimesthecapacitanceinthecommonemitteramplifier. 

Whymightthisbe? Acommon-emitteramplifierinvertsthesignalfrom 

basetocollector. Theinvertedcollectorsignalfedbacktothebaseopposestheinputonthe 

base. Thecollectorsignalisbetatimeslargerthantheinput. ForthePN2222A, β=50–300. 

Thus,the9pFC-Ecapacitancelookslike9·50=450pFto9·300=2700pF. 

Thesolutiontothejunctioncapacitanceproblemistoselectahighfrequencytransistorfor 

widebandwidthapplications—RF(radiofrequency)ormicrowavetransistor.Thebandwidth 

canbeextendedfurtherbyusingthecommon-baseinsteadofthecommon-emitterconfiguration. 

Thegroundedbaseshieldstheemitterinputfromcapacitivecollectorfeedback. A 

two-transistorcascodearrangementwillyieldthesamebandwidthasthecommon-base,with 

thehigherinputimpedanceofthecommon-emitter. 

• REVIEW: 

• Transistoramplifiersexhibitdistortionbecauseof βvariationwithcollectorcurrent. 

• Ic,VBE, βandjunctioncapacitancevarywithtemperature. 

• AnincreaseintemperaturecancauseanincreaseinIC,causinganincreaseintemperature,aviciouscycleknownasthermalrunaway. 

• Junctioncapacitancelimitshighfrequencygainofatransistor.TheMillereffectmakes 

Ccblook βtimeslargeratthebaseofaCEamplifier. 

• Transistornoiselimitstheabilitytoamplifysmallsignals. Noisefigureisafigureof 

meritconcerningtransistornoise. 

• Whenparallelingpowertransistorsforincreasedcurrent,insertballastresistorsinseries 

withtheemitterstoequalizecurrent. 

• FT istheabsoluteupperfrequencylimitforaCEamplifier,smallsignalcurrentgain 

fallstounity,hfe=1. 

• Fmaxistheupperfrequencylimitforanoscillatorunderthemostidealconditions. 

Bibliography 

[1] A.G.ThieleinLoydP.Hunter,“HandbookofSemiconductorElectronics,”LowFrequency 

Amplifiers,ISBN-07-031305-9,1970 

[2] “GETransistorManual”,GeneralElectric,1964. 

[3] R. Victor Jones, “Basic BJT Amplifier Configurations”, November 7, 2001. at 

http://people.seas.harvard.edu/˜jones/es154/lectures/lecture 3/ 

bjt amps/bjt amps.html


[4] Tony Kuphaldt,“Lessons in Electric Circuits”, Vol. 1, DC, DC Network Analysis, 

Thevenin’s Theorem, at http://www.openbookproject.net/electricCircuits/ 

DC/DC 10.html#xtocid102679 

[5] “PN2222 Datasheet”,Fairchild Semiconductor Corporation, 2007 at 

http://www.fairchildsemi.com/ds/PN/PN2222A.pdf

280 CHAPTER4. BIPOLARJUNCTIONTRANSISTORS

Chapter5 

JUNCTIONFIELD-EFFECT 

TRANSISTORS 

Contents 


5.2 Thetransistorasaswitch . . . . . . . . . . . . . . . . . . . . . . . . . . . . .283 

5.3 Metercheckofatransistor. . . . . . . . . . . . . . . . . . . . . . . . . . . . .286 

5.4 Active-modeoperation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .288 

5.5 Thecommon-sourceamplifier–PENDING...................297 

5.6 Thecommon-drainamplifier–PENDING. . . . . . . . . . . . . . . . . . . .298 

5.7 Thecommon-gateamplifier–PENDING . . . . . . . . . . . . . . . . . . . .298 

5.8 Biasingtechniques–PENDING..........................298 

5.9 Transistorratingsandpackages–PENDING . . . . . . . . . . . . . . . . .299 

5.10 JFETquirks–PENDING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .299 

***INCOMPLETE*** 


Atransistorisalinearsemiconductordevicethatcontrolscurrentwiththeapplicationofa 

lower-powerelectricalsignal. Transistorsmayberoughlygroupedintotwomajordivisions: 

bipolarandfield-effect.Inthelastchapterwestudiedbipolartransistors,whichutilizeasmall 

currenttocontrolalargecurrent. Inthischapter,we’llintroducethegeneralconceptofthe 

field-effecttransistor–adeviceutilizingasmallvoltagetocontrolcurrent–andthenfocus 

ononeparticulartype: thejunctionfield-effecttransistor. Inthenextchapterwe’llexplore 

anothertypeoffield-effecttransistor,theinsulatedgatevariety. 

Allfield-effecttransistorsareunipolarratherthanbipolardevices.Thatis,themaincurrentthroughthemiscomprisedeitherofelectronsthroughanN-typesemiconductororholes 

281

282 CHAPTER5. JUNCTIONFIELD-EFFECTTRANSISTORS 

throughaP-typesemiconductor. Thisbecomesmoreevidentwhenaphysicaldiagramofthe 

deviceisseen: 

gate 

drain 

source 

N-channel JFET 

gate 

drain 

P N 

source 

schematic symbol physical diagram 

Inajunctionfield-effecttransistor,orJFET,thecontrolledcurrentpassesfromsourceto 

drain,orfromdraintosourceasthecasemaybe.Thecontrollingvoltageisappliedbetween 

thegateandsource. NotehowthecurrentdoesnothavetocrossthroughaPNjunctionon 

itswaybetweensourceanddrain: thepath(calledachannel)isanuninterruptedblockof 

semiconductormaterial. Intheimagejustshown,thischannelisanN-typesemiconductor. 

P-typechannelJFETsarealsomanufactured: 

gate 

drain 

source 

P-channel JFET 

gate 

drain 


N 

P 

source 

Generally,N-channelJFETsaremorecommonlyusedthanP-channel.Thereasonsforthis 

havetodowithobscuredetailsofsemiconductortheory,whichI’drathernotdiscussinthis 

chapter.Aswithbipolartransistors,Ibelievethebestwaytointroducefield-effecttransistor 

usageistoavoidtheorywheneverpossibleandconcentrateinsteadonoperationalcharacteristics. 

TheonlypracticaldifferencebetweenN-andP-channelJFETsyouneedtoconcern 

yourselfwithnowisbiasingofthePNjunctionformedbetweenthegatematerialandthe 

channel.


Withnovoltageappliedbetweengateandsource,thechannelisawide-openpathforelectronstoflow.However,ifavoltageisappliedbetweengateandsourceofsuchpolaritythatitreverse-biasesthePNjunction,theflowbetweensourceanddrainconnectionsbecomeslimited,orregulated,justasitwasforbipolartransistorswithasetamountofbasecurrent. 

Maximumgate-sourcevoltage”pinchesoff”allcurrentthroughsourceanddrain,thusforcing 

theJFETintocutoffmode. ThisbehaviorisduetothedepletionregionofthePNjunction 

expandingundertheinfluenceofareverse-biasvoltage,eventuallyoccupyingtheentirewidth 

ofthechannelifthevoltageisgreatenough.Thisactionmaybelikenedtoreducingtheflowof 

aliquidthroughaflexiblehosebysqueezingit:withenoughforce,thehosewillbeconstricted 

enoughtocompletelyblocktheflow. 

water 

water 

hose nozzle 

Hose constricted by squeezing, 

water flow reduced or stopped 

Notehowthisoperationalbehaviorisexactlyoppositeofthebipolarjunctiontransistor. 

Bipolartransistorsarenormally-offdevices:nocurrentthroughthebase,nocurrentthrough 

thecollectorortheemitter. JFETs,ontheotherhand,arenormally-ondevices: novoltage 

appliedtothegateallowsmaximumcurrentthroughthesourceanddrain. Alsotakenote 

thattheamountofcurrentallowedthroughaJFETisdeterminedbyavoltagesignalrather 

thanacurrentsignalaswithbipolartransistors. Infact,withthegate-sourcePNjunction 

reverse-biased,thereshouldbenearlyzerocurrentthroughthegateconnection. Forthis 

reason,weclassifytheJFETasavoltage-controlleddevice,andthebipolartransistorasa 

current-controlleddevice. 

Ifthegate-sourcePNjunctionisforward-biasedwithasmallvoltage,theJFETchannel 

will”open”alittlemoretoallowgreatercurrentsthrough. However,thePNjunctionofa 

JFETisnotbuilttohandleanysubstantialcurrentitself,andthusitisnotrecommendedto 

forward-biasthejunctionunderanycircumstances. 

ThisisaverycondensedoverviewofJFEToperation.Inthenextsection,we’llexplorethe 

useoftheJFETasaswitchingdevice. 

5.2 Thetransistorasaswitch 

Likeitsbipolarcousin,thefield-effecttransistormaybeusedasanon/offswitchcontrolling 

electricalpowertoaload. Let’sbeginourinvestigationoftheJFETasaswitchwithour 

familiarswitch/lampcircuit:


switch 

RememberingthatthecontrolledcurrentinaJFETflowsbetweensourceanddrain,we 

substitutethesourceanddrainconnectionsofaJFETforthetwoendsoftheswitchinthe 

abovecircuit: 

Ifyouhaven’tnoticedbynow,thesourceanddrainconnectionsonaJFETlookidentical 

ontheschematicsymbol. Unlikethebipolarjunctiontransistorwheretheemitterisclearly 

distinguishedfromthecollectorbythearrowhead,aJFET’ssourceanddrainlinesbothrun 

perpendicularintothebarrepresentingthesemiconductorchannel.Thisisnoaccident,asthe 

sourceanddrainlinesofaJFETareofteninterchangeableinpractice!Inotherwords,JFETs 

areusuallyabletohandlechannelcurrentineitherdirection,fromsourcetodrainorfrom 

draintosource. 

NowallweneedinthecircuitisawaytocontroltheJFET’sconduction.Withzeroapplied 

voltagebetweengateandsource,theJFET’schannelwillbe”open,”allowingfullcurrentto 

thelamp.Inordertoturnthelampoff,wewillneedtoconnectanothersourceofDCvoltage 

betweenthegateandsourceconnectionsoftheJFETlikethis: 

switch 

Closingthisswitchwill”pinchoff”theJFET’schannel,thusforcingitintocutoffandturningthelampoff: 

switch


Notethatthereisnocurrentgoingthroughthegate. Asareverse-biasedPNjunction,it 

firmlyopposestheflowofanyelectronsthroughit. Asavoltage-controlleddevice,theJFET 

requiresnegligibleinputcurrent.ThisisanadvantageoustraitoftheJFEToverthebipolar 

transistor:thereisvirtuallyzeropowerrequiredofthecontrollingsignal. 

Openingthecontrolswitchagainshoulddisconnectthereverse-biasingDCvoltagefrom 

thegate,thusallowingthetransistortoturnbackon.Ideally,anyway,thisishowitworks.In 

practicethismaynotworkatall: 

switch 

No lamp current after the switch opens! 

Whyisthis?Whydoesn’ttheJFET’schannelopenupagainandallowlampcurrentthrough 

likeitdidbeforewithnovoltageappliedbetweengateandsource?Theanswerliesintheoperationofthereverse-biasedgate-sourcejunction.Thedepletionregionwithinthatjunctionacts 

asaninsulatingbarrierseparatinggatefromsource.Assuch,itpossessesacertainamountof 

capacitancecapableofstoringanelectricchargepotential.Afterthisjunctionhasbeenforcibly 

reverse-biasedbytheapplicationofanexternalvoltage,itwilltendtoholdthatreverse-biasing 

voltageasastoredchargeevenafterthesourceofthatvoltagehasbeendisconnected.What 

isneededtoturntheJFETonagainistobleedoffthatstoredchargebetweenthegateand 

sourcethrougharesistor: 

switch 

Resistor bleeds off stored charge in 

PN junction to allow transistor to 

turn on once again. 

Thisresistor’svalueisnotveryimportant.ThecapacitanceoftheJFET’sgate-sourcejunctionisverysmall,andsoevenaratherhigh-valuebleedresistorcreatesafastRCtimeconstant,allowingthetransistortoresumeconductionwithlittledelayoncetheswitchisopened. 

Likethebipolartransistor,itmatterslittlewhereorwhatthecontrollingvoltagecomes 

from.Wecoulduseasolarcell,thermocouple,oranyothersortofvoltage-generatingdeviceto 

supplythevoltagecontrollingtheJFET’sconduction.Allthatisrequiredofavoltagesource 

forJFETswitchoperationissufficientvoltagetoachievepinch-offoftheJFETchannel.This 

levelisusuallyintherealmofafewvoltsDC,andistermedthepinch-offorcutoffvoltage. 

Theexactpinch-offvoltageforanygivenJFETisafunctionofitsuniquedesign,andisnota


universalfigurelike0.7voltsisforasiliconBJT’sbase-emitterjunctionvoltage. 

• REVIEW: 

• Field-effecttransistorscontrolthecurrentbetweensourceanddrainconnectionsbya 

voltageappliedbetweenthegateandsource.Inajunctionfield-effecttransistor(JFET), 

thereisaPNjunctionbetweenthegateandsourcewhichisnormallyreverse-biasedfor 

controlofsource-draincurrent. 

• JFETsarenormally-on(normally-saturated)devices.Theapplicationofareverse-biasing 

voltagebetweengateandsourcecausesthedepletionregionofthatjunctiontoexpand, 

thereby”pinchingoff”thechannelbetweensourceanddrainthroughwhichthecontrolled 

currenttravels. 

• Itmaybenecessarytoattacha”bleed-off”resistorbetweengateandsourcetodischarge 

thestoredchargebuiltupacrossthejunction’snaturalcapacitancewhenthecontrolling 

voltageisremoved. Otherwise,achargemayremaintokeeptheJFETincutoffmode 

evenafterthevoltagesourcehasbeendisconnected. 

5.3 Metercheckofatransistor 

TestingaJFETwithamultimetermightseemtobearelativelyeasytask,seeingashowit 

hasonlyonePNjunctiontotest:eithermeasuredbetweengateandsource,orbetweengate 

anddrain. 

V A 

V 

V A 

V 

A 

A 

OFF 

OFF 

COM 

COM 

A 

A 

gate 

drain 

source 

N-channel transistor 

gate 

- 

- 

drain 

+ 

P N 

+ 

source 

physical diagram 

Both meters show non-continuity 

(high resistance) through gatechannel 

junction.


V A 

V 

V A 

V 

A 

A 

OFF 

OFF 

COM 

COM 

A 

A 

gate 

drain 

source 

N-channel transistor 

+ 

gate 

+ 

drain 

- 

P N 

- 

source 

physical diagram 

Both meters show continuity (low 

resistance) through gate-channel 

junction. 

Testingcontinuitythroughthedrain-sourcechannelisanothermatter,though. Rememberfromthelastsectionhowastoredchargeacrossthecapacitanceofthegate-channelPN 

junctioncouldholdtheJFETinapinched-offstatewithoutanyexternalvoltagebeingapplied 

acrossit? Thiscanoccurevenwhenyou’reholdingtheJFETinyourhandtotestit! Consequently,anymeterreadingofcontinuitythroughthatchannelwillbeunpredictable,sinceyou 

don’tnecessarilyknowifachargeisbeingstoredbythegate-channeljunction.Ofcourse,ifyou 

knowbeforehandwhichterminalsonthedevicearethegate,source,anddrain,youmayconnectajumperwirebetweengateandsourcetoeliminateanystoredchargeandthenproceed 

totestsource-draincontinuitywithnoproblem.However,ifyoudon’tknowwhichterminals 

arewhich,theunpredictabilityofthesource-drainconnectionmayconfuseyourdetermination 

ofterminalidentity. 

AgoodstrategytofollowwhentestingaJFETistoinsertthepinsofthetransistorinto 

anti-staticfoam(thematerialusedtoshipandstorestatic-sensitiveelectroniccomponents) 

justpriortotesting.Theconductivityofthefoamwillmakearesistiveconnectionbetweenall 

terminalsofthetransistorwhenitisinserted. Thisconnectionwillensurethatallresidual 

voltagebuiltupacrossthegate-channelPNjunctionwillbeneutralized,thus”openingup”the 

channelforanaccuratemetertestofsource-to-draincontinuity. 

SincetheJFETchannelisasingle,uninterruptedpieceofsemiconductormaterial,thereis 

usuallynodifferencebetweenthesourceanddrainterminals.Aresistancecheckfromsource 

todrainshouldyieldthesamevalueasacheckfromdraintosource.Thisresistanceshouldbe 

relativelylow(afewhundredohmsatmost)whenthegate-sourcePNjunctionvoltageiszero. 

Byapplyingareverse-biasvoltagebetweengateandsource,pinch-offofthechannelshouldbe 

apparentbyanincreasedresistancereadingonthemeter.


5.4 Active-modeoperation 

JFETs,likebipolartransistors,areableto”throttle”currentinamodebetweencutoffand 

saturationcalledtheactivemode.TobetterunderstandJFEToperation,let’ssetupaSPICE 

simulationsimilartotheoneusedtoexplorebasicbipolartransistorfunction: 

V in 

jfet simulation 

vin 0 1 dc 1 

j1 2 1 0 mod1 


v1 3 0 dc 

.model mod1 njf 

.dc v1 0 2 0.05 

.plot dc i(vammeter) 

.end 

1 

Q 1 

V ammeter 

2 3 

0 V 

0 0 0 

Notethatthetransistorlabeled”Q1”intheschematicisrepresentedintheSPICEnetlistas 

j1.Althoughalltransistortypesarecommonlyreferredtoas”Q”devicesincircuitschematics 

–justasresistorsarereferredtoby”R”designations,andcapacitorsby”C”–SPICEneedsto 

betoldwhattypeoftransistorthisisbymeansofadifferentletterdesignation: qforbipolar 

junctiontransistors,and jforjunctionfield-effecttransistors. 

V 1

5.4. ACTIVE-MODEOPERATION 289 

Here,thecontrollingsignalisasteadyvoltageof1volt,appliedwithnegativetowardsthe 

JFETgateandpositivetowardtheJFETsource,toreverse-biasthePNjunction.Inthefirst 

BJTsimulationofchapter4,aconstant-currentsourceof20 µAwasusedforthecontrolling 

signal,butrememberthataJFETisavoltage-controlleddevice,notacurrent-controlleddevice 

likethebipolarjunctiontransistor. 

LiketheBJT,theJFETtendstoregulatethecontrolledcurrentatafixedlevelabovea 

certainpowersupplyvoltage,nomatterhowhighthatvoltagemayclimb. Ofcourse,this 

currentregulationhaslimitsinreallife–notransistorcanwithstandinfinitevoltagefrom 

apowersource–andwithenoughdrain-to-sourcevoltagethetransistorwill”breakdown” 

anddraincurrentwillsurge. ButwithinnormaloperatinglimitstheJFETkeepsthedrain 

currentatasteadylevelindependentofpowersupplyvoltage.Toverifythis,we’llrunanother 

computersimulation,thistimesweepingthepowersupplyvoltage(V1)allthewayto50volts: 


vin 0 1 dc 1 

j1 2 1 0 mod1 


v1 3 0 dc 


.dc v1 0 50 2 


.end


Sureenough,thedraincurrentremainssteadyatavalueof100 µA(1.000E-04amps)no 

matterhowhighthepowersupplyvoltageisadjusted. 

BecausetheinputvoltagehascontrolovertheconstrictionoftheJFET’schannel,itmakes 

sensethatchangingthisvoltageshouldbetheonlyactioncapableofalteringthecurrent 

regulationpointfortheJFET,justlikechangingthebasecurrentonaBJTistheonlyaction 

capableofalteringcollectorcurrentregulation.Let’sdecreasetheinputvoltagefrom1voltto 

0.5voltsandseewhathappens: 


vin 0 1 dc 0.5 

j1 2 1 0 mod1 


v1 3 0 dc 


.dc v1 0 50 2 


.end


Asexpected,thedraincurrentisgreaternowthanitwasintheprevioussimulation.With 

lessreverse-biasvoltageimpressedacrossthegate-sourcejunction,thedepletionregionisnot 

aswideasitwasbefore,thus”opening”thechannelforchargecarriersandincreasingthe 

draincurrentfigure. 

Pleasenote,however,theactualvalueofthisnewcurrentfigure:225 µA(2.250E-04amps). 

Thelastsimulationshowedadraincurrentof100 µA,andthatwaswithagate-sourcevoltage 

of1volt.Nowthatwe’vereducedthecontrollingvoltagebyafactorof2(from1voltdownto 

0.5volts),thedraincurrentincreased,butnotbythesame2:1proportion! Let’sreduceour 

gate-sourcevoltageoncemorebyanotherfactorof2(downto0.25volts)andseewhathappens: 


vin 0 1 dc 0.25 

j1 2 1 0 mod1 


v1 3 0 dc 


.dc v1 0 50 2 


.end


Withthegate-sourcevoltagesetto0.25volts,one-halfwhatitwasbefore,thedraincurrent 

is306.3 µA.Althoughthisisstillanincreaseoverthe225 µAfromthepriorsimulation,itisn’t 

proportionaltothechangeofthecontrollingvoltage. 

Toobtainabetterunderstandingofwhatisgoingonhere,weshouldrunadifferentkind 

ofsimulation:onethatkeepsthepowersupplyvoltageconstantandinsteadvariesthecontrolling(voltage)signal. 

WhenthiskindofsimulationwasrunonaBJT,theresultwasa 

straight-linegraph,showinghowtheinputcurrent/outputcurrentrelationshipofaBJTis 

linear.Let’sseewhatkindofrelationshipaJFETexhibits: 


vin 0 1 dc 

j1 2 1 0 mod1 


v1 3 0 dc 25 


.dc vin 0 2 0.1 


.end


Thissimulationdirectlyrevealsanimportantcharacteristicofthejunctionfield-effecttransistor:thecontroleffectofgatevoltageoverdraincurrentisnonlinear.Noticehowthedrain 

currentdoesnotdecreaselinearlyasthegate-sourcevoltageisincreased. Withthebipolar 

junctiontransistor,collectorcurrentwasdirectlyproportionaltobasecurrent:outputsignal 

proportionatelyfollowedinputsignal. NotsowiththeJFET!Thecontrollingsignal(gatesourcevoltage)haslessandlesseffectoverthedraincurrentasitapproachescutoff.Inthis 

simulation,mostofthecontrollingaction(75percentofdraincurrentdecrease–from400 

µAto100 µA)takesplacewithinthefirstvoltofgate-sourcevoltage(from0to1volt),while 

theremaining25percentofdraincurrentreductiontakesanotherwholevoltworthofinput 

signal.Cutoffoccursat2voltsinput. 

Linearityisgenerallyimportantforatransistorbecauseitallowsittofaithfullyamplifya 

waveformwithoutdistortingit. Ifatransistorisnonlinearinitsinput/outputamplification, 

theshapeoftheinputwaveformwillbecomecorruptedinsomeway,leadingtotheproduction 

ofharmonicsintheoutputsignal. Theonlytimelinearityisnotimportantinatransistor 

circuitiswhenitsbeingoperatedattheextremelimitsofcutoffandsaturation(offandon, 

respectively,likeaswitch). 

AJFET’scharacteristiccurvesdisplaythesamecurrent-regulatingbehaviorasforaBJT, 

andthenonlinearitybetweengate-to-sourcevoltageanddraincurrentisevidentinthedisproportionateverticalspacingsbetweenthecurves:


I drain 

Below pinch-off 

Triode region 

Ohmic region 

|V DS| = |V P| - |V GS| 

Above pinch-off 

Saturation region 

V gate-to-source = 



E drain-to-source 

1 V 

0 V 

V gate-to-source = 0.5 V 

2 V = V P 

(pinch-off) 

Tobettercomprehendthecurrent-regulatingbehavioroftheJFET,itmightbehelpfulto 

drawamodelmadeupofsimpler,morecommoncomponents,justaswedidfortheBJT: 

G 

N-channel JFET diode-regulating diode model 

G 

D 

S 

InthecaseoftheJFET,itisthevoltageacrossthereverse-biasedgate-sourcediodewhich 

setsthecurrentregulationpointforthepairofconstant-currentdiodes. Apairofopposing 

constant-currentdiodesisincludedinthemodeltofacilitatecurrentineitherdirectionbe- 

D 

S


tweensourceanddrain,atraitmadepossiblebytheunipolarnatureofthechannel. With 

noPNjunctionsforthesource-draincurrenttotraverse,thereisnopolaritysensitivityinthe 

controlledcurrent.Forthisreason,JFETsareoftenreferredtoasbilateraldevices. 

AcontrastoftheJFET’scharacteristiccurvesagainstthecurvesforabipolartransistor 

revealsanotabledifference:thelinear(straight)portionofeachcurve’snon-horizontalareais 

surprisinglylongcomparedtotherespectiveportionsofaBJT’scharacteristiccurves: 

I drain 

I collector 

"Ohmic regions" 





0 V 

V gate-to-source = 0.5 V 





1 V 


2 V (pinch-off) 

AJFETtransistoroperatedinthetrioderegiontendstoactverymuchlikeaplainresistor 

asmeasuredfromdraintosource. Likeallsimpleresistances,itscurrent/voltagegraphisa 

straightline.Forthisreason,thetrioderegion(non-horizontal)portionofaJFET’scharacteristiccurveissometimesreferredtoastheohmicregion.Inthismodeofoperationwherethere


isn’tenoughdrain-to-sourcevoltagetobringdraincurrentuptotheregulatedpoint,thedrain 

currentisdirectlyproportionaltothedrain-to-sourcevoltage.Inacarefullydesignedcircuit, 

thisphenomenoncanbeusedtoanadvantage.Operatedinthisregionofthecurve,theJFET 

actslikeavoltage-controlledresistanceratherthanavoltage-controlledcurrentregulator,and 

theappropriatemodelforthetransistorisdifferent: 

G 

D 

S 

N-channel JFET diode-rheostat model 

(for saturation, or "ohmic," mode only!) 

G 

Hereandherealonetherheostat(variableresistor)modelofatransistorisaccurate. It 

mustberemembered,however,thatthismodelofthetransistorholdstrueonlyforanarrow 

rangeofitsoperation:whenitisextremelysaturated(farlessvoltageappliedbetweendrain 

andsourcethanwhatisneededtoachievefullregulatedcurrentthroughthedrain). The 

amountofresistance(measuredinohms)betweendrainandsourceinthismodeiscontrolled 

byhowmuchreverse-biasvoltageisappliedbetweengateandsource.Thelessgate-to-source 

voltage,thelessresistance(steeperlineongraph). 

BecauseJFETsarevoltage-controlledcurrentregulators(atleastwhenthey’reallowedto 

operateintheiractive),theirinherentamplificationfactorcannotbeexpressedasaunitless 

ratioaswithBJTs.Inotherwords,thereisno βratioforaJFET.Thisistrueforallvoltagecontrolledactivedevices,includingothertypesoffield-effecttransistorsandevenelectron 

tubes.Thereis,however,anexpressionofcontrolled(drain)currenttocontrolling(gate-source) 

voltage,anditiscalledtransconductance.ItsunitisSiemens,thesameunitforconductance 

(formerlyknownasthemho). 

Whythischoiceofunits?Becausetheequationtakesonthegeneralformofcurrent(output 

signal)dividedbyvoltage(inputsignal). 

D 

S

5.5. THECOMMON-SOURCEAMPLIFIER–PENDING 297 

g fs = ∆I D 

∆V GS 

Where, 

gfs = Transconductance in Siemens 

∆ID = Change in drain current 

∆VGS = Change in gate-source voltage 

Unfortunately,thetransconductancevalueforanyJFETisnotastablequantity:itvaries 

significantlywiththeamountofgate-to-sourcecontrolvoltageappliedtothetransistor.Aswe 

sawintheSPICEsimulations,thedraincurrentdoesnotchangeproportionallywithchanges 

ingate-sourcevoltage. Tocalculatedraincurrentforanygivengate-sourcevoltage,thereis 

anotherequationthatmaybeused.Itisobviouslynonlinearuponinspection(notethepower 

of2),reflectingthenonlinearbehaviorwe’vealreadyexperiencedinsimulation: 

I D = I DSS ( 1 - 

Where, 

• REVIEW: 

V GS 

V GS(cutoff) 

I D = Drain current 

) 2 

I DSS = Drain current with gate shorted to source 

V GS = Gate-to-source voltage 

V GS(cutoff) = Pinch-off gate-to-source voltage 

• Intheiractivemodes,JFETsregulatedraincurrentaccordingtotheamountofreversebiasvoltageappliedbetweengateandsource,muchlikeaBJTregulatescollectorcurrent 

accordingtobasecurrent. Themathematicalratiobetweendraincurrent(output)and 

gate-to-sourcevoltage(input)iscalledtransconductance,anditismeasuredinunitsof 

Siemens. 

• Therelationshipbetweengate-source(control)voltageanddrain(controlled)currentis 

nonlinear: asgate-sourcevoltageisdecreased,draincurrentincreasesexponentially. 

Thatistosay,thetransconductanceofaJFETisnotconstantoveritsrangeofoperation. 

• Intheirtrioderegion,JFETsregulatedrain-to-sourceresistanceaccordingtotheamount 

ofreverse-biasvoltageappliedbetweengateandsource. Inotherwords,theyactlike 

voltage-controlledresistances. 

5.5 Thecommon-sourceamplifier–PENDING 

***PENDING***


• REVIEW: 

• 

• 

• 

5.6 Thecommon-drainamplifier–PENDING 

***PENDING*** 

• REVIEW: 

• 

• 

• 

5.7 Thecommon-gateamplifier–PENDING 

***PENDING*** 

• REVIEW: 

• 

• 

• 

5.8 Biasingtechniques–PENDING 

***PENDING*** 

• REVIEW: 

• 

• 

•

5.9. TRANSISTORRATINGSANDPACKAGES–PENDING 299 

5.9 Transistorratingsandpackages–PENDING 

***PENDING*** 

• REVIEW: 

• 

• 

• 

5.10 JFETquirks–PENDING 

***PENDING*** 

• REVIEW: 

• 

• 

•

300 CHAPTER5. JUNCTIONFIELD-EFFECTTRANSISTORS

Chapter6 

INSULATED-GATE 

FIELD-EFFECTTRANSISTORS 

Contents 


6.2 Depletion-typeIGFETs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .302 

6.3 Enhancement-typeIGFETs–PENDING. . . . . . . . . . . . . . . . . . . . .311 

6.4 Active-modeoperation–PENDING . . . . . . . . . . . . . . . . . . . . . . .311 

6.5 Thecommon-sourceamplifier–PENDING...................312 

6.6 Thecommon-drainamplifier–PENDING. . . . . . . . . . . . . . . . . . . .312 

6.7 Thecommon-gateamplifier–PENDING . . . . . . . . . . . . . . . . . . . .312 

6.8 Biasingtechniques–PENDING..........................312 

6.9 Transistorratingsandpackages–PENDING . . . . . . . . . . . . . . . . .312 

6.10 IGFETquirks–PENDING . . . . . . . . . . . . . . . . . . . . . . . . . . . . .313 

6.11 MESFETs–PENDING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .313 

6.12 IGBTs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .313 



Aswasstatedinthelastchapter,thereismorethanonetypeoffield-effecttransistor. The 

junctionfield-effecttransistor,orJFET,usesvoltageappliedacrossareverse-biasedPNjunctiontocontrolthewidthofthatjunction’sdepletionregion,whichthencontrolstheconductivityofasemiconductorchannelthroughwhichthecontrolledcurrentmoves. 

Anothertype 

offield-effectdevice–theinsulatedgatefield-effecttransistor,orIGFET–exploitsasimilar 

principleofadepletionregioncontrollingconductivitythroughasemiconductorchannel,but 

itdiffersprimarilyfromtheJFETinthatthereisnodirectconnectionbetweenthegatelead 

301

302 CHAPTER6. INSULATED-GATEFIELD-EFFECTTRANSISTORS 

andthesemiconductormaterialitself. Rather,thegateleadisinsulatedfromthetransistor 

bodybyathinbarrier,hencetheterminsulatedgate.Thisinsulatingbarrieractslikethedielectriclayerofacapacitor,andallowsgate-to-sourcevoltagetoinfluencethedepletionregion 

electrostaticallyratherthanbydirectconnection. 

InadditiontoachoiceofN-channelversusP-channeldesign,IGFETscomeintwomajor 

types:enhancementanddepletion.ThedepletiontypeismorecloselyrelatedtotheJFET,so 

wewillbeginourstudyofIGFETswithit. 

6.2 Depletion-typeIGFETs 

Insulatedgatefield-effecttransistorsareunipolardevicesjustlikeJFETs: thatis,thecontrolledcurrentdoesnothavetocrossaPNjunction.ThereisaPNjunctioninsidethetransistor,butitsonlypurposeistoprovidethatnonconductingdepletionregionwhichisusedto 

restrictcurrentthroughthechannel. 

HereisadiagramofanN-channelIGFETofthe”depletion”type: 

gate 

drain 

source 

N-channel, D-type IGFET 

substrate 

gate 

insulating 

barrier 

drain 


N 

P 

source 

substrate 

NoticehowthesourceanddrainleadsconnecttoeitherendoftheNchannel,andhowthe 

gateleadattachestoametalplateseparatedfromthechannelbyathininsulatingbarrier. 

Thatbarrierissometimesmadefromsilicondioxide(theprimarychemicalcompoundfoundin 

sand),whichisaverygoodinsulator.DuetothisMetal(gate)-Oxide(barrier)-Semiconductor 

(channel)construction,theIGFETissometimesreferredtoasaMOSFET.Thereareother 

typesofIGFETconstruction,though,andso”IGFET”isthebetterdescriptorforthisgeneral 

classoftransistors. 

NoticealsohowtherearefourconnectionstotheIGFET.Inpractice,thesubstratelead 

isdirectlyconnectedtothesourceleadtomakethetwoelectricallycommon. Usually,this 

connectionismadeinternallytotheIGFET,eliminatingtheseparatesubstrateconnection, 

resultinginathree-terminaldevicewithaslightlydifferentschematicsymbol:

6.2. DEPLETION-TYPEIGFETS 303 

gate 

drain 

source 

N-channel, D-type IGFET 

gate 

insulating 

barrier 

drain 


N 

P 

source 

substrate 

Withsourceandsubstratecommontoeachother,theNandPlayersoftheIGFETendup 

beingdirectlyconnectedtoeachotherthroughtheoutsidewire.Thisconnectionpreventsany 

voltagefrombeingimpressedacrossthePNjunction. Asaresult,adepletionregionexists 

betweenthetwomaterials,butitcanneverbeexpandedorcollapsed.JFEToperationisbased 

ontheexpansionofthePNjunction’sdepletionregion,buthereintheIGFETthatcannot 

happen,soIGFEToperationmustbebasedonadifferenteffect. 

Indeeditis,forwhenacontrollingvoltageisappliedbetweengateandsource,theconductivityofthechannelischangedasaresultofthedepletionregionmovingclosertoorfurther 

awayfromthegate. Inotherwords,thechannel’seffectivewidthchangesjustaswiththe 

JFET,butthischangeinchannelwidthisduetodepletionregiondisplacementratherthan 

depletionregionexpansion. 

InanN-channelIGFET,acontrollingvoltageappliedpositive(+)tothegateandnegative 

(-)tothesourcehastheeffectofrepellingthePNjunction’sdepletionregion,expandingthe 

N-typechannelandincreasingconductivity: 

controlling 

voltage 

gate 

drain 

N 

source 

P 

R load 

Channel expands for greater conductivity 

Reversingthecontrollingvoltage’spolarityhastheoppositeeffect,attractingthedepletion 

regionandnarrowingthechannel,consequentlyreducingchannelconductivity:


controlling 

voltage 

gate 

drain 

N 

source 

P 

R load 

Channel narrows for less conductivity 

Theinsulatedgateallowsforcontrollingvoltagesofanypolaritywithoutdangerofforwardbiasingajunction,aswastheconcernwithJFETs. 

ThistypeofIGFET,althoughitscalled 

a”depletion-type,”actuallyhasthecapabilityofhavingitschanneleitherdepleted(channel 

narrowed)orenhanced(channelexpanded).Inputvoltagepolaritydetermineswhichwaythe 

channelwillbeinfluenced. 

Understandingwhichpolarityhaswhicheffectisnotasdifficultasitmayseem.Thekey 

istoconsiderthetypeofsemiconductordopingusedinthechannel(N-channelorP-channel?), 

thenrelatethatdopingtypetothesideoftheinputvoltagesourceconnectedtothechannelby 

meansofthesourcelead.IftheIGFETisanN-channelandtheinputvoltageisconnectedso 

thatthepositive(+)sideisonthegatewhilethenegative(-)sideisonthesource,thechannel 

willbeenhancedasextraelectronsbuilduponthechannelsideofthedielectricbarrier.Think, 

”negative(-)correlateswithN-type,thusenhancingthechannelwiththerighttypeofcharge 

carrier(electrons)andmakingitmoreconductive.”Conversely,iftheinputvoltageisconnected 

toanN-channelIGFETtheotherway,sothatnegative(-)connectstothegatewhilepositive 

(+)connectstothesource,freeelectronswillbe”robbed”fromthechannelasthegate-channel 

capacitorcharges,thusdepletingthechannelofmajoritychargecarriersandmakingitless 

conductive. 

ForP-channelIGFETs,theinputvoltagepolarityandchanneleffectsfollowthesamerule. 

Thatistosay,ittakesjusttheoppositepolarityasanN-channelIGFETtoeitherdepleteor 

enhance:


controlling 

voltage 

controlling 

voltage 

gate 

drain 

source 

P N 

R load 

Channel expands for greater conductivity 

gate 

drain 

P N 

source 

R load 

Channel narrows for less conductivity 

IllustratingtheproperbiasingpolaritieswithstandardIGFETsymbols:


Enhanced 

(more drain 

current) 

Depleted 

(less drain 

current) 

N-channel P-channel 

+ 

- 

Whenthereiszerovoltageappliedbetweengateandsource,theIGFETwillconductcurrentbetweensourceanddrain,butnotasmuchcurrentasitwouldifitwereenhancedby 

thepropergatevoltage.Thisplacesthedepletion-type,orsimplyD-type,IGFETinacategory 

ofitsowninthetransistorworld.Bipolarjunctiontransistorsarenormally-offdevices:with 

nobasecurrent,theyblockanycurrentfromgoingthroughthecollector.Junctionfield-effect 

transistorsarenormally-ondevices:withzeroappliedgate-to-sourcevoltage,theyallowmaximumdraincurrent(actually,youcancoaxaJFETintogreaterdraincurrentsbyapplying 

averysmallforward-biasvoltagebetweengateandsource,butthisshouldneverbedonein 

practiceforriskofdamagingitsfragilePNjunction).D-typeIGFETs,however,arenormally 

half-ondevices:withnogate-to-sourcevoltage,theirconductionlevelissomewherebetween 

cutoffandfullsaturation.Also,theywilltolerateappliedgate-sourcevoltagesofanypolarity, 

thePNjunctionbeingimmunefromdamageduetotheinsulatingbarrierandespeciallythe 

directconnectionbetweensourceandsubstratepreventinganyvoltagedifferentialacrossthe 

junction. 

Ironically,theconductionbehaviorofaD-typeIGFETisstrikinglysimilartothatofanelectrontubeofthetriode/tetrode/pentodevariety.Thesedeviceswerevoltage-controlledcurrent 

regulatorsthatlikewiseallowedcurrentthroughthemwithzerocontrollingvoltageapplied.A 

controllingvoltageofonepolarity(gridnegativeandcathodepositive)woulddiminishconductivitythroughthetubewhileavoltageoftheotherpolarity(gridpositiveandcathodenegative) 

wouldenhanceconductivity.Ifinditcuriousthatoneofthelatertransistordesignsinvented 

exhibitsthesamebasicpropertiesoftheveryfirstactive(electronic)device. 

AfewSPICEanalyseswilldemonstratethecurrent-regulatingbehaviorofD-typeIGFETs. 

First,atestwithzeroinputvoltage(gateshortedtosource)andthepowersupplysweptfrom 

0to50volts.Thegraphshowsdraincurrent: 

- 

+ 

- 

+ 

+ 

-


Q 1 

n-channel igfet characteristic curve 

m1 1 0 0 0 mod1 


v1 2 0 

.model mod1 nmos vto=-1 

.dc v1 0 50 2 


.end 

0 

0 

V ammeter 

1 2 

0 V 

Asexpectedforanytransistor,thecontrolledcurrentholdssteadyataregulatedvalueover 

awiderangeofpowersupplyvoltages.Inthiscase,thatregulatedpointis10 µA(1.000E-05). 

Nowlet’sseewhathappenswhenweapplyanegativevoltagetothegate(withreferenceto 

thesource)andsweepthepowersupplyoverthesamerangeof0to50volts: 

0 

V 1


3 

0.5 V 

Q 1 


m1 1 3 0 0 mod1 

vin 0 3 dc 0.5 


v1 2 0 


.dc v1 0 50 2 


.end 

0 

V ammeter 

1 2 

Notsurprisingly,thedraincurrentisnowregulatedatalowervalueof2.5 µA(downfrom 

10 µAwithzeroinputvoltage).Nowlet’sapplyaninputvoltageoftheotherpolarity,toenhance 

theIGFET: 

0 V 

0 

V 1


3 

0.5 V 

Q 1 


m1 1 3 0 0 mod1 

vin 3 0 dc 0.5 


v1 2 0 


.dc v1 0 50 2 


.end 

0 

V ammeter 

1 2 

Withthetransistorenhancedbythesmallcontrollingvoltage,thedraincurrentisnow 

atanincreasedvalueof22.5 µA(2.250E-05). Itshouldbeapparentfromthesethreesets 

ofvoltageandcurrentfiguresthattherelationshipofdraincurrenttogate-sourcevoltageis 

nonlinearjustasitwaswiththeJFET.With1/2voltofdepletingvoltage,thedraincurrentis 

2.5 µA;with0voltsinputthedraincurrentgoesupto10 µA;andwith1/2voltofenhancing 

voltage,thecurrentisat22.5 µA.Toobtainabetterunderstandingofthisnonlinearity,we 

0 V 

0 

V 1


canuseSPICEtoplotthedraincurrentoverarangeofinputvoltagevalues,sweepingfrom 

anegative(depleting)figuretoapositive(enhancing)figure,maintainingthepowersupply 

voltageofV1ataconstantvalue: 

n-channel igfet 

m1 1 3 0 0 mod1 

vin 3 0 


v1 2 0 dc 24 


.dc vin -1 1 0.1 


.end 

JustasitwaswithJFETs,thisinherentnonlinearityoftheIGFEThasthepotentialto 

causedistortioninanamplifiercircuit,astheinputsignalwillnotbereproducedwith100 

percentaccuracyattheoutput. Alsonoticethatagate-sourcevoltageofabout1voltinthe 

depletingdirectionisabletopinchoffthechannelsothatthereisvirtuallynodraincurrent. 

D-typeIGFETs,likeJFETs,haveacertainpinch-offvoltagerating. Thisratingvarieswith 

thepreciseuniqueofthetransistor,andmaynotbethesameasinoursimulationhere. 

PlottingasetofcharacteristiccurvesfortheIGFET,weseeapatternnotunlikethatofthe 

JFET:

6.3. ENHANCEMENT-TYPEIGFETS–PENDING 311 

• REVIEW: 

• 

• 

• 

I drain 





+0.5 V 

0 V 

-0.5 V 

6.3 Enhancement-typeIGFETs–PENDING 

• REVIEW: 

• 

• 

• 

6.4 Active-modeoperation–PENDING 

• REVIEW: 

• 

• 

•


6.5 Thecommon-sourceamplifier–PENDING 

• REVIEW: 

• 

• 

• 

6.6 Thecommon-drainamplifier–PENDING 

• REVIEW: 

• 

• 

• 

6.7 Thecommon-gateamplifier–PENDING 

• REVIEW: 

• 

• 

• 

6.8 Biasingtechniques–PENDING 

• REVIEW: 

• 

• 

• 

6.9 Transistorratingsandpackages–PENDING 

• REVIEW: 

• 

• 

•

6.10. IGFETQUIRKS–PENDING 313 

6.10 IGFETquirks–PENDING 

• REVIEW: 

• 

• 

• 

6.11 MESFETs–PENDING 

• REVIEW: 

• 

• 

• 

6.12 IGBTs 

Becauseoftheirinsulatedgates,IGFETsofalltypeshaveextremelyhighcurrentgain:there 

canbenosustainedgatecurrentifthereisnocontinuousgatecircuitinwhichelectronsmay 

continuallyflow. TheonlycurrentweseethroughthegateterminalofanIGFET,then,is 

whatevertransient(briefsurge)mayberequiredtochargethegate-channelcapacitanceand 

displacethedepletionregionasthetransistorswitchesfroman”on”statetoan”off”state,or 

viceversa. 

ThishighcurrentgainwouldatfirstseemtoplaceIGFETtechnologyatadecidedadvantageoverbipolartransistorsforthecontrolofverylargecurrents. 

Ifabipolarjunction 

transistorisusedtocontrolalargecollectorcurrent,theremustbeasubstantialbasecurrent 

sourcedorsunkbysomecontrolcircuitry,inaccordancewiththe βratio.Togiveanexample, 

inorderforapowerBJTwithaβof20toconductacollectorcurrentof100amps,theremustbe 

atleast5ampsofbasecurrent,asubstantialamountofcurrentinitselfforminiaturediscrete 

orintegratedcontrolcircuitrytohandle: 

Control 

circuitry 

5 A 

R load 

β = 20 

100 A 

105 A


Itwouldbenicefromthestandpointofcontrolcircuitrytohavepowertransistorswithhigh 

currentgain,sothatfarlesscurrentisneededforcontrolofloadcurrent. Ofcourse,wecan 

useDarlingtonpairtransistorstoincreasethecurrentgain,butthiskindofarrangementstill 

requiresfarmorecontrollingcurrentthananequivalentpowerIGFET: 

Control 

circuitry 

Control 

circuitry 

0.238 A 

≈ 0 A 

5 A 

R load 

β = 20 

R load 

100 A 

105 A 

100 A 

100 A 

Unfortunately,though,IGFETshaveproblemsoftheirowncontrollinghighcurrent:they 

typicallyexhibitgreaterdrain-to-sourcevoltagedropwhilesaturatedthanthecollector-toemittervoltagedropofasaturatedBJT.Thisgreatervoltagedropequatestohigherpowerdissipationforthesameamountofloadcurrent,limitingtheusefulnessofIGFETsashighpowerdevices.Althoughsomespecializeddesignssuchastheso-calledVMOStransistorhave 

beendesignedtominimizethisinherentdisadvantage,thebipolarjunctiontransistorisstill 

superiorinitsabilitytoswitchhighcurrents. 

AninterestingsolutiontothisdilemmaleveragesthebestfeaturesofIGFETswiththe 

bestoffeaturesofBJTs,inonedevicecalledanInsulated-GateBipolarTransistor,orIGBT. 

AlsoknownasanBipolar-modeMOSFET,aConductivity-ModulatedField-EffectTransistor 

(COMFET),orsimplyasanInsulated-GateTransistor(IGT),itisequivalenttoaDarlington 

pairofIGFETandBJT:

6.12. IGBTS 315 

Gate 

Insulated-Gate Bipolar Transistor (IGBT) 

(N-channel) 

Schematic symbols Equivalent circuit 

Collector 

Emitter 

Gate 

Collector 

Emitter 

Gate 

Collector 

Emitter 

Inessence,theIGFETcontrolsthebasecurrentofaBJT,whichhandlesthemainload 

currentbetweencollectorandemitter. Thisway,thereisextremelyhighcurrentgain(since 

theinsulatedgateoftheIGFETdrawspracticallynocurrentfromthecontrolcircuitry),but 

thecollector-to-emittervoltagedropduringfullconductionisaslowasthatofanordinaryBJT. 

OnedisadvantageoftheIGBToverastandardBJTisitsslowerturn-offtime. Forfast 

switchingandhighcurrent-handlingcapacity,itsdifficulttobeatthebipolarjunctiontransistor.Fasterturn-offtimesfortheIGBTmaybeachievedbycertainchangesindesign,butonly 

attheexpenseofahighersaturatedvoltagedropbetweencollectorandemitter.However,the 

IGBTprovidesagoodalternativetoIGFETsandBJTsforhigh-powercontrolapplications. 

• REVIEW: 

• 

• 

•

316 CHAPTER6. INSULATED-GATEFIELD-EFFECTTRANSISTORS

Chapter7 

THYRISTORS 

Contents 

7.1 Hysteresis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .317 

7.2 Gasdischargetubes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .318 

7.3 TheShockleyDiode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .322 

7.4 TheDIAC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .329 

7.5 TheSilicon-ControlledRectifier(SCR) . . . . . . . . . . . . . . . . . . . . .329 

7.6 TheTRIAC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .341 

7.7 Optothyristors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .344 

7.8 TheUnijunctionTransistor(UJT) . . . . . . . . . . . . . . . . . . . . . . . .344 

7.9 TheSilicon-ControlledSwitch(SCS). . . . . . . . . . . . . . . . . . . . . . .350 

7.10 Field-effect-controlledthyristors . . . . . . . . . . . . . . . . . . . . . . . . .352 

Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .354 

7.1 Hysteresis 

Thyristorsareaclassofsemiconductorcomponentsexhibitinghysteresis,thatpropertywhereby 

asystemfailstoreturntoitsoriginalstateaftersomecauseofstatechangehasbeenremoved. 

Averysimpleexampleofhysteresisisthemechanicalactionofatoggleswitch: whenthe 

leverispushed,itflipstooneoftwoextremestates(positions)andwillremainthereeven 

afterthesourceofmotionisremoved(afteryouremoveyourhandfromtheswitchlever).To 

illustratetheabsenceofhysteresis,considertheactionofa”momentary”pushbuttonswitch, 

whichreturnstoitsoriginalstateafterthebuttonisnolongerpressed:whenthestimulusis 

removed(yourhand),thesystem(switch)immediatelyandfullyreturnstoitspriorstatewith 

no”latching”behavior. 

Bipolar,junctionfield-effect,andinsulatedgatefield-effecttransistorsareallnon-hysteric 

devices.Thatis,thesedonotinherently”latch”intoastateafterbeingstimulatedbyavoltage 

orcurrentsignal. Foranygiveninputsignalatanygiventime,atransistorwillexhibita 

317

318 CHAPTER7. THYRISTORS 

predictableoutputresponseasdefinedbyitscharacteristiccurve. Thyristors,ontheother 

hand,aresemiconductordevicesthattendtostay”on”onceturnedon,andtendtostay”off” 

onceturnedoff. Amomentaryeventisabletoflipthesedevicesintoeithertheironoroff 

stateswherethesewillremainthatwayontheirown,evenafterthecauseofthestatechange 

istakenaway.Assuch,theseareusefulonlyason/offswitchingdevices–muchlikeatoggle 

switch–andcannotbeusedasanalogsignalamplifiers. 

Thyristorsareconstructedusingthesametechnologyasbipolarjunctiontransistors,and 

infactmaybeanalyzedascircuitscomprisedoftransistorpairs.Howthen,canahystericdevice(athyristor)bemadefromnon-hystericdevices(transistors)?Theanswertothisquestion 

ispositivefeedback,alsoknownasregenerativefeedback.Asyoushouldrecall,feedbackisthe 

conditionwhereapercentageoftheoutputsignalis”fedback”totheinputofanamplifying 

device. Negative,ordegenerative,feedbackresultsinadiminishingofvoltagegainwithincreasesinstability,linearity,andbandwidth.Positivefeedback,ontheotherhand,resultsin 

akindofinstabilitywheretheamplifier’soutputtendsto”saturate.”Inthecaseofthyristors, 

thissaturatingtendencyequatestothedevice”wanting”tostayononceturnedon,andoff 

onceturnedoff. 

Inthischapterwewillexploreseveraldifferentkindsofthyristors,mostofwhichstemfrom 

asingle,basictwo-transistorcorecircuit.Beforewedothat,though,itwouldbebeneficialto 

studythetechnologicalpredecessortothyristors:gasdischargetubes. 

7.2 Gasdischargetubes 

Ifyou’veeverwitnessedalightningstorm,you’veseenelectricalhysteresisinaction(and 

probablydidn’trealizewhatyouwereseeing). Theactionofstrongwindandrainaccumulatestremendousstaticelectricchargesbetweencloudandearth,andbetweencloudsaswell.Electricchargeimbalancesmanifestthemselvesashighvoltages,andwhentheelectricalresistanceofaircannolongerholdthesehighvoltagesatbay,hugesurgesofcurrenttravel 

betweenopposingpolesofelectricalchargewhichwecall”lightning.” 

Thebuildupofhighvoltagesbywindandrainisafairlycontinuousprocess,therateof 

chargeaccumulationincreasingundertheproperatmosphericconditions.However,lightning 

boltsareanythingbutcontinuous:theyexistasrelativelybriefsurgesratherthancontinuous 

discharges.Whyisthis?Whydon’tweseesoft,glowinglightningarcsinsteadofviolentlybrief 

lightningbolts?Theanswerliesinthenonlinear(andhysteric)resistanceofair. 

Underordinaryconditions,airhasanextremelyhighamountofresistance.Itissohigh,in 

fact,thatwetypicallytreatitsresistanceasinfiniteandelectricalconductionthroughtheair 

asnegligible.Thepresenceofwateranddustinairlowersitsresistancesome,butitisstillan 

insulatorformostpracticalpurposes.Whenenoughhighvoltageisappliedacrossadistance 

ofair,though,itselectricalpropertieschange:electronsbecome”stripped”fromtheirnormal 

positionsaroundtheirrespectiveatomsandareliberatedtoconstituteacurrent.Inthisstate, 

airisconsideredtobeionizedandiscalledaplasmaratherthanagas.Thisusageoftheword 

”plasma”isnottobeconfusedwiththemedicalterm(meaningthefluidportionofblood),but 

isafourthstateofmatter,theotherthreebeingsolid,liquid,andvapor(gas). Plasmaisa 

relativelygoodconductorofelectricity,itsspecificresistancebeingmuchlowerthanthatofthe 

samesubstanceinitsgaseousstate. 

Asanelectriccurrentmovesthroughtheplasma,thereisenergydissipatedintheplasma

7.2. GASDISCHARGETUBES 319 

intheformofheat,justascurrentthroughasolidresistordissipatesenergyintheformofheat. 

Inthecaseoflightning,thetemperaturesinvolvedareextremelyhigh.Hightemperaturesare 

alsosufficienttoconvertgaseousairintoaplasmaormaintainplasmainthatstatewithout 

thepresenceofhighvoltage. Asthevoltagebetweencloudandearth,orbetweencloudand 

cloud,decreasesasthechargeimbalanceisneutralizedbythecurrentofthelightningbolt,the 

heatdissipatedbytheboltmaintainstheairpathinaplasmastate,keepingitsresistancelow. 

Thelightningboltremainsaplasmauntilthevoltagedecreasestotoolowaleveltosustain 

enoughcurrenttodissipateenoughheat.Finally,theairreturnstoagaseousstateandstops 

conductingcurrent,thusallowingvoltagetobuilduponcemore. 

Notehowthroughoutthiscycle,theairexhibitshysteresis.Whennotconductingelectricity, 

ittendstoremainaninsulatoruntilvoltagebuildsuppastacriticalthresholdpoint. Then, 

onceitchangesstateandbecomesaplasma,ittendstoremainaconductoruntilvoltagefalls 

belowalowercriticalthresholdpoint.Once”turnedon”ittendstostay”on,”andonce”turned 

off”ittendstostay”off.”Thishysteresis,combinedwithasteadybuildupofvoltageduetothe 

electrostaticeffectsofwindandrain,explainstheactionoflightningasbriefbursts. 

Inelectronicterms,whatwehavehereintheactionoflightningisasimplerelaxationoscillator.Oscillatorsareelectroniccircuitsthatproduceanoscillating(AC)voltagefromasteady 

supplyofDCpower. Arelaxationoscillatorisonethatworksontheprincipleofacharging 

capacitorthatissuddenlydischargedeverytimeitsvoltagereachesacriticalthresholdvalue. 

Oneofthesimplestrelaxationoscillatorsinexistenceiscomprisedofthreecomponents(not 

countingtheDCpowersupply):aresistor,capacitor,andneonlampinFigure7.1. 

R 

C Neon lamp 

Figure7.1:Simplerelaxationoscillator 

Neonlampsarenothingmorethantwometalelectrodesinsideasealedglassbulb,separatedbytheneongasinside. 

Atroomtemperaturesandwithnoappliedvoltage,thelamp 

hasnearlyinfiniteresistance.However,onceacertainthresholdvoltageisexceeded(thisvoltagedependsonthegaspressureandgeometryofthelamp),theneongaswillbecomeionized 

(turnedintoaplasma)anditsresistancedramaticallyreduced. Ineffect,theneonlampexhibitsthesamecharacteristicsasairinalightningstorm,completewiththeemissionoflight 

asaresultofthedischarge,albeitonamuchsmallerscale. 

Thecapacitorintherelaxationoscillatorcircuitshownabovechargesataninverseexponentialratedeterminedbythesizeoftheresistor. 

Whenitsvoltagereachesthethreshold 

voltageofthelamp,thelampsuddenly”turnson”andquicklydischargesthecapacitortoa 

lowvoltagevalue.Oncedischarged,thelamp”turnsoff”andallowsthecapacitortobuildupa


chargeoncemore.Theresultisaseriesofbriefflashesoflightfromthelamp,therateofwhich 

isdictatedbybatteryvoltage,resistorresistance,capacitorcapacitance,andlampthreshold 

voltage. 

Whilegas-dischargelampsaremorecommonlyusedassourcesofillumination,theirhystericpropertieswereleveragedinslightlymoresophisticatedvariantsknownasthyratron 

tubes.Essentiallyagas-filledtriodetube(atriodebeingathree-elementvacuumelectrontube 

performingmuchasimilarfunctiontotheN-channel,D-typeIGFET),thethyratrontubecould 

beturnedonwithasmallcontrolvoltageappliedbetweengridandcathode,andturnedoffby 

reducingtheplate-to-cathodevoltage. 

control 

voltage 

+ 

- 

R load 

Thyratron 

Tube 

Figure7.2:Simplethyratroncontrolcircuit 

high voltage 

AC source 

Inessence,thyratrontubeswerecontrolledversionsofneonlampsbuiltspecificallyfor 

switchingcurrenttoaload.Thedotinsidethecircleoftheschematicsymbolindicatesagas 

fill,asopposedtothehardvacuumnormallyseeninotherelectrontubedesigns.Inthecircuit 

shownaboveinFigure7.2.thethyratrontubeallowscurrentthroughtheloadinonedirection 

(notethepolarityacrosstheloadresistor)whentriggeredbythesmallDCcontrolvoltage 

connectedbetweengridandcathode.Notethattheload’spowersourceisAC,whichprovidesa 

clueabouthowthethyratronturnsoffafteritsbeentriggeredon:sinceACvoltageperiodically 

passesthroughaconditionof0voltsbetweenhalf-cycles,thecurrentthroughanAC-powered 

loadmustalsoperiodicallyhalt. Thisbriefpauseofcurrentbetweenhalf-cyclesgivesthe 

tube’sgastimetocool,lettingitreturntoitsnormal”off”state.Conductionmayresumeonly 

ifenoughvoltageisappliedbytheACpowersource(someothertimeinthewave’scycle)and 

iftheDCcontrolvoltageallowsit. 

AnoscilloscopedisplayofloadvoltageinsuchacircuitwouldlooksomethinglikeFigure7.3. 

AstheACsupplyvoltageclimbsfromzerovoltstoitsfirstpeak,theloadvoltageremains 

atzero(noloadcurrent)untilthethresholdvoltageisreached.Atthatpoint,thetubeswitches 

”on”andbeginstoconduct,theloadvoltagenowfollowingtheACvoltagethroughtherestof 

thehalfcycle.Loadvoltageexists(andthusloadcurrent)evenwhentheACvoltagewaveform 

hasdroppedbelowthethresholdvalueofthetube.Thisishysteresisatwork:thetubestays 

initsconductivemodepastthepointwhereitfirstturnedon,continuingtoconductuntil 

therethesupplyvoltagedropsofftoalmostzerovolts. Becausethyratrontubesareone-way 

(diode)devices,novoltagedevelopsacrosstheloadthroughthenegativehalf-cycleofAC.In

7.2. GASDISCHARGETUBES 321 

Load voltage 

AC supply voltage 

Figure7.3:Thyratronwaveforms 

Threshold voltage 

practicalthyratroncircuits,multipletubesarrangedinsomeformoffull-waverectifiercircuit 

tofacilitatefull-waveDCpowertotheload. 

Thethyratrontubehasbeenappliedtoarelaxationoscillatorcircuit. [1]Thefrequency 

iscontrolledbyasmallDCvoltagebetweengridandcathode. (SeeFigure7.4)ThisvoltagecontrolledoscillatorisknownasaVCO.Relaxationoscillatorsproduceaverynon-sinusoidal 

output,andtheyexistmostlyasdemonstrationcircuits(asisthecasehere)orinapplications 

wheretheharmonicrichwaveformisdesirable.[2] 

R 

C 

Controlling 

voltage 

Figure7.4:Voltagecontrolledthyratronrelaxationoscillator 

Ispeakofthyratrontubesinthepasttenseforgoodreason:modernsemiconductorcomponentshaveobsoletedthyratrontubetechnologyforallbutafewveryspecialapplications. 

It 

isnocoincidencethatthewordthyristorbearssomuchsimilaritytothewordthyratron,for 

thisclassofsemiconductorcomponentsdoesmuchthesamething:usehystereticallyswitch 

currentonandoff.Itisthesemoderndevicesthatwenowturnourattentionto. 

• REVIEW: 

• Electricalhysteresis,thetendencyforacomponenttoremain”on”(conducting)afterit 

beginstoconductandtoremain”off”(nonconducting)afteritceasestoconduct,helpsto 

explainwhylightningboltsexistasmomentarysurgesofcurrentratherthancontinuous 

dischargesthroughtheair. 

• Simplegas-dischargetubessuchasneonlampsexhibitelectricalhysteresis.


• Moreadvancedgas-dischargetubeshavebeenmadewithcontrolelementssothattheir 

”turn-on”voltagecouldbeadjustedbyanexternalsignal. Themostcommonofthese 

tubeswascalledthethyratron. 

• Simpleoscillatorcircuitscalledrelaxationoscillatorsmaybecreatedwithnothingmore 

thanaresistor-capacitorchargingnetworkandahystereticdeviceconnectedacrossthe 

capacitor. 

7.3 TheShockleyDiode 

Ourexplorationofthyristorsbeginswithadevicecalledthefour-layerdiode,alsoknownas 

aPNPNdiode,oraShockleydiodeafteritsinventor,WilliamShockley. Thisisnottobe 

confusedwithaSchottkydiode,thattwo-layermetal-semiconductordeviceknownforitshigh 

switchingspeed.AcrudeillustrationoftheShockleydiode,oftenseenintextbooks,isafourlayersandwichofP-N-P-Nsemiconductormaterial,Figure7.5. 

P 

N 

P 

N 

Anode 

Cathode 

Figure7.5:Shockleyor4-layerdiode 

Unfortunately,thissimpleillustrationdoesnothingtoenlightenthevieweronhowitworks 

orwhy.Consideranalternativerenderingofthedevice’sconstructioninFigure7.6. 

P 

N 

P 

Anode 

N 

P 

N 

Cathode 

Figure7.6:TransistorequivalentofShockleydiode

7.3. THESHOCKLEYDIODE 323 

Shownlikethis,itappearstobeasetofinterconnectedbipolartransistors,onePNPand 

theotherNPN.Drawnusingstandardschematicsymbols,andrespectingthelayerdoping 

concentrationsnotshowninthelastimage,theShockleydiodelookslikethis(Figure7.7) 

Anode 

P 

N 

P 

N 

P 

N 

Anode 

Cathode Cathode 

Physical diagram Equivalent schematic Schematic symbol 

Figure7.7:Shockleydiode:physicaldiagram,equivalentschematicdiagram,andschematic 

symbol. 

Let’sconnectoneofthesedevicestoasourceofvariablevoltageandseewhathappens: 

(Figure7.8) 

Figure7.8:PoweredShockleydiodeequivalentcircuit. 

Withnovoltageapplied,ofcoursetherewillbenocurrent.Asvoltageisinitiallyincreased, 

therewillstillbenocurrentbecauseneithertransistorisabletoturnon:bothwillbeincutoff 

mode.Tounderstandwhythisis,considerwhatittakestoturnabipolarjunctiontransistor 

on: currentthroughthebase-emitterjunction. Asyoucanseeinthediagram,basecurrent 

throughthelowertransistoriscontrolledbytheuppertransistor,andthebasecurrentthrough 

theuppertransistoriscontrolledbythelowertransistor. Inotherwords,neithertransistor 

canturnonuntiltheothertransistorturnson. Whatwehavehere,invernacularterms,is 

knownasaCatch-22. 

SohowcanaShockleydiodeeverconductcurrent,ifitsconstituenttransistorsstubbornly 

maintainthemselvesinastateofcutoff? Theanswerliesinthebehaviorofrealtransistors 

asopposedtoidealtransistors.Anidealbipolartransistorwillneverconductcollectorcurrent 

ifnobasecurrentflows,nomatterhowmuchorlittlevoltageweapplybetweencollectorand


emitter.Realtransistors,ontheotherhand,havedefinitelimitstohowmuchcollector-emitter 

voltageeachcanwithstandbeforeonebreaksdownandconduct. Iftworealtransistorsare 

connectedinthisfashiontoformaShockleydiode,eachonewillconductifsufficientvoltageis 

appliedbythebatterybetweenanodeandcathodetocauseoneofthemtobreakdown.Once 

onetransistorbreaksdownandbeginstoconduct,itwillallowbasecurrentthroughtheother 

transistor,causingittoturnoninanormalfashion,whichthenallowsbasecurrentthrough 

thefirsttransistor.Theendresultisthatbothtransistorswillbesaturated,nowkeepingeach 

otherturnedoninsteadofoff. 

So,wecanforceaShockleydiodetoturnonbyapplyingsufficientvoltagebetweenanode 

andcathode.Aswehaveseen,thiswillinevitablycauseoneofthetransistorstoturnon,which 

thenturnstheothertransistoron,ultimately”latching”bothtransistorsonwhereeachwill 

tendtoremain.Buthowdowenowgetthetwotransistorstoturnoffagain?Eveniftheapplied 

voltageisreducedtoapointwellbelowwhatittooktogettheShockleydiodeconducting,it 

willremainconductingbecausebothtransistorsnowhavebasecurrenttomaintainregular, 

controlledconduction.Theanswertothisistoreducetheappliedvoltagetoamuchlowerpoint 

wheretoolittlecurrentflowstomaintaintransistorbias,atwhichpointoneofthetransistors 

willcutoff,whichthenhaltsbasecurrentthroughtheothertransistor,sealingbothtransistors 

inthe”off”stateaseachonewasbeforeanyvoltagewasappliedatall. 

IfwegraphthissequenceofeventsandplottheresultsonanI/Vgraph,thehysteresis 

isevident. First,wewillobservethecircuitastheDCvoltagesource(battery)issettozero 

voltage:(Figure7.9) 

Circuit 

current 

Applied voltage 

Figure7.9:Zeroappliedvoltage;zerocurrent 

Next,wewillsteadilyincreasetheDCvoltage.Currentthroughthecircuitisatornearly 

atzero,asthebreakdownlimithasnotbeenreachedforeithertransistor:(Figure7.10) 

Whenthevoltagebreakdownlimitofonetransistorisreached,itwillbegintoconduct 

collectorcurrenteventhoughnobasecurrenthasgonethroughityet. Normally,thissort 

oftreatmentwoulddestroyabipolarjunctiontransistor,butthePNPjunctionscomprisinga 

Shockleydiodeareengineeredtotakethiskindofabuse,similartothewayaZenerdiodeis 

builttohandlereversebreakdownwithoutsustainingdamage.ForthesakeofillustrationI’ll 

assumethelowertransistorbreaksdownfirst,sendingcurrentthroughthebaseoftheupper 

transistor:(Figure7.11) 

Astheuppertransistorreceivesbasecurrent,itturnsonasexpected. Thisactionallows 

thelowertransistortoconductnormally,thetwotransistors”sealing”themselvesinthe”on”


Circuit 

current 


Figure7.10:Someappliedvoltage;stillnocurrent 

Circuit 

current 


Figure7.11:Morevoltageapplied;lowertransistorbreaksdown


state.Fullcurrentisquicklyseeninthecircuit:(Figure7.12) 

Circuit 

current 


Figure7.12:Transistorsarenowfullyconducting. 

Thepositivefeedbackmentionedearlierinthischapterisclearlyevidenthere.Whenone 

transistorbreaksdown,itallowscurrentthroughthedevicestructure. Thiscurrentmaybe 

viewedasthe”output”signalofthedevice. Onceanoutputcurrentisestablished,itworks 

toholdbothtransistorsinsaturation,thusensuringthecontinuationofasubstantialoutput 

current.Inotherwords,anoutputcurrent”feedsback”positivelytotheinput(transistorbase 

current)tokeepbothtransistorsinthe”on”state,thusreinforcing(orregenerating)itself. 

Withbothtransistorsmaintainedinastateofsaturationwiththepresenceofamplebase 

current,eachwillcontinuetoconducteveniftheappliedvoltageisgreatlyreducedfromthe 

breakdownlevel.Theeffectofpositivefeedbackistokeepbothtransistorsinastateofsaturationdespitethelossofinputstimulus(theoriginal,highvoltageneededtobreakdownone 

transistorandcauseabasecurrentthroughtheothertransistor):(Figure7.13) 

Circuit 

current 


Figure7.13:Currentmaintainedevenwhenvoltageisreduced 

IftheDCvoltagesourceisturneddowntoofar,though,thecircuitwilleventuallyreacha 

pointwherethereisn’tenoughcurrenttosustainbothtransistorsinsaturation.Asonetransistorpasseslessandlesscollectorcurrent,itreducesthebasecurrentfortheothertransistor, 

thusreducingbasecurrentforthefirsttransistor. Theviciouscyclecontinuesrapidlyuntil 

bothtransistorsfallintocutoff:(Figure7.14) 

Here,positivefeedbackisagainatwork:thefactthatthecause/effectcyclebetweenboth


Circuit 

current 


Figure7.14:Ifvoltagedropstoolow,bothtransistorsshutoff. 

transistorsis”vicious”(adecreaseincurrentthroughoneworkstodecreasecurrentthrough 

theother,furtherdecreasingcurrentthroughthefirsttransistor)indicatesapositiverelationshipbetweenoutput(controlledcurrent)andinput(controllingcurrentthroughthetransistors’ 

bases). 

Theresultingcurveonthegraphisclassicallyhysteretic:astheinputsignal(voltage)is 

increasedanddecreased,theoutput(current)doesnotfollowthesamepathgoingdownasit 

didgoingup:(Figure7.15) 

Circuit 

current 


Figure7.15:Hystereticcurve 

Putinsimpleterms,theShockleydiodetendstostayononceitsturnedon,andstayoff 

onceitsturnedoff. No”in-between”or”active”modeinitsoperation:itisapurelyonoroff 

device,asareallthyristors. 

AfewspecialtermsapplytoShockleydiodesandallotherthyristordevicesbuiltuponthe 

Shockleydiodefoundation.Firstisthetermusedtodescribeits”on”state:latched.Theword 

”latch”isreminiscentofadoorlockmechanism,whichtendstokeepthedoorclosedonceithas 

beenpushedshut.Thetermfiringreferstotheinitiationofalatchedstate.TogetaShockley 

diodetolatch,theappliedvoltagemustbeincreaseduntilbreakoverisattained.Thoughthis 

actionisbestdescribedastransistorbreakdown,thetermbreakoverisusedinsteadbecause 

theresultisapairoftransistorsinmutualsaturationratherthandestructionofthetransistor. 

AlatchedShockleydiodeisre-setbackintoitsnonconductingstatebyreducingcurrent 

throughituntillow-currentdropoutoccurs. 

NotethatShockleydiodesmaybefiredinawayotherthanbreakover: excessivevoltage


rise,ordv/dt. Iftheappliedvoltageacrossthediodeincreasesatahighrateofchange,it 

maytrigger. Thisisabletocauselatching(turningon)ofthediodeduetoinherentjunction 

capacitanceswithinthetransistors.Capacitors,asyoumayrecall,opposechangesinvoltage 

bydrawingorsupplyingcurrent. IftheappliedvoltageacrossaShockleydioderisesattoo 

fastarate,thosetinycapacitanceswilldrawenoughcurrentduringthattimetoactivatethe 

transistorpair,turningthembothon.Usually,thisformoflatchingisundesirable,andcanbe 

minimizedbyfilteringhigh-frequency(fastvoltagerises)fromthediodewithseriesinductors 

andparallelresistor-capacitornetworkscalledsnubbers:(Figure7.16) 

Shockley 

diode 

Series inductor 

RC "snubber" 

Figure7.16: Boththeseriesinductorandparallelresistor-capacitor“snubber”circuithelp 

minimizetheShockleydiode’sexposuretoexcessivelyrisingvoltage. 

ThevoltageriselimitofaShockleydiodeisreferredtoasthecriticalrateofvoltagerise. 

Manufacturersusuallyprovidethisspecificationforthedevicestheysell. 

• REVIEW: 

• Shockleydiodesarefour-layerPNPNsemiconductordevices. Thesebehaveasapairof 

interconnectedPNPandNPNtransistors. 

• Likeallthyristors,Shockleydiodestendtostayononceturnedon(latched),andstayoff 

onceturnedoff. 

• TolatchaShockleydiodeexceedtheanode-to-cathodebreakovervoltage,orexceedthe 

anode-to-cathodecriticalrateofvoltagerise. 

• TocauseaShockleydiodetostopconducting,reducethecurrentgoingthroughittoa 

levelbelowitslow-currentdropoutthreshold.

7.4. THEDIAC 329 

7.4 TheDIAC 

Likealldiodes,Shockleydiodesareunidirectionaldevices;thatis,theseonlyconductcurrent 

inonedirection.Ifbidirectional(AC)operationisdesired,twoShockleydiodesmaybejoined 

inparallelfacingdifferentdirectionstoformanewkindofthyristor,theDIAC:(Figure7.17) 

DIAC equivalent circuit DIAC schematic symbol 

Figure7.17:TheDIAC 

ADIACoperatedwithaDCvoltageacrossitbehavesexactlythesameasaShockleydiode. 

WithAC,however,thebehaviorisdifferentfromwhatonemightexpect.Becausealternating 

currentrepeatedlyreversesdirection,DIACswillnotstaylatchedlongerthanone-halfcycle.If 

aDIACbecomeslatched,itwillcontinuetoconductcurrentonlyaslongasvoltageisavailable 

topushenoughcurrentinthatdirection. WhentheACpolarityreverses,asitmusttwice 

percycle,theDIACwilldropoutduetoinsufficientcurrent,necessitatinganotherbreakover 

beforeitconductsagain.TheresultisthecurrentwaveforminFigure7.18. 

DIAC current 


Figure7.18:DIACwaveforms 

Breakover voltage 


DIACsarealmostneverusedalone,butinconjunctionwithotherthyristordevices. 

7.5 TheSilicon-ControlledRectifier(SCR) 

Shockleydiodesarecuriousdevices,butratherlimitedinapplication. Theirusefulnessmay 

beexpanded,however,byequippingthemwithanothermeansoflatching. Indoingso,each 

becomestrueamplifyingdevices(ifonlyinanon/offmode),andwerefertotheseassiliconcontrolledrectifiers,orSCRs.


TheprogressionfromShockleydiodetoSCRisachievedwithonesmalladdition,actually 

nothingmorethanathirdwireconnectiontotheexistingPNPNstructure:(Figure7.19) 

Anode 

Gate 

P 

N 

P 

N 

P 

N 

Anode 

Gate 


Gate 

Anode 

Cathode 


Figure7.19:TheSilicon-ControlledRectifier(SCR) 

IfanSCR’sgateisleftfloating(disconnected),itbehavesexactlyasaShockleydiode. It 

maybelatchedbybreakovervoltageorbyexceedingthecriticalrateofvoltagerisebetween 

anodeandcathode,justaswiththeShockleydiode. Dropoutisaccomplishedbyreducing 

currentuntiloneorbothinternaltransistorsfallintocutoffmode,alsoliketheShockleydiode. 

However,becausethegateterminalconnectsdirectlytothebaseofthelowertransistor,it 

maybeusedasanalternativemeanstolatchtheSCR.Byapplyingasmallvoltagebetween 

gateandcathode,thelowertransistorwillbeforcedonbytheresultingbasecurrent,which 

willcausetheuppertransistortoconduct,whichthensuppliesthelowertransistor’sbase 

withcurrentsothatitnolongerneedstobeactivatedbyagatevoltage. Thenecessarygate 

currenttoinitiatelatch-up,ofcourse,willbemuchlowerthanthecurrentthroughtheSCR 

fromcathodetoanode,sotheSCRdoesachieveameasureofamplification. 

ThismethodofsecuringSCRconductioniscalledtriggering,anditisbyfarthemostcommonwaythatSCRsarelatchedinactualpractice. 

Infact,SCRsareusuallychosensothat 

theirbreakovervoltageisfarbeyondthegreatestvoltageexpectedtobeexperiencedfromthe 

powersource,sothatitcanbeturnedononlybyanintentionalvoltagepulseappliedtothe 

gate. 

ItshouldbementionedthatSCRsmaysometimesbeturnedoffbydirectlyshortingtheir 

gateandcathodeterminalstogether,orby”reverse-triggering”thegatewithanegativevoltage 

(inreferencetothecathode),sothatthelowertransistorisforcedintocutoff. Isaythisis 

”sometimes”possiblebecauseitinvolvesshuntingalloftheuppertransistor’scollectorcurrent 

pastthelowertransistor’sbase. Thiscurrentmaybesubstantial,makingtriggeredshut-off 

ofanSCRdifficultatbest.AvariationoftheSCR,calledaGate-Turn-Offthyristor,orGTO, 

makesthistaskeasier.ButevenwithaGTO,thegatecurrentrequiredtoturnitoffmaybe 

asmuchas20%oftheanode(load)current!TheschematicsymbolforaGTOisshowninthe 

followingillustration:(Figure7.20) 

SCRsandGTOssharethesameequivalentschematics(twotransistorsconnectedina 

positive-feedbackfashion),theonlydifferencesbeingdetailsofconstructiondesignedtogrant 

theNPNtransistoragreater βthanthePNP.Thisallowsasmallergatecurrent(forwardor 

reverse)toexertagreaterdegreeofcontroloverconductionfromcathodetoanode,withthe 

PNPtransistor’slatchedstatebeingmoredependentupontheNPN’sthanviceversa. The

7.5. THESILICON-CONTROLLEDRECTIFIER(SCR) 331 

Anode 

Gate 

Cathode 

Figure7.20:TheGateTurn-Offthyristor(GTO) 

Gate-Turn-OffthyristorisalsoknownbythenameofGate-ControlledSwitch,orGCS. 

ArudimentarytestofSCRfunction,oratleastterminalidentification,maybeperformed 

withanohmmeter.BecausetheinternalconnectionbetweengateandcathodeisasinglePN 

junction,ametershouldindicatecontinuitybetweentheseterminalswiththeredtestleadon 

thegateandtheblacktestleadonthecathodelikethis:(Figure7.21) 

V A 

V 

A 

OFF 

COM 

A 

gate 

cathode 

Figure7.21:RudimentarytestofSCR 

AllothercontinuitymeasurementsperformedonanSCRwillshow”open”(”OL”onsome 

digitalmultimeterdisplays). Itmustbeunderstoodthatthistestisverycrudeanddoesnot 

constituteacomprehensiveassessmentoftheSCR.ItispossibleforanSCRtogivegood 

ohmmeterindicationsandstillbedefective. Ultimately,theonlywaytotestanSCRisto 

subjectittoaloadcurrent. 

Ifyouareusingamultimeterwitha”diodecheck”function,thegate-to-cathodejunction 

voltageindicationyougetmayormaynotcorrespondtowhat’sexpectedofasiliconPNjunction(approximately0.7volts). 

Insomecases,youwillreadamuchlowerjunctionvoltage: 

merehundredthsofavolt.Thisisduetoaninternalresistorconnectedbetweenthegateand 

cathodeincorporatedwithinsomeSCRs.ThisresistorisaddedtomaketheSCRlesssusceptibletofalsetriggeringbyspuriousvoltagespikes,fromcircuit”noise”orfromstaticelectric 

discharge. Inotherwords,havingaresistorconnectedacrossthegate-cathodejunctionrequiresthatastrongtriggeringsignal(substantialcurrent)beappliedtolatchtheSCR.This


featureisoftenfoundinlargerSCRs,notonsmallSCRs.BearinmindthatanSCRwithan 

internalresistorconnectedbetweengateandcathodewillindicatecontinuityinbothdirections 

betweenthosetwoterminals:(Figure7.22) 

Gate 

Gate-to-Cathode 

resistor 

Anode 

Cathode 

Figure7.22:LargerSCRshavegatetocathoderesistor. 

”Normal”SCRs,lackingthisinternalresistor,aresometimesreferredtoassensitivegate 

SCRsduetotheirabilitytobetriggeredbytheslightestpositivegatesignal. 

ThetestcircuitforanSCRisbothpracticalasadiagnostictoolforcheckingsuspectedSCRs 

andalsoanexcellentaidtounderstandingbasicSCRoperation.ADCvoltagesourceisused 

forpoweringthecircuit,andtwopushbuttonswitchesareusedtolatchandunlatchtheSCR, 

respectively:(Figure7.23) 

off 

on 

SCR under 

test 

Figure7.23:SCRtestingcircuit 

Actuatingthenormally-open”on”pushbuttonswitchconnectsthegatetotheanode,allowingcurrentfromthenegativeterminalofthebattery,throughthecathode-gatePNjunction, 

throughtheswitch,throughtheloadresistor,andbacktothebattery.Thisgatecurrentshould 

forcetheSCRtolatchon,allowingcurrenttogodirectlyfromcathodetoanodewithoutfurther 

triggeringthroughthegate.Whenthe”on”pushbuttonisreleased,theloadshouldremainenergized. 

Pushingthenormally-closed”off”pushbuttonswitchbreaksthecircuit,forcingcurrent 

throughtheSCRtohalt,thusforcingittoturnoff(low-currentdropout).


IftheSCRfailstolatch,theproblemmaybewiththeloadandnottheSCR.Acertain 

minimumamountofloadcurrentisrequiredtoholdtheSCRlatchedinthe”on”state. This 

minimumcurrentleveliscalledtheholdingcurrent.Aloadwithtoogreataresistancevalue 

maynotdrawenoughcurrenttokeepanSCRlatchedwhengatecurrentceases,thusgiving 

thefalseimpressionofabad(unlatchable)SCRinthetestcircuit.Holdingcurrentvaluesfor 

differentSCRsshouldbeavailablefromthemanufacturers. Typicalholdingcurrentvalues 

rangefrom1milliampto50milliampsormoreforlargerunits. 

Forthetesttobefullycomprehensive,morethanthetriggeringactionneedstobetested. 

TheforwardbreakovervoltagelimitoftheSCRcouldbetestedbyincreasingtheDCvoltage 

supply(withnopushbuttonsactuated)untiltheSCRlatchesallonitsown. Bewarethat 

abreakovertestmayrequireveryhighvoltage: manypowerSCRshavebreakovervoltage 

ratingsof600voltsormore!Also,ifapulsevoltagegeneratorisavailable,thecriticalrateof 

voltagerisefortheSCRcouldbetestedinthesameway:subjectittopulsingsupplyvoltages 

ofdifferentV/timerateswithnopushbuttonswitchesactuatedandseewhenitlatches. 

Inthissimpleform,theSCRtestcircuitcouldsufficeasastart/stopcontrolcircuitforaDC 

motor,lamp,orotherpracticalload:(Figure7.24) 

Motor 

off 

on 

SCR under 

test 

Figure7.24:DCmotorstart/stopcontrolcircuit 

AnotherpracticalusefortheSCRinaDCcircuitisasacrowbardeviceforovervoltage 

protection. A”crowbar”circuitconsistsofanSCRplacedinparallelwiththeoutputofa 

DCpowersupply,forplacingadirectshort-circuitontheoutputofthatsupplytoprevent 

excessivevoltagefromreachingtheload.DamagetotheSCRandpowersupplyisprevented 

bythejudiciousplacementofafuseorsubstantialseriesresistanceaheadoftheSCRtolimit 

short-circuitcurrent:(Figure7.25) 

SomedeviceorcircuitsensingtheoutputvoltagewillbeconnectedtothegateoftheSCR, 

sothatwhenanovervoltageconditionoccurs,voltagewillbeappliedbetweenthegateand 

cathode,triggeringtheSCRandforcingthefusetoblow.Theeffectwillbeapproximatelythe 

sameasdroppingasolidsteelcrowbardirectlyacrosstheoutputterminalsofthepowersupply, 

hencethenameofthecircuit. 

MostapplicationsoftheSCRareforACpowercontrol,despitethefactthatSCRsareinherentlyDC(unidirectional)devices.Ifbidirectionalcircuitcurrentisrequired,multipleSCRs 

maybeused,withoneormorefacingeachdirectiontohandlecurrentthroughbothhalf-cycles 

oftheACwave. TheprimaryreasonSCRsareusedatallforACpowercontrolapplications 

istheuniqueresponseofathyristortoanalternatingcurrent.Aswesaw,thethyratrontube 

(theelectrontubeversionoftheSCR)andtheDIAC,ahystereticdevicetriggeredonduringa


AC 

power 

source 

Transformer 

Rectifier 

Filter 

Fuse 

Load 

Crowbar 

(triggering circuit 

omitted for simplicity) 

Figure7.25:CrowbarcircuitusedinDCpowersupply 

portionofanAChalf-cyclewilllatchandremainonthroughouttheremainderofthehalf-cycle 

untiltheACcurrentdecreasestozero,asitmusttobeginthenexthalf-cycle.Justpriortothe 

zero-crossoverpointofthecurrentwaveform,thethyristorwillturnoffduetoinsufficientcurrent(thisbehaviorisalsoknownasnaturalcommutation)andmustbefiredagainduringthe 

nextcycle.Theresultisacircuitcurrentequivalenttoa”choppedup”sinewave.Forreview, 

hereisthegraphofaDIAC’sresponsetoanACvoltagewhosepeakexceedsthebreakover 

voltageoftheDIAC:(Figure7.26) 

DIAC current 


Figure7.26:DIACbidirectionalresponse 



WiththeDIAC,thatbreakovervoltagelimitwasafixedquantity.WiththeSCR,wehave 

controloverexactlywhenthedevicebecomeslatchedbytriggeringthegateatanypointin 

timealongthewaveform. ByconnectingasuitablecontrolcircuittothegateofanSCR,we 

can”chop”thesinewaveatanypointtoallowfortime-proportionedpowercontroltoaload. 

TakethecircuitinFigure7.27asanexample. Here,anSCRispositionedinacircuitto 

controlpowertoaloadfromanACsource. 

Beingaunidirectional(one-way)device,atmostwecanonlydeliverhalf-wavepowerto 

theload,inthehalf-cycleofACwherethesupplyvoltagepolarityispositiveonthetopand 

negativeonthebottom. However,fordemonstratingthebasicconceptoftime-proportional 

control,thissimplecircuitisbetterthanonecontrollingfull-wavepower(whichwouldrequire 

twoSCRs).


AC 

source 

Load 

SCR 

Figure7.27:SCRcontrolofACpower 

Withnotriggeringtothegate,andtheACsourcevoltagewellbelowtheSCR’sbreakover 

voltagerating,theSCRwillneverturnon. ConnectingtheSCRgatetotheanodethrough 

astandardrectifyingdiode(topreventreversecurrentthroughthegateintheeventofthe 

SCRcontainingabuilt-ingate-cathoderesistor),willallowtheSCRtobetriggeredalmost 

immediatelyatthebeginningofeverypositivehalf-cycle:(Figure7.28) 

AC 

source 

AC source voltage 

Load 

Load current 

Figure7.28: Gateconnecteddirectlytoanodethroughadiode; nearlycompletehalf-wave 

currentthroughload. 

WecandelaythetriggeringoftheSCR,however,byinsertingsomeresistanceintothe 

gatecircuit,thusincreasingtheamountofvoltagedroprequiredbeforeenoughgatecurrent 

triggerstheSCR.Inotherwords,ifwemakeitharderforelectronstoflowthroughthegateby 

addingaresistance,theACvoltagewillhavetoreachahigherpointinitscyclebeforethere 

willbeenoughgatecurrenttoturntheSCRon.TheresultisinFigure7.29. 

Withthehalf-sinewavechoppeduptoagreaterdegreebydelayedtriggeringoftheSCR, 

theloadreceiveslessaveragepower(powerisdeliveredforlesstimethroughoutacycle).By 

makingtheseriesgateresistorvariable,wecanmakeadjustmentstothetime-proportioned 

power:(Figure7.30) 

Unfortunately,thiscontrolschemehasasignificantlimitation. InusingtheACsource 

waveformforourSCRtriggeringsignal,welimitcontroltothefirsthalfofthewaveform’s 

half-cycle.Inotherwords,itisnotpossibleforustowaituntilafterthewave’speaktotrigger 

theSCR.ThismeanswecanturndownthepoweronlytothepointwheretheSCRturnsonat


AC 

source 

AC source voltage 

Load 

Load current 

Figure7.29:Resistanceinsertedingatecircuit;lessthanhalf-wavecurrentthroughload. 

AC 

source 

Load 

trigger 

threshold 

Figure7.30: Increasingtheresistanceraisesthethresholdlevel,causinglesspowertobe 

deliveredtotheload.Decreasingtheresistancelowersthethresholdlevel,causingmorepower 

tobedeliveredtotheload.


theverypeakofthewave:(Figure7.31) 

AC 

source 

Load 

Figure7.31:Circuitatminimumpowersetting 

trigger 

threshold 

Raisingthetriggerthresholdanymorewillcausethecircuittonottriggeratall,sincenot 

eventhepeakoftheACpowervoltagewillbeenoughtotriggertheSCR.Theresultwillbeno 

powertotheload. 

Aningenioussolutiontothiscontroldilemmaisfoundintheadditionofaphase-shifting 

capacitortothecircuit:(Figure7.32) 

AC 

source 

Capacitor voltage 

Load 

Figure7.32:Additionofaphase-shiftingcapacitortothecircuit 

Thesmallerwaveformshownonthegraphisvoltageacrossthecapacitor.Forthesakeof 

illustratingthephaseshift,I’massumingaconditionofmaximumcontrolresistancewherethe 

SCRisnottriggeringatallwithnoloadcurrent,saveforwhatlittlecurrentgoesthroughthe 

controlresistorandcapacitor.Thiscapacitorvoltagewillbephase-shiftedanywherefrom0 o to 

90 o laggingbehindthepowersourceACwaveform.Whenthisphase-shiftedvoltagereachesa


highenoughlevel,theSCRwilltrigger. 

WithenoughvoltageacrossthecapacitortoperiodicallytriggertheSCR,theresultingload 

currentwaveformwilllooksomethinglikeFigure7.33) 

AC 

source 

Capacitor voltage 

Load 

load 

current 

trigger 

threshold 

Figure7.33:Phase-shiftedsignaltriggersSCRintoconduction. 

BecausethecapacitorwaveformisstillrisingafterthemainACpowerwaveformhas 

reacheditspeak,itbecomespossibletotriggertheSCRatathresholdlevelbeyondthatpeak, 

thuschoppingtheloadcurrentwavefurtherthanitwaspossiblewiththesimplercircuit. 

Inreality,thecapacitorvoltagewaveformisabitmorecomplexthatwhatisshownhere,its 

sinusoidalshapedistortedeverytimetheSCRlatcheson.However,whatI’mtryingtoillustratehereisthedelayedtriggeringactiongainedwiththephase-shiftingRCnetwork;thus,a 

simplified,undistortedwaveformservesthepurposewell. 

SCRsmayalsobetriggered,or”fired,”bymorecomplexcircuits. Whilethecircuitpreviouslyshownissufficientforasimpleapplicationlikealampcontrol,largeindustrialmotor 

controlsoftenrelyonmoresophisticatedtriggeringmethods.Sometimes,pulsetransformers 

areusedtocoupleatriggeringcircuittothegateandcathodeofanSCRtoprovideelectrical 

isolationbetweenthetriggeringandpowercircuits:(Figure7.34) 

. . . 

to triggering 

circuit 

. . . 

pulse 

transformer 

SCR 

. . . 

to power 

circuit 

Figure7.34:Transformercouplingoftriggersignalprovidesisolation. 

WhenmultipleSCRsareusedtocontrolpower,theircathodesareoftennotelectricallycommon,makingitdifficulttoconnectasingletriggeringcircuittoallSCRsequally.Anexample 

. . .


ofthisisthecontrolledbridgerectifiershowninFigure7.35. 

SCR 1 

SCR 2 

SCR 4 

SCR 3 

Figure7.35:Controlledbridgerectifier 

Load 

Inanybridgerectifiercircuit,therectifyingdiodes(inthisexample,therectifyingSCRs) 

mustconductinoppositepairs.SCR1andSCR3mustbefiredsimultaneously,andSCR2and 

SCR4mustbefiredtogetherasapair.Asyouwillnotice,though,thesepairsofSCRsdonot 

sharethesamecathodeconnections,meaningthatitwouldnotworktosimplyparalleltheir 

respectivegateconnectionsandconnectasinglevoltagesourcetotriggerboth:(Figure7.36) 

SCR 1 

SCR 2 

SCR 4 

SCR 3 

Load 

triggering 

voltage 

(pulse voltage 

source) 

Figure7.36:ThisstrategywillnotworkfortriggeringSCR2andSCR4asapair. 

AlthoughthetriggeringvoltagesourceshownwilltriggerSCR4,itwillnottriggerSCR2 

properlybecausethetwothyristorsdonotshareacommoncathodeconnectiontoreference 

thattriggeringvoltage. Pulsetransformersconnectingthetwothyristorgatestoacommon 

triggeringvoltagesourcewillwork,however:(Figure7.37) 

BearinmindthatthiscircuitonlyshowsthegateconnectionsfortwooutofthefourSCRs. 

PulsetransformersandtriggeringsourcesforSCR1andSCR3,aswellasthedetailsofthe 

pulsesourcesthemselves,havebeenomittedforthesakeofsimplicity. 

Controlledbridgerectifiersarenotlimitedtosingle-phasedesigns.Inmostindustrialcontrolsystems,ACpowerisavailableinthree-phaseformformaximumefficiency,andsolid-state


SCR 1 

SCR 2 

SCR 4 pulse 

voltage 

source 

SCR 3 

Load 

Figure7.37:TransformercouplingofthegatesallowstriggeringofSCR2andSCR4. 

controlcircuitsarebuilttotakeadvantageofthat. Athree-phasecontrolledrectifiercircuit 

builtwithSCRs,withoutpulsetransformersortriggeringcircuitryshown,wouldlooklike 

Figure7.38. 

• REVIEW: 

3-phase source 

Controlled 

rectifier 

Figure7.38:Three-phasebridgeSCRcontrolofload 

+ 

Load 

- 

• ASilicon-ControlledRectifier,orSCR,isessentiallyaShockleydiodewithanextraterminaladded. 

Thisextraterminaliscalledthegate,anditisusedtotriggerthedevice 

intoconduction(latchit)bytheapplicationofasmallvoltage. 

• Totrigger,orfire,anSCR,voltagemustbeappliedbetweenthegateandcathode,positive 

tothegateandnegativetothecathode.WhentestinganSCR,amomentaryconnection 

betweenthegateandanodeissufficientinpolarity,intensity,anddurationtotriggerit. 

• SCRsmaybefiredbyintentionaltriggeringofthegateterminal,excessivevoltage(breakdown)betweenanodeandcathode,orexcessiverateofvoltagerisebetweenanodeand

7.6. THETRIAC 341 

cathode.SCRsmaybeturnedoffbyanodecurrentfallingbelowtheholdingcurrentvalue 

(low-currentdropout),orby”reverse-firing”thegate(applyinganegativevoltagetothe 

gate).Reverse-firingisonlysometimeseffective,andalwaysinvolveshighgatecurrent. 

• AvariantoftheSCR,calledaGate-Turn-Offthyristor(GTO),isspecificallydesignedto 

beturnedoffbymeansofreversetriggering.Eventhen,reversetriggeringrequiresfairly 

highcurrent:typically20%oftheanodecurrent. 

• SCRterminalsmaybeidentifiedbyacontinuitymeter:theonlytwoterminalsshowing 

anycontinuitybetweenthematallshouldbethegateandcathode. Gateandcathode 

terminalsconnecttoaPNjunctioninsidetheSCR,soacontinuitymetershouldobtain 

adiode-likereadingbetweenthesetwoterminalswiththered(+)leadonthegateand 

theblack(-)leadonthecathode.Beware,though,thatsomelargeSCRshaveaninternal 

resistorconnectedbetweengateandcathode,whichwillaffectanycontinuityreadings 

takenbyameter. 

• SCRsaretruerectifiers: theyonlyallowcurrentthroughtheminonedirection. This 

meanstheycannotbeusedaloneforfull-waveACpowercontrol. 

• IfthediodesinarectifiercircuitarereplacedbySCRs,youhavethemakingsofacontrolledrectifiercircuit,wherebyDCpowertoaloadmaybetime-proportionedbytriggeringtheSCRsatdifferentpointsalongtheACpowerwaveform. 

7.6 TheTRIAC 

SCRsareunidirectional(one-way)currentdevices,makingthemusefulforcontrollingDC 

only.IftwoSCRsarejoinedinback-to-backparallelfashionjustliketwoShockleydiodeswere 

joinedtogethertoformaDIAC,wehaveanewdeviceknownastheTRIAC:(Figure7.39) 

Gate 

Main Terminal 2 

(MT 2) 


(MT1) Main Terminal 2 

(MT 2) 

Gate 


(MT1) TRIAC equivalent circuit TRIAC schematic symbol 

Figure7.39:TheTRIACSCRequivalentand,TRIACschematicsymbol 

BecauseindividualSCRsaremoreflexibletouseinadvancedcontrolsystems,theseare 

morecommonlyseenincircuitslikemotordrives;TRIACsareusuallyseeninsimple,lowpowerapplicationslikehouseholddimmerswitches.Asimplelampdimmercircuitisshownin


Figure7.40,completewiththephase-shiftingresistor-capacitornetworknecessaryforafterpeakfiring. 

AC 

source 

Lamp 

Figure7.40:TRIACphase-controlofpower 

TRIACsarenotoriousfornotfiringsymmetrically.Thismeanstheseusuallywon’ttrigger 

attheexactsamegatevoltagelevelforonepolarityasfortheother.Generallyspeaking,this 

isundesirable,becauseunsymmetricalfiringresultsinacurrentwaveformwithagreatervarietyofharmonicfrequencies.Waveformsthataresymmetricalaboveandbelowtheiraverage 

centerlinesarecomprisedofonlyodd-numberedharmonics. Unsymmetricalwaveforms,on 

theotherhand,containeven-numberedharmonics(whichmayormaynotbeaccompaniedby 

odd-numberedharmonicsaswell). 

Intheinterestofreducingtotalharmoniccontentinpowersystems,thefewerandless 

diversetheharmonics,thebetter–onemorereasonindividualSCRsarefavoredoverTRIACs 

forcomplex,high-powercontrolcircuits. OnewaytomaketheTRIAC’scurrentwaveform 

moresymmetricalistouseadeviceexternaltotheTRIACtotimethetriggeringpulse. A 

DIACplacedinserieswiththegatedoesafairjobofthis:(Figure7.41) 

AC 

source 

Lamp 

Figure7.41:DIACimprovessymmetryofcontrol 

DIACbreakovervoltagestendtobemuchmoresymmetrical(thesameinonepolarity 

astheother)thanTRIACtriggeringvoltagethresholds. SincetheDIACpreventsanygate 

currentuntilthetriggeringvoltagehasreachedacertain,repeatablelevelineitherdirection, 

thefiringpointoftheTRIACfromonehalf-cycletothenexttendstobemoreconsistent,and 

thewaveformmoresymmetricalaboveandbelowitscenterline. 

PracticallyallthecharacteristicsandratingsofSCRsapplyequallytoTRIACs,except 

thatTRIACsofcoursearebidirectional(canhandlecurrentinbothdirections). Notmuch 

moreneedstobesaidaboutthisdeviceexceptforanimportantcaveatconcerningitsterminal 

designations.

7.6. THETRIAC 343 

Fromtheequivalentcircuitdiagramshownearlier,onemightthinkthatmainterminals 

1and2wereinterchangeable. Thesearenot! AlthoughitishelpfultoimaginetheTRIAC 

asbeingcomposedoftwoSCRsjoinedtogether,itinfactisconstructedfromasinglepieceof 

semiconductingmaterial,appropriatelydopedandlayered.Theactualoperatingcharacteristicsmaydifferslightlyfromthatoftheequivalentmodel. 

Thisismademostevidentbycontrastingtwosimplecircuitdesigns,onethatworksand 

onethatdoesn’t.Thefollowingtwocircuitsareavariationofthelampdimmercircuitshown 

earlier,thephase-shiftingcapacitorandDIACremovedforsimplicity’ssake. Althoughthe 

resultingcircuitlacksthefinecontrolabilityofthemorecomplexversion(withcapacitorand 

DIAC),itdoesfunction:(Figure7.42) 

AC 

source 

Lamp 

Figure7.42:ThiscircuitwiththegatetoMT2doesfunction. 

SupposeweweretoswapthetwomainterminalsoftheTRIACaround. Accordingtothe 

equivalentcircuitdiagramshownearlierinthissection,theswapshouldmakenodifference. 

Thecircuitoughttowork:(Figure7.43) 

AC 

source 

Lamp 

Figure7.43:WiththegateswappedtoMT1,thiscircuitdoesnotfunction. 

However,ifthiscircuitisbuilt,itwillbefoundthatitdoesnotwork!Theloadwillreceive 

nopower,theTRIACrefusingtofireatall,nomatterhowloworhigharesistancevaluethe 

controlresistorissetto.ThekeytosuccessfullytriggeringaTRIACistomakesurethegate 

receivesitstriggeringcurrentfromthemainterminal2sideofthecircuit(themainterminal 

ontheoppositesideoftheTRIACsymbolfromthegateterminal). IdentificationoftheMT1 

andMT2terminalsmustbedoneviatheTRIAC’spartnumberwithreferencetoadatasheet 

orbook. 

• REVIEW: 

• ATRIACactsmuchliketwoSCRsconnectedback-to-backforbidirectional(AC)operation.


• TRIACcontrolsaremoreoftenseeninsimple,low-powercircuitsthancomplex,highpowercircuits.Inlargepowercontrolcircuits,multipleSCRstendtobefavored. 

• WhenusedtocontrolACpowertoaload,TRIACsareoftenaccompaniedbyDIACsconnectedinserieswiththeirgateterminals.TheDIAChelpstheTRIACfiremoresymmetrically(moreconsistentlyfromonepolaritytoanother). 

• Mainterminals1and2onaTRIACarenotinterchangeable. 

• TosuccessfullytriggeraTRIAC,gatecurrentmustcomefromthemainterminal2(MT2) 

sideofthecircuit! 

7.7 Optothyristors 

Likebipolartransistors,SCRsandTRIACsarealsomanufacturedaslight-sensitivedevices, 

theactionofimpinginglightreplacingthefunctionoftriggeringvoltage. 

Optically-controlledSCRsareoftenknownbytheacronymLASCR,orLightActivated 

SCR.Itssymbol,notsurprisingly,lookslikeFigure7.44. 

Light Activated SCR 

LASCR 

Figure7.44:LightactivatedSCR 

Optically-controlledTRIACsdon’treceivethehonorofhavingtheirownacronym,butinsteadarehumblyknownasopto-TRIACs.TheirschematicsymbolisshowninFigure7.45. 

Opto-TRIAC 

Figure7.45:Opto-TRIAC 

Optothyristors(ageneraltermforeithertheLASCRortheopto-TRIAC)arecommonly 

foundinsidesealed”optoisolator”modules. 

7.8 TheUnijunctionTransistor(UJT) 

Unijunctiontransistor:Althoughaunijunctiontransistorisnotathyristor,thisdevicecan 

triggerlargerthyristorswithapulseatbaseB1.Aunijunctiontransistoriscomposedofabar

7.8. THEUNIJUNCTIONTRANSISTOR(UJT) 345 

ofN-typesiliconhavingaP-typeconnectioninthemiddle.SeeFigure7.46(a).Theconnections 

attheendsofthebarareknownasbasesB1andB2;theP-typemid-pointistheemitter. 

Withtheemitterdisconnected,thetotalresistanceRBBO,adatasheetitem,isthesumofRB1 

andRB2asshowninFigure7.46(b).RBBOrangesfrom4-12kΩfordifferentdevicetypes.The 

intrinsicstandoffratio ηistheratioofRB1toRBBO. Itvariesfrom0.4to0.8fordifferent 

devices.TheschematicsymbolisFigure7.46(c) 

E 

B2 

P 

N 

B1 

(a) 

B2 

B1 

(b) 

R B2 

R B1 

R BB0 = R B1 + R B2 

η = 

η = 

R B1 

R B1 + R B2 

R B1 

R BB0 

Figure7.46:Unijunctiontransistor:(a)Construction,(b)Model,(c)Symbol 

TheUnijunctionemittercurrentvsvoltagecharacteristiccurve(Figure7.47(a))shows 

thatasVEincreases,currentIEincreasesupIP atthepeakpoint. Beyondthepeakpoint, 

currentincreasesasvoltagedecreasesinthenegativeresistanceregion.Thevoltagereachesa 

minimumatthevalleypoint.TheresistanceofRB1,thesaturationresistanceislowestatthe 

valleypoint. 

IPandIV,aredatasheetparameters;Fora2n2647,IPandIV are2µAand4mA,respectively.[5]VPisthevoltagedropacrossRB1plusa0.7Vdiodedrop;seeFigure7.47(b).VV 

is 

estimatedtobeapproximately10%ofVBB. 

TherelaxationoscillatorinFigure7.48isanapplicationoftheunijunctionoscillator. RE 

chargesCEuntilthepeakpoint. Theunijunctionemitterterminalhasnoeffectonthecapacitoruntilthispointisreached. 

Oncethecapacitorvoltage,VE,reachesthepeakvoltage 

pointVP,theloweredemitter-base1E-B1resistancequicklydischargesthecapacitor. Once 

thecapacitordischargesbelowthevalleypointVV,theE-RB1resistancerevertsbacktohigh 

resistance,andthecapacitorisfreetochargeagain. 

DuringcapacitordischargethroughtheE-B1saturationresistance,apulsemaybeseenon 

theexternalB1andB2loadresistors,Figure7.48.TheloadresistoratB1needstobelowto 

notaffectthedischargetime.TheexternalresistoratB2isoptional.Itmaybereplacedbya 

shortcircuit.Theapproximatefrequencyisgivenby1/f=T=RC.Amoreaccurateexpression 

forfrequencyisgiveninFigure7.48. 

ThechargingresistorREmustfallwithincertainlimits.Itmustbesmallenoughtoallow 

IPtoflowbasedontheVBBsupplylessVP.ItmustbelargeenoughtosupplyIVbasedonthe 

VBBsupplylessVV.[6]Theequationsandanexamplefora2n2647: 

E 

(c) 

B2 

B1


V E 

V P 

V V 

Peak 

point 

I P 

negative resistance 

Valley point 

I V 

(a) 

saturation 

I E 

R E 

(b) 

B2 

B1 

R B2 

0.7V 

+ - 

+ 

+ 

VBB ηVBB - 

RB1 - 

V P 

V P = 0.7 + ηV BB 

V V ≈ 0.10(V BB) 

Figure7.47:Unijunctiontransistor:(a)emittercharacteristiccurve,(b)modelforVP. 

f = 

R E 

100k 

C E 

10nF 

V BB 

E 

10V 

470Ω 

B2 

B1 

47Ω 

2n2647 R BBO = 4.7— 9.1k η=0.68—0.82 I V= 8mA I P=2µA 

1 

RC ln(1/(1- η)) 

= 

V RE 

V CE 

V RB1 

1 

(100k)(10nF) ln(1/(1- 0.75)) 

= 1.39kHz 

Figure7.48:Unijunctiontransistorrelaxationoscillatorandwaveforms.OscillatordrivesSCR. 

R E 

100k 

C E 

10nF 

V BB 

E 

10V 

470Ω 

B2 

B1


V P = 0.7 + ηV BB 

VBB - VV < RE < 

IV VBB - VP IP 2n2647 R BBO =4.7— 9.1k η=0.68—0.82 I V= 8mA I P=2µA 

V P = 0.7 + 0.75(10) = 8.2V 

V V = 0.10(V BB) V V = 0.10(10) = 1V 

10 - 1 

8mA 

1.125k 

< R E < 

10 - 8.2 

2µA 

< R E < 900k 

ProgrammableUnijunctionTransistor(PUT):Althoughtheunijunctiontransistoris 

listedasobsolete(readexpensiveifobtainable),theprogrammableunijunctiontransistoris 

aliveandwell.Itisinexpensiveandinproduction.Thoughitservesafunctionsimilartothe 

unijunctiontransistor,thePUTisathreeterminalthyristor. ThePUTsharesthefour-layer 

structuretypicalofthyristorsshowninFigure7.49.Notethatthegate,anN-typelayernear 

theanode,isknownasan“anodegate”. Moreover,thegateleadontheschematicsymbolis 

attachedtotheanodeendofthesymbol. 

V V 

V P 

V A 

I P IV 

I A 

Figure7.49:Programmableunijunctiontransistor:Characteristiccurve,internalconstruction, 


ThecharacteristiccurvefortheprogrammableunijunctiontransistorinFigure7.49issimilartothatoftheunijunctiontransistor. 

ThisisaplotofanodecurrentIAversusanode 

voltageVA. Thegateleadvoltagesets,programs,thepeakanodevoltageVP. Asanodecurrentinceases,voltageincreasesuptothepeakpoint.Thereafter,increasingcurrentresultsin 

decreasingvoltage,downtothevalleypoint. 

ThePUTequivalentoftheunijunctiontransistorisshowninFigure7.50. ExternalPUT 

resistorsR1andR2replaceunijunctiontransistorinternalresistorsRB1andRB2,respectively. 

Theseresistorsallowthecalculationoftheintrinsicstandoffratio η. 

Figure7.51showsthePUTversionoftheunijunctionrelaxationoscillatorFigure7.48. 

ResistorRchargesthecapacitoruntilthepeakpoint,Figure7.49,thenheavyconduction 

movestheoperatingpointdownthenegativeresistanceslopetothevalleypoint. Acurrent 

spikeflowsthroughthecathodeduringcapacitordischarge,developingavoltagespikeacross 

thecathoderesistors.Aftercapacitordischarge,theoperatingpointresetsbacktotheslopeup 

G 

A 

P 

N 

P 

N 

K 

G 

A 

K


E 

tothepeakpoint. 

B1 

Unijunction PUT equivalent 

R 

C 

B2 

B1 

E 

A 

K 

G 

B2 

R2 

V S 

R1 

R BB0 = R1 + R2 

η = 

R1 

R1 + R2 

V S = ηV BB 

V P = V T + V S 

Figure7.50:PUTequivalentofunijunctiontransistor 

V BB 

47Ω 

K 

10V 

V C 

V RK 

R1⋅R2 

RG = 

R1 + R2 

A G VG VP 

V RK 

R2 

R1 

Figure7.51:PUTrelaxationoscillator 

Problem: WhatistherangeofsuitablevaluesforRinFigure7.51,arelaxationoscillator? 

ThechargingresistormustbesmallenoughtosupplyenoughcurrenttoraisetheanodetoVP 

thepeakpoint(Figure7.49)whilechargingthecapacitor.OnceVPisreached,anodevoltage 

decreasesascurrentincreases(negativeresistance),whichmovestheoperatingpointtothe 

valley. ItisthejobofthecapacitortosupplythevalleycurrentIV. Onceitisdischarged, 

theoperatingpointresetsbacktotheupwardslopetothepeakpoint. Theresistormustbe 

largeenoughsothatitwillneversupplythehighvalleycurrentIP. Ifthechargingresistor 

evercouldsupplythatmuchcurrent,theresistorwouldsupplythevalleycurrentafterthe 

capacitorwasdischargedandtheoperatingpointwouldneverresetbacktothehighresistance 

conditiontotheleftofthepeakpoint. 

WeselectthesameVBB=10Vusedfortheunijunctiontransistorexample.Weselectvalues 

ofR1andR2sothat ηisabout2/3.Wecalculate ηandVS.TheparallelequivalentofR1,R2is 

RG,whichisonlyusedtomakeselectionsfromTable7.1.AlongwithVS=10,theclosestvalue 

0V


toour6.3,wefindVT=0.6V,inTable7.1andcalculateVP. 

R1 = 27k R2 = 16k VBB = 10V 

η = 

R1 

R1 + R2 

VS = ηVBB R1⋅R2 

RG = 

R1 + R2 

V P = V T + V S 

η = 

27 

27 + 16 

= 0.6279 

V S = 0.6279(10) = 6.279V 

27k⋅16k 

RG = = 10k 

27k + 16k 

For R G=10k and V S=10V, V T = 0.6V 

V P = 0.6 + 6.3 = 6.9V 

WealsofindIPandIV,thepeakandvalleycurrents,respectivelyinTable7.1.Westillneed 

VV,thevalleyvoltage. Weused10%ofVBB=1V,inthepreviousunijunctionexample. Consultingthedatasheet,wefindtheforwardvoltageVF=0.8VatIF=50mA.Thevalleycurrent 

IV=70µAismuchlessthanIF=50mA.Therefore,VV mustbelessthanVF=0.8V.Howmuch 

less?TobesafewesetVV=0V.Thiswillraisethelowerlimitontheresistorrangealittle. 

For RG=10k and VS=10V, IP = 4.0µA 

V V = 0.10(V BB) not used V V = 0V 

VBB - VV < RE < 

IV VBB - VP IP For R G=10k and V S=10V, I V = 70µA 

10 - 0 

70µA 

143k 

< R E < 

10 - 6.9 

4µA 

< R E < 755k 

ChoosingR>143kguaranteesthattheoperatingpointcanresetfromthevalleypointafter 

capacitordischarge.R


applicationofaPUTtriggeringanSCRisalsoshown. ThiscircuitneedsaVBBunfiltered 

supply(notshown)divideddownfromthebridgerectifiertoresettherelaxationoscillator 

aftereachpowerzerocrossing.Thevariableresistorshouldhaveaminimumresistorinseries 

withittopreventalowpotsettingfromhangingatthevalleypoint. 

R 

270k 

V BB 

C 

K 

3.7nF 

47Ω 

10V 

A G 

V RK 

R2 

16k 

V G 

R1 

27k 

V BB 

R 

270k 

A G 

C 

K 

33 PUT 

nF 

Figure7.52:PUTrelaxationoscillatorwithcomponentvalues.PUTdrivesSCRlampdimmer. 

PUTtimingcircuitsaresaidtobeusableto10kHz.Ifalinearrampisrequiredinsteadof 

anexponentialramp,replacethechargingresistorwithaconstantcurrentsourcesuchasa 

FETbasedconstantcurrentdiode.AsubstitutePUTmaybebuiltfromaPNPandNPNsilicon 

transistorasshownfortheSCSequivalentcircuitinFigure7.53byomittingthecathodegate 

andusingtheanodegate. 

• REVIEW: 

• Aunijunctiontransistorconsistsoftwobases(B1,B2)attachedtoaresistivebarofsilicon,andanemitterinthecenter.TheE-B1junctionhasnegativeresistanceproperties; 

itcanswitchbetweenhighandlowresistance. 

• APUT(programmableunijunctiontransistor)isa3-terminal4-layerthyristoractinglike 

aunijunctiontransistor.Anexternalresistornetwork“programs” η. 

• Theintrinsicstandoffratiois η=R1/(R1+R2)foraPUT;substituteRB1andRB2,respectively,foraunijunctiontransistor.Thetriggervoltageisdeterminedby 

η. 

• Unijunctiontransistorsandprogrammableunijunctiontransistorsareappliedtooscillators,timingcircuits,andthyristortriggering. 

R2 

16k 

V G 

R1 

27k 

SCR 

7.9 TheSilicon-ControlledSwitch(SCS) 

IfwetaketheequivalentcircuitforanSCRandaddanotherexternalterminal,connectedto 

thebaseofthetoptransistorandthecollectorofthebottomtransistor,wehaveadeviceknown 

asasilicon-controlled-switch,orSCS:(Figure7.53)

7.9. THESILICON-CONTROLLEDSWITCH(SCS) 351 

Anode 

Cathode 

Gate 

P 

N 

P 

N 

P 

N 

Anode 

Gate 

Anode 

Cathode 

Gate 


Anode 

Gate 

Anode 

Anode 

Cathode Gate 

Gate 

Cathode 


Figure7.53:TheSilicon-ControlledSwitch(SCS) 

Thisextraterminalallowsmorecontroltobeexertedoverthedevice,particularlyinthe 

modeofforcedcommutation,whereanexternalsignalforcesittoturnoffwhilethemain 

currentthroughthedevicehasnotyetfallenbelowtheholdingcurrentvalue. Notethatthe 

motorisintheanodegatecircuitinFigure7.54.Thisiscorrect,althoughitdoesn’tlookright. 

TheanodeleadisrequiredtoswitchtheSCSoff.Thereforethemotorcannotbeinserieswith 

theanode. 

+ 

− 

on 

R 1 

off 

Motor 

R 2 

SCS 

+ 

− 

on 

R 1 

off 

Motor 

R 2 

SCS 

Figure7.54:SCS:Motorstart/stopcircuit,equivalentcircuitwithtwotransistors. 

Whenthe”on”pushbuttonswitchisactuated,thevoltageappliedbetweenthecathodegate 

andthecathode,forward-biasesthelowertransistor’sbase-emitterjunction,andturningiton. 

ThetoptransistoroftheSCSisreadytoconduct,havingbeensuppliedwithacurrentpath 

fromitsemitterterminal(theSCS’sanodeterminal)throughresistorR2tothepositivesideof 

thepowersupply.AsinthecaseoftheSCR,bothtransistorsturnonandmaintaineachother 

inthe”on”mode.Whenthelowertransistorturnson,itconductsthemotor’sloadcurrent,and 

themotorstartsandruns. 

Themotormaybestoppedbyinterruptingthepowersupply,aswithanSCR,andthisis 

callednaturalcommutation. However,theSCSprovidesuswithanothermeansofturning


off: forcedcommutationbyshortingtheanodeterminaltothecathode. [3]Ifthisisdone 

(byactuatingthe”off”pushbuttonswitch),theuppertransistorwithintheSCSwillloseits 

emittercurrent,thushaltingcurrentthroughthebaseofthelowertransistor.Whenthelower 

transistorturnsoff,itbreaksthecircuitforbasecurrentthroughthetoptransistor(securing 

its”off”state),andthemotor(makingitstop).TheSCSwillremainintheoffconditionuntil 

suchtimethatthe”on”pushbuttonswitchisre-actuated. 

• REVIEW: 

• Asilicon-controlledswitch,orSCS,isessentiallyanSCRwithanextragateterminal. 

• Typically,theloadcurrentthroughanSCSiscarriedbytheanodegateandcathode 

terminals,withthecathodegateandanodeterminalssufficingascontrolleads. 

• AnSCSisturnedonbyapplyingapositivevoltagebetweenthecathodegateandcathode 

terminals. Itmaybeturnedoff(forcedcommutation)byapplyinganegativevoltage 

betweentheanodeandcathodeterminals,orsimplybyshortingthosetwoterminals 

together.Theanodeterminalmustbekeptpositivewithrespecttothecathodeinorder 

fortheSCStolatch. 

7.10 Field-effect-controlledthyristors 

Tworelativelyrecenttechnologiesdesignedtoreducethe”driving”(gatetriggercurrent)requirementsofclassicthyristordevicesaretheMOS-gatedthyristorandtheMOSControlled 

Thyristor,orMCT. 

TheMOS-gatedthyristorusesaMOSFETtoinitiateconductionthroughtheupper(PNP) 

transistorofastandardthyristorstructure,thustriggeringthedevice. SinceaMOSFETrequiresnegligiblecurrentto”drive”(causeittosaturate),thismakesthethyristorasawhole 

veryeasytotrigger:(Figure7.55) 

MOS-gated thyristor 

equivalent circuit 

Gate 

Cathode 

Anode 

Figure7.55:MOS-gatedthyristorequivalentcircuit 

GiventhefactthatordinarySCRsarequiteeasyto”drive”asitis,thepracticaladvantage 

ofusinganevenmoresensitivedevice(aMOSFET)toinitiatetriggeringisdebatable. Also,

7.10. FIELD-EFFECT-CONTROLLEDTHYRISTORS 353 

placingaMOSFETatthegateinputofthethyristornowmakesitimpossibletoturnitoffbya 

reverse-triggeringsignal.Onlylow-currentdropoutcanmakethisdevicestopconductingafter 

ithasbeenlatched. 

Adeviceofarguablygreatervaluewouldbeafully-controllablethyristor,wherebyasmall 

gatesignalcouldbothtriggerthethyristorandforceittoturnoff.Suchadevicedoesexist,and 

itiscalledtheMOSControlledThyristor,orMCT.ItusesapairofMOSFETsconnectedtoa 

commongateterminal,onetotriggerthethyristorandtheotherto”untrigger”it:(Figure7.56) 

MOS Controlled Thyristor 

(MCT) equivalent circuit 

Gate 

Cathode 

Anode 

Figure7.56:MOS-controlledthyristor(MCT)equivalentcircuit 

Apositivegatevoltage(withrespecttothecathode)turnsontheupper(N-channel)MOS- 

FET,allowingbasecurrentthroughtheupper(PNP)transistor,whichlatchesthetransistor 

pairinan”on”state.Oncebothtransistorsarefullylatched,therewillbelittlevoltagedropped 

betweenanodeandcathode,andthethyristorwillremainlatchedaslongasthecontrolled 

currentexceedstheminimum(holding)currentvalue. However,ifanegativegatevoltageis 

applied(withrespecttotheanode,whichisatnearlythesamevoltageasthecathodeinthe 

latchedstate),thelowerMOSFETwillturnonand”short”betweenthelower(NPN)transistor’sbaseandemitterterminals,thusforcingitintocutoff.OncetheNPNtransistorcutsoff, 

thePNPtransistorwilldropoutofconduction,andthewholethyristorturnsoff.Gatevoltage 

hasfullcontroloverconductionthroughtheMCT:toturnitonandtoturnitoff. 

Thisdeviceisstillathyristor,though.Ifzerovoltageisappliedbetweengateandcathode, 

neitherMOSFETwillturnon.Consequently,thebipolartransistorpairwillremaininwhateverstateitwaslastin(hysteresis).So,abriefpositivepulsetothegateturnstheMCTon,a 

briefnegativepulseforcesitoff,andnoappliedgatevoltageletsitremaininwhateverstate 

itisalreadyin.Inessence,theMCTisalatchingversionoftheIGBT(InsulatedGateBipolar 

Transistor). 

• REVIEW:


• AMOS-gatedthyristorusesanN-channelMOSFETtotriggerathyristor,resultinginan 

extremelylowgatecurrentrequirement. 

• AMOSControlledThyristor,orMCT,usestwoMOSFETStoexertfullcontroloverthe 

thyristor. Apositivegatevoltagetriggersthedevice;anegativegatevoltageforcesit 

toturnoff. Zerogatevoltageallowsthethyristortoremaininwhateverstateitwas 

previouslyin(off,orlatchedon). 

Bibliography 

[1] “PhattytronPT-1VacuumTubeSynthesizer”,TheAudioPlaygroundSynthesizerMuseumat 

http://www.keyboardmuseum.com/ar/m/meta/pt1.html 

[2] “At last, a pitch source with tube power”, METASONIX, PMB 109, 881 

11th Street, Lakeport CA 95453 USA at http://www.metasonix.com/i 

ndex.php?option=com content&task=view&id=14&Itemid=31 

[3] “SiliconContolledSwitches”, GETransistorManual, TheGeneralElectricCompany, 

1964,Figure16.19(M). 

[4] “2N6027, 2N6028 Programmable Unijunction Transistor ”, datasheet at 

http://www.onsemi.com/pub link/Collateral/2N6027-D.PDF 

[5] “Unijunction Transistor ”, American Microsemiconductor, at 

http://www.americanmicrosemi.com/tutorials/unijunction.htm 

[6] Matthew H. Williams, “Unijunction Transistor ”, at 

http://baec.tripod.com/DEC90/uni tran.htm Unijunction Transistor by 

http://baec.tripod.com/DEC90/unitran.htm

Chapter8 

OPERATIONALAMPLIFIERS 

Contents 


8.2 Single-endedanddifferentialamplifiers . . . . . . . . . . . . . . . . . . . .356 

8.3 The”operational”amplifier . . . . . . . . . . . . . . . . . . . . . . . . . . . .360 

8.4 Negativefeedback . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .366 

8.5 Dividedfeedback . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .369 

8.6 Ananalogyfordividedfeedback . . . . . . . . . . . . . . . . . . . . . . . . .372 

8.7 Voltage-to-currentsignalconversion . . . . . . . . . . . . . . . . . . . . . .378 

8.8 Averagerandsummercircuits . . . . . . . . . . . . . . . . . . . . . . . . . .380 

8.9 Buildingadifferentialamplifier . . . . . . . . . . . . . . . . . . . . . . . . .382 

8.10 Theinstrumentationamplifier . . . . . . . . . . . . . . . . . . . . . . . . . .384 

8.11 Differentiatorandintegratorcircuits......................385 

8.12 Positivefeedback...................................388 

8.13 Practicalconsiderations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .392 

8.13.1 Common-modegain. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .393 

8.13.2 Offsetvoltage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .396 

8.13.3 Biascurrent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .398 

8.13.4 Drift . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .404 

8.13.5 Frequencyresponse. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .404 

8.13.6 Inputtooutputphaseshift. . . . . . . . . . . . . . . . . . . . . . . . . . .405 

8.14 Operationalamplifiermodels . . . . . . . . . . . . . . . . . . . . . . . . . . .408 

8.15 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .413 


Theoperationalamplifierisarguablythemostusefulsingledeviceinanalogelectroniccircuitry.Withonlyahandfulofexternalcomponents,itcanbemadetoperformawidevariety 

355

356 CHAPTER8. OPERATIONALAMPLIFIERS 

ofanalogsignalprocessingtasks.Itisalsoquiteaffordable,mostgeneral-purposeamplifiers 

sellingforunderadollarapiece. Moderndesignshavebeenengineeredwithdurabilityin 

mindaswell: several”op-amps”aremanufacturedthatcansustaindirectshort-circuitson 

theiroutputswithoutdamage. 

Onekeytotheusefulnessoftheselittlecircuitsisintheengineeringprincipleoffeedback, 

particularlynegativefeedback,whichconstitutesthefoundationofalmostallautomaticcontrol 

processes. Theprinciplespresentedhereinoperationalamplifiercircuits,therefore,extend 

wellbeyondtheimmediatescopeofelectronics.Itiswellworththeelectronicsstudent’stime 

tolearntheseprinciplesandlearnthemwell. 

8.2 Single-endedanddifferentialamplifiers 

Foreaseofdrawingcomplexcircuitdiagrams,electronicamplifiersareoftensymbolizedbya 

simpletriangleshape,wheretheinternalcomponentsarenotindividuallyrepresented.This 

symbologyisveryhandyforcaseswhereanamplifier’sconstructionisirrelevanttothegreater 

functionoftheoverallcircuit,anditisworthyoffamiliarization: 

General amplifier circuit symbol 

+V supply 

Input Output 

-V supply 

The+Vand-VconnectionsdenotethepositiveandnegativesidesoftheDCpowersupply, 

respectively.Theinputandoutputvoltageconnectionsareshownassingleconductors,because 

itisassumedthatallsignalvoltagesarereferencedtoacommonconnectioninthecircuitcalled 

ground.Often(butnotalways!),onepoleoftheDCpowersupply,eitherpositiveornegative, 

isthatgroundreferencepoint.Apracticalamplifiercircuit(showingtheinputvoltagesource, 

loadresistance,andpowersupply)mightlooklikethis: 

V input 

+V 


-V 

R load 

30 V 

Withouthavingtoanalyzetheactualtransistordesignoftheamplifier,youcanreadily 

discernthewholecircuit’sfunction:totakeaninputsignal(Vin),amplifyit,anddriveaload 

+ 

-

8.2. SINGLE-ENDEDANDDIFFERENTIALAMPLIFIERS 357 

resistance(Rload). Tocompletetheaboveschematic,itwouldbegoodtospecifythegainsof 

thatamplifier(AV,AI,AP)andtheQ(bias)pointforanyneededmathematicalanalysis. 

IfitisnecessaryforanamplifiertobeabletooutputtrueACvoltage(reversingpolarity) 

totheload,asplitDCpowersupplymaybeused,wherebythegroundpointiselectrically 

”centered”between+Vand-V.Sometimesthesplitpowersupplyconfigurationisreferredto 

asadualpowersupply. 

V input 

+V 


-V 

R load 

15 V 

15 V 

Theamplifierisstillbeingsuppliedwith30voltsoverall,butwiththesplitvoltageDC 

powersupply,theoutputvoltageacrosstheloadresistorcannowswingfromatheoretical 

maximumof+15voltsto-15volts,insteadof+30voltsto0volts. Thisisaneasywayto 

gettruealternatingcurrent(AC)outputfromanamplifierwithoutresortingtocapacitiveor 

inductive(transformer)couplingontheoutput.Thepeak-to-peakamplitudeofthisamplifier’s 

outputbetweencutoffandsaturationremainsunchanged. 

Bysignifyingatransistoramplifierwithinalargercircuitwithatrianglesymbol,weease 

thetaskofstudyingandanalyzingmorecomplexamplifiersandcircuits. Oneofthesemore 

complexamplifiertypesthatwe’llbestudyingiscalledthedifferentialamplifier.Unlikenormalamplifiers,whichamplifyasingleinputsignal(oftencalledsingle-endedamplifiers),differentialamplifiersamplifythevoltagedifferencebetweentwoinputsignals.Usingthesimplified 

triangleamplifiersymbol,adifferentialamplifierlookslikethis: 

Input 1 


Differential amplifier 

− 

+ 

+V supply 

-V supply 

Output 

Thetwoinputleadscanbeseenontheleft-handsideofthetriangularamplifiersymbol,the 

outputleadontheright-handside,andthe+Vand-Vpowersupplyleadsontopandbottom. 

Aswiththeotherexample,allvoltagesarereferencedtothecircuit’sgroundpoint.Noticethat 

oneinputleadismarkedwitha(-)andtheotherismarkedwitha(+).Becauseadifferential 

amplifieramplifiesthedifferenceinvoltagebetweenthetwoinputs,eachinputinfluencesthe 

+ 

- 

+ 

-


outputvoltageinoppositeways. Considerthefollowingtableofinput/outputvoltagesfora 

differentialamplifierwithavoltagegainof4: 

(-) Input 1 

(+) Input 2 

Output 

0 

0 

0 

0 0 0 1 2.5 7 

1 2.5 7 

0 0 0 

4 10 28 -4 -10 -28 

Voltage output equation: V out = A V(Input 2 - Input 1) 

or 

V out = A V(Input (+) - Input (-)) 

3 

3 

-3 

3 

0 24 

Anincreasinglypositivevoltageonthe(+)inputtendstodrivetheoutputvoltagemore 

positive,andanincreasinglypositivevoltageonthe(-)inputtendstodrivetheoutputvoltage 

morenegative.Likewise,anincreasinglynegativevoltageonthe(+)inputtendstodrivethe 

outputnegativeaswell,andanincreasinglynegativevoltageonthe(-)inputdoesjustthe 

opposite.Becauseofthisrelationshipbetweeninputsandpolarities,the(-)inputiscommonly 

referredtoastheinvertinginputandthe(+)asthenoninvertinginput. 

Itmaybehelpfultothinkofadifferentialamplifierasavariablevoltagesourcecontrolled 

byasensitivevoltmeter,assuch: 

- 

+ 

- 

G 

+ 

+V 

-V 

Bearinmindthattheaboveillustrationisonlyamodeltoaidinunderstandingthebehaviorofadifferentialamplifier.Itisnotarealisticschematicofitsactualdesign.The”G”symbolrepresentsagalvanometer,asensitivevoltmetermovement.Thepotentiometerconnectedbetween+Vand-Vprovidesavariablevoltageattheoutputpin(withreferencetoonesideof 

theDCpowersupply),thatvariablevoltagesetbythereadingofthegalvanometer.Itmustbe 

understoodthatanyloadpoweredbytheoutputofadifferentialamplifiergetsitscurrentfrom 

theDCpowersource(battery),nottheinputsignal. Theinputsignal(tothegalvanometer) 

merelycontrolstheoutput. 

Thisconceptmayatfirstbeconfusingtostudentsnewtoamplifiers.Withallthesepolaritiesandpolaritymarkings(-and+)around,itseasytogetconfusedandnotknowwhatthe 

outputofadifferentialamplifierwillbe. Toaddressthispotentialconfusion,here’sasimple 

ruletoremember: 

-2 

-7 

-20

8.2. SINGLE-ENDEDANDDIFFERENTIALAMPLIFIERS 359 

Differential 

input voltage 

Differential 

input voltage 

- 

+ 

- 

− 

+ 

+ − 

+ 

+ 

- 

Output 

voltage 

- 

Output 

voltage 

+ 

Whenthepolarityofthedifferentialvoltagematchesthemarkingsforinvertingandnoninvertinginputs,theoutputwillbepositive.Whenthepolarityofthedifferentialvoltageclasheswiththeinputmarkings,theoutputwillbenegative.Thisbearssomesimilaritytothemathematicalsigndisplayedbydigitalvoltmetersbasedoninputvoltagepolarity.Theredtestlead 

ofthevoltmeter(oftencalledthe”positive”leadbecauseofthecolorred’spopularassociation 

withthepositivesideofapowersupplyinelectronicwiring)ismorepositivethantheblack, 

themeterwilldisplayapositivevoltagefigure,andviceversa: 

Differential 

input voltage 

Differential 

input voltage 

blk 

- 

6 V 

+ red 

blk 

+ 

6 V 

- 

red 

- 

+ 

- 

+ 

+ 6.00 V 

Digital Voltmeter 

- 6.00 V 

Digital Voltmeter 

Justasavoltmeterwillonlydisplaythevoltagebetweenitstwotestleads,anidealdifferentialamplifieronlyamplifiesthepotentialdifferencebetweenitstwoinputconnections,notthevoltagebetweenanyoneofthoseconnectionsandground.Theoutputpolarityofadifferentialamplifier,justlikethesignedindicationofadigitalvoltmeter,dependsontherelative 

polaritiesofthedifferentialvoltagebetweenthetwoinputconnections. 

Iftheinputvoltagestothisamplifierrepresentedmathematicalquantities(asisthecase 

withinanalogcomputercircuitry),orphysicalprocessmeasurements(asisthecasewithin 

analogelectronicinstrumentationcircuitry),youcanseehowadevicesuchasadifferential 

amplifiercouldbeveryuseful. Wecoulduseittocomparetwoquantitiestoseewhichis 

greater(bythepolarityoftheoutputvoltage),orperhapswecouldcomparethedifference 

betweentwoquantities(suchasthelevelofliquidintwotanks)andflaganalarm(basedonthe 

absolutevalueoftheamplifieroutput)ifthedifferencebecametoogreat.Inbasicautomatic 

controlcircuitry,thequantitybeingcontrolled(calledtheprocessvariable)iscomparedwith 

atargetvalue(calledthesetpoint),anddecisionsaremadeastohowtoactbasedonthe 

discrepancybetweenthesetwovalues.Thefirststepinelectronicallycontrollingsuchascheme


istoamplifythedifferencebetweentheprocessvariableandthesetpointwithadifferential 

amplifier.Insimplecontrollerdesigns,theoutputofthisdifferentialamplifiercanbedirectly 

utilizedtodrivethefinalcontrolelement(suchasavalve)andkeeptheprocessreasonably 

closetosetpoint. 

• REVIEW: 

• A”shorthand”symbolforanelectronicamplifierisatriangle,thewideendsignifying 

theinputsideandthenarrowendsignifyingtheoutput. Powersupplylinesareoften 

omittedinthedrawingforsimplicity. 

• TofacilitatetrueACoutputfromanamplifier,wecanusewhatiscalledasplitordual 

powersupply,withtwoDCvoltagesourcesconnectedinserieswiththemiddlepoint 

grounded,givingapositivevoltagetoground(+V)andanegativevoltagetoground(-V). 

Splitpowersupplieslikethisarefrequentlyusedindifferentialamplifiercircuits. 

• Mostamplifiershaveoneinputandoneoutput.Differentialamplifiershavetwoinputs 

andoneoutput,theoutputsignalbeingproportionaltothedifferenceinsignalsbetween 

thetwoinputs. 

• Thevoltageoutputofadifferentialamplifierisdeterminedbythefollowingequation: 

Vout=AV(Vnoninv-Vinv) 

8.3 The”operational”amplifier 

Longbeforetheadventofdigitalelectronictechnology,computerswerebuilttoelectronically 

performcalculationsbyemployingvoltagesandcurrentstorepresentnumericalquantities. 

Thiswasespeciallyusefulforthesimulationofphysicalprocesses.Avariablevoltage,forinstance,mightrepresentvelocityorforceinaphysicalsystem. 

Throughtheuseofresistive 

voltagedividersandvoltageamplifiers,themathematicaloperationsofdivisionandmultiplicationcouldbeeasilyperformedonthesesignals. 

Thereactivepropertiesofcapacitorsandinductorslendthemselveswelltothesimulation 

ofvariablesrelatedbycalculusfunctions. Rememberhowthecurrentthroughacapacitor 

wasafunctionofthevoltage’srateofchange,andhowthatrateofchangewasdesignated 

incalculusasthederivative? Well,ifvoltageacrossacapacitorweremadetorepresentthe 

velocityofanobject,thecurrentthroughthecapacitorwouldrepresenttheforcerequiredto 

accelerateordeceleratethatobject,thecapacitor’scapacitancerepresentingtheobject’smass: 

i C = C dv 

dt 

F = m dv 

dt 

Where, Where, 

i C = 

C = 

dv 

Instantaneous current 

through capacitor 

Capacitance in farads 

dt = Rate of change of 

voltage over time 

F = Force applied to object 

m = 

dv 

dt = 

Mass of object 

Rate of change of 

velocity over time

8.3. THE”OPERATIONAL”AMPLIFIER 361 

Thisanalogelectroniccomputationofthecalculusderivativefunctionistechnicallyknown 

asdifferentiation,anditisanaturalfunctionofacapacitor’scurrentinrelationtothevoltage 

appliedacrossit.Notethatthiscircuitrequiresno”programming”toperformthisrelatively 

advancedmathematicalfunctionasadigitalcomputerwould. 

Electroniccircuitsareveryeasyandinexpensivetocreatecomparedtocomplexphysical 

systems,sothiskindofanalogelectronicsimulationwaswidelyusedintheresearchand 

developmentofmechanicalsystems.Forrealisticsimulation,though,amplifiercircuitsofhigh 

accuracyandeasyconfigurabilitywereneededintheseearlycomputers. 

Itwasfoundinthecourseofanalogcomputerdesignthatdifferentialamplifierswithextremelyhighvoltagegainsmettheserequirementsofaccuracyandconfigurabilitybetterthan 

single-endedamplifierswithcustom-designedgains. Usingsimplecomponentsconnectedto 

theinputsandoutputofthehigh-gaindifferentialamplifier,virtuallyanygainandanyfunctioncouldbeobtainedfromthecircuit,overall,withoutadjustingormodifyingtheinternal 

circuitryoftheamplifieritself. Thesehigh-gaindifferentialamplifierscametobeknownas 

operationalamplifiers,orop-amps,becauseoftheirapplicationinanalogcomputers’mathematicaloperations. 

Modernop-amps,likethepopularmodel741,arehigh-performance,inexpensiveintegrated 

circuits. Theirinputimpedancesarequitehigh,theinputsdrawingcurrentsintherangeof 

halfamicroamp(maximum)forthe741,andfarlessforop-ampsutilizingfield-effectinput 

transistors.Outputimpedanceistypicallyquitelow,about75 Ωforthemodel741,andmany 

modelshavebuilt-inoutputshortcircuitprotection,meaningthattheiroutputscanbedirectly 

shortedtogroundwithoutcausingharmtotheinternalcircuitry.Withdirectcouplingbetween 

op-amps’internaltransistorstages,theycanamplifyDCsignalsjustaswellasAC(upto 

certainmaximumvoltage-risetimelimits).Itwouldcostfarmoreinmoneyandtimetodesign 

acomparablediscrete-transistoramplifiercircuittomatchthatkindofperformance,unless 

highpowercapabilitywasrequired.Forthesereasons,op-ampshaveallbutobsoleteddiscretetransistorsignalamplifiersinmanyapplications. 

Thefollowingdiagramshowsthepinconnectionsforsingleop-amps(741included)when 

housedinan8-pinDIP(DualInlinePackage)integratedcircuit:


Typical 8-pin "DIP" op-amp 

integrated circuit 

No 

connection 

+V 

8 7 6 

− 

Output 

+ 

5 

1 2 3 4 

Offset 

null 

Offset 

null 

Somemodelsofop-ampcometwotoapackage,includingthepopularmodelsTL082and 

1458.Thesearecalled”dual”units,andaretypicallyhousedinan8-pinDIPpackageaswell, 

withthefollowingpinconnections: 

8 7 6 

5 

1 2 3 4 

-V 

Dual op-amp in 8-pin DIP 

+V 

+ 

− 

Operationalamplifiersarealsoavailablefourtoapackage,usuallyin14-pinDIParrangements. 

Unfortunately,pinassignmentsaren’tasstandardforthese”quad”op-ampsasthey 

areforthe”dual”orsingleunits.Consultthemanufacturerdatasheet(s)fordetails. 

Practicaloperationalamplifiervoltagegainsareintherangeof200,000ormore,which 

− 

+ 

-V


makesthemalmostuselessasananalogdifferentialamplifierbythemselves.Foranop-amp 

withavoltagegain(AV)of200,000andamaximumoutputvoltageswingof+15V/-15V,all 

itwouldtakeisadifferentialinputvoltageof75 µV(microvolts)todriveittosaturationor 

cutoff!Beforewetakealookathowexternalcomponentsareusedtobringthegaindowntoa 

reasonablelevel,let’sinvestigateapplicationsforthe”bare”op-ampbyitself. 

Oneapplicationiscalledthecomparator. Forallpracticalpurposes,wecansaythatthe 

outputofanop-ampwillbesaturatedfullypositiveifthe(+)inputismorepositivethanthe(-) 

input,andsaturatedfullynegativeifthe(+)inputislesspositivethanthe(-)input.Inother 

words,anop-amp’sextremelyhighvoltagegainmakesitusefulasadevicetocomparetwo 

voltagesandchangeoutputvoltagestateswhenoneinputexceedstheotherinmagnitude. 

V in 

− 

+ 

+V 

-V 

LED 

Intheabovecircuit,wehaveanop-ampconnectedasacomparator,comparingtheinput 

voltagewithareferencevoltagesetbythepotentiometer(R1).IfVindropsbelowthevoltage 

setbyR1,theop-amp’soutputwillsaturateto+V,therebylightinguptheLED.Otherwise,if 

Vinisabovethereferencevoltage,theLEDwillremainoff.IfVinisavoltagesignalproduced 

byameasuringinstrument,thiscomparatorcircuitcouldfunctionasa”low”alarm,withthe 

trip-pointsetbyR1.InsteadofanLED,theop-ampoutputcoulddrivearelay,atransistor,an 

SCR,oranyotherdevicecapableofswitchingpowertoaloadsuchasasolenoidvalve,totake 

actionintheeventofalowalarm. 

Anotherapplicationforthecomparatorcircuitshownisasquare-waveconverter.Suppose 

thattheinputvoltageappliedtotheinverting(-)inputwasanACsinewaveratherthana 

stableDCvoltage.Inthatcase,theoutputvoltagewouldtransitionbetweenopposingstates 

ofsaturationwhenevertheinputvoltagewasequaltothereferencevoltageproducedbythe 

potentiometer.Theresultwouldbeasquarewave:


V in 

V in 

− 

+ 

+V 

-V 

V out 

Adjustmentstothepotentiometersettingwouldchangethereferencevoltageappliedto 

thenoninverting(+)input,whichwouldchangethepointsatwhichthesinewavewouldcross, 

changingtheon/offtimes,ordutycycleofthesquarewave: 

V in 

V in 

− 

+ 

+V 

-V 

V out 

ItshouldbeevidentthattheACinputvoltagewouldnothavetobeasinewaveinparticular 

forthiscircuittoperformthesamefunction. Theinputvoltagecouldbeatrianglewave, 

sawtoothwave,oranyothersortofwavethatrampedsmoothlyfrompositivetonegativeto 

positiveagain. Thissortofcomparatorcircuitisveryusefulforcreatingsquarewavesof 

varyingdutycycle. Thistechniqueissometimesreferredtoaspulse-widthmodulation,or 

PWM(varying,ormodulatingawaveformaccordingtoacontrollingsignal,inthiscasethe 

signalproducedbythepotentiometer). 

Anothercomparatorapplicationisthatofthebargraphdriver.Ifwehadseveralop-amps 

V out 

V out


connectedascomparators,eachwithitsownreferencevoltageconnectedtotheinvertinginput, 

buteachonemonitoringthesamevoltagesignalontheirnoninvertinginputs,wecouldbuilda 

bargraph-stylemetersuchaswhatiscommonlyseenonthefaceofstereotunersandgraphic 

equalizers. Asthesignalvoltage(representingradiosignalstrengthoraudiosoundlevel) 

increased,eachcomparatorwould”turnon”insequenceandsendpowertoitsrespectiveLED. 

Witheachcomparatorswitching”on”atadifferentlevelofaudiosound,thenumberofLED’s 

illuminatedwouldindicatehowstrongthesignalwas. 

+V 

-V 

V in 

Simple bargraph driver circuit 

− 

+ 

− 

+ 

− 

+ 

− 

+ 

LED 4 

LED 3 

LED 2 

LED 1 

Inthecircuitshownabove,LED1wouldbethefirsttolightupastheinputvoltageincreased 

inapositivedirection. Astheinputvoltagecontinuedtoincrease,theotherLED’swould 

illuminateinsuccession,untilallwerelit. 

Thisverysametechnologyisusedinsomeanalog-to-digitalsignalconverters,namelythe 

flashconverter,totranslateananalogsignalquantityintoaseriesofon/offvoltagesrepresentingadigitalnumber. 

• REVIEW: 

• Atriangleshapeisthegenericsymbolforanamplifiercircuit,thewideendsignifying 

theinputandthenarrowendsignifyingtheoutput. 

• Unlessotherwisespecified,allvoltagesinamplifiercircuitsarereferencedtoacommon 

groundpoint,usuallyconnectedtooneterminalofthepowersupply. Thisway,wecan 

speakofacertainamountofvoltagebeing”on”asinglewire,whilerealizingthatvoltage 

isalwaysmeasuredbetweentwopoints. 

-V


• Adifferentialamplifierisoneamplifyingthevoltagedifferencebetweentwosignalinputs. 

Insuchacircuit,oneinputtendstodrivetheoutputvoltagetothesamepolarityofthe 

inputsignal,whiletheotherinputdoesjusttheopposite.Consequently,thefirstinputis 

calledthenoninverting(+)inputandthesecondiscalledtheinverting(-)input. 

• Anoperationalamplifier(orop-ampforshort)isadifferentialamplifierwithanextremely 

highvoltagegain(AV =200,000ormore).Itsnamehailsfromitsoriginaluseinanalog 

computercircuitry(performingmathematicaloperations). 

• Op-ampstypicallyhaveveryhighinputimpedancesandfairlylowoutputimpedances. 

• Sometimesop-ampsareusedassignalcomparators,operatinginfullcutofforsaturation 

modedependingonwhichinput(invertingornoninverting)hasthegreatestvoltage. 

Comparatorsareusefulindetecting”greater-than”signalconditions(comparingoneto 

theother). 

• Onecomparatorapplicationiscalledthepulse-widthmodulator,andismadebycomparingasine-waveACsignalagainstaDCreferencevoltage. 

AstheDCreferencevoltage 

isadjusted,thesquare-waveoutputofthecomparatorchangesitsdutycycle(positive 

versusnegativetimes).Thus,theDCreferencevoltagecontrols,ormodulatesthepulse 

widthoftheoutputvoltage. 

8.4 Negativefeedback 

Ifweconnecttheoutputofanop-amptoitsinvertinginputandapplyavoltagesignalto 

thenoninvertinginput,wefindthattheoutputvoltageoftheop-ampcloselyfollowsthat 

inputvoltage(I’veneglectedtodrawinthepowersupply,+V/-Vwires,andgroundsymbolfor 

simplicity): 

V in 

− 

+ 

AsVinincreases,Voutwillincreaseinaccordancewiththedifferentialgain. However,as 

Voutincreases,thatoutputvoltageisfedbacktotheinvertinginput,therebyactingtodecrease 

thevoltagedifferentialbetweeninputs,whichactstobringtheoutputdown.Whatwillhappen 

foranygivenvoltageinputisthattheop-ampwilloutputavoltageverynearlyequaltoVin, 

butjustlowenoughsothatthere’senoughvoltagedifferenceleftbetweenVinandthe(-)input 

tobeamplifiedtogeneratetheoutputvoltage. 

Thecircuitwillquicklyreachapointofstability(knownasequilibriuminphysics),where 

theoutputvoltageisjusttherightamounttomaintaintherightamountofdifferential,which 

inturnproducestherightamountofoutputvoltage.Takingtheop-amp’soutputvoltageand 

couplingittotheinvertinginputisatechniqueknownasnegativefeedback,anditisthekey 

tohavingaself-stabilizingsystem(thisistruenotonlyofop-amps,butofanydynamicsystem 

ingeneral).Thisstabilitygivestheop-ampthecapacitytoworkinitslinear(active)mode,as 

V out

8.4. NEGATIVEFEEDBACK 367 

opposedtomerelybeingsaturatedfully”on”or”off”asitwaswhenusedasacomparator,with 

nofeedbackatall. 

Becausetheop-amp’sgainissohigh,thevoltageontheinvertinginputcanbemaintained 

almostequaltoVin.Let’ssaythatourop-amphasadifferentialvoltagegainof200,000.IfVin 

equals6volts,theoutputvoltagewillbe5.999970000149999volts. Thiscreatesjustenough 

differentialvoltage(6volts-5.999970000149999volts=29.99985 µV)tocause5.999970000149999 

voltstobemanifestedattheoutputterminal,andthesystemholdsthereinbalance.Asyou 

cansee,29.99985 µVisnotalotofdifferential,soforpracticalcalculations,wecanassume 

thatthedifferentialvoltagebetweenthetwoinputwiresisheldbynegativefeedbackexactly 

at0volts. 

29.99985 µV 

The effects of negative feedback 

6 V 

− 

+ 

The effects of negative feedback 

(rounded figures) 

0 V 

6 V 

− 

+ 

5.999970000149999 V 

Onegreatadvantagetousinganop-ampwithnegativefeedbackisthattheactualvoltage 

gainoftheop-ampdoesn’tmatter,solongasitsverylarge. Iftheop-amp’sdifferentialgain 

were250,000insteadof200,000,allitwouldmeanisthattheoutputvoltagewouldholdjust 

alittleclosertoVin(lessdifferentialvoltageneededbetweeninputstogeneratetherequired 

output).Inthecircuitjustillustrated,theoutputvoltagewouldstillbe(forallpracticalpurposes)equaltothenon-invertinginputvoltage. 

Op-ampgains,therefore,donothavetobe 

preciselysetbythefactoryinorderforthecircuitdesignertobuildanamplifiercircuitwith 

6 V


precisegain.Negativefeedbackmakesthesystemself-correcting.Theabovecircuitasawhole 

willsimplyfollowtheinputvoltagewithastablegainof1. 

Goingbacktoourdifferentialamplifiermodel,wecanthinkoftheoperationalamplifier 

asbeingavariablevoltagesourcecontrolledbyanextremelysensitivenulldetector,thekind 

ofmetermovementorothersensitivemeasurementdeviceusedinbridgecircuitstodetecta 

conditionofbalance(zerovolts).The”potentiometer”insidetheop-ampcreatingthevariable 

voltagewillmovetowhateverpositionitmustto”balance”theinvertingandnoninverting 

inputvoltagessothatthe”nulldetector”haszerovoltageacrossit: 

6 V 

0 V 

- 

+ 

null 

+V 

-V 

Asthe”potentiometer”willmovetoprovideanoutputvoltagenecessarytosatisfythe”null 

detector”atan”indication”ofzerovolts,theoutputvoltagebecomesequaltotheinputvoltage: 

inthiscase,6volts.Iftheinputvoltagechangesatall,the”potentiometer”insidetheop-amp 

willchangepositiontoholdthe”nulldetector”inbalance(indicatingzerovolts),resultingin 

anoutputvoltageapproximatelyequaltotheinputvoltageatalltimes. 

Thiswillholdtruewithintherangeofvoltagesthattheop-ampcanoutput.Withapower 

supplyof+15V/-15V,andanidealamplifierthatcanswingitsoutputvoltagejustasfar,it 

willfaithfully”follow”theinputvoltagebetweenthelimitsof+15voltsand-15volts.Forthis 

reason,theabovecircuitisknownasavoltagefollower. Likeitsone-transistorcounterpart, 

thecommon-collector(”emitter-follower”)amplifier,ithasavoltagegainof1,ahighinput 

impedance,alowoutputimpedance,andahighcurrentgain.Voltagefollowersarealsoknown 

asvoltagebuffers,andareusedtoboostthecurrent-sourcingabilityofvoltagesignalstooweak 

(toohighofsourceimpedance)todirectlydriveaload. Theop-ampmodelshowninthelast 

illustrationdepictshowtheoutputvoltageisessentiallyisolatedfromtheinputvoltage,so 

thatcurrentontheoutputpinisnotsuppliedbytheinputvoltagesourceatall,butrather 

fromthepowersupplypoweringtheop-amp. 

Itshouldbementionedthatmanyop-ampscannotswingtheiroutputvoltagesexactlyto 

+V/-Vpowersupplyrailvoltages.Themodel741isoneofthosethatcannot:whensaturated, 

itsoutputvoltagepeakswithinaboutonevoltofthe+Vpowersupplyvoltageandwithinabout 

2voltsofthe-Vpowersupplyvoltage. Therefore,withasplitpowersupplyof+15/-15volts, 

a741op-amp’soutputmaygoashighas+14voltsoraslowas-13volts(approximately),but 

nofurther. Thisisduetoitsbipolartransistordesign. Thesetwovoltagelimitsareknown 

6 V

8.5. DIVIDEDFEEDBACK 369 

asthepositivesaturationvoltageandnegativesaturationvoltage,respectively.Otherop-amps, 

suchasthemodel3130withfield-effecttransistorsinthefinaloutputstage,havetheabilityto 

swingtheiroutputvoltageswithinmillivoltsofeitherpowersupplyrailvoltage.Consequently, 

theirpositiveandnegativesaturationvoltagesarepracticallyequaltothesupplyvoltages. 

• REVIEW: 

• Connectingtheoutputofanop-amptoitsinverting(-)inputiscallednegativefeedback. 

Thistermcanbebroadlyappliedtoanydynamicsystemwheretheoutputsignalis”fed 

back”totheinputsomehowsoastoreachapointofequilibrium(balance). 

• Whentheoutputofanop-ampisdirectlyconnectedtoitsinverting(-)input,avoltage 

followerwillbecreated.Whateversignalvoltageisimpresseduponthenoninverting(+) 

inputwillbeseenontheoutput. 

• Anop-ampwithnegativefeedbackwilltrytodriveitsoutputvoltagetowhateverlevel 

necessarysothatthedifferentialvoltagebetweenthetwoinputsispracticallyzero.The 

highertheop-ampdifferentialgain,thecloserthatdifferentialvoltagewillbetozero. 

• Someop-ampscannotproduceanoutputvoltageequaltotheirsupplyvoltagewhensaturated.Themodel741isoneofthese.Theupperandlowerlimitsofanop-amp’soutput 

voltageswingareknownaspositivesaturationvoltageandnegativesaturationvoltage, 

respectively. 

8.5 Dividedfeedback 

Ifweaddavoltagedividertothenegativefeedbackwiringsothatonlyafractionoftheoutput 

voltageisfedbacktotheinvertinginputinsteadofthefullamount,theoutputvoltagewillbe 

amultipleoftheinputvoltage(pleasebearinmindthatthepowersupplyconnectionstothe 

op-amphavebeenomittedonceagainforsimplicity’ssake): 

The effects of divided negative feedback 

6 mA R1 6 V 

R2 6 mA 

0 V 

1 kΩ 1 kΩ 

6 V 

− 

6 V 

+ 

12 V 

All voltage figures shown in 

reference to ground


IfR1andR2arebothequalandVinis6volts,theop-ampwilloutputwhatevervoltageis 

neededtodrop6voltsacrossR1(tomaketheinvertinginputvoltageequalto6volts,aswell, 

keepingthevoltagedifferencebetweenthetwoinputsequaltozero). Withthe2:1voltage 

dividerofR1andR2,thiswilltake12voltsattheoutputoftheop-amptoaccomplish. 

Anotherwayofanalyzingthiscircuitistostartbycalculatingthemagnitudeanddirection 

ofcurrentthroughR1,knowingthevoltageoneitherside(andtherefore,bysubtraction,the 

voltageacrossR1),andR1’sresistance.Sincetheleft-handsideofR1isconnectedtoground(0 

volts)andtheright-handsideisatapotentialof6volts(duetothenegativefeedbackholding 

thatpointequaltoVin),wecanseethatwehave6voltsacrossR1.Thisgivesus6mAofcurrent 

throughR1fromlefttoright.Becauseweknowthatbothinputsoftheop-amphaveextremely 

highimpedance,wecansafelyassumetheywon’taddorsubtractanycurrentthroughthe 

divider. Inotherwords,wecantreatR1andR2asbeinginserieswitheachother:allofthe 

electronsflowingthroughR1mustflowthroughR2.KnowingthecurrentthroughR2andthe 

resistanceofR2,wecancalculatethevoltageacrossR2(6volts),anditspolarity.Countingup 

voltagesfromground(0volts)totheright-handsideofR2,wearriveat12voltsontheoutput. 

Uponexaminingthelastillustration,onemightwonder,”wheredoesthat6mAofcurrent 

go?”Thelastillustrationdoesn’tshowtheentirecurrentpath,butinrealityitcomesfromthe 

negativesideoftheDCpowersupply,throughground,throughR1,throughR2,throughthe 

outputpinoftheop-amp,andthenbacktothepositivesideoftheDCpowersupplythroughthe 

outputtransistor(s)oftheop-amp.Usingthenulldetector/potentiometermodeloftheop-amp, 

thecurrentpathlookslikethis: 

R 1 

6 V 

- 

+ 

null 

R 2 

1 kΩ 1 kΩ 

The6voltsignalsourcedoesnothavetosupplyanycurrentforthecircuit: itmerely 

commandstheop-amptobalancevoltagebetweentheinverting(-)andnoninverting(+)input 

pins,andinsodoingproduceanoutputvoltagethatistwicetheinputduetothedividingeffect 

ofthetwo1kΩresistors. 

Wecanchangethevoltagegainofthiscircuit,overall,justbyadjustingthevaluesofR1 

andR2(changingtheratioofoutputvoltagethatisfedbacktotheinvertinginput).Gaincan 

becalculatedbythefollowingformula: 

+V 

-V

8.5. DIVIDEDFEEDBACK 371 

AV = R2 + 1 

R1 Notethatthevoltagegainforthisdesignofamplifiercircuitcanneverbelessthan1. If 

weweretolowerR2toavalueofzeroohms,ourcircuitwouldbeessentiallyidenticaltothe 

voltagefollower,withtheoutputdirectlyconnectedtotheinvertinginput. Sincethevoltage 

followerhasagainof1,thissetsthelowergainlimitofthenoninvertingamplifier.However, 

thegaincanbeincreasedfarbeyond1,byincreasingR2inproportiontoR1. 

Alsonotethatthepolarityoftheoutputmatchesthatoftheinput,justaswithavoltage 

follower. Apositiveinputvoltageresultsinapositiveoutputvoltage,andviceversa(with 

respecttoground).Forthisreason,thiscircuitisreferredtoasanoninvertingamplifier. 

Justaswiththevoltagefollower,weseethatthedifferentialgainoftheop-ampisirrelevant,solongasitsveryhigh. 

Thevoltagesandcurrentsinthiscircuitwouldhardlychange 

atalliftheop-amp’svoltagegainwere250,000insteadof200,000.Thisstandsasastarkcontrasttosingle-transistoramplifiercircuitdesigns,wheretheBetaoftheindividualtransistor 

greatlyinfluencedtheoverallgainsoftheamplifier. Withnegativefeedback,wehaveaselfcorrectingsystemthatamplifiesvoltageaccordingtotheratiossetbythefeedbackresistors, 

notthegainsinternaltotheop-amp. 

Let’sseewhathappensifweretainnegativefeedbackthroughavoltagedivider,butapply 

theinputvoltageatadifferentlocation: 

6 V 

6 mA R1 0 V R2 6 mA 

1 kΩ 1 kΩ 

− 

0 V 

+ 

-6 V 

All voltage figures shown in 

reference to ground 

Bygroundingthenoninvertinginput,thenegativefeedbackfromtheoutputseekstohold 

theinvertinginput’svoltageat0volts,aswell.Forthisreason,theinvertinginputisreferred 

tointhiscircuitasavirtualground,beingheldatgroundpotential(0volts)bythefeedback, 

yetnotdirectlyconnectedto(electricallycommonwith)ground. Theinputvoltagethistime 

isappliedtotheleft-handendofthevoltagedivider(R1=R2=1kΩagain),sotheoutput 

voltagemustswingto-6voltsinordertobalancethemiddleatgroundpotential(0volts). 

Usingthesametechniquesaswiththenoninvertingamplifier,wecananalyzethiscircuit’s 

operationbydeterminingcurrentmagnitudesanddirections,startingwithR1,andcontinuing 

ontodeterminingtheoutputvoltage. 

Wecanchangetheoverallvoltagegainofthiscircuit,overall,justbyadjustingthevalues 

ofR1andR2(changingtheratioofoutputvoltagethatisfedbacktotheinvertinginput).Gain 

canbecalculatedbythefollowingformula: 

AV = R − 2 

R1 Notethatthiscircuit’svoltagegaincanbelessthan1,dependingsolelyontheratioofR2


toR1. Alsonotethattheoutputvoltageisalwaystheoppositepolarityoftheinputvoltage. 

Apositiveinputvoltageresultsinanegativeoutputvoltage,andviceversa(withrespectto 

ground).Forthisreason,thiscircuitisreferredtoasaninvertingamplifier.Sometimes,the 

gainformulacontainsanegativesign(beforetheR2/R1fraction)toreflectthisreversalof 

polarities. 

Thesetwoamplifiercircuitswe’vejustinvestigatedservethepurposeofmultiplyingor 

dividingthemagnitudeoftheinputvoltagesignal. Thisisexactlyhowthemathematical 

operationsofmultiplicationanddivisionaretypicallyhandledinanalogcomputercircuitry. 

• REVIEW: 

• Byconnectingtheinverting(-)inputofanop-ampdirectlytotheoutput,wegetnegative 

feedback,whichgivesusavoltagefollowercircuit.Byconnectingthatnegativefeedback 

througharesistivevoltagedivider(feedingbackafractionoftheoutputvoltagetothe 

invertinginput),theoutputvoltagebecomesamultipleoftheinputvoltage. 

• Anegative-feedbackop-ampcircuitwiththeinputsignalgoingtothenoninverting(+) 

inputiscalledanoninvertingamplifier.Theoutputvoltagewillbethesamepolarityas 

theinput.Voltagegainisgivenbythefollowingequation:AV=(R2/R1)+1 

• Anegative-feedbackop-ampcircuitwiththeinputsignalgoingtothe”bottom”ofthe 

resistivevoltagedivider,withthenoninverting(+)inputgrounded,iscalledaninverting 

amplifier. Itsoutputvoltagewillbetheoppositepolarityoftheinput. Voltagegainis 

givenbythefollowingequation:AV =-R2/R1 

8.6 Ananalogyfordividedfeedback 

Ahelpfulanalogyforunderstandingdividedfeedbackamplifiercircuitsisthatofamechanical 

lever,withrelativemotionofthelever’sendsrepresentingchangeininputandoutputvoltages, 

andthefulcrum(pivotpoint)representingthelocationofthegroundpoint,realorvirtual. 

Takeforexamplethefollowingnoninvertingop-ampcircuit.Weknowfromthepriorsection 

thatthevoltagegainofanoninvertingamplifierconfigurationcanneverbelessthanunity(1). 

Ifwedrawaleverdiagramnexttotheamplifierschematic,withthedistancebetweenfulcrum 

andleverendsrepresentativeofresistorvalues,themotionoftheleverwillsignifychangesin 

voltageattheinputandoutputterminalsoftheamplifier:

8.6. ANANALOGYFORDIVIDEDFEEDBACK 373 

0 V 

R 1 

R 1 

1 kΩ 1 kΩ 

− 

V in 

V in 

+ 

R 2 

R 2 

V out 

V out 

V out = 2(V in) 

Physicistscallthistypeoflever,withtheinputforce(effort)appliedbetweenthefulcrum 

andoutput(load),athird-classlever.Itischaracterizedbyanoutputdisplacement(motion)at 

leastaslargethantheinputdisplacement–a”gain”ofatleast1–andinthesamedirection. 

Applyingapositiveinputvoltagetothisop-ampcircuitisanalogoustodisplacingthe”input” 

pointontheleverupward:


0 V 

R 1 

1 kΩ 1 kΩ 

− 

V in 

+ 

- 

V in 

+ 

R 2 

V out 

V out 


Duetothedisplacement-amplifyingcharacteristicsofthelever,the”output”pointwillmove 

twiceasfarasthe”input”point,andinthesamedirection.Intheelectroniccircuit,theoutput 

voltagewillequaltwicetheinput,withthesamepolarity.Applyinganegativeinputvoltageis 

analogoustomovingtheleverdownwardfromitslevel”zero”position,resultinginanamplified 

outputdisplacementthatisalsonegative: 

0 V 

R 1 

1 kΩ 1 kΩ 

− 

V in 

- 

+ 

V in 

+ 

R 2 

V out 

V out 

+ 

- 


- 

+


IfwealtertheresistorratioR2/R1,wechangethegainoftheop-ampcircuit.Inleverterms, 

thismeansmovingtheinputpointinrelationtothefulcrumandleverend,whichsimilarly 

changesthedisplacement”gain”ofthemachine: 

0 V 

R 1 

V in 

R 1 

1 kΩ 

V in 

R 2 

− 

+ 

R 2 

3 kΩ 

V out 

V out 


Now,anyinputsignalwillbecomeamplifiedbyafactoroffourinsteadofbyafactoroftwo:


0 V 

V in 

R 1 

1 kΩ 

V in 

+ 

- 

− 

+ 

R 2 

3 kΩ 

V out 

V out 


Invertingop-ampcircuitsmaybemodeledusingtheleveranalogyaswell.Withtheinvertingconfiguration,thegroundpointofthefeedbackvoltagedivideristheop-amp’sinverting 

inputwiththeinputtotheleftandtheoutputtotheright.Thisismechanicallyequivalentto 

afirst-classlever,wheretheinputforce(effort)isontheoppositesideofthefulcrumfromthe 

output(load): 

V in 

V in 

R 1 

R 1 

1 kΩ 1 kΩ 

− 

+ 

R 2 

R 2 

V out 

+ 

- 

V out 

V out = -(V in) 

Withequal-valueresistors(equal-lengthsofleveroneachsideofthefulcrum),theoutput 

voltage(displacement)willbeequalinmagnitudetotheinputvoltage(displacement),butof 

theoppositepolarity(direction).Apositiveinputresultsinanegativeoutput:


V in 

V in 

+ 

- 

R 1 

1 kΩ 1 kΩ 

− 

+ 

R 2 

V out 

V out 

V out = -(V in) 

ChangingtheresistorratioR2/R1changesthegainoftheamplifiercircuit,justaschanging 

thefulcrumpositionontheleverchangesitsmechanicaldisplacement”gain.”Considerthe 

followingexample,whereR2ismadetwiceaslargeasR1: 

V in 

V in 

+ 

- 

R 1 

1 kΩ 

− 

+ 

R 2 

2 kΩ 

V out 

- 

V out 

- 

+ 

+ 

V out = -2(V in) 

Withtheinvertingamplifierconfiguration,though,gainsoflessthan1arepossible,just 

aswithfirst-classlevers. ReversingR2andR1valuesisanalogoustomovingthefulcrumto 

itscomplementarypositiononthelever:one-thirdofthewayfromtheoutputend.There,the 

outputdisplacementwillbeone-halftheinputdisplacement:


V in 

V in 

+ 

- 

R 1 

2 kΩ 

− 

+ 

R 2 

1 kΩ 

V out 

- 

V out 

8.7 Voltage-to-currentsignalconversion 

V out = -0.5(V in) 

Ininstrumentationcircuitry,DCsignalsareoftenusedasanalogrepresentationsofphysical 

measurementssuchastemperature,pressure,flow,weight,andmotion.Mostcommonly,DC 

currentsignalsareusedinpreferencetoDCvoltagesignals,becausecurrentsignalsareexactlyequalinmagnitudethroughouttheseriescircuitloopcarryingcurrentfromthesource 

(measuringdevice)totheload(indicator,recorder,orcontroller),whereasvoltagesignalsin 

aparallelcircuitmayvaryfromoneendtotheotherduetoresistivewirelosses. Furthermore,current-sensinginstrumentstypicallyhavelowimpedances(whilevoltage-sensinginstrumentshavehighimpedances),whichgivescurrent-sensinginstrumentsgreaterelectrical 

noiseimmunity. 

Inordertousecurrentasananalogrepresentationofaphysicalquantity,wehavetohave 

somewayofgeneratingapreciseamountofcurrentwithinthesignalcircuit. Buthowdo 

wegenerateaprecisecurrentsignalwhenwemightnotknowtheresistanceoftheloop? 

Theansweristouseanamplifierdesignedtoholdcurrenttoaprescribedvalue,applying 

asmuchoraslittlevoltageasnecessarytotheloadcircuittomaintainthatvalue. Suchan 

amplifierperformsthefunctionofacurrentsource. Anop-ampwithnegativefeedbackisa 

perfectcandidateforsuchatask: 

+

8.7. VOLTAGE-TO-CURRENTSIGNALCONVERSION 379 

250 Ω 

− 

4 to 20 mA 

+ 

4 to 20 mA 

+ 

Vin 1 to 5 volt signal range 

- 

Theinputvoltagetothiscircuitisassumedtobecomingfromsometypeofphysicaltransducer/amplifierarrangement,calibratedtoproduce1voltat0percentofphysicalmeasurement,and5voltsat100percentofphysicalmeasurement.Thestandardanalogcurrentsignal 

rangeis4mAto20mA,signifying0%to100%ofmeasurementrange,respectively.At5volts 

input,the250 Ω(precision)resistorwillhave5voltsappliedacrossit,resultingin20mAof 

currentinthelargeloopcircuit(withRload).ItdoesnotmatterwhatresistancevalueRloadis, 

orhowmuchwireresistanceispresentinthatlargeloop,solongastheop-amphasahigh 

enoughpowersupplyvoltagetooutputthevoltagenecessarytoget20mAflowingthrough 

Rload. The250 Ωresistorestablishestherelationshipbetweeninputvoltageandoutputcurrent,inthiscasecreatingtheequivalenceof1-5Vin/4-20mAout.Ifwewereconvertingthe 

1-5voltinputsignaltoa10-50mAoutputsignal(anolder,obsoleteinstrumentationstandard 

forindustry),we’dusea100 Ωprecisionresistorinstead. 

Anothernameforthiscircuitistransconductanceamplifier. Inelectronics,transconductanceisthemathematicalratioofcurrentchangedividedbyvoltagechange(∆I/∆V),anditismeasuredintheunitofSiemens,thesameunitusedtoexpressconductance(themathematicalreciprocalofresistance:current/voltage).Inthiscircuit,thetransconductanceratiois 

fixedbythevalueofthe250 Ωresistor,givingalinearcurrent-out/voltage-inrelationship. 

• REVIEW: 

• Inindustry,DCcurrentsignalsareoftenusedinpreferencetoDCvoltagesignalsas 

analogrepresentationsofphysicalquantities. Currentinaseriescircuitisabsolutely 

equalatallpointsinthatcircuitregardlessofwiringresistance,whereasvoltageina 

parallel-connectedcircuitmayvaryfromendtoendbecauseofwireresistance,making 

current-signalingmoreaccuratefromthe”transmitting”tothe”receiving”instrument. 

• Voltagesignalsarerelativelyeasytoproducedirectlyfromtransducerdevices,whereas 

accuratecurrentsignalsarenot.Op-ampscanbeusedto”convert”avoltagesignalinto 

acurrentsignalquiteeasily. Inthismode,theop-ampwilloutputwhatevervoltageis 

necessarytomaintaincurrentthroughthesignalingcircuitatthepropervalue. 

- 

R load 

+


8.8 Averagerandsummercircuits 

Ifwetakethreeequalresistorsandconnectoneendofeachtoacommonpoint,thenapply 

threeinputvoltages(onetoeachoftheresistors’freeends),thevoltageseenatthecommon 

pointwillbethemathematicalaverageofthethree. 

V 1 V 2 V 3 

"Passive averager" circuit 

R 1 

R 2 

R 3 

V out 

= 

V1 R1 + 

V2 R2 + 

V3 R3 1 1 1 

R + + 

1 R2 R3 

With equal value resistors: 

Vout = V1 + V2 3 

+ V3 ThiscircuitisreallynothingmorethanapracticalapplicationofMillman’sTheorem: 

R 1 R 2 R 3 

V 1 V 2 V 3 

V out 

= 

V1 R1 + 

V2 R2 + 

V3 R3 1 1 1 

R + + 

1 R2 R3 

Thiscircuitiscommonlyknownasapassiveaverager,becauseitgeneratesanaveragevoltagewithnon-amplifyingcomponents.Passivesimplymeansthatitisanunamplifiedcircuit. 

ThelargeequationtotherightoftheaveragercircuitcomesfromMillman’sTheorem,which 

describesthevoltageproducedbymultiplevoltagesourcesconnectedtogetherthroughindividualresistances.Sincethethreeresistorsintheaveragercircuitareequaltoeachother,we 

cansimplifyMillman’sformulabywritingR1,R2,andR3simplyasR(one,equalresistance 

insteadofthreeindividualresistances):

8.8. AVERAGERANDSUMMERCIRCUITS 381 

V out = 

V out = 

V1 R 

V2 + R 

V3 + R 

1 

R + 

1 

R + 

1 

R 

V1 + V2 R 

3 

R 

+ V3 Vout = V1 + V2 + V3 3 

Ifwetakeapassiveaverageranduseittoconnectthreeinputvoltagesintoanop-amp 

amplifiercircuitwithagainof3,wecanturnthisaveragingfunctionintoanadditionfunction. 

Theresultiscalledanoninvertingsummercircuit: 

V 1 

V 2 

V 3 

1 kΩ 2 kΩ 

R 

R 

R 

− 

+ 

Withavoltagedividercomposedofa2kΩ/1kΩcombination,thenoninvertingamplifier 

circuitwillhaveavoltagegainof3. Bytakingthevoltagefromthepassiveaverager,which 

isthesumofV1,V2,andV3dividedby3,andmultiplyingthataverageby3,wearriveatan 

outputvoltageequaltothesumofV1,V2,andV3: 

V out = 3 V 1 + V 2 + V 3 

3 

V out = V 1 + V 2 + V 3 

Muchthesamecanbedonewithaninvertingop-ampamplifier,usingapassiveaverager 

aspartofthevoltagedividerfeedbackcircuit.Theresultiscalledaninvertingsummercircuit: 

V out


V 1 

V 2 

V 3 

R 

R 

R 

I 1 

I 2 

I 3 

0 V 

0 V 

− 

+ 

R 

I 1 + I 2 + I 3 

Now,withtheright-handsidesofthethreeaveragingresistorsconnectedtothevirtual 

groundpointoftheop-amp’sinvertinginput,Millman’sTheoremnolongerdirectlyappliesas 

itdidbefore.Thevoltageatthevirtualgroundisnowheldat0voltsbytheop-amp’snegative 

feedback,whereasbeforeitwasfreetofloattotheaveragevalueofV1,V2,andV3.However, 

withallresistorvaluesequaltoeachother,thecurrentsthrougheachofthethreeresistors 

willbeproportionaltotheirrespectiveinputvoltages.Sincethosethreecurrentswilladdat 

thevirtualgroundnode,thealgebraicsumofthosecurrentsthroughthefeedbackresistorwill 

produceavoltageatVoutequaltoV1+V2+V3,exceptwithreversedpolarity.Thereversalin 

polarityiswhatmakesthiscircuitaninvertingsummer: 

V out = -(V 1 + V 2 + V 3) 

Summer(adder)circuitsarequiteusefulinanalogcomputerdesign,justasmultiplierand 

dividercircuitswouldbe.Again,itistheextremelyhighdifferentialgainoftheop-ampwhich 

allowsustobuildtheseusefulcircuitswithabareminimumofcomponents. 

• REVIEW: 

• Asummercircuitisonethatsums,oradds,multipleanalogvoltagesignalstogether. 

Therearetwobasicvarietiesofop-ampsummercircuits:noninvertingandinverting. 

8.9 Buildingadifferentialamplifier 

Anop-ampwithnofeedbackisalreadyadifferentialamplifier,amplifyingthevoltagedifferencebetweenthetwoinputs.However,itsgaincannotbecontrolled,anditisgenerallytoohigh 

tobeofanypracticaluse.Sofar,ourapplicationofnegativefeedbacktoop-ampshasresulting 

inthepracticallossofoneoftheinputs,theresultingamplifieronlygoodforamplifyingasinglevoltagesignalinput.Withalittleingenuity,however,wecanconstructanop-ampcircuit 

maintainingbothvoltageinputs,yetwithacontrolledgainsetbyexternalresistors. 

V out

8.9. BUILDINGADIFFERENTIALAMPLIFIER 383 

V 1 

V 2 

R R 

− 

+ 

R R 

Ifalltheresistorvaluesareequal,thisamplifierwillhaveadifferentialvoltagegainof1. 

Theanalysisofthiscircuitisessentiallythesameasthatofaninvertingamplifier,exceptthat 

thenoninvertinginput(+)oftheop-ampisatavoltageequaltoafractionofV2,ratherthan 

beingconnecteddirectlytoground.Aswouldstandtoreason,V2functionsasthenoninverting 

inputandV1functionsastheinvertinginputofthefinalamplifiercircuit.Therefore: 

V out = V 2 - V 1 

Ifwewantedtoprovideadifferentialgainofanythingotherthan1,wewouldhaveto 

adjusttheresistancesinbothupperandlowervoltagedividers,necessitatingmultipleresistor 

changesandbalancingbetweenthetwodividersforsymmetricaloperation.Thisisnotalways 

practical,forobviousreasons. 

Anotherlimitationofthisamplifierdesignisthefactthatitsinputimpedancesarerather 

lowcomparedtothatofsomeotherop-ampconfigurations,mostnotablythenoninverting 

(single-endedinput)amplifier. Eachinputvoltagesourcehastodrivecurrentthrougharesistance,whichconstitutesfarlessimpedancethanthebareinputofanop-ampalone. 

The 

solutiontothisproblem,fortunately,isquitesimple.Allweneedtodois”buffer”eachinput 

voltagesignalthroughavoltagefollowerlikethis: 

V 1 

V 2 

+ 

− 

− 

+ 

R R 

− 

+ 

R R 

NowtheV1andV2inputlinesareconnectedstraighttotheinputsoftwovoltage-follower 

op-amps,givingveryhighimpedance.Thetwoop-ampsontheleftnowhandlethedrivingof 

currentthroughtheresistorsinsteadoflettingtheinputvoltagesources(whatevertheymay 

be)doit.Theincreasedcomplexitytoourcircuitisminimalforasubstantialbenefit. 

V out 

V out


8.10 Theinstrumentationamplifier 

Assuggestedbefore,itisbeneficialtobeabletoadjustthegainoftheamplifiercircuitwithout 

havingtochangemorethanoneresistorvalue,asisnecessarywiththepreviousdesignof 

differentialamplifier. Theso-calledinstrumentationbuildsonthelastversionofdifferential 

amplifiertogiveusthatcapability: 

V 1 

V 2 

+ 

− 

− 

+ 

R 

R gain 

R 

3 

4 

1 

2 

R R 

− 

+ 

R R 

Thisintimidatingcircuitisconstructedfromabuffereddifferentialamplifierstagewith 

threenewresistorslinkingthetwobuffercircuitstogether.Considerallresistorstobeofequal 

valueexceptforRgain. Thenegativefeedbackoftheupper-leftop-ampcausesthevoltageat 

point1(topofRgain)tobeequaltoV1. Likewise,thevoltageatpoint2(bottomofRgain)is 

heldtoavalueequaltoV2. ThisestablishesavoltagedropacrossRgainequaltothevoltage 

differencebetweenV1andV2.ThatvoltagedropcausesacurrentthroughRgain,andsincethe 

feedbackloopsofthetwoinputop-ampsdrawnocurrent,thatsameamountofcurrentthrough 

Rgainmustbegoingthroughthetwo”R”resistorsaboveandbelowit.Thisproducesavoltage 

dropbetweenpoints3and4equalto: 

V3-4 = (V2 - V1)(1 + 2R ) 

Rgain Theregulardifferentialamplifierontheright-handsideofthecircuitthentakesthisvoltagedropbetweenpoints3and4,andamplifiesitbyagainof1(assumingagainthatall”R” 

resistorsareofequalvalue).Thoughthislookslikeacumbersomewaytobuildadifferential 

amplifier,ithasthedistinctadvantagesofpossessingextremelyhighinputimpedancesonthe 

V1andV2inputs(becausetheyconnectstraightintothenoninvertinginputsoftheirrespectiveop-amps),andadjustablegainthatcanbesetbyasingleresistor.Manipulatingtheabove 

formulaabit,wehaveageneralexpressionforoverallvoltagegainintheinstrumentation 

amplifier: 

A 2R 

V = (1 + ) 

Rgain Thoughitmaynotbeobviousbylookingattheschematic,wecanchangethedifferential 

gainoftheinstrumentationamplifiersimplybychangingthevalueofoneresistor:Rgain.Yes, 

wecouldstillchangetheoverallgainbychangingthevaluesofsomeoftheotherresistors, 

V out

8.11. DIFFERENTIATORANDINTEGRATORCIRCUITS 385 

butthiswouldnecessitatebalancedresistorvaluechangesforthecircuittoremainsymmetrical. 

PleasenotethatthelowestgainpossiblewiththeabovecircuitisobtainedwithRgain 

completelyopen(infiniteresistance),andthatgainvalueis1. 

• REVIEW: 

• Aninstrumentationamplifierisadifferentialop-ampcircuitprovidinghighinputimpedances 

witheaseofgainadjustmentthroughthevariationofasingleresistor. 

8.11 Differentiatorandintegratorcircuits 

Byintroducingelectricalreactanceintothefeedbackloopsofop-ampamplifiercircuits,wecan 

causetheoutputtorespondtochangesintheinputvoltageovertime. Drawingtheirnames 

fromtheirrespectivecalculusfunctions,theintegratorproducesavoltageoutputproportional 

totheproduct(multiplication)oftheinputvoltageandtime;andthedifferentiator(nottobe 

confusedwithdifferential)producesavoltageoutputproportionaltotheinputvoltage’srateof 

change. 

Capacitancecanbedefinedasthemeasureofacapacitor’soppositiontochangesinvoltage. 

Thegreaterthecapacitance,themoretheopposition. Capacitorsopposevoltagechangeby 

creatingcurrentinthecircuit:thatis,theyeitherchargeordischargeinresponsetoachange 

inappliedvoltage.So,themorecapacitanceacapacitorhas,thegreateritschargeordischarge 

currentwillbeforanygivenrateofvoltagechangeacrossit. Theequationforthisisquite 

simple: 

Changing 

DC 

voltage 

i = C dv 

dt 

Thedv/dtfractionisacalculusexpressionrepresentingtherateofvoltagechangeover 

time.IftheDCsupplyintheabovecircuitweresteadilyincreasedfromavoltageof15volts 

toavoltageof16voltsoveratimespanof1hour,thecurrentthroughthecapacitorwould 

mostlikelybeverysmall,becauseoftheverylowrateofvoltagechange(dv/dt=1volt/3600 

seconds). However,ifwesteadilyincreasedtheDCsupplyfrom15voltsto16voltsovera 

shortertimespanof1second,therateofvoltagechangewouldbemuchhigher,andthusthe 

chargingcurrentwouldbemuchhigher(3600timeshigher,tobeexact). Sameamountof 

changeinvoltage,butvastlydifferentratesofchange,resultinginvastlydifferentamountsof 

currentinthecircuit. 

Toputsomedefinitenumberstothisformula,ifthevoltageacrossa47 µFcapacitorwas 

changingatalinearrateof3voltspersecond,thecurrent”through”thecapacitorwouldbe 

(47 µF)(3V/s)=141 µA. 

Wecanbuildanop-ampcircuitwhichmeasureschangeinvoltagebymeasuringcurrent 

throughacapacitor,andoutputsavoltageproportionaltothatcurrent: 

C


V in 

C 

Differentiator 

0 V 

0 V 

0 V 

− 

+ 

Theright-handsideofthecapacitorisheldtoavoltageof0volts,duetothe”virtualground” 

effect.Therefore,current”through”thecapacitorissolelyduetochangeintheinputvoltage. 

Asteadyinputvoltagewon’tcauseacurrentthroughC,butachanginginputvoltagewill. 

Capacitorcurrentmovesthroughthefeedbackresistor,producingadropacrossit,which 

isthesameastheoutputvoltage. Alinear,positiverateofinputvoltagechangewillresult 

inasteadynegativevoltageattheoutputoftheop-amp. Conversely,alinear,negativerate 

ofinputvoltagechangewillresultinasteadypositivevoltageattheoutputoftheop-amp. 

Thispolarityinversionfrominputtooutputisduetothefactthattheinputsignalisbeing 

sent(essentially)totheinvertinginputoftheop-amp,soitactsliketheinvertingamplifier 

mentionedpreviously. Thefastertherateofvoltagechangeattheinput(eitherpositiveor 

negative),thegreaterthevoltageattheoutput. 

Theformulafordeterminingvoltageoutputforthedifferentiatorisasfollows: 

V out = -RC dv in 

dt 

Applicationsforthis,besidesrepresentingthederivativecalculusfunctioninsideofananalogcomputer,includerate-of-changeindicatorsforprocessinstrumentation.Onesuchrateof-changesignalapplicationmightbeformonitoring(orcontrolling)therateoftemperaturechangeinafurnace,wheretoohighortoolowofatemperatureriseratecouldbedetrimental.TheDCvoltageproducedbythedifferentiatorcircuitcouldbeusedtodriveacomparator, 

whichwouldsignalanalarmoractivateacontroliftherateofchangeexceededapre-setlevel. 

Inprocesscontrol,thederivativefunctionisusedtomakecontroldecisionsformaintaining 

aprocessatsetpoint,bymonitoringtherateofprocesschangeovertimeandtakingactionto 

preventexcessiveratesofchange,whichcanleadtoanunstablecondition.Analogelectronic 

controllersusevariationsofthiscircuitrytoperformthederivativefunction. 

Ontheotherhand,thereareapplicationswhereweneedpreciselytheoppositefunction, 

calledintegrationincalculus.Here,theop-ampcircuitwouldgenerateanoutputvoltageproportionaltothemagnitudeanddurationthataninputvoltagesignalhasdeviatedfrom0volts.Stateddifferently,aconstantinputsignalwouldgenerateacertainrateofchangeintheoutputvoltage:differentiationinreverse.Todothis,allwehavetodoisswapthecapacitorand 

resistorinthepreviouscircuit: 

R 

V out

8.11. DIFFERENTIATORANDINTEGRATORCIRCUITS 387 

V in 

R 

Integrator 

0 V 

0 V 

0 V 

− 

+ 

Asbefore,thenegativefeedbackoftheop-ampensuresthattheinvertinginputwillbeheld 

at0volts(thevirtualground).Iftheinputvoltageisexactly0volts,therewillbenocurrent 

throughtheresistor,thereforenochargingofthecapacitor,andthereforetheoutputvoltage 

willnotchange.Wecannotguaranteewhatvoltagewillbeattheoutputwithrespecttoground 

inthiscondition,butwecansaythattheoutputvoltagewillbeconstant. 

However,ifweapplyaconstant,positivevoltagetotheinput,theop-ampoutputwillfall 

negativeatalinearrate,inanattempttoproducethechangingvoltageacrossthecapacitor 

necessarytomaintainthecurrentestablishedbythevoltagedifferenceacrosstheresistor. 

Conversely,aconstant,negativevoltageattheinputresultsinalinear,rising(positive)voltage 

attheoutput.Theoutputvoltagerate-of-changewillbeproportionaltothevalueoftheinput 

voltage. 

C 

V out 

Theformulafordeterminingvoltageoutputfortheintegratorisasfollows: 

dv out 

dt 

= - V in 

RC 

or 

t 

V out = ∫ - 

0 

V in 

RC 

dt + c 

Where, 

c = Output voltage at start time (t=0) 

Oneapplicationforthisdevicewouldbetokeepa”runningtotal”ofradiationexposure, 

ordosage,iftheinputvoltagewasaproportionalsignalsuppliedbyanelectronicradiation 

detector.Nuclearradiationcanbejustasdamagingatlowintensitiesforlongperiodsoftime 

asitisathighintensitiesforshortperiodsoftime. Anintegratorcircuitwouldtakeboth 

theintensity(inputvoltagemagnitude)andtimeintoaccount,generatinganoutputvoltage 

representingtotalradiationdosage. 

Anotherapplicationwouldbetointegrateasignalrepresentingwaterflow,producinga 

signalrepresentingtotalquantityofwaterthathaspassedbytheflowmeter.Thisapplication 

ofanintegratorissometimescalledatotalizerintheindustrialinstrumentationtrade.


• REVIEW: 

• Adifferentiatorcircuitproducesaconstantoutputvoltageforasteadilychanginginput 

voltage. 

• Anintegratorcircuitproducesasteadilychangingoutputvoltageforaconstantinput 

voltage. 

• Bothtypesofdevicesareeasilyconstructed,usingreactivecomponents(usuallycapacitorsratherthaninductors)inthefeedbackpartofthecircuit. 

8.12 Positivefeedback 

Aswe’veseen,negativefeedbackisanincrediblyusefulprinciplewhenappliedtooperational 

amplifiers. Itiswhatallowsustocreateallthesepracticalcircuits,beingabletoprecisely 

setgains,rates,andothersignificantparameterswithjustafewchangesofresistorvalues. 

Negativefeedbackmakesallthesecircuitsstableandself-correcting. 

Thebasicprincipleofnegativefeedbackisthattheoutputtendstodriveinadirection 

thatcreatesaconditionofequilibrium(balance).Inanop-ampcircuitwithnofeedback,there 

isnocorrectivemechanism,andtheoutputvoltagewillsaturatewiththetiniestamountof 

differentialvoltageappliedbetweentheinputs.Theresultisacomparator: 

Withnegativefeedback(theoutputvoltage”fedback”somehowtotheinvertinginput),the 

circuittendstopreventitselffromdrivingtheoutputtofullsaturation. Rather,theoutput 

voltagedrivesonlyashighoraslowasneededtobalancethetwoinputs’voltages: 

0 V 

V in 

Negative feedback 

− 

+ 

V out = V in 

Whethertheoutputisdirectlyfedbacktotheinverting(-)inputorcoupledthroughasetof 

components,theeffectisthesame:theextremelyhighdifferentialvoltagegainoftheop-amp 

willbe”tamed”andthecircuitwillrespondaccordingtothedictatesofthefeedback”loop” 

connectingoutputtoinvertinginput. 

Anothertypeoffeedback,namelypositivefeedback,alsofindsapplicationinop-ampcircuits. 

Unlikenegativefeedback,wheretheoutputvoltageis”fedback”totheinverting(-) 

input,withpositivefeedbacktheoutputvoltageissomehowroutedbacktothenoninverting 

V out

8.12. POSITIVEFEEDBACK 389 

(+)input.Initssimplestform,wecouldconnectastraightpieceofwirefromoutputtononinvertinginputandseewhathappens: 

Positive feedback 

+ 

− 

Theinvertinginputremainsdisconnectedfromthefeedbackloop,andisfreetoreceivean 

externalvoltage.Let’sseewhathappensifwegroundtheinvertinginput: 

0 V 

+ 

− 

Withtheinvertinginputgrounded(maintainedatzerovolts),theoutputvoltagewillbe 

dictatedbythemagnitudeandpolarityofthevoltageatthenoninvertinginput.Ifthatvoltage 

happenstobepositive,theop-ampwilldriveitsoutputpositiveaswell,feedingthatpositive 

voltagebacktothenoninvertinginput,whichwillresultinfullpositiveoutputsaturation.On 

theotherhand,ifthevoltageonthenoninvertinginputhappenstostartoutnegative,theopamp’soutputwilldriveinthenegativedirection,feedingbacktothenoninvertinginputand 

resultinginfullnegativesaturation. 

Whatwehavehereisacircuitwhoseoutputisbistable: stableinoneoftwostates(saturatedpositiveorsaturatednegative). 

Onceithasreachedoneofthosesaturatedstates,it 

willtendtoremaininthatstate,unchanging.Whatisnecessarytogetittoswitchstatesisa 

voltageplacedupontheinverting(-)inputofthesamepolarity,butofaslightlygreatermagnitude.Forexample,ifourcircuitissaturatedatanoutputvoltageof+12volts,itwilltakean 

inputvoltageattheinvertinginputofatleast+12voltstogettheoutputtochange.Whenit 

changes,itwillsaturatefullynegative. 

So,anop-ampwithpositivefeedbacktendstostayinwhateveroutputstateitsalreadyin. 

It”latches”betweenoneoftwostates,saturatedpositiveorsaturatednegative. Technically, 

thisisknownashysteresis. 

Hysteresiscanbeausefulpropertyforacomparatorcircuittohave.Aswe’veseenbefore, 

comparatorscanbeusedtoproduceasquarewavefromanysortoframpingwaveform(sine 

wave,trianglewave,sawtoothwave,etc.) input. IftheincomingACwaveformisnoise-free 

(thatis,a”pure”waveform),asimplecomparatorwillworkjustfine. 

V out 

V out


V in 

− 

+ 

+V 

-V 

Square wave 

output voltage 

AC input 

voltage 

V out 

A "clean" AC input waveform produces predictable 

transition points on the output voltage square wave 

DC reference 

voltage 

However,ifthereexistanyanomaliesinthewaveformsuchasharmonicsor”spikes”which 

causethevoltagetoriseandfallsignificantlywithinthetimespanofasinglecycle,acomparator’soutputmightswitchstatesunexpectedly: 

V in 

− 

+ 

+V 

-V 

Square wave 


AC input 

voltage 

V out 

DC reference 

voltage 

Anytimethereisatransitionthroughthereferencevoltagelevel,nomatterhowtinythat 

transitionmaybe,theoutputofthecomparatorwillswitchstates,producingasquarewave 

with”glitches.” 

Ifweaddalittlepositivefeedbacktothecomparatorcircuit,wewillintroducehysteresis 

intotheoutput.Thishysteresiswillcausetheoutputtoremaininitscurrentstateunlessthe 

ACinputvoltageundergoesamajorchangeinmagnitude.

8.12. POSITIVEFEEDBACK 391 

V in 

− 

+ 

+V 

-V 

V out 

Positive feedback 

resistor 

Whatthisfeedbackresistorcreatesisadual-referenceforthecomparatorcircuit. The 

voltageappliedtothenoninverting(+)inputasareferencewhichtocomparewiththeincoming 

ACvoltagechangesdependingonthevalueoftheop-amp’soutputvoltage. Whentheopampoutputissaturatedpositive,thereferencevoltageatthenoninvertinginputwillbemore 

positivethanbefore.Conversely,whentheop-ampoutputissaturatednegative,thereference 

voltageatthenoninvertinginputwillbemorenegativethanbefore. Theresultiseasierto 

understandonagraph: 

square wave 


AC input 

voltage 

DC reference voltages 

upper center lower 

Whentheop-ampoutputissaturatedpositive,theupperreferencevoltageisineffect,and 

theoutputwon’tdroptoanegativesaturationlevelunlesstheACinputrisesabovethatupper 

referencelevel.Conversely,whentheop-ampoutputissaturatednegative,thelowerreference 

voltageisineffect,andtheoutputwon’trisetoapositivesaturationlevelunlesstheACinput 

dropsbelowthatlowerreferencelevel.Theresultisacleansquare-waveoutputagain,despite 

significantamountsofdistortionintheACinputsignal. Inorderfora”glitch”tocausethe 

comparatortoswitchfromonestatetoanother,itwouldhavetobeatleastasbig(tall)asthe 

differencebetweentheupperandlowerreferencevoltagelevels,andattherightpointintime 

tocrossboththoselevels. 

Anotherapplicationofpositivefeedbackinop-ampcircuitsisintheconstructionofoscillatorcircuits.Anoscillatorisadevicethatproducesanalternating(AC),oratleastpulsing, 

outputvoltage.Technically,itisknownasanastabledevice:havingnostableoutputstate(no 

equilibriumwhatsoever). Oscillatorsareveryusefuldevices,andtheyareeasilymadewith 

justanop-ampandafewexternalcomponents.


V ref 

Oscillator circuit using positive feedback 

C 

R 

V ramp 

V ramp 

V ref 

− 

+ 

R 

R 

V out 

V out is a square wave just like V ref, only taller 

Whentheoutputissaturatedpositive,theVref willbepositive,andthecapacitorwill 

chargeupinapositivedirection.WhenVrampexceedsVrefbythetiniestmargin,theoutput 

willsaturatenegative,andthecapacitorwillchargeintheoppositedirection(polarity). Oscillationoccursbecausethepositivefeedbackisinstantaneousandthenegativefeedbackis 

delayed(bymeansofanRCtimeconstant).Thefrequencyofthisoscillatormaybeadjusted 

byvaryingthesizeofanycomponent. 

• REVIEW: 

• Negativefeedbackcreatesaconditionofequilibrium(balance).Positivefeedbackcreates 

aconditionofhysteresis(thetendencyto”latch”inoneoftwoextremestates). 

• Anoscillatorisadeviceproducinganalternatingorpulsingoutputvoltage. 

8.13 Practicalconsiderations 

Realoperationalhavesomeimperfectionscomparedtoan“ideal”model.Arealdevicedeviates 

fromaperfectdifferenceamplifier.Oneminusonemaynotbezero.Itmayhavehaveanoffset 

likeananalogmeterwhichisnotzeroed. Theinputsmaydrawcurrent. Thecharacteristics 

maydriftwithageandtemperature. Gainmaybereducedathighfrequencies,andphase 

mayshiftfrominputtooutput. Theseimperfectionmaycausenonoticableerrorsinsome 

applications,unacceptableerrorsinothers. Insomecasestheseerrorsmaybecompensated 

for.Sometimesahigherquality,highercostdeviceisrequired.

8.13. PRACTICALCONSIDERATIONS 393 

8.13.1 Common-modegain 

Asstatedbefore,anidealdifferentialamplifieronlyamplifiesthevoltagedifferencebetween 

itstwoinputs. Ifthetwoinputsofadifferentialamplifierweretobeshortedtogether(thus 

ensuringzeropotentialdifferencebetweenthem),thereshouldbenochangeinoutputvoltage 

foranyamountofvoltageappliedbetweenthosetwoshortedinputsandground: 

V common-mode 

− 

+ 

V out 

V out should remain the same 

regardless of V common-mode 

Voltagethatiscommonbetweeneitheroftheinputsandground,as”Vcommon−mode”is 

inthiscase,iscalledcommon-modevoltage. Aswevarythiscommonvoltage,theperfect 

differentialamplifier’soutputvoltageshouldholdabsolutelysteady(nochangeinoutputfor 

anyarbitrarychangeincommon-modeinput).Thistranslatestoacommon-modevoltagegain 

ofzero. 

A V = Change in V out 

Change in V in 

. . . if change in V out = 0 . . . 

0 

Change in V in 

A V = 0 

= 0 

Theoperationalamplifier,beingadifferentialamplifierwithhighdifferentialgain,would 

ideallyhavezerocommon-modegainaswell.Inreallife,however,thisisnoteasilyattained. 

Thus,common-modevoltageswillinvariablyhavesomeeffectontheop-amp’soutputvoltage. 

Theperformanceofarealop-ampinthisregardismostcommonlymeasuredintermsofits 

differentialvoltagegain(howmuchitamplifiesthedifferencebetweentwoinputvoltages)versusitscommon-modevoltagegain(howmuchitamplifiesacommon-modevoltage).Theratio 

oftheformertothelatteriscalledthecommon-moderejectionratio,abbreviatedasCMRR: 

Differential AV CMRR = 

Common-mode AV Anidealop-amp,withzerocommon-modegainwouldhaveaninfiniteCMRR.Realop-amps 

havehighCMRRs,theubiquitous741havingsomethingaround70dB,whichworksouttoa


littleover3,000intermsofaratio. 

Becausethecommonmoderejectionratioinatypicalop-ampissohigh,common-modegain 

isusuallynotagreatconcernincircuitswheretheop-ampisbeingusedwithnegativefeedback.Ifthecommon-modeinputvoltageofanamplifiercircuitweretosuddenlychange,thusproducingacorrespondingchangeintheoutputduetocommon-modegain,thatchangeinoutputwouldbequicklycorrectedasnegativefeedbackanddifferentialgain(beingmuchgreater 

thancommon-modegain)workedtobringthesystembacktoequilibrium. Sureenough,a 

changemightbeseenattheoutput,butitwouldbealotsmallerthanwhatyoumightexpect. 

Aconsiderationtokeepinmind,though,iscommon-modegainindifferentialop-ampcircuitssuchasinstrumentationamplifiers.Outsideoftheop-amp’ssealedpackageandextremelyhighdifferentialgain,wemayfindcommon-modegainintroducedbyanimbalanceof 

resistorvalues. Todemonstratethis,we’llrunaSPICEanalysisonaninstrumentationamplifierwithinputsshortedtogether(nodifferentialvoltage),imposingacommon-modevoltage 

toseewhathappens. First,we’llruntheanalysisshowingtheoutputvoltageofaperfectly 

balancedcircuit. Weshouldexpecttoseenochangeinoutputvoltageasthecommon-mode 

voltagechanges: 

V 1 

0 

R jump 

(jumper 

wire) 

instrumentation amplifier 

v1 1 0 

rin1 1 0 9e12 

rjump 1 4 1e-12 

rin2 4 0 9e12 

e1 3 0 1 2 999k 

e2 6 0 4 5 999k 

e3 9 0 8 7 999k 

rload 9 0 10k 

r1 2 3 10k 

rgain 2 5 10k 

r2 5 6 10k 

r3 3 7 10k 

r4 7 9 10k 

r5 6 8 10k 

2 

5 

1 

4 

+ 

− 

− 

+ 

E 1 

E 2 

R 1 

R gain 

R 2 

3 

6 

2 

5 

R 3 

R 5 

7 

8 

7 

8 

− 

+ 

E 3 

R 4 

R 6 

9 

9 

0 

V out


r6 8 0 10k 

.dc v1 0 10 1 

.print dc v(9) 

.end 

v1 v(9) 

0.000E+00 0.000E+00 

1.000E+00 1.355E-16 

2.000E+00 2.710E-16 

3.000E+00 0.000E+00 As you can see, the output voltage v(9) 

4.000E+00 5.421E-16 hardly changes at all for a common-mode 

5.000E+00 0.000E+00 input voltage (v1) that sweeps from 0 

6.000E+00 0.000E+00 to 10 volts. 

7.000E+00 0.000E+00 

8.000E+00 1.084E-15 

9.000E+00 -1.084E-15 

1.000E+01 0.000E+00 

Asidefromverysmalldeviations(actuallyduetoquirksofSPICEratherthanrealbehavior 

ofthecircuit),theoutputremainsstablewhereitshouldbe:at0volts,withzeroinputvoltage 

differential.However,let’sintroducearesistorimbalanceinthecircuit,increasingthevalueof 

R5from10,000 Ωto10,500 Ω,andseewhathappens(thenetlisthasbeenomittedforbrevity 

–theonlythingalteredisthevalueofR5): 

v1 v(9) 

0.000E+00 0.000E+00 

1.000E+00 -2.439E-02 

2.000E+00 -4.878E-02 

3.000E+00 -7.317E-02 This time we see a significant variation 

4.000E+00 -9.756E-02 (from 0 to 0.2439 volts) in output voltage 

5.000E+00 -1.220E-01 as the common-mode input voltage sweeps 

6.000E+00 -1.463E-01 from 0 to 10 volts as it did before. 

7.000E+00 -1.707E-01 

8.000E+00 -1.951E-01 

9.000E+00 -2.195E-01 

1.000E+01 -2.439E-01 

Ourinputvoltagedifferentialisstillzerovolts,yettheoutputvoltagechangessignificantly 

asthecommon-modevoltageischanged.Thisisindicativeofacommon-modegain,something 

we’retryingtoavoid. Morethanthat,itsacommon-modegainofourownmaking,having 

nothingtodowithimperfectionsintheop-ampsthemselves.Withamuch-tempereddifferentialgain(actuallyequalto3inthisparticularcircuit)andnonegativefeedbackoutsidethe 

circuit,thiscommon-modegainwillgouncheckedinaninstrumentsignalapplication. 

Thereisonlyonewaytocorrectthiscommon-modegain,andthatistobalancealltheresistorvalues.Whendesigninganinstrumentationamplifierfromdiscretecomponents(rather 

thanpurchasingoneinanintegratedpackage),itiswisetoprovidesomemeansofmaking


fineadjustmentstoatleastoneofthefourresistorsconnectedtothefinalop-amptobeableto 

”trimaway”anysuchcommon-modegain.Providingthemeansto”trim”theresistornetwork 

hasadditionalbenefitsaswell. Supposethatallresistorvaluesareexactlyastheyshould 

be,butacommon-modegainexistsduetoanimperfectioninoneoftheop-amps. Withthe 

adjustmentprovision,theresistancecouldbetrimmedtocompensateforthisunwantedgain. 

Onequirkofsomeop-ampmodelsisthatofoutputlatch-up,usuallycausedbythecommonmodeinputvoltageexceedingallowablelimits.Ifthecommon-modevoltagefallsoutsideofthe 

manufacturer’sspecifiedlimits,theoutputmaysuddenly”latch”inthehighmode(saturateat 

fulloutputvoltage).InJFET-inputoperationalamplifiers,latch-upmayoccurifthecommonmodeinputvoltageapproachestoocloselytothenegativepowersupplyrailvoltage. 

Onthe 

TL082op-amp,forexample,thisoccurswhenthecommon-modeinputvoltagecomeswithin 

about0.7voltsofthenegativepowersupplyrailvoltage.Suchasituationmayeasilyoccurin 

asingle-supplycircuit,wherethenegativepowersupplyrailisground(0volts),andtheinput 

signalisfreetoswingto0volts. 

Latch-upmayalsobetriggeredbythecommon-modeinputvoltageexceedingpowersupply 

railvoltages,negativeorpositive. Asarule,youshouldneveralloweitherinputvoltageto 

riseabovethepositivepowersupplyrailvoltage,orsinkbelowthenegativepowersupply 

railvoltage,eveniftheop-ampinquestionisprotectedagainstlatch-up(asarethe741and 

1458op-ampmodels).Attheveryleast,theop-amp’sbehaviormaybecomeunpredictable.At 

worst,thekindoflatch-uptriggeredbyinputvoltagesexceedingpowersupplyvoltagesmay 

bedestructivetotheop-amp. 

Whilethisproblemmayseemeasytoavoid,itspossibilityismorelikelythanyoumight 

think. Considerthecaseofanoperationalamplifiercircuitduringpower-up. Ifthecircuit 

receivesfullinputsignalvoltagebeforeitsownpowersupplyhashadtimeenoughtocharge 

thefiltercapacitors,thecommon-modeinputvoltagemayeasilyexceedthepowersupplyrail 

voltagesforashorttime. Iftheop-ampreceivessignalvoltagefromacircuitsuppliedbya 

differentpowersource,anditsownpowersourcefails,thesignalvoltage(s)mayexceedthe 

powersupplyrailvoltagesforanindefiniteamountoftime! 

8.13.2 Offsetvoltage 

Anotherpracticalconcernforop-ampperformanceisvoltageoffset. Thatis,effectofhaving 

theoutputvoltagesomethingotherthanzerovoltswhenthetwoinputterminalsareshorted 

together. Rememberthatoperationalamplifiersaredifferentialamplifiersaboveall:they’re 

supposedtoamplifythedifferenceinvoltagebetweenthetwoinputconnectionsandnothing 

more.Whenthatinputvoltagedifferenceisexactlyzerovolts,wewould(ideally)expecttohave 

exactlyzerovoltspresentontheoutput.However,intherealworldthisrarelyhappens.Even 

iftheop-ampinquestionhaszerocommon-modegain(infiniteCMRR),theoutputvoltagemay 

notbeatzerowhenbothinputsareshortedtogether.Thisdeviationfromzeroiscalledoffset.


+15 V 

− 

+ 

-15 V 

V out = +14.7 V (saturated +) 

Aperfectop-ampwouldoutputexactlyzerovoltswithbothitsinputsshortedtogetherand 

grounded. However,mostop-ampsofftheshelfwilldrivetheiroutputstoasaturatedlevel, 

eithernegativeorpositive.Intheexampleshownabove,theoutputvoltageissaturatedata 

valueofpositive14.7volts,justabitlessthan+V(+15volts)duetothepositivesaturation 

limitofthisparticularop-amp. Becausetheoffsetinthisop-ampisdrivingtheoutputtoa 

completelysaturatedpoint,there’snowayoftellinghowmuchvoltageoffsetispresentatthe 

output.Ifthe+V/-Vsplitpowersupplywasofahighenoughvoltage,whoknows,maybethe 

outputwouldbeseveralhundredvoltsonewayortheotherduetotheeffectsofoffset! 

Forthisreason,offsetvoltageisusuallyexpressedintermsoftheequivalentamountof 

inputvoltagedifferentialproducingthiseffect. Inotherwords,weimaginethattheop-amp 

isperfect(nooffsetwhatsoever),andasmallvoltageisbeingappliedinserieswithoneofthe 

inputstoforcetheoutputvoltageonewayortheotherawayfromzero. Beingthatop-amp 

differentialgainsaresohigh,thefigurefor”inputoffsetvoltage”doesn’thavetobemuchto 

accountforwhatweseewithshortedinputs: 

+15 V 

− 

+ 

-15 V 

Input offset voltage 

(internal to the real op-amp, 

external to this ideal op-amp) 

V out = +14.7 V (saturated +) 

Offsetvoltagewilltendtointroduceslighterrorsinanyop-ampcircuit. Sohowdowe 

compensateforit?Unlikecommon-modegain,thereareusuallyprovisionsmadebythemanufacturertotrimtheoffsetofapackagedop-amp.Usually,twoextraterminalsontheop-amp 

packagearereservedforconnectinganexternal”trim”potentiometer.Theseconnectionpoints 

arelabeledoffsetnullandareusedinthisgeneralway:


-15 V 

+15 V 

− 

+ 

V out 

Potentiometer adjusted so that 

V out = 0 volts with inputs shorted together 

Onsingleop-ampssuchasthe741and3130,theoffsetnullconnectionpointsarepins1 

and5onthe8-pinDIPpackage.Othermodelsofop-ampmayhavetheoffsetnullconnections 

locatedondifferentpins,and/orrequireaslightlydifferenceconfigurationoftrimpotentiometerconnection.Someop-ampsdon’tprovideoffsetnullpinsatall!Consultthemanufacturer’s 

specificationsfordetails. 

8.13.3 Biascurrent 

Inputsonanop-amphaveextremelyhighinputimpedances.Thatis,theinputcurrentsenteringorexitinganop-amp’stwoinputsignalconnectionsareextremelysmall.Formostpurposesofop-ampcircuitanalysis,wetreatthemasthoughtheydon’texistatall.Weanalyzethecircuitasthoughtherewasabsolutelyzerocurrententeringorexitingtheinputconnections. 

Thisidyllicpicture,however,isnotentirelytrue.Op-amps,especiallythoseop-ampswith 

bipolartransistorinputs,havetohavesomeamountofcurrentthroughtheirinputconnectionsinorderfortheirinternalcircuitstobeproperlybiased. 

Thesecurrents,logically,are 

calledbiascurrents.Undercertainconditions,op-ampbiascurrentsmaybeproblematic.The 

followingcircuitillustratesoneofthoseproblemconditions: 

Thermocouple Vout + 

Atfirstglance,weseenoapparentproblemswiththiscircuit.Athermocouple,generatinga 

smallvoltageproportionaltotemperature(actually,avoltageproportionaltothedifferencein 

temperaturebetweenthemeasurementjunctionandthe”reference”junctionformedwhenthe 

alloythermocouplewiresconnectwiththecopperwiresleadingtotheop-amp)drivestheopampeitherpositiveornegative.Inotherwords,thisisakindofcomparatorcircuit,comparing 

thetemperaturebetweentheendthermocouplejunctionandthereferencejunction(nearthe 

op-amp). Theproblemisthis: thewireloopformedbythethermocoupledoesnotprovidea 

− 

+V 

-V


pathforbothinputbiascurrents,becausebothbiascurrentsaretryingtogothesameway 

(eitherintotheop-amporoutofit). 

I ? 

Thermocouple 

I ? 

+ 

Vout -V 

− 

+V 

This comparator circuit won’t work 

Inorderforthiscircuittoworkproperly,wemustgroundoneoftheinputwires,thus 

providingapathto(orfrom)groundforbothcurrents: 

Thermocouple 

+ 

Vout I I 

-V 

I 

− 

+V 

This comparator circuit will work 

Notnecessarilyanobviousproblem,butaveryrealone! 

Anotherwayinputbiascurrentsmaycausetroubleisbydroppingunwantedvoltagesacross 

circuitresistances.Takethiscircuitforexample: 

Voltage drop due 

to bias current: 

- Rin + 

V in 

I bias 

Voltage at (+) op-amp input 

will not be exactly equal to V in 

Weexpectavoltagefollowercircuitsuchastheoneabovetoreproducetheinputvoltage 

preciselyattheoutput.Butwhatabouttheresistanceinserieswiththeinputvoltagesource? 

Ifthereisanybiascurrentthroughthenoninverting(+)inputatall,itwilldropsomevoltage 

acrossRin,thusmakingthevoltageatthenoninvertinginputunequaltotheactualVinvalue. 

Biascurrentsareusuallyinthemicroamprange,sothevoltagedropacrossRinwon’tbevery 

much,unlessRinisverylarge. Oneexampleofanapplicationwheretheinputresistance 

− 

+ 

+V 

-V 

V out


(Rin)wouldbeverylargeisthatofpHprobeelectrodes,whereoneelectrodecontainsanionpermeableglassbarrier(averypoorconductor,withmillionsof 

Ωofresistance). 

Ifwewereactuallybuildinganop-ampcircuitforpHelectrodevoltagemeasurement,we’d 

probablywanttouseaFETorMOSFET(IGFET)inputop-ampinsteadofonebuiltwith 

bipolartransistors(forlessinputbiascurrent).Buteventhen,whatslightbiascurrentsmay 

remaincancausemeasurementerrorstooccur,sowehavetofindsomewaytomitigatethem 

throughgooddesign. 

Onewaytodosoisbasedontheassumptionthatthetwoinputbiascurrentswillbethe 

same.Inreality,theyareoftenclosetobeingthesame,thedifferencebetweenthemreferred 

toastheinputoffsetcurrent. Iftheyarethesame,thenweshouldbeabletocanceloutthe 

effectsofinputresistancevoltagedropbyinsertinganequalamountofresistanceinseries 

withtheotherinput,likethis: 

V in 

I bias 

R in(-) 

- + 

R in(+) 

- + 

I bias 

− 

+ 

Withtheadditionalresistanceaddedtothecircuit,theoutputvoltagewillbeclosertoVin 

thanbefore,evenifthereissomeoffsetbetweenthetwoinputcurrents. 

Forbothinvertingandnoninvertingamplifiercircuits,thebiascurrentcompensatingresistorisplacedinserieswiththenoninverting(+)inputtocompensateforbiascurrentvoltage 

dropsinthedividernetwork: 

V in 

+V 

-V 

Noninverting amplifier with 

compensating resistor 

R 1 

R comp 

− 

+ 

R 2 

R comp = R 1 // R 2 

V out 

V out


V in 

R 1 

Inverting amplifier with 

compensating resistor 

R comp 

Rcomp = R1 // R2 Ineithercase,thecompensatingresistorvalueisdeterminedbycalculatingtheparallel 

resistancevalueofR1andR2.WhyisthevalueequaltotheparallelequivalentofR1andR2? 

WhenusingtheSuperpositionTheoremtofigurehowmuchvoltagedropwillbeproducedby 

theinverting(-)input’sbiascurrent,wetreatthebiascurrentasthoughitwerecomingfrom 

acurrentsourceinsidetheop-ampandshort-circuitallvoltagesources(VinandVout). This 

givestwoparallelpathsforbiascurrent(throughR1andthroughR2,bothtoground). We 

wanttoduplicatethebiascurrent’seffectonthenoninverting(+)input,sotheresistorvalue 

wechoosetoinsertinserieswiththatinputneedstobeequaltoR1inparallelwithR2. 

Arelatedproblem,occasionallyexperiencedbystudentsjustlearningtobuildoperational 

amplifiercircuits,iscausedbyalackofacommongroundconnectiontothepowersupply.Itis 

imperativetoproperop-ampfunctionthatsometerminaloftheDCpowersupplybecommon 

tothe”ground”connectionoftheinputsignal(s). Thisprovidesacompletepathforthebias 

currents,feedbackcurrent(s),andfortheload(output)current.Takethiscircuitillustration, 

forinstance,showingaproperlygroundedpowersupply: 

R 1 

6 V 

- 

+ 

null 

R 2 

1 kΩ 1 kΩ 

Here,arrowsdenotethepathofelectronflowthroughthepowersupplybatteries,bothfor 

poweringtheop-amp’sinternalcircuitry(the”potentiometer”insideofitthatcontrolsoutput 

− 

+ 

+V 

-V 

R 2 

V out


voltage),andforpoweringthefeedbackloopofresistorsR1andR2.Suppose,however,thatthe 

groundconnectionforthis”split”DCpowersupplyweretoberemoved.Theeffectofdoingthis 

isprofound: 

A power supply ground is essential to circuit operation! 

R 1 

6 V 

- 

+ 

null 

R 2 

1 kΩ 1 kΩ 

+V 

-V 

broken 

connection 

Noelectronsmayflowinoroutoftheop-amp’soutputterminal,becausethepathwaytothe 

powersupplyisa”deadend.”Thus,noelectronsflowthroughthegroundconnectiontotheleft 

ofR1,neitherthroughthefeedbackloop. Thiseffectivelyrenderstheop-ampuseless:itcan 

neithersustaincurrentthroughthefeedbackloop,northroughagroundedload,sincethereis 

noconnectionfromanypointofthepowersupplytoground. 

Thebiascurrentsarealsostopped,becausetheyrelyonapathtothepowersupplyandback 

totheinputsourcethroughground.Thefollowingdiagramshowsthebiascurrents(only),as 

theygothroughtheinputterminalsoftheop-amp,throughthebaseterminalsoftheinput 

transistors,andeventuallythroughthepowersupplyterminal(s)andbacktoground.


Bias current paths shown, through power supply 

6 V 

I bias 

I bias 

- 

+ 

Withoutagroundreferenceonthepowersupply,thebiascurrentswillhavenocomplete 

pathforacircuit,andtheywillhalt.Sincebipolarjunctiontransistorsarecurrent-controlled 

devices,thisrenderstheinputstageoftheop-ampuselessaswell,asbothinputtransistors 

willbeforcedintocutoffbythecompletelackofbasecurrent. 

• REVIEW: 

• Op-ampinputsusuallyconductverysmallcurrents,calledbiascurrents,neededtoproperlybiasthefirsttransistoramplifierstageinternaltotheop-amps’circuitry.Biascurrentsaresmall(inthemicroamprange),butlargeenoughtocauseproblemsinsome 

applications. 

• Biascurrentsinbothinputsmusthavepathstoflowtoeitheroneofthepowersupply 

”rails”ortoground.Itisnotenoughtojusthaveaconductivepathfromoneinputtothe 

other. 

• Tocancelanyoffsetvoltagescausedbybiascurrentflowingthroughresistances,justadd 

anequivalentresistanceinserieswiththeotherop-ampinput(calledacompensating 

resistor). Thiscorrectivemeasureisbasedontheassumptionthatthetwoinputbias 

currentswillbeequal. 

• Anyinequalitybetweenbiascurrentsinanop-ampconstituteswhatiscalledaninput 

offsetcurrent. 

• Itisessentialforproperop-ampoperationthattherebeagroundreferenceonsometerminalofthepowersupply,toformcompletepathsforbiascurrents,feedbackcurrent(s), 

andloadcurrent. 

+V 

-V


8.13.4 Drift 

Beingsemiconductordevices,op-ampsaresubjecttoslightchangesinbehaviorwithchanges 

inoperatingtemperature. Anychangesinop-ampperformancewithtemperaturefallunder 

thecategoryofop-ampdrift.Driftparameterscanbespecifiedforbiascurrents,offsetvoltage, 

andthelike.Consultthemanufacturer’sdatasheetforspecificsonanyparticularop-amp. 

Tominimizeop-ampdrift,wecanselectanop-ampmadetohaveminimumdrift,and/orwe 

candoourbesttokeeptheoperatingtemperatureasstableaspossible.Thelatteractionmay 

involveprovidingsomeformoftemperaturecontrolfortheinsideoftheequipmenthousing 

theop-amp(s). Thisisnotasstrangeasitmayfirstseem. Laboratory-standardprecision 

voltagereferencegenerators,forexample,aresometimesknowntoemploy”ovens”forkeeping 

theirsensitivecomponents(suchaszenerdiodes)atconstanttemperatures.Ifextremelyhigh 

accuracyisdesiredovertheusualfactorsofcostandflexibility,thismaybeanoptionworth 

lookingat. 

• REVIEW: 

• Op-amps,beingsemiconductordevices,aresusceptibletovariationsintemperature.Any 

variationsinamplifierperformanceresultingfromchangesintemperatureisknownas 

drift.Driftisbestminimizedwithenvironmentaltemperaturecontrol. 

8.13.5 Frequencyresponse 

Withtheirincrediblyhighdifferentialvoltagegains,op-ampsareprimecandidatesforaphenomenonknownasfeedbackoscillation. 

You’veprobablyheardtheequivalentaudioeffect 

whenthevolume(gain)onapublic-addressorothermicrophoneamplifiersystemisturned 

toohigh:thathighpitchedsquealresultingfromthesoundwaveform”feedingback”through 

themicrophonetobeamplifiedagain. Anop-ampcircuitcanmanifestthissameeffect,with 

thefeedbackhappeningelectricallyratherthanaudibly. 

Acaseexampleofthisisseeninthe3130op-amp,ifitisconnectedasavoltagefollower 

withthebareminimumofwiringconnections(thetwoinputs,output,andthepowersupply 

connections). Theoutputofthisop-ampwillself-oscillateduetoitshighgain,nomatter 

whattheinputvoltage. Tocombatthis,asmallcompensationcapacitormustbeconnected 

totwospecially-providedterminalsontheop-amp. Thecapacitorprovidesahigh-impedance 

pathfornegativefeedbacktooccurwithintheop-amp’scircuitry,thusdecreasingtheACgain 

andinhibitingunwantedoscillations. Iftheop-ampisbeingusedtoamplifyhigh-frequency 

signals,thiscompensationcapacitormaynotbeneeded,butitisabsolutelyessentialforDCor 

low-frequencyACsignaloperation. 

Someop-amps,suchasthemodel741,haveacompensationcapacitorbuiltintominimize 

theneedforexternalcomponents.Thisimprovedsimplicityisnotwithoutacost:duetothat 

capacitor’spresenceinsidetheop-amp,thenegativefeedbacktendstogetstrongerasthe 

operatingfrequencyincreases(thatcapacitor’sreactancedecreaseswithhigherfrequencies). 

Asaresult,theop-amp’sdifferentialvoltagegaindecreasesasfrequencygoesup:itbecomes 

alesseffectiveamplifierathigherfrequencies. 

Op-ampmanufacturerswillpublishthefrequencyresponsecurvesfortheirproducts.Since 

asufficientlyhighdifferentialgainisabsolutelyessentialtogoodfeedbackoperationinop-amp


circuits,thegain/frequencyresponseofanop-ampeffectivelylimitsits”bandwidth”ofoperation.Thecircuitdesignermusttakethisintoaccountifgoodperformanceistobemaintained 

overtherequiredrangeofsignalfrequencies. 

• REVIEW: 

• Duetocapacitanceswithinop-amps,theirdifferentialvoltagegaintendstodecreaseas 

theinputfrequencyincreases.Frequencyresponsecurvesforop-ampsareavailablefrom 

themanufacturer. 

8.13.6 Inputtooutputphaseshift 

Inordertoillustratethephaseshiftfrominputtooutputofanoperationalamplifier(op-amp), 

theOPA227wastestedinourlab. TheOPA227wasconstructedinatypicalnon-inverting 

configuration(Figure8.1). 

Figure8.1:OPA227Non-invertingstage 

Thecircuitconfigurationcallsforasignalgainof ∼ =34V/Vor ∼ =50dB.Theinputexcitation 

atVsrcwassetto10mVp,andthreefrequenciesofinterest:2.2kHz,22kHz,and220MHz. 

TheOPA227’sopenloopgainandphasecurvevs.frequencyisshowninFigure8.2. 

Tohelppredicttheclosedloopphaseshiftfrominputtooutput,wecanusetheopenloop 

gainandphasecurve. Sincethecircuitconfigurationcallsforaclosedloopgain,or1/β,of 

∼=50dB,theclosedloopgaincurveintersectstheopenloopgaincurveatapproximately22 

kHz.Afterthisintersection,theclosedloopgaincurverollsoffatthetypical20dB/decadefor 

voltagefeedbackamplifiers,andfollowstheopenloopgaincurve. 

Whatisactuallyatworkhereisthenegativefeedbackfromtheclosedloopmodifiesthe 

openloopresponse. Closingtheloopwithnegativefeedbackestablishesaclosedlooppoleat 

22kHz.Muchlikethedominantpoleintheopenloopphasecurve,wewillexpectphaseshift 

intheclosedloopresponse.Howmuchphaseshiftwillwesee? 

Sincethenewpoleisnowat22kHz,thisisalsothe-3dBpointasthepolestartstorolloff 

theclosedloopagainat20dBperdecadeasstatedearlier. Aswithanypoleinbasiccontrol 

theory,phaseshiftstartstooccuronedecadeinfrequencybeforethepole,andendsat90 o of 

phaseshiftonedecadeinfrequencyafterthepole.Sowhatdoesthispredictfortheclosedloop 

responseinourcircuit?


Figure8.2:AVand Φvs.Frequencyplot 

Thiswillpredictphaseshiftstartingat2.2kHz,with45 o ofphaseshiftatthe-3dBpointof 

22kHz,andfinallyendingwith90 o ofphaseshiftat220kHz.ThethreeFiguresshownbelow 

areoscilloscopecapturesatthefrequenciesofinterestforourOPA227circuit. Figure8.3is 

setfor2.2kHz,andnonoticeablephaseshiftispresent. Figure8.4issetfor220kHz,and 

∼=45 o ofphaseshiftisrecorded.Finally,Figure8.5issetfor220MHz,andtheexpected ∼ =90 o 

ofphaseshiftisrecorded.ThescopeplotswerecapturedusingaLeCroy44xWavesurfer.The 

finalscopeplotusedax1probewiththetriggersettoHFreject. 

Figure8.3:OPA227Av=50dB@2.2kHz


Figure8.4:OPA227Av=50dB@22kHz 

Figure8.5:OPA227Av=50dB@220kHz


8.14 Operationalamplifiermodels 

Whilementionofoperationalamplifierstypicallyprovokesvisionsofsemiconductordevices 

builtasintegratedcircuitsonaminiaturesiliconchip,thefirstop-ampswereactuallyvacuum 

tubecircuits.Thefirstcommercial,generalpurposeoperationalamplifierwasmanufactured 

bytheGeorgeA.PhilbrickResearches,Incorporated,in1952. DesignatedtheK2-W,itwas 

builtaroundtwotwin-triodetubesmountedinanassemblywithanoctal(8-pin)socketforeasy 

installationandservicinginelectronicequipmentchassisofthatera. Theassemblylooked 

somethinglikethis: 

approx. 

4 inches 

The Philbrick Researches 

op-amp, model K2-W 

GAP/R 

MODEL 

K2-W 

Theschematicdiagramshowsthetwotubes,alongwithtenresistorsandtwocapacitors,a 

fairlysimplecircuitdesignevenby1952standards: 

Inverting (-) 

input 

Noninverting (+) 

input 

+300 V 

12AX7 

-300 V 

The Philbrick Researches op-amp, model K2-W 

220 kΩ 

220 kΩ 

500 pF 

510 kΩ 

1 MΩ 

2.2 MΩ 

12AX7 

221 kΩ 

9.1 kΩ 

680 kΩ 

7.5 pF 

120 kΩ 4.7 MΩ 

NE-68 

Output 

Incaseyou’reunfamiliarwiththeoperationofvacuumtubes,theyoperatesimilarlytoN-

8.14. OPERATIONALAMPLIFIERMODELS 409 

channeldepletion-typeIGFETtransistors:thatis,theyconductmorecurrentwhenthecontrol 

grid(thedashedline)ismademorepositivewithrespecttothecathode(thebentlinenearthe 

bottomofthetubesymbol),andconductlesscurrentwhenthecontrolgridismadelesspositive 

(ormorenegative)thanthecathode.Thetwintriodetubeontheleftfunctionsasadifferential 

pair,convertingthedifferentialinputs(invertingandnoninvertinginputvoltagesignals)into 

asingle,amplifiedvoltagesignalwhichisthenfedtothecontrolgridofthelefttriodeof 

thesecondtriodepairthroughavoltagedivider(1MΩ −−2.2MΩ). Thattriodeamplifies 

andinvertstheoutputofthedifferentialpairforalargervoltagegain,thentheamplified 

signaliscoupledtothesecondtriodeofthesamedual-triodetubeinanoninvertingamplifier 

configurationforalargercurrentgain. Thetwoneon”glowtubes”actasvoltageregulators, 

similartothebehaviorofsemiconductorzenerdiodes,toprovideabiasvoltageinthecoupling 

betweenthetwosingle-endedamplifiertriodes. 

Withadual-supplyvoltageof+300/-300volts,thisop-ampcouldonlyswingitsoutput+/- 

50volts,whichisverypoorbytoday’sstandards. Ithadanopen-loopvoltagegainof15,000 

to20,000,aslewrateof+/-12volts/µsecond,amaximumoutputcurrentof1mA,aquiescent 

powerconsumptionofover3watts(notincludingpowerforthetubes’filaments!),andcost 

about$24in1952dollars.Betterperformancecouldhavebeenattainedusingamoresophisticatedcircuitdesign,butonlyattheexpenseofgreaterpowerconsumption,greatercost,and 

decreasedreliability. 

Withtheadventofsolid-statetransistors,op-ampswithfarlessquiescentpowerconsumptionandincreasedreliabilitybecamefeasible,butmanyoftheotherperformanceparametersremainedaboutthesame.TakeforinstancePhilbrick’smodelP55A,ageneral-purposesolidstateop-ampcirca1966. 

TheP55Asportedanopen-loopgainof40,000,aslewrateof1.5 

volt/µsecondandanoutputswingof+/-11volts(atapowersupplyvoltageof+/-15volts), 

amaximumoutputcurrentof2.2mA,andacostof$49(orabout$21forthe”utilitygrade” 

version).TheP55A,aswellasotherop-ampsinPhilbrick’slineupofthetime,wasofdiscretecomponentconstruction,itsconstituenttransistors,resistors,andcapacitorshousedinasolid 

”brick”resemblingalargeintegratedcircuitpackage. 

Itisn’tverydifficulttobuildacrudeoperationalamplifierusingdiscretecomponents. A 

schematicofonesuchcircuitisshowninFigure8.6. 

Whileitsperformanceisratherdismalbymodernstandards,itdemonstratesthatcomplexityisnotnecessarytocreateaminimallyfunctionalop-amp.TransistorsQ3andQ4form 

theheartofanotherdifferentialpaircircuit,thesemiconductorequivalentofthefirsttriode 

tubeintheK2-Wschematic. Asitwasinthevacuumtubecircuit,thepurposeofadifferentialpairistoamplifyandconvertadifferentialvoltagebetweenthetwoinputterminalstoa 

single-endedoutputvoltage. 

Withtheadventofintegrated-circuit(IC)technology,op-ampdesignsexperiencedadramaticincreaseinperformance,reliability,density,andeconomy. 

Betweentheyearsof1964 

and1968,theFairchildcorporationintroducedthreemodelsofICop-amps:the702,709,and 

thestill-popular741.Whilethe741isnowconsideredoutdatedintermsofperformance,itis 

stillafavoriteamonghobbyistsforitssimplicityandfaulttolerance(short-circuitprotection 

ontheoutput,forinstance).Personalexperienceabusingmany741op-ampshasledmetothe 

conclusionthatitisahardchiptokill... 

Theinternalschematicdiagramforamodel741op-ampisshowninFigure8.7. 

Byintegratedcircuitstandards,the741isaverysimpledevice: anexampleofsmallscaleintegration,orSSItechnology. 

Itwouldbenosmallmattertobuildthiscircuitusing


input (+) 

Q 5 

+V 

Q 1 

Q 3 

-V 

Q 6 

Q 2 

Q 4 

(-) input 

Output 

A simple operational 

amplifier made from 

discrete components 

Figure8.6:Asimpleoperationalamplifiermadefromdiscretecomponents. 

(-) input 

(+) input 

offset null 

offset null 

R 1 

Q 1 

Q 3 

Q 5 

-V 

+V 

Q 7 

R 3 

Q 8 Q 9 Q 12 

Q 2 

Q 4 

Q 6 

R 2 

Q 10 

Internal schematic of a model 741 operational amplifier 

R 4 

R 5 

Q 11 

C 1 

Q 23 

Figure8.7:Schematicdiagramofamodel741op-amp. 

R 9 

Q 16 

Q 13 

Q 17 

R 8 

Q 24 

Q 18 

R 10 

Q 22 

Q 19 

R 11 

Q 15 

Q 21 

Q 14 

Q 20 

R 6 

R 7 

Output

8.14. OPERATIONALAMPLIFIERMODELS 411 

discretecomponents,soyoucanseetheadvantagesofeventhemostprimitiveintegrated 

circuittechnologyoverdiscretecomponentswherehighpartscountsareinvolved. 

Forthehobbyist,student,orengineerdesiringgreaterperformance,thereareliterallyhundredsofop-ampmodelstochoosefrom. 

Manysellforlessthanadollarapiece,evenretail! 

Special-purposeinstrumentationandradio-frequency(RF)op-ampsmaybequiteabitmore 

expensive.InthissectionIwillshowcaseseveralpopularandaffordableop-amps,comparing 

andcontrastingtheirperformancespecifications. Thevenerable741isincludedasa”benchmark”forcomparison,althoughitis,asIsaidbefore,consideredanobsoletedesign. 

Table8.1:Widelyusedoperationalamplifiers 

Model Devices/ Power Bandwidth Bias Slew Output 

package supply current rate current 

number (count) (V) (MHz) (nA) (V/µS) (mA) 

TL082 2 12/36 4 8 13 17 

LM301A 1 10/36 1 250 0.5 25 

LM318 1 10/40 15 500 70 20 

LM324 4 3/32 1 45 0.25 20 

LF353 2 12/36 4 8 13 20 

LF356 1 10/36 5 8 12 25 

LF411 1 10/36 4 20 15 25 

741C 1 10/36 1 500 0.5 25 

LM833 2 10/36 15 1050 7 40 

LM1458 2 6/36 1 800 10 45 

CA3130 1 5/16 15 0.05 10 20 

ListedinTable 8.1arebutafewofthelow-costoperationalamplifiermodelswidelyavailablefromelectronicssuppliers.Mostofthemareavailablethroughretailsupplystoressuchas 

RadioShack.Allareunder$1.00costdirectfromthemanufacturer(year2001prices).Asyou 

cansee,thereissubstantialvariationinperformancebetweensomeoftheseunits. Takefor 

instancetheparameterofinputbiascurrent:theCA3130winstheprizeforlowest,at0.05nA 

(or50pA),andtheLM833hasthehighestatslightlyover1µA.ThemodelCA3130achieves 

itsincrediblylowbiascurrentthroughtheuseofMOSFETtransistorsinitsinputstage.One 

manufactureradvertisesthe3130’sinputimpedanceas1.5tera-ohms,or1.5x10 12 Ω!Other 

op-ampsshownherewithlowbiascurrentfiguresuseJFETinputtransistors,whilethehigh 

biascurrentmodelsusebipolarinputtransistors. 

Whilethe741isspecifiedinmanyelectronicprojectschematicsandshowcasedinmany 

textbooks,itsperformancehaslongbeensurpassedbyotherdesignsineverymeasure.Even 

somedesignsoriginallybasedonthe741havebeenimprovedovertheyearstofarsurpass 

originaldesignspecifications. Onesuchexampleisthemodel1458,twoop-ampsinan8-pin 

DIPpackage,whichatonetimehadtheexactsameperformancespecificationsasthesingle 

741. Initslatestincarnationitboastsawiderpowersupplyvoltagerange,aslewrate50 

timesasgreat,andalmosttwicetheoutputcurrentcapabilityofa741,whilestillretaining 

theoutputshort-circuitprotectionfeatureofthe741.Op-ampswithJFETandMOSFETinput 

transistorsfarexceedthe741’sperformanceintermsofbiascurrent,andgenerallymanageto 

beatthe741intermsofbandwidthandslewrateaswell.


Myownpersonalrecommendationsforop-ampsareassuch: whenlowbiascurrentisa 

priority(suchasinlow-speedintegratorcircuits),choosethe3130. Forgeneral-purposeDC 

amplifierwork,the1458offersgoodperformance(andyougettwoop-ampsinthespaceof 

onepackage).Foranupgradeinperformance,choosethemodel353,asitisapin-compatible 

replacementforthe1458. The353isdesignedwithJFETinputcircuitryforverylowbias 

current,andhasabandwidth4timesaregreatasthe1458,althoughitsoutputcurrentlimit 

islower(butstillshort-circuitprotected).Itmaybemoredifficulttofindontheshelfofyour 

localelectronicssupplyhouse,butitisjustasreasonablypricedasthe1458. 

Iflowpowersupplyvoltageisarequirement,Irecommendthemodel324,asitfunctions 

onaslowas3voltsDC.Itsinputbiascurrentrequirementsarealsolow,anditprovidesfour 

op-ampsinasingle14-pinchip.Itsmajorweaknessisspeed,limitedto1MHzbandwidthand 

anoutputslewrateofonly0.25voltsper µs.Forhigh-frequencyACamplifiercircuits,the318 

isaverygood”generalpurpose”model. 

Special-purposeop-ampsareavailableformodestcostwhichprovidebetterperformance 

specifications.Manyofthesearetailoredforaspecifictypeofperformanceadvantage,suchas 

maximumbandwidthorminimumbiascurrent.Takeforinstancetheop-amps,bothdesigned 

forhighbandwidthinTable 8.2. 

Table8.2:Highbandwidthoperationalamplifiers 




CLC404 1 10/14 232 44,000 2600 70 

CLC425 1 5/14 1900 40,000 350 90 

TheCLC404listsat$21.80(almostasmuchasGeorgePhilbrick’sfirstcommercialopamp,albeitwithoutcorrectionforinflation),whiletheCLC425isquiteabitlessexpensiveat 

$3.23perunit.Inbothcaseshighspeedisachievedattheexpenseofhighbiascurrentsand 

restrictivepowersupplyvoltageranges. Someop-amps,designedforhighpoweroutputare 

listedinTable8.3. 

Table8.3:Highcurrentoperationalamplifiers 




LM12CL 1 15/80 0.7 1000 9 13,000 

LM7171 1 5.5/36 200 12,000 4100 100 

Yes,theLM12CLactuallyhasanoutputcurrentratingof13amps(13,000milliamps)! 

Itlistsat$14.40,whichisnotalotofmoney,consideringtherawpowerofthedevice. The 

LM7171,ontheotherhand,tradeshighcurrentoutputabilityforfastvoltageoutputability 

(ahighslewrate).Itlistsat$1.19,aboutaslowassome”generalpurpose”op-amps. 

Amplifierpackagesmayalsobepurchasedascompleteapplicationcircuitsasopposedto 

bareoperationalamplifiers. TheBurr-BrownandAnalogDevicescorporations,forexample,

8.15. DATA 413 

bothlongknownfortheirprecisionamplifierproductlines,offerinstrumentationamplifiers 

inpre-designedpackagesaswellasotherspecializedamplifierdevices.Indesignswherehigh 

precisionandrepeatabilityafterrepairisimportant,itmightbeadvantageousforthecircuit 

designertochoosesuchapre-engineeredamplifier”block”ratherthanbuildthecircuitfrom 

individualop-amps.Ofcourse,theseunitstypicallycostquiteabitmorethanindividualopamps. 

8.15 Data 

Parametricaldataforallsemiconductorop-ampmodelsexcepttheCA3130comesfromNationalSemiconductor’sonlineresources,availableatthiswebsite: 

(http://www.national.com). 

DatafortheCA3130comesfromHarrisSemiconductor’sCA3130/CA3130Adatasheet(file 

number817.4). 

Contributors 



WayneLittle(June2007):Author,“Inputtooutputphaseshift”subsection,in“Practical 

considerations”section.

414 CHAPTER8. OPERATIONALAMPLIFIERS

Chapter9 

PRACTICALANALOG 

SEMICONDUCTORCIRCUITS 

Contents 

9.1 ElectroStaticDischarge. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .415 

9.1.1 ESDDamagePrevention. . . . . . . . . . . . . . . . . . . . . . . . . . . .416 

9.1.2 StorageandTransportationofESDsensitivecomponentandboards. . .419 

9.1.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .420 

9.2 Powersupplycircuits–INCOMPLETE . . . . . . . . . . . . . . . . . . . . .420 

9.2.1 Unregulated . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .421 

9.2.2 Linearregulated . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .421 

9.2.3 Switching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .421 

9.2.4 Rippleregulated. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .422 

9.3 Amplifiercircuits–PENDING. . . . . . . . . . . . . . . . . . . . . . . . . . .422 

9.4 Oscillatorcircuits–INCOMPLETE. . . . . . . . . . . . . . . . . . . . . . . .422 

9.4.1 Varactormultiplier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .422 

9.5 Phase-lockedloops–PENDING..........................424 

9.6 Radiocircuits–INCOMPLETE . . . . . . . . . . . . . . . . . . . . . . . . . .424 

9.7 Computationalcircuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .433 

9.8 Measurementcircuits–INCOMPLETE . . . . . . . . . . . . . . . . . . . . .455 

9.9 Controlcircuits–PENDING . . . . . . . . . . . . . . . . . . . . . . . . . . . .456 

Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .456 


9.1 ElectroStaticDischarge 

VolumeIchapter1.1discussesstaticelectricity,andhowitiscreated. Thishasalotmore 

significancethanmightbefirstassumed,ascontrolofstaticelectricityplaysalargepartin 

415

416 CHAPTER9. PRACTICALANALOGSEMICONDUCTORCIRCUITS 

modernelectronicsandotherprofessions. AnElectroStaticDischargeeventiswhenastatic 

chargeisbledoffinanuncontrolledfashion,andwillbereferredtoasESDhereafter. 

ESDcomesinmanyforms,itcanbeassmallas50voltsofelectricitybeingequalizedup 

totensofthousandsofvolts. Theactualpowerisextremelysmall,sosmallthatnodanger 

isgenerallyofferedtosomeonewhoisinthedischargepathofESD.Itusuallytakesseveral 

thousandvoltsforapersontoevennoticeESDintheformofasparkandthefamiliarzap 

thataccompaniesit.TheproblemwithESDisevenasmalldischargethatcangocompletely 

unnoticedcanruinsemiconductors.Astaticchargeofthousandsofvoltsiscommon,however 

thereasonitisnotathreatisthereisnocurrentofanysubstantialdurationbehindit.These 

extremevoltagesdoallowionizationoftheairandallowothermaterialstobreakdown,which 

istherootofwherethedamagecomesfrom. 

ESDisnotanewproblem.Blackpowdermanufacturingandotherpyrotechnicindustries 

havealwaysbeendangerousifanESDeventoccursinthewrongcircumstance. Duringthe 

eraoftubes(AKAvalves)ESDwasanonexistentissueforelectronics,butwiththeadventof 

semiconductors,andtheincreaseinminiaturization,ithasbecomemuchmoreserious. 

Damagetocomponentscan,andusuallydo,occurwhenthepartisintheESDpath.Many 

parts,suchaspowerdiodes,areveryrobustandcanhandlethedischarge,butifaparthas 

asmallorthingeometryaspartoftheirphysicalstructurethenthevoltagecanbreakdown 

thatpartofthesemiconductor.Currentsduringtheseeventsbecomequitehigh,butareinthe 

nanosecondtomicrosecondtimeframe. Partofthecomponentisleftpermanentlydamaged 

bythis,whichcancausetwotypesoffailuremodes. Catastrophicistheeasyone,leaving 

thepartcompletelynonfunctional.Theothercanbemuchmoreserious.Latentdamagemay 

allowtheproblemcomponenttoworkforhours,daysorevenmonthsaftertheinitialdamage 

beforecatastrophicfailure.Manytimesthesepartsarereferredtoas”walkingwounded”,since 

theyareworkingbutbad.Figure9.1isshownanexampleoflatent(”walkingwounded”)ESD 

damage. Ifthesecomponentsendupinalifesupportrole,suchasmedicalormilitaryuse, 

thentheconsequencescanbegrim.Formosthobbyistsitisaninconvenience,butitcanbean 

expensiveone. 

EvencomponentsthatareconsideredfairlyruggedcanbedamagedbyESD.Bipolartransistors,theearliestofthesolidstateamplifiers,arenotimmune,thoughlesssusceptible.Someofthenewerhighspeedcomponentscanberuinedwithaslittleas3volts.Therearecomponentsthatmightnotbeconsideredatrisk,suchassomespecializedresistorsandcapacitors 

manufacturedusingMOS(MetalOxideSemiconductor)technology,thatcanbedamagedvia 

ESD. 

9.1.1 ESDDamagePrevention 

BeforeESDcanbepreventeditisimportanttounderstandwhatcausesit.Generallymaterials 

aroundtheworkbenchcanbebrokenupinto3categories. TheseareESDGenerative,ESD 

Neutral,andESDDissipative(orESDConductive).ESDGenerativematerialsareactivestatic 

generators,suchasmostplastics,cathair,andpolyesterclothing.ESDNeutralmaterialsare 

generallyinsulative,butdon’ttendtogenerateorholdstaticchargesverywell.Examplesof 

thisincludewood,paper,andcotton.Thisisnottosaytheycannotbestaticgeneratorsoran 

ESDhazard,buttheriskissomewhatminimizedbyotherfactors.Woodandwoodproducts, 

forexample,tendtoholdmoisture,whichcanmakethemslightlyconductive.Thisistrueof 

alotoforganicmaterials.Ahighlypolishedtablewouldnotfallunderthiscategory,because

9.1. ELECTROSTATICDISCHARGE 417 

Figure9.1: 

theglossisusuallyplastic,orvarnish,whicharehighlyefficientinsulators.ESDConductive 

materialsareprettyobvious,theyarethemetaltoolslayingaround. Plastichandlescanbe 

aproblem,butthemetalwillbleedastaticchargeawayasfastasitisgeneratedifitisona 

groundedsurface.Therearealotofothermaterials,suchassomeplastics,thataredesigned 

tobeconductive.TheywouldfallundertheheadingofESDDissipative.Dirtandconcreteare 

alsoconductive,andfallundertheESDDissipativeheading. 

Therearealotofactivitiesthatgeneratestatic,whichyouneedtobeawareofaspartof 

anESDcontrolregimen.Thesimpleactofpullingtapeoffadispensercangenerateextreme 

voltage. Rollingaroundinachairisanotherstaticgenerator,asisscratching. Infact,any 

activitythatallows2ormoresurfacestorubagainsteachotherisprettycertaintogenerate 

somestaticcharge.Thiswasmentionedinthebeginningofthisbook,butrealworldexamples 

canbesubtle.Thisiswhyamethodforcontinuouslybleedingoffthisvoltageisneeded.Things 

thatgeneratehugeamountsofstaticshouldbeavoidedwhileworkingoncomponents. 

Plasticisusuallyassociatedwiththegenerationofstatic.Thishasbeengottenaroundin 

theformofconductiveplastics.Theusualwaytomakeconductiveplasticisanadditivethat 

changestheelectricalcharacteristicsoftheplasticfromaninsulatortoaconductor,although 

itwilllikelystillhavearesistanceofmillionsofohmspersquareinch. Plasticshavebeen 

developedthatcanbeusedasconductorsisinlowweightapplications,suchasthoseinthe 

airlineindustries.Thesearespecialistapplications,andarenotgenerallyassociatedwithESD 

control. 

ItisnotallbadnewsforESDprotection. Thehumanbodyisaprettydecentconductor. 

Highhumidityintheairwillalsoallowastaticchargetodissipateharmlesslyaway,aswell 

asmakingESDNeutralmaterialsmoreconductive. Thisiswhycoldwinterdays,wherethe 

humidityinsideahousecanbequitelow,canincreasethenumberofsparksonadoorknob. 

Summer,orrainydays,youwouldhavetoworkquitehardtogenerateasubstantialamountof 

static.Industrycleanroomsandfactoryfloorsgotheefforttoregulatebothtemperatureand 

humidityforthisreason. Concretefloorsarealsoconductive,sotheremaybesomeexisting 

componentsinthehomethatcanaidinsettingupprotections.


ToestablishESDprotectiontherehastobeastandardvoltagelevelthateverythingis 

referencedto. Suchalevelexistsintheformofground. Thereareverygoodsafetyreasons 

thatgroundisusedaroundthehouseinoutlets. Insomewaysthisrelatestostatic,butnot 

directly.Itdoesgiveusaplacetodumpourexcesselectrons,oracquiresomeifweareshort, 

toneutralizeanychargesourbodiesandtoolsmightacquire.Ifeverythingonaworkbenchis 

connecteddirectlyorindirectlytogroundviaaconductorthenstaticwilldissipatelongbefore 

anESDeventhasachancetooccur. 

Agoodgroundingpointcanbemadeseveraldifferentways.Inhouseswithmodernwiring 

thatisuptocodethegroundpinontheACplugincanbeused,orthescrewthatholdsthe 

outletscoverplateon. Thisisbecausehousewiringactuallyhasawireorspikegoinginto 

theearthsomewherewherethepoweristappedfromthemainpowerlines.Forpeoplewhose 

housewiringisn’tquiterightaspikedrivenintotheearthatleast3feetorasimpleelectrical 

connectiontometalplumbing(worstoption)canbeused. Themainthingistoestablishan 

electricalpathtotheearthoutsidethehouse. 

TenmegohmsisconsideredaconductorintheworldofESDcontrol. Staticelectricityis 

voltagewithnorealcurrent,andifachargeisbledoffsecondsafterbeinggenerateditis 

nullified.Generallya1to10megohmresistorisusedtoconnectanyESDprotectionforthis 

reason.IthasthebenefitofslowingthedischargerateduringanESDevent,whichincreases 

thelikelihoodofacomponentsurvivingundamaged.Thefasterthedischarge,thehigherthe 

currentspikegoingthoughthecomponent. Anotherreasonsucharesistanceisconsidered 

desirableisiftheuserisaccidentallyshortedtohighvoltage,suchashouseholdcurrent,it 

won’tbetheESDprotectionsthatkillthem. 

AlargeindustryhasgrownuparoundcontrollingESDintheelectronicsindustry. The 

stapleofanyelectronicsconstructionistheworkbenchwithastaticconductiveordissipative 

surface.Thissurfacecanbeboughtcommercially,orhomemadeintheformofasheetofmetal 

orfoil.Inthecaseofametalsurfaceitmightbeagoodideatolaythinpaperontop,althoughit 

isnotnecessaryifyouarenotdoinganypoweredtestsonthesurface.Thecommercialversion 

isusuallysomeformofconductiveplasticwhoseresistanceishighenoughnottobeaproblem, 

whichisabettersolution. Ifyouaremakingyourownsurfacefortheworkbenchbesureto 

addthe10megohmresistortoground,otherwiseyouhavenoprotectionatall. 

TheotherbigitemthatneedsESDgroundedisyou.Peoplearewalkingstaticgenerators. 

Yourbodybeingconductiveitisrelativelyeasytogrounditthough,thisisusuallydonewith 

awriststrap.Commercialversionsalreadyhavetheresistorbuiltin,andhaveawidestrapto 

offeragoodcontactsurfacewithyourskin.Disposableversionscanbeboughtforafewdollars. 

AmetalwatchbandisalsoagoodESDprotectionconnectionpoint.Justaddawire(withthe 

resistor)toyourgroundingpoint.Mostindustriestaketheissueseriouslyenoughtousereal 

timemonitorsthatwillsoundanalarmiftheoperatorisnotproperlygrounded. 

Anotherwayofgroundingyourselfisaheelstrap. Aconductiveplasticpartiswrapped 

aroundtheheelofyourshoe,withaconductiveplasticstrapgoingupandunderyoursockfor 

goodcontactwiththeskin.Itonlyworksonfloorswithconductivewaxorconcrete.Themethod 

willkeepapersonfromgeneratinglargechargesthatcanoverwhelmotherESDprotections, 

andisnotconsideredadequateinandofitself.Youcangetthesameeffectbywalkingbarefoot 

onaconcretefloor. 

YetanotherESDprotectionistowearESDconductivesmocks.Liketheheelstrap,thisis 

asecondaryprotection,notmeanttoreplacethewriststrap.Theyaremeanttoshortcircuit 

anychargesthatyourclothesmaygenerate.

9.1. ELECTROSTATICDISCHARGE 419 

Figure9.2: 

Movingaircanalsogeneratesubstantialstaticcharges.Whenyoublowdustoffyourelectronicstheirwillbestaticgenerated.Anindustrialsolutiontotheproblemtothisissueistwo 

fold: Firstly,airgunshaveasmall,wellshieldedradioactivematerialimplantedwithinthe 

airguntoionizetheair.Ionizedairisaconductor,andwillbleedoffstaticchargesquitewell. 

Secondly,usehighvoltageelectricitytoionizetheaircomingoutofafan,whichhasthesame 

effectastheairgun. ThiswilleffectivelyhelpaworkstationreducethepotentialforESD 

generationbyalargeamount. 

AnotherESDprotectionisthesimplestofall,distance.Manyindustrieshaverulesstating 

allNeutralandGenerativematerialswillbeatleast12inchesormorefromanyworkin 

progress. 

TheusercanalsoreducethepossibilityofESDdamagebysimplynotremovingthepart 

outofitsprotectivepackaginguntilitistimetoinsertitintothecircuit.Thiswillreducethe 

likelihoodofESDexposure,andwhilethecircuitwillstillbevulnerable,thecomponentwill 

havesomeminorprotectionfromtherestofthecomponents,astheothercomponentswilloffer 

differentdischargepathsforESD. 

9.1.2 StorageandTransportationofESDsensitivecomponentand 

boards 

ItdoesnogoodtofollowESDprotectionsontheworkbenchifthepartsarebeingdamaged 

whilestoringorcarryingthem. ThemostcommonmethodistouseavariationofaFaraday 

cage,anESDbag.AnESDbagsurroundsthecomponentwithaconductiveshield,andusually 

hasanonstaticgeneratinginsulativelayerinside.InpermanentFaradaycagesthisshieldis 

grounded,asinthecaseofRFIrooms,butwithportablecontainersthisisn’tpractical. By


puttingaESDbagonagroundedsurfacethesamethingisaccomplished.Faradaycageswork 

byroutingtheelectricchargearoundthecontentsandgroundingthemimmediately. Acar 

struckbylightningisanextremeexampleofaFaradaycage. 

Staticbagsarebyfarthemostcommonmethodofstoringcomponentsandboards. They 

aremadeusingextremelythinlayersofmetal,sothinastobealmosttransparent.Abagwith 

ahole,evensmallones,oronethatisnotfoldedontoptosealthecontentfromoutsidecharges 

isineffective. 

Anothermethodofprotectingpartsinstorageistotesortubes.Inthesecasesthepartsare 

putintoconductiveboxes,withalidofthesamematerial. ThiseffectivelyformsaFaraday 

cage. AtubeismeantforICsandotherdeviceswithalotofpins,andstoresthepartsina 

moldedconductiveplastictubethatkeepsthepartssafebothmechanicallyandelectrically. 

9.1.3 Conclusion 

Figure9.3: 

ESDcanbeaminorunfelteventmeasuringafewvolts,oramassiveeventpresentingreal 

dangerstooperators.AllESDprotectionscanbeoverwhelmedbycircumstance,butthiscan 

becircumventedbyawarenessofwhatitisandhowtopreventit. Manyprojectshavebeen 

builtwithnoESDprotectionsatallandworkedwell.Giventhatprotectingtheseprojectsisa 

minorinconvenienceitisbettertomaketheeffort. 

Industrytakestheproblemveryseriously,asbothapotentiallifethreateningissueanda 

qualityissue.Someonewhobuysanexpensivepieceofelectronicsorhightechhardwareisnot 

goingtobehappyiftheyhavetoreturnitin6months.Whenareputationisonthelineitis 

easiertodotherightthing. 

9.2 Powersupplycircuits–INCOMPLETE 

Therearethreemajorkindsofpowersupplies: unregulated(alsocalledbruteforce),linear 

regulated,andswitching.Afourthtypeofpowersupplycircuitcalledtheripple-regulated,isa 

hybridbetweenthe”bruteforce”and”switching”designs,andmeritsasubsectiontoitself.

9.2. POWERSUPPLYCIRCUITS–INCOMPLETE 421 

9.2.1 Unregulated 

Anunregulatedpowersupplyisthemostrudimentarytype,consistingofatransformer,rectifier,andlow-passfilter. 

Thesepowersuppliestypicallyexhibitalotofripplevoltage(i.e. 

rapidly-varyinginstability)andotherAC”noise”superimposedontheDCpower.Iftheinput 

voltagevaries,theoutputvoltagewillvarybyaproportionalamount. Theadvantageofan 

unregulatedsupplyisthatitscheap,simple,andefficient. 

9.2.2 Linearregulated 

Alinearregulatedsupplyissimplya”bruteforce”(unregulated)powersupplyfollowedbya 

transistorcircuitoperatinginits”active,”or”linear”mode,hencethenamelinearregulator. 

(Obviousinretrospect,isn’tit?)Atypicallinearregulatorisdesignedtooutputafixedvoltage 

forawiderangeofinputvoltages,anditsimplydropsanyexcessinputvoltagetoallowa 

maximumoutputvoltagetotheload. Thisexcessvoltagedropresultsinsignificantpower 

dissipationintheformofheat.Iftheinputvoltagegetstoolow,thetransistorcircuitwilllose 

regulation,meaningthatitwillfailtokeepthevoltagesteady.Itcanonlydropexcessvoltage, 

notmakeupforadeficiencyinvoltagefromthebruteforcesectionofthecircuit.Therefore,you 

havetokeeptheinputvoltageatleast1to3voltshigherthanthedesiredoutput,depending 

ontheregulatortype. Thismeansthepowerequivalentofatleast1to3voltsmultipliedby 

thefullloadcurrentwillbedissipatedbytheregulatorcircuit,generatingalotofheat.This 

makeslinearregulatedpowersuppliesratherinefficient.Also,togetridofallthatheatthey 

havetouselargeheatsinkswhichmakesthemlarge,heavy,andexpensive. 

9.2.3 Switching 

Aswitchingregulatedpowersupply(”switcher”)isanefforttorealizetheadvantagesofboth 

bruteforceandlinearregulateddesigns(small,efficient,andcheap,butalso”clean,”stable 

outputvoltage).SwitchingpowersuppliesworkontheprincipleofrectifyingtheincomingAC 

powerlinevoltageintoDC,re-convertingitintohigh-frequencysquare-waveACthroughtransistorsoperatedason/offswitches,steppingthatACvoltageupordownbyusingalightweighttransformer,thenrectifyingthetransformer’sACoutputintoDCandfilteringforfinaloutput. 

Voltageregulationisachievedbyalteringthe”dutycycle”oftheDC-to-ACinversionon 

thetransformer’sprimaryside.Inadditiontolighterweightbecauseofasmallertransformer 

core,switchershaveanothertremendousadvantageoverthepriortwodesigns: thistypeof 

powersupplycanbemadesototallyindependentoftheinputvoltagethatitcanworkonany 

electricpowersystemintheworld;thesearecalled”universal”powersupplies. 

Thedownsideofswitchersisthattheyaremorecomplex,andduetotheiroperationthey 

tendtogeneratealotofhigh-frequencyAC”noise”onthepowerline.Mostswitchersalsohave 

significantripplevoltageontheiroutputs.Withthecheapertypes,thisnoiseandripplecanbe 

asbadasforanunregulatedpowersupply;suchlow-endswitchersaren’tworthless,because 

theystillprovideastableaverageoutputvoltage,andthere’sthe”universal”inputcapability. 

Expensiveswitchersareripple-freeandhavenoisenearlyaslowasforsomealineartypes; 

theseswitcherstendtobeasexpensiveaslinearsupplies. Thereasontouseanexpensive 

switcherinsteadofagoodlinearisifyouneeduniversalpowersystemcompatibilityorhigh


efficiency.Highefficiency,lightweight,andsmallsizearethereasonsswitchingpowersupplies 

arealmostuniversallyusedforpoweringdigitalcomputercircuitry. 

9.2.4 Rippleregulated 

Aripple-regulatedpowersupplyisanalternativetothelinearregulateddesignscheme: a 

”bruteforce”powersupply(transformer,rectifier,filter)constitutesthe”frontend”ofthecircuit,butatransistoroperatedstrictlyinitson/off(saturation/cutoff)modestransfersDCpowertoalargecapacitorasneededtomaintaintheoutputvoltagebetweenahighandalowsetpoint. 

Asinswitchers,thetransistorinarippleregulatorneverpassescurrentwhileinits 

”active,”or”linear,”modeforanysubstantiallengthoftime,meaningthatverylittleenergy 

willbewastedintheformofheat.However,thebiggestdrawbacktothisregulationschemeis 

thenecessarypresenceofsomeripplevoltageontheoutput,astheDCvoltagevariesbetween 

thetwovoltagecontrolsetpoints. Also,thisripplevoltagevariesinfrequencydependingon 

loadcurrent,whichmakesfinalfilteringoftheDCpowermoredifficult. 

Rippleregulatorcircuitstendtobequiteabitsimplerthanswitchercircuitry,andthey 

neednothandlethehighpowerlinevoltagesthatswitchertransistorsmusthandle,making 

themsafertoworkon. 

9.3 Amplifiercircuits–PENDING 

Note,Q3andQ4inFigure9.4arecomplementary,NPNandPNPrespectively. Thiscircuit 

workswellformoderatepoweraudioamplifiers.Foranexplanationofthiscircuitsee“Direct 

coupledcomplementary-pair,” 

(page255). 

9.4 Oscillatorcircuits–INCOMPLETE 

ThephaseshiftoscillatorofFigure9.5producesasinewaveoutputintheaudiofrequency 

range. Resistivefeedbackfromthecollectorwouldbenegativefeedbackdueto180 o phasing 

(basetocollectorphaseinversion). However,thethree60 o RCphaseshifters(R1C1,R2C2, 

andR3C3)provideanadditional180 o foratotalof360 o . Thisin-phasefeedbackconstitutes 

positivefeedback.Oscillationsresultiftransistorgainexceedsfeedbacknetworklosses. 

9.4.1 Varactormultiplier 

AVaractororvariablecapacitancediodewithanonlinearcapacitancevsfrequencycharacteristicdistortstheappliedsinewavef1inFigure9.6,generatingharmonics,f3. 

Thefundamentalfilterpassesf1,blockingtheharmonicsfromreturningtothegenerator. 

ThechokepassesDC,andblocksradiofrequencies(RF)fromenteringtheVbiassupply. The 

harmonicfilterpassesthedesiredharmonic,saythe3rd,totheoutput,f3. Thecapacitorat 

thebottomoftheinductorisalargevalue,lowreactance,toblockDCbutgroundtheinductor

9.4. OSCILLATORCIRCUITS–INCOMPLETE 423 

R 1 

39 kΩ 

input 

C 1 

220 nF 

R 2 

120 kΩ 

R 3 

47kΩ 

C 2 

25µF 

C 3 

250 µF 

R 5 

22Ω 

Q 1 

R 4 

390 Ω 

R 6 

Q 2 

2.2 kΩ 

C 4 

3.3 nF 

R 7 

15 Ω 

R 8 

R 9 

2.2 Ω 

R 10 

2.2 Ω 

560Ω 

Q 3 

Q 4 

+22V 

C 5 

4000 µF 

Figure9.4:Directcoupledcomplementarysymmetry3waudioamplifier.AfterMullard.[2] 

R 5 

C 1 C 2 C 3 

R 1 R 2 R 3 R 4 

Figure9.5:Phaseshiftoscillator.R1C1,R2C2,andR3C3eachprovide60 o ofphaseshift. 

R 6 

Vcc 

C 4


capacitance 

voltage 

f1 

fundamental 

filter 

varactor 

diode 

Vbias RF blocking 

choke 

harmonic 

filter 

Resonant 

inductor 

DC blocking 

capacitor 

Figure9.6:Varactordiode,havinganonlinearcapacitancevsvoltagecharacteristic,servesin 

frequencymultiplier. 

forRF.Thevaricapdiodeinparallelwiththeindctorconstitutesaparallelresonantnetwork. 

Itistunedtothedesiredharmonic.Notethatthereversebias,Vbias,isfixed. 

Thevaricapmultiplierisprimarilyusedtogeneratemicrowavesignalswhichcannotbe 

directlyproducedbyoscillators. ThelumpedcircuitrepresentationinFigure9.6isactually 

striplineorwaveguidesections.FrequeniesuptohundredsofgHzmaybeproducedbyvaractor 

multipliers. 

9.5 Phase-lockedloops–PENDING 

9.6 Radiocircuits–INCOMPLETE 

L1 

240 

µΗ 

(a) 

C1 

365 

pF 

C2 

1000 

pf 

(b) 

(c) 

(d) 

Figure9.7:(a)Crystalradio.(b)ModulatedRFatantenna.(c)RectifiedRFatdiodecathode, 

withoutC2filtercapacitor.(d)Demodualtedaudiotoheadphones. 

Anantennagroundsystem,tankcircuit,peakdetector,andheadphonesarethethemain 

componentsofacrystalradio. SeeFigure9.7(a). Theantennaabsorbstransimttedradio 

signals(b)whichflowtogroundviatheothercomponents. ThecombinationofC1andL1 

comprisearesonantcircuit,referedtoasatankcircuit.Itspurposeistoselectoneoutofmany 

f3

9.6. RADIOCIRCUITS–INCOMPLETE 425 

availableradiossignals. ThevariablecapacitorC1allowsfortuningtothevarioussignals. 

ThediodepassesthepositivehalfcyclesoftheRF,removingthenegativehalfcycles(c). C2 

issizedtofiltertheradiofrequenciesfromtheRFenvelope(c),passingaudiofrequencies(d) 

totheheadset.Notethatnopowersupplyisrequiredforacrystalradio.Agermaniumdiode, 

whichhasalowerforwardvoltagedropprovidesgreatersensitvitythanasilicondiode. 

While2000Ωmagneticheadphonesareshownabove,aceramicearphone,sometimescalled 

acrystalearphone,ismoresensitive.Theceramicearphoneisdesirableforallbutthestrongest 

radiosignals 

ThecircuitinFigure9.8producesastrongeroutputthanthecrystaldetector. Sincethe 

transistorisnotbiasedinthelinearregion(nobasebiasresistor),itonlyconductsforpositive 

halfcyclesofRFinput,detectingtheaudiomodulation.Anadvantageofatransistordetector 

isamplificationinadditiontodetection. Thismorepowerfulcircuitcanreadilydrive2000Ω 

magneticheadphones.NotethetransistorisagermanuimPNPdevice.Thisisprobablymore 

sensitive,duetothelower0.2VVBE,comparedwithsilicon.However,asilicondeviceshould 

stillwork.ReversebatterypolarityforNPNsilicondevices. 

365 

pF 

Ge 

transistor 

1.5V 

+ 

5nf 

- 

2000Ω double headphones 

Coil - #34 AWG magnet wire 

close wound over 1 in. length on 

1 1/4 in. dia. form. Tap 1/4 in. 

from bottom. 

Figure9.8:TROne,onetransistorradio.No-bias-resistorcausesoperationasadetector.After 

Stoner,Figure4.4A.[8] 

The2000Ωheadphonesarenolongerawidelyavailableitem.However,thelowimpedance 

earbudscommonlyusedwithportableaudioequipmentmaybesubstitutedwhenpairedwith 

asuitableaudiotransformer.SeeVolume6Experiments,ACCircuits,Sensitiveaudiodetector 

fordetails. 

ThecircuitinFigure9.9addsanaudioamplifiertothecrystaldetectorforgreaterheadphonevolume. 

Theoriginalcircuitusedagermaniumdiodeandtransistor. [8]Aschottky 

diodemaybesubstitutedforthegermaniumdiode. Asilicontransistormaybeusedifthe 

base-biasresistorischangedaccordingtothetable. 

Formorecrystalradiocircuits,simpleone-transistorradios,andmoreadvancedlowtransistorcountradios,seeWenzel[9] 

ThecircuitinFigure9.11isanintegratedcircuitAMradiocontainingalltheactiveradio 

frequencycircuitrywithinasingleIC.Allcapacitorsandinductors,alongwithafewresistors, 

areexternaltotheIC.The370PfvariablecapacitortunesthedesiredRFsignal. The320 

pFvariablecapacitortunesthelocaloscillator455KHzabovetheRFinputsignal. TheRF 

signalandlocaloscillatorfrequenciesmixproducingthesunanddifferenceofthetwoatpin 

15.Theexternal455KHzceramicfilterbetweenpins15and12,selectsthe455KHzdifference 

frequency. Mostoftheamplificationisintheintermediatefrequency(IF)amplifierbetween


365 

pF 

Ge diode 

500 

pF 

5 

nf 

1.5-6V 

− 

+ 

2000Ω double 

headphones 

Resistor 

1.5V 6V 

Ge 47k 220k 

Si 120k 1Meg 

Coil - #34 AWG magnet 

wire close wound over 

1 in. length on 1 1/4 in. 

dia. form. Tap 1/4 in. 

from bottom. 

Figure9.9:Crystalradiowithonetransistoraudioamplifer,base-bias. AfterStoner,Figure 

4.3A.[8] 

pins12and7.Adiodeatpin7recoversaudiofromtheIF.Someautomaticgaincontrol(AGC) 

isrecoveredandfilteredtoDCandfedbackintopin9. 

Figure9.12showsconventionalmecahnicaltuning(a)oftheRFinputtunerandthelocal 

oscillatorwithvaractordiodetuning(b).Themeshedplatesofadualvariablecapacitormake 

forabulkycomponent.Itisecconomictoreplaceitwithvaricaptuningdiodes.Increasingthe 

reversebiasVtunedecreasescapacitancewhichincreasesfrequency. Vtunecouldbeproduced 

byapotentiometer. 

Figure9.13showsanevenlowerpartscountAMradio.Sonyengineershaveincludedthe 

intermediatefrequency(IF)bandpassfilterwithinthe8-pinIC.ThiseliminatesexternalIF 

transformersandanIFceramicfilter.L-Ctuningcomponentsarestillrequiredfortheradio 

frequency(RF)inputandthelocaloscillator.Though,thevariablecapacitorscouldbereplaced 

byvaricaptuningdiodes. 

Figure9.14showsalow-parts-countFMradiobasedonaTDA7021Tintegratedcircuitby 

NXPWireless. ThebulkyexternalIFfiltertransformershavebeenreplacedbyR-Cfilters. 

Theresistorsareintegrated,thecapacitorsexternal. Thiscircuithasbeensimplifiedfrom 

Figure5intheNXPDatasheet. SeeFigure5or8ofthedatasheetfortheomittedsignal 

strengthcircuit. ThesimpletuningcircuitisfromtheFigure5TestCircuit. Figure8hasa 

moreelaboratetuner.DatasheetFigure8showsastereoFMradiowithanaudioamplifierfor 

drivingaspeaker.[7] 

Foraconstructionproject,thesimplifiedFMRadioinFigure9.14isrecommended.Forthe 

56nHinductor,wind8turnsof#22AWGbarewireormagnetwireona0.125inchdrillbitor 

othermandrel.Removethemandrelandstrechto0.6inchlength.Thetuningcapacitormay 

beaminiaturetrimmercapacitor. 

Figure9.15isanexampleofacommon-base(CB)RFamplifier. Itisagoodillustration 

becauseitlookslikeaCBforlackofabiasnetwork. Sincethereisnobias,thisisaclassC 

amplifier.Thetransistorconductsforlessthan180 o oftheinputsignalbecauseatleast0.7V 

biaswouldberequiredfor180 o classB.Thecommon-baseconfigurationhashigherpowergain 

athighRFfrequenciesthancommon-emitter.Thisisapoweramplifier(3/4W)asopposedto 

asmallsignalamplifier.Theinputandoutput π-networksmatchtheemitterandcollectorto 

the50 Ωinputandoutputcoaxialterminations,respectively.Theoutput π-networkalsohelps


560 Ω 560 Ω 

268 

pF 

volume 

1 K 

20,000 pF 

− + 

2 µF 

Q3 

Q2 

Q1 

1000 

pF 

Q4 

10,000 

pF 

20,000 

pF 

3.9 K 

1000 pF 

50,000 

pF 

1000 pF 

50,000 

pF 

1 K + 

10 K 

2.7 K 

40 µF 

40 

µF 

Figure9.10:RegencyTR1:Firstmassproducedtransistorradio,1954. 

− 

33 K 

2.7 K 

560 Ω 

1000 

pF 

2.2 K 

2.2 K 

2.2 K 

470 K 

100 K 

22.5 V 

+ 

+ 

5 µF 

− 

−


370pF 

RF in 

320pF 

330pF 

370pF 

10nF 

RF in 

320pF 

Vcc 

10nF 

330pF 

100nF 

Vcc 

2 

1 

6 

5 

4 

Vcc 

Vcc 

RF 16 14 

IF 

Osc. 

8 15 12 

1.5nF 

47pF 

11 13 

100nF 

100nF 

455 kHz 

Ceramic filter 

3 

TCA440 

10 

8.2K 25µF 

Figure9.11:ICradio,AfterSignetics[3] 

2 

1 

6 

5 

4 

8 

Vcc 

7 

9 

47pF 

5µF 

39K 

6 

5 

4 

12K 

TCA440 TCA440 

BB113 

RF in 

RF 330nF 

10nF 

2 

1 RF 

Osc 

+Vtune 

BB113 

270K 

(a) (b) 

Figure9.12: ICradiocomparisonof(a)mechanicaltuningto(b)electronicvaricapdiode 

tuning.[3] 

330pF 

8 

Osc 

AF 

3.3nF


560 

µH 

160 

µF 

RF in 

8 

7 

1 2 3 4 

6 

Lo Osc 

5 

Vcc 

RF Amp Mixer Osc 

Overload 

& AGC 

AGC 

OL AGC 

Vol 

BPF IF Amp 

AGC Vol Gnd 

22 

µF 

4.7 

µF 

130 

µH 

100K 

1500 

µF 

CXA1600MP 

160 

µF 

Detector 

Audio 

Amp 

0.1 

µF 

Audio 

22 

µF 

220 

µF 

3 V 

220µF 

Figure9.13:CompactICradioeliminatesexternalIFfilters.AfterSony[4] 

+ 

-


- 

+ 

3V 

100 

nF 

16 

15 

14 

13 

1 2 3 4 5 6 7 8 

10 

nF 

3.3 

nF 

Demodulator 

100 

nF 

audio 

TDA7021T 

10 

nF 

220 

pF 

RF 

56 

nH 

antenna 

Mixer 

VCO 

220 

pF 

12 

40 

pF 

11 

4.7 

nF 

100 

nF 

IF 

10 

Field 

strength 

Figure9.14:ICFMradio,signalstrengthcircuitnotshown.AfterNXPWirelessFigure5.[7] 

1.5 

nF 

9 

820 

pF


filterharmonicsgeneratedbytheclassCamplifier. Though,moresectionswouldlikelybe 

requiredbymodernradiatedemissionsstandards. 

+10V 

100pF 

100pF 

0.68µH 

RFC 

100pF 

45-380 

pF 

9-180 

pF 

8-60 

pF 

9-180 

pF 

L1 

25nH 

L2 

25nH 

1.2µH 

RFC 

2N2863 

Figure9.15:ClassCcommon-base750mWRFpoweramplifier.L1=#10Cuwire1/2turn,5/8 

in.IDby3/4in.high.L2=#14tinnedCuwire11/2turns,1/2in.IDby1/3in.spacing.After 

TexasInstruments[5] 

Anexampleofahighgaincommon-baseRFamplifierisshowninFigure9.16.Thecommon- 

basecircuitcanbepushedtoahigherfrequencythanotherconfigurations.Thisisacommon 

baseconfigurationbecausethetransistorbasesaregroundedforACby1000pFcapacitors. 

Thecapacitorsarenecessary(unliketheclassC,Figure9.15)toallowthe1KΩ-4KΩvoltage 

dividertobiasthetransistorbaseforclassAoperation. The500Ωresistorsareemitterbias 

resistors.Theystablizethecollectorcurrent.The850ΩresistorsarecollectorDCloads.The 

threestageamplifierprovidesanoverallgainof38dBat100MHzwitha9MHzbandwidth. 

1000 

pF 

4-30 

pF 

10nH 

2N1141 

1K 

500 

Ω 

80nH 

68 

pF 

1000 

pF 

4-30 

pF 

4K 

2 

nF 

100µH RFC 

820 

Ω 

1000 

pF 

2N1141 

1K 

500 

Ω 

1000 

pF 

4K 

2 

nF 

100µH RFC 

820 

Ω 

80nH 

4-30 

pF 

1000 

pF 

2N1141 

1K 

500 

Ω 

4K 

2 

nF 

100nH 

4-30 

pF 

820 

Ω 

-25 V 

1000 

pF 

Figure9.16:ClassAcommon-basesmall-signalhighgainamplifier.AfterTexasInstruments 

[6] 

Acascodeamplifierhasawidebandwdthlikeacommon-baseamplifierandamoderately 

highinputimpedancelikeacommonemitterarrangement. Thebiasingforthiscascodeam- 

plifier(Figure9.17)isworkedoutinanexampleproblem(page246). 

Thiscircuit(Figure9.17)issimulatedinthe“Cascode”sectionoftheBJTchapter(page 

219).UseRFormicrowavetransistorsforbesthighfrequencyresponse.


C1 

10nF 

Vi 

R1 

150k 

R2 

220k 

R3 

1Meg 

R4 

87k 

C2 

10nF 

V B2 

V CC 

R L 

4.7k 

Q1 

Q2 

20V 

Vo 

C3 

10nF 

Figure9.17:ClassAcascodesmall-signalhighgainamplifier. 

1 K 1 K 

Transmitter Receiver 

Transmit 

Receive 

10 V 

10 V 10 V 

1 K 

Figure9.18:PINdiodeT/Rswitchdisconnectsreceiverfromantennaduringtransmit. 

left antenna right antenna 

1 K 

right 

left 

5 V 

-5 V 

RFC 

1 K 

Receiver 

Figure9.19:PINdiodeantennaswitchfordirectionfinderreceiver. 

1 K

9.7. COMPUTATIONALCIRCUITS 433 

330 

V control = 0 to 5 V 

47 nF 47 nF 330 

47 nF 

1.25 V 

150 150 

47 nF 47 nF 

Figure9.20:PINdiodeattenuator:PINdiodesfunctionasvoltagevariableresistors.AfterLin 

[1]. 

ThePINdiodesarearrangedinaπ-attenuatornetwork.Theanti-seriesdiodescancelsome 

harmonicdistortioncomparedwithasingleseriesdiode. Thefixed1.25Vsupplyforward 

biasestheparalleldiodes,whichnotonlyconductingDCcurrentfromgroundviatheresistors, 

butalso,conductRFtogroundthroughthediodes’capacitors. ThecontrolvoltageVcontrol, 

increasescurrentthroughtheparalleldiodesasitincreases. Thisdecreasestheresistance 

andattenuation,passingmoreRFfrominputtooutput.Attenuationisabout3dBatVcontrol= 

5V.Attenuationis40dBatVcontrol=1Vwithflatfrequencyresponseto2gHz.AtVcontrol= 

0.5V,attenuationis80dBat10MHz. However,thefrequencyresponsevariestoomuchto 

use.[1] 

9.7 Computationalcircuits 

Whensomeonementionstheword”computer,”adigitaldeviceiswhatusuallycomestomind. 

Digitalcircuitsrepresentnumericalquantitiesinbinaryformat:patternsof1’sand0’srepresentedbyamultitudeoftransistorcircuitsoperatinginsaturatedorcutoffstates. 

However, 

analogcircuitrymayalsobeusedtorepresentnumericalquantitiesandperformmathematical 

calculations,byusingvariablevoltagesignalsinsteadofdiscreteon/offstates. 

Hereisasimpleexampleofbinary(digital)representationversusanalogrepresentationof 

thenumber”twenty-five:” 

330


A digital circuit representing the number 25: 

16 + 8 + 1 = 25 

1 

2 

4 

8 

16 

32 

An analog circuit representing the number 25: 

100 V 0 

Voltmeter 

Digitalcircuitsareverydifferentfromcircuitsbuiltonanalogprinciples. Digitalcomputationalcircuitscanbeincrediblycomplex,andcalculationsmustoftenbeperformedinsequential”steps”toobtainafinalanswer,muchasahumanbeingwouldperformarithmeticalcalculationsinstepswithpencilandpaper. 

Analogcomputationalcircuits,ontheother 

hand,arequitesimpleincomparison,andperformtheircalculationsincontinuous,real-time 

fashion.Thereisadisadvantagetousinganalogcircuitrytorepresentnumbers,though:imprecision. 

Thedigitalcircuitshownaboveisrepresentingthenumbertwenty-five,precisely. 

Theanalogcircuitshownabovemayormaynotbeexactlycalibratedto25.000volts,butis 

subjectto”drift”anderror. 

50 

100


Inapplicationswhereprecisionisnotcritical,analogcomputationalcircuitsareverypracticalandelegant.Shownhereareafewop-ampcircuitsforperforminganalogcomputation: 



Input (-) 

Input (+) 

Analog summer (adder) circuit 

R 

R 

1 kΩ 

− 

+ 

1 kΩ 

Output = Input 1 + Input 2 

Analog subtractor circuit 

R R 

− 

+ 

R R 

Output = Input (+) - Input (-) 

Output 

Output




Analog averager circuit 

R 

R 

− 

+ 

Output = Input 1 + Input 2 

2 

Output 

(Buffer optional) 

Analog inverter (sign reverser) circuit 


R 

− 

+ 

R 

Output = - Input 

Output 

Analog "multiply-by-constant" circuit 


K 

− 

+ 

Output = (K)(Input) 

Output



Analog "divide-by-constant" circuit 

K 

− 

+ 

Output = 

Output 

(Buffer optional) 


K 

Analog inverting "multiply/divideby-constant" 

circuit 


K 

− 

+ 

Output = - (K)(Input) 

Output 

Eachofthesecircuitsmaybeusedinmodularfashiontocreateacircuitcapableofmultiple 

calculations.Forinstance,supposethatweneededtosubtractacertainfractionofonevariable 

fromanothervariable.Bycombiningadivide-by-constantcircuitwithasubtractorcircuit,we 

couldobtaintherequiredfunction:



Divide-by-constant 

K 

Output = Input 1 - 

− 

+ 



K 

Subtractor 

R R 

− 

+ 

R R 

Output 

Devicescalledanalogcomputersusedtobecommoninuniversitiesandengineeringshops, 

wheredozensofop-ampcircuitscouldbe”patched”togetherwithremovablejumperwiresto 

modelmathematicalstatements,usuallyforthepurposeofsimulatingsomephysicalprocess 

whoseunderlyingequationswereknown.Digitalcomputershavemadeanalogcomputersall 

butobsolete,butanalogcomputationalcircuitrycannotbebeatenbydigitalintermsofsheer 

eleganceandeconomyofnecessarycomponents. 

Analogcomputationalcircuitryexcelsatperformingthecalculusoperationsintegrationand 

differentiationwithrespecttotime,byusingcapacitorsinanop-ampfeedbackloop. Tofully 

understandthesecircuits’operationandapplications,though,wemustfirstgraspthemeaning 

ofthesefundamentalcalculusconcepts.Fortunately,theapplicationofop-ampcircuitstorealworldproblemsinvolvingcalculusservesasanexcellentmeanstoteachbasiccalculus. 

In 

thewordsofJohnI.Smith,takenfromhisoutstandingtextbook,ModernOperationalCircuit 

Design: 

”Anoteofencouragementisofferedtocertainreaders:integralcalculusisoneof 

themathematicaldisciplinesthatoperational[amplifier]circuitryexploitsand,in 

theprocess,ratherdemolishesasabarriertounderstanding.”(pg.4) 

Mr. Smith’ssentimentsonthepedagogicalvalueofanalogcircuitryasalearningtoolfor 

mathematicsarenotunique.ConsidertheopinionofengineerGeorgeFoxLang,inanarticle 

hewrotefortheAugust2000issueofthejournalSoundandVibration,entitled,”Analogwas 

notaComputerTrademark!”: 

”Creatingarealphysicalentity(acircuit)governedbyaparticularsetofequationsandinteractingwithitprovidesuniqueinsightintothosemathematicalstatements.Thereisnobetterwaytodevelopa”gutfeel”fortheinterplaybetweenphysics 

andmathematicsthantoexperiencesuchaninteraction.Theanalogcomputerwas 

apowerfulinterdisciplinaryteachingtool;itsobsolescenceismournedbymanyeducatorsinavarietyoffields.”(pg.23)


Differentiationisthefirstoperationtypicallylearnedbybeginningcalculusstudents.Simplyput,differentiationisdeterminingtheinstantaneousrate-of-changeofonevariableasit 

relatestoanother. Inanalogdifferentiatorcircuits,theindependentvariableistime,andso 

theratesofchangewe’redealingwithareratesofchangeforanelectronicsignal(voltageor 

current)withrespecttotime. 

Supposeweweretomeasurethepositionofacar,travelinginadirectpath(noturns),from 

itsstartingpoint. Letuscallthismeasurement,x. Ifthecarmovesataratesuchthatits 

distancefrom”start”increasessteadilyovertime,itspositionwillplotonagraphasalinear 

function(straightline): 

x 

x 

Position 

Time 

Ifweweretocalculatethederivativeofthecar’spositionwithrespecttotime(thatis, 

determinetherate-of-changeofthecar’spositionwithrespecttotime),wewouldarriveat 

aquantityrepresentingthecar’svelocity. Thedifferentiationfunctionisrepresentedbythe 

fractionalnotationd/d,sowhendifferentiatingposition(x)withrespecttotime(t),wedenote 

theresult(thederivative)asdx/dt: 

x 

x 

Position 

Time 

dx 

dt 

Velocity 

Time 

Foralineargraphofxovertime,thederivateofposition(dx/dt),otherwiseandmore 

commonlyknownasvelocity,willbeaflatline,unchanginginvalue. Thederivativeofa 

mathematicalfunctionmaybegraphicallyunderstoodasitsslopewhenplottedonagraph,


andherewecanseethattheposition(x)graphhasaconstantslope,whichmeansthatits 

derivative(dx/dt)mustbeconstantovertime. 

Now,supposethedistancetraveledbythecarincreasedexponentiallyovertime:thatis,it 

beganitstravelinslowmovements,butcoveredmoreadditionaldistancewitheachpassing 

periodintime.Wewouldthenseethatthederivativeofposition(dx/dt),otherwiseknownas 

velocity(v),wouldnotbeconstantovertime,butwouldincrease: 

x 

x 

Position 

Time 

dx 

dt 

Velocity 

Time 

Theheightofpointsonthevelocitygraphcorrespondtotherates-of-change,orslope,of 

pointsatcorrespondingtimesonthepositiongraph: 

x 

Position 

Time 

dx 

dt 

Velocity 

Time 

Whatdoesthishavetodowithanalogelectroniccircuits?Well,ifweweretohaveananalog 

voltagesignalrepresentthecar’sposition(thinkofahugepotentiometerwhosewiperwas 

attachedtothecar,generatingavoltageproportionaltothecar’sposition),wecouldconnecta 

differentiatorcircuittothissignalandhavethecircuitcontinuouslycalculatethecar’svelocity, 

displayingtheresultviaavoltmeterconnectedtothedifferentiatorcircuit’soutput:


x 

Position 

x 

+ 

V 

- 


− 

+ 

Velocity 

- 

dx 

V 

dt 

+ 

Recallfromthelastchapterthatadifferentiatorcircuitoutputsavoltageproportionalto 

theinputvoltage’srate-of-changeovertime(d/dt).Thus,iftheinputvoltageischangingover 

timeataconstantrate,theoutputvoltagewillbeataconstantvalue.Ifthecarmovesinsuch 

awaythatitselapseddistanceovertimebuildsupatasteadyrate,thenthatmeansthecar 

istravelingataconstantvelocity,andthedifferentiatorcircuitwilloutputaconstantvoltage 

proportionaltothatvelocity. Ifthecar’selapseddistanceovertimechangesinanon-steady 

manner,thedifferentiatorcircuit’soutputwilllikewisebenon-steady,butalwaysatalevel 

representativeoftheinput’srate-of-changeovertime. 

Notethatthevoltmeterregisteringvelocity(attheoutputofthedifferentiatorcircuit)is 

connectedin”reverse”polaritytotheoutputoftheop-amp.Thisisbecausethedifferentiator 

circuitshownisinverting: outputtinganegativevoltageforapositiveinputvoltagerate-ofchange.Ifwewishtohavethevoltmeterregisterapositivevalueforvelocity,itwillhavetobeconnectedtotheop-ampasshown.Asimpracticalasitmaybetoconnectagiantpotentiometertoamovingobjectsuchasanautomobile,theconceptshouldbeclear: 

byelectronically 

performingthecalculusfunctionofdifferentiationonasignalrepresentingposition,weobtain 

asignalrepresentingvelocity. 

Beginningcalculusstudentslearnsymbolictechniquesfordifferentiation. However,this 

requiresthattheequationdescribingtheoriginalgraphbeknown.Forexample,calculusstudentslearnhowtotakeafunctionsuchasy=3xandfinditsderivativewithrespecttox(d/dx), 

3,simplybymanipulatingtheequation.Wemayverifytheaccuracyofthismanipulationby 

comparingthegraphsofthetwofunctions:


y = 3x 

y 

x = 2.5; slope = 3 

x = 2; slope = 3 

x = 1; slope = 3 

x 

x = 1; y = 3 

d 

3x = 3 

dx 

(y = 3) 

y 

x = 2; y = 3 

x = 2.5; y = 3 

x 

Nonlinearfunctionssuchasy=3x 2 mayalsobedifferentiatedbysymbolicmeans.Inthis 

case,thederivativeofy=3x 2 withrespecttoxis6x: 

y = 3x 2 

y 

x = 2; slope = 12 

x = 1; slope = 6 

x 

x = 0; slope = 0 

x = 0; y = 0 

3x 

dx 

2 d 

= 6x 

(y = 6x) 

y 

x = 2; y = 12 

x = 1; y = 6 

Inreallife,though,weoftencannotdescribethebehaviorofanyphysicaleventbyasimple 

equationlikey=3x,andsosymbolicdifferentiationofthetypelearnedbycalculusstudents 

maybeimpossibletoapplytoaphysicalmeasurement. Ifsomeonewishedtodeterminethe 

derivativeofourhypotheticalcar’sposition(dx/dt=velocity)bysymbolicmeans,theywould 

firsthavetoobtainanequationdescribingthecar’spositionovertime,basedonpositionmeasurementstakenfromarealexperiment–anearlyimpossibletaskunlessthecarisoperated 

undercarefullycontrolledconditionsleadingtoaverysimplepositiongraph. However,an 

analogdifferentiatorcircuit,byexploitingthebehaviorofacapacitorwithrespecttovoltage, 

current,andtimei=C(dv/dt),naturallydifferentiatesanyrealsignalinrelationtotime,and 

wouldbeabletooutputasignalcorrespondingtoinstantaneousvelocity(dx/dt)atanymoment. 

Byloggingthecar’spositionsignalalongwiththedifferentiator’soutputsignalusing 

achartrecorderorotherdataacquisitiondevice,bothgraphswouldnaturallypresentthem- 

x


selvesforinspectionandanalysis. 

Wemaytaketheprincipleofdifferentiationonestepfurtherbyapplyingittothevelocity 

signalusinganotherdifferentiatorcircuit.Inotherwords,useittocalculatetherate-of-change 

ofvelocity,whichweknowistherate-of-changeofposition.Whatpracticalmeasurewouldwe 

arriveatifwedidthis? Thinkofthisintermsoftheunitsweusetomeasurepositionand 

velocity.Ifweweretomeasurethecar’spositionfromitsstartingpointinmiles,thenwewould 

probablyexpressitsvelocityinunitsofmilesperhour(dx/dt).Ifweweretodifferentiatethe 

velocity(measuredinmilesperhour)withrespecttotime,wewouldendupwithaunitofmiles 

perhourperhour. Introductoryphysicsclassesteachstudentsaboutthebehavioroffalling 

objects,measuringpositioninmeters,velocityinmeterspersecond,andchangeinvelocityover 

timeinmeterspersecond,persecond. Thisfinalmeasureiscalledacceleration: therateof 

changeofvelocityovertime: 

x 

x 

Position 

Time 

dx 

dt 

Velocity 

Time 

d 2 x 

dt 2 

Differentiation Differentiation 

Acceleration 

Time 

Theexpressiond 2 x/dt 2 iscalledthesecondderivativeofposition(x)withregardtotime(t). 

Ifweweretoconnectaseconddifferentiatorcircuittotheoutputofthefirst,thelastvoltmeter 

wouldregisteracceleration:


x 

Position 

+ 

V 

- 

x 


− 

+ 

Velocity 

- 

dx 

V 

dt 

+ 


− 

+ 

+ d 

V 

Acceleration - 

2 x 

dt 2 

Derivingvelocityfromposition,andaccelerationfromvelocity,weseetheprincipleofdifferentiationveryclearlyillustrated.Thesearenottheonlyphysicalmeasurementsrelatedto 

eachotherinthisway,buttheyare,perhaps,themostcommon.Anotherexampleofcalculus 

inactionistherelationshipbetweenliquidflow(q)andliquidvolume(v)accumulatedina 

vesselovertime: 

Water 

supply 

dv 

dt 

= flow 

Water 

LT 

v = volume 

A”LevelTransmitter”devicemountedonawaterstoragetankprovidesasignaldirectly 

proportionaltowaterlevelinthetank,which–ifthetankisofconstantcross-sectionalarea 

throughoutitsheight–directlyequateswatervolumestored.Ifweweretotakethisvolume 

signalanddifferentiateitwithrespecttotime(dv/dt),wewouldobtainasignalproportional 

tothewaterflowratethroughthepipecarryingwatertothetank. Adifferentiatorcircuit


connectedinsuchawayastoreceivethisvolumesignalwouldproduceanoutputsignalproportionaltoflow,possiblysubstitutingforaflow-measurementdevice(”FlowTransmitter”) 

installedinthepipe. 

Returningtothecarexperiment,supposethatourhypotheticalcarwereequippedwitha 

tachogeneratorononeofthewheels,producingavoltagesignaldirectlyproportionaltovelocity. 

Wecoulddifferentiatethesignaltoobtainaccelerationwithonecircuit,likethis: 

x 

v 

Velocity 

+ 

V 

- 

+ - 

Gen 


− 

+ 

Acceleration 

- 

V 

+ 

dv 

dt = 

Byitsverynature,thetachogeneratordifferentiatesthecar’spositionwithrespecttotime, 

generatingavoltageproportionaltohowrapidlythewheel’sangularpositionchangesover 

time.Thisprovidesuswitharawsignalalreadyrepresentativeofvelocity,withonlyasingle 

stepofdifferentiationneededtoobtainanaccelerationsignal. Atachogeneratormeasuring 

velocity,ofcourse,isafarmorepracticalexampleofautomobileinstrumentationthanagiantpotentiometermeasuringitsphysicalposition,butwhatwegaininpracticalitywelosein 

positionmeasurement. Nomatterhowmanytimeswedifferentiate,wecanneverinferthe 

car’spositionfromavelocitysignal.Iftheprocessofdifferentiationbroughtusfromposition 

tovelocitytoacceleration,thensomehowweneedtoperformthe”reverse”processofdifferentiationtogofromvelocitytoposition.Suchamathematicalprocessdoesexist,anditiscalled 

integration.The”integrator”circuitmaybeusedtoperformthisfunctionofintegrationwith 

respecttotime: 

d 2 x 

dt 2


x 

v 

Velocity 

+ 

V 

- 

+ - 

Gen 


− 

+ 


− 

+ 

Acceleration 

- 

V ∫ v dt = x 

+ 

- 

V 

+ 

dv 

dt = 

Recallfromthelastchapterthatanintegratorcircuitoutputsavoltagewhoserate-ofchangeovertimeisproportionaltotheinputvoltage’smagnitude. 

Thus,givenaconstant 

inputvoltage,theoutputvoltagewillchangeataconstantrate.Ifthecartravelsataconstant 

velocity(constantvoltageinputtotheintegratorcircuitfromthetachogenerator),thenits 

distancetraveledwillincreasesteadilyastimeprogresses,andtheintegratorwilloutputa 

steadilychangingvoltageproportionaltothatdistance. Ifthecar’svelocityisnotconstant, 

thenneitherwilltherate-of-changeovertimebeoftheintegratorcircuit’soutput,butthe 

outputvoltagewillfaithfullyrepresenttheamountofdistancetraveledbythecaratanygiven 

pointintime. 

Thesymbolforintegrationlookssomethinglikeaverynarrow,cursiveletter”S”( ).The 

equationutilizingthissymbol( vdt=x)tellsusthatweareintegratingvelocity(v)with 

respecttotime(dt),andobtainingposition(x)asaresult. 

So,wemayexpressthreemeasuresofthecar’smotion(position,velocity,andacceleration) 

intermsofvelocity(v)justaseasilyaswecouldintermsofposition(x): 

Position 

d 2 x 

dt 2


∫ v dt 

x 

Position 

Time 

v 

Integration 

Velocity 

Time 

dv 

dt 

Differentiation 

Acceleration 

Time 

Ifwehadanaccelerometerattachedtothecar,generatingasignalproportionaltotherate 

ofaccelerationordeceleration,wecould(hypothetically)obtainavelocitysignalwithonestep 

ofintegration,andapositionsignalwithasecondstepofintegration:


x 

a 

Acceleration 

+ 

V 

- 

Accel. 


− 

+ 


− 

+ 

+ 

V ∫∫ a dt = x 

Position - 

Velocity 

- 

V ∫ a dt = v 

+ 

Thus,allthreemeasuresofthecar’smotion(position,velocity,andacceleration)maybe 

expressedintermsofacceleration: 

x 

Position 

∫∫ a dt ∫ a dt 

Time 

Velocity 

Time 

Integration Integration 

a 

Acceleration 

Time


Asyoumighthavesuspected,theprocessofintegrationmaybeillustratedin,andapplied 

to,otherphysicalsystemsaswell.Takeforexamplethewaterstoragetankandflowexample 

shownearlier. Ifflowrateisthederivativeoftankvolumewithrespecttotime(q=dv/dt), 

thenwecouldalsosaythatvolumeistheintegralofflowratewithrespecttotime: 

Water 

supply 

FT f = flow 

Water 

∫ f dt = volume 

Ifweweretousea”FlowTransmitter”devicetomeasurewaterflow,thenbytime-integration 

wecouldcalculatethevolumeofwateraccumulatedinthetankovertime.Althoughitistheoreticallypossibletouseacapacitiveop-ampintegratorcircuittoderiveavolumesignalfromaflowsignal,mechanicalanddigitalelectronic”integrator”devicesaremoresuitableforintegrationoverlongperiodsoftime,andfindfrequentuseinthewatertreatmentanddistribution 

industries. 

Justastherearesymbolictechniquesfordifferentiation,therearealsosymbolictechniques 

forintegration,althoughtheytendtobemorecomplexandvaried.Applyingsymbolicintegrationtoareal-worldproblemliketheaccelerationofacar,though,isstillcontingentontheavailabilityofanequationpreciselydescribingthemeasuredsignal–oftenadifficultorimpossiblethingtoderivefrommeasureddata. 

However,electronicintegratorcircuitsperform 

thismathematicalfunctioncontinuously,inrealtime,andforanyinputsignalprofile,thus 

providingapowerfultoolforscientistsandengineers. 

Havingsaidthis,therearecaveatstotheusingcalculustechniquestoderiveonetype 

ofmeasurementfromanother. Differentiationhastheundesirabletendencyofamplifying 

”noise”foundinthemeasuredvariable,sincethenoisewilltypicallyappearasfrequencies 

muchhigherthanthemeasuredvariable,andhighfrequenciesbytheirverynaturepossess 

highrates-of-changeovertime. 

Toillustratethisproblem,supposewewerederivingameasurementofcaracceleration 

fromthevelocitysignalobtainedfromatachogeneratorwithwornbrushesorcommutator 

bars.Pointsofpoorcontactbetweenbrushandcommutatorwillproducemomentary”dips”in 

thetachogenerator’soutputvoltage,andthedifferentiatorcircuitconnectedtoitwillinterpret 

thesedipsasveryrapidchangesinvelocity. Foracarmovingatconstantspeed–neither 

acceleratingnordecelerating–theaccelerationsignalshouldbe0volts,but”noise”inthe 

velocitysignalcausedbyafaultytachogeneratorwillcausethedifferentiated(acceleration) 

signaltocontain”spikes,”falselyindicatingbriefperiodsofhighaccelerationanddeceleration:


x 


− 

- 

+ 

V 

v V + 

Acceleration + 

- 

Velocity 

+ - 

Gen 

Noisevoltagepresentinasignaltobedifferentiatedneednotbeofsignificantamplitudeto 

causetrouble:allthatisrequiredisthatthenoiseprofilehavefastriseorfalltimes.Inother 

words,anyelectricalnoisewithahighdv/dtcomponentwillbeproblematicwhendifferentiated,evenifitisoflowamplitude. 

Itshouldbenotedthatthisproblemisnotanartifact(anidiosyncraticerrorofthemeasuring/computinginstrument)oftheanalogcircuitry;rather,itisinherenttotheprocessof 

differentiation. Nomatterhowwemightperformthedifferentiation,”noise”inthevelocity 

signalwillinvariablycorrupttheoutputsignal.Ofcourse,ifweweredifferentiatingasignal 

twice,aswedidtoobtainbothvelocityandaccelerationfromapositionsignal,theamplifiednoisesignaloutputbythefirstdifferentiatorcircuitwillbeamplifiedagainbythenext 

differentiator,thuscompoundingtheproblem: 

dv 

dt


little noise 

x 

Position 

+ 

V 

- 

x 


− 

+ 

more noise even more noise! 

Velocity 

- 

dx 

V 

dt 

+ 


− 

+ 

+ d 

V 

Acceleration - 

2 x 

dt 2 

Integrationdoesnotsufferfromthisproblem,becauseintegratorsactaslow-passfilters, 

attenuatinghigh-frequencyinputsignals.Ineffect,allthehighandlowpeaksresultingfrom 

noiseonthesignalbecomeaveragedtogetherovertime,foradiminishednetresult. One 

mightsuppose,then,thatwecouldavoidalltroublebymeasuringaccelerationdirectlyand 

integratingthatsignaltoobtainvelocity;ineffect,calculatingin”reverse”fromthewayshown 

previously:


x 

a 

Acceleration 

+ 

V 

- 

Accel. 


− 

+ 

Velocity 

- 

V ∫ a dt = v 

+ 

Unfortunately,followingthismethodologymightleadusintootherdifficulties,onebeinga 

commonartifactofanalogintegratorcircuitsknownasdrift.Allop-ampshavesomeamountof 

inputbiascurrent,andthiscurrentwilltendtocauseachargetoaccumulateonthecapacitor 

inadditiontowhateverchargeaccumulatesasaresultoftheinputvoltagesignal. Inother 

words,allanalogintegratorcircuitssufferfromthetendencyofhavingtheiroutputvoltage 

”drift”or”creep”evenwhenthereisabsolutelynovoltageinput,accumulatingerrorovertime 

asaresult. Also,imperfectcapacitorswilltendtolosetheirstoredchargeovertimedue 

tointernalresistance,resultingin”drift”towardzerooutputvoltage. Theseproblemsare 

artifactsoftheanalogcircuitry,andmaybeeliminatedthroughtheuseofdigitalcomputation. 

Circuitartifactsnotwithstanding,possibleerrorsmayresultfromtheintegrationofone 

measurement(suchasacceleration)toobtainanother(suchasvelocity)simplybecauseofthe 

wayintegrationworks.Ifthe”zero”calibrationpointoftherawsignalsensorisnotperfect,it 

willoutputaslightpositiveornegativesignaleveninconditionswhenitshouldoutputnothing.Consideracarwithanimperfectlycalibratedaccelerometer,oronethatisinfluencedby 

gravitytodetectaslightaccelerationunrelatedtocarmotion.Evenwithaperfectintegrating 

computer,thissensorerrorwillcausetheintegratortoaccumulateerror,resultinginanoutput 

signalindicatingachangeofvelocitywhenthecarisneitheracceleratingnordecelerating.


(slight positive 

voltage) 

(no motion) 

x 

a 

Acceleration 

+ 

V 

- 

(calibration error) 

Accel. 


− 

+ 

Velocity 

- 

V ∫ a dt = v 

+ 

(small rate 

of change) 

Aswithdifferentiation,thiserrorwillalsocompounditselfiftheintegratedsignalispassed 

ontoanotherintegratorcircuit,sincethe”drifting”outputofthefirstintegratorwillverysoon 

presentasignificantpositiveornegativesignalforthenextintegratortointegrate.Therefore, 

careshouldbetakenwhenintegratingsensorsignals:ifthe”zero”adjustmentofthesensoris 

notperfect,theintegratedresultwilldrift,eveniftheintegratorcircuititselfisperfect. 

Sofar,theonlyintegrationerrorsdiscussedhavebeenartificialinnature:originatingfrom 

imperfectionsinthecircuitryandsensors.Therealsoexistsasourceoferrorinherenttothe 

processofintegrationitself,andthatistheunknownconstantproblem.Beginningcalculusstudentslearnthatwheneverafunctionisintegrated,thereexistsanunknownconstant(usually 

representedasthevariableC)addedtotheresult.Thisuncertaintyiseasiesttounderstand 

bycomparingthederivativesofseveralfunctionsdifferingonlybytheadditionofaconstant 

value:


y 

y = 3x 2 + 4 

y = 3x 2 

y = 3x 2 - 6 

dx d 

dx d 

3x 2 + 4 = 6x 

3x 

dx 

2 d = 6x 

3x 2 - 6 = 6x 

(y’ = 6x) y’ 

x x 

Notehoweachoftheparaboliccurves(y=3x 2 +C)sharetheexactsameshape,differing 

fromeachotherinregardtotheirverticaloffset. However,theyallsharetheexactsame 

derivativefunction:y’=(d/dx)(3x 2 +C)=6x,becausetheyallshareidenticalratesofchange 

(slopes)atcorrespondingpointsalongthexaxis.Whilethisseemsquitenaturalandexpected 

fromtheperspectiveofdifferentiation(differentequationssharingacommonderivative),it 

usuallystrikesbeginningstudentsasoddfromtheperspectiveofintegration,becausethereare 

multiplecorrectanswersfortheintegralofafunction.Goingfromanequationtoitsderivative, 

thereisonlyoneanswer,butgoingfromthatderivativebacktotheoriginalequationleadsus 

toarangeofcorrectsolutions.Inhonorofthisuncertainty,thesymbolicfunctionofintegration 

iscalledtheindefiniteintegral. 

Whenanintegratorperformslivesignalintegrationwithrespecttotime,theoutputis 

thesumoftheintegratedinputsignalovertimeandaninitialvalueofarbitrarymagnitude, 

representingtheintegrator’spre-existingoutputatthetimeintegrationbegan.Forexample, 

ifIintegratethevelocityofacardrivinginastraightlineawayfromacity,calculatingthata 

constantvelocityof50milesperhouroveratimeof2hourswillproduceadistance( vdt)of 

100miles,thatdoesnotnecessarilymeanthecarwillbe100milesawayfromthecityafter2 

hours.Allittellsusisthatthecarwillbe100milesfurtherawayfromthecityafter2hoursof 

driving.Theactualdistancefromthecityafter2hoursofdrivingdependsonhowfarthecar 

wasfromthecitywhenintegrationbegan.Ifwedonotknowthisinitialvaluefordistance,we 

cannotdeterminethecar’sexactdistancefromthecityafter2hoursofdriving. 

Thissameproblemappearswhenweintegrateaccelerationwithrespecttotimetoobtain 

velocity:

9.8. MEASUREMENTCIRCUITS–INCOMPLETE 455 

x 

a 

Acceleration 

+ 

V 

- 

Accel. 


− 

+ 

∫ dt 

Velocity 

- 

V 

+ 

∫ a dt = v + v0 Where, 

v0 = Initial velocity 

Inthisintegratorsystem,thecalculatedvelocityofthecarwillonlybevalidiftheintegrator 

circuitisinitializedtoanoutputvalueofzerowhenthecarisstationary(v=0). Otherwise, 

theintegratorcouldverywellbeoutputtinganon-zerosignalforvelocity(v0)whenthecar 

isstationary,fortheaccelerometercannottellthedifferencebetweenastationarystate(0 

milesperhour)andastateofconstantvelocity(say,60milesperhour,unchanging). This 

uncertaintyinintegratoroutputisinherenttotheprocessofintegration,andnotanartifact 

ofthecircuitryorofthesensor. 

Insummary,ifmaximumaccuracyisdesiredforanyphysicalmeasurement,itisbestto 

measurethatvariabledirectlyratherthancomputeitfromothermeasurements.Thisisnot 

tosaythatcomputationisworthless.Quitetothecontrary,oftenitistheonlypracticalmeans 

ofobtainingadesiredmeasurement.However,thelimitsofcomputationmustbeunderstood 

andrespectedinorderthatprecisemeasurementsbeobtained. 

9.8 Measurementcircuits–INCOMPLETE 

Figure9.21showsaphotodiodeamplifierformeasuringlowlevelsoflight. Bestsensitivity 

andbandwidthareobtainedwithatransimpedanceamplifier,acurrenttovoltageamplifier, 

insteadofaconventionaloperationalamplifier. Thephotodioderemainsreversebiasedfor 

lowestdiodecapacitance,hencewiderbandwidth,andlowernoise.Thefeedbackresistorsets 

the“gain”,thecurrenttovoltageamplificationfactor.Typicalvaluesare1to10Meg Ω.Higher 

valuesyieldhighergain.AcapacitorofafewpFmayberequiredtocompensateforphotodiode 

capacitance,andpreventsinstabilityatthehighgain.Thewiringatthesummingnodemust 

beascompactaspossible. Thispointissensitivetocircuitboardcontaminantsandmustbe 

thoroughlycleaned.Themostsensitiveamplifierscontainthephotodiodeandamplifierwithin 

ahybridmicrocircuitpackageorsingledie.


− 

+ 

Vo 

Figure9.21:Photodiodeamplifier. 

9.9 Controlcircuits–PENDING 

Contributors 



WarrenYoung(August2002): Initialideaandtextfor”Powersupplycircuits”section. 

ParagraphsmodifiedbyTonyKuphaldt(changesinvocabulary,plusinclusionofadditional 

concepts). 

BillMarsden(April2008)Authorof“ElectroStaticDischarge”section. 

Bibliography 

[1] Chin-Leong Lim, Lim Yeam Ch’ng, Goh Swee Chye, “Diode Quad Is 

Foundation For PIN Diode Attenuator,” Microwaves & RF, May 2006, at 

http://www.mwrf.com/Articles/Index.cfm?Ad=1&ArticleID=12523 

[2] “TransistorAudioandRadioCircuits,”TP1399,2ndEd.,pp39-40,Mullard,London,1972. 

[3] “AMReceiverCircuitTCA440,”AnalogDataManual,2ndEd.,pp14-20to14-26,Signetics,1982. 

[4] Sony “8-pin Single-Chip AM Radio with Builot-in Power Amplifier,” pp 5, at 

http://www.datasheetcatalog.com/datasheets pdf/C/X/A/1/CXA1600.shtml 

[5] TexasInstruments“SolidStateCommunications,”pp318,McGraw-Hill,N.Y.,1966. 

[6] TexasInstruments“TransistorCircuitDesign,”pp290,McGraw-Hill,N.Y.,1963. 

[7] “Datasheet TDA7021T”, STR-NXP Wireless, at http://www.nxp.com/ 

acrobat download/datasheets/TDA7021T CNV 2.pdf 

[8] DonaldL.Stoner,L.A.Earnshaw,“TheTransistorRadioHandbook,”pp76,Editorsand 

Eenineers,Sumerland,CA,1963.


[9] ,Charles Wenzel, “Crystal Radio Circuits,” at http://www.techlib.com/e 

lectronics/crystal.html.

458 CHAPTER9. PRACTICALANALOGSEMICONDUCTORCIRCUITS

Chapter10 

ACTIVEFILTERS 

Contents 

***PENDING*** 

459

460 CHAPTER10. ACTIVEFILTERS

Chapter11 

DCMOTORDRIVES 

Contents 

11.1 PulseWidthModulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .461 


11.1 PulseWidthModulation 

PulseWidthModulation(PWM)usesdigitalsignalstocontrolpowerapplications,aswellas 

beingfairlyeasytoconvertbacktoanalogwithaminimumofhardware. 

Analogsystems,suchaslinearpowersupplies,tendtogeneratealotofheatsincetheyare 

basicallyvariableresistorscarryingalotofcurrent.Digitalsystemsdon’tgenerallygenerate 

asmuchheat. Almostalltheheatgeneratedbyaswitchingdeviceisduringthetransition 

(whichisdonequickly),whilethedeviceisneitheronnoroff,butinbetween.Thisisbecause 

powerfollowsthefollowingformula: 

P=EI,orWatts=VoltageXCurrent 

Ifeithervoltageorcurrentisnearzerothenpowerwillbenearzero. PWMtakesfull 

advantageofthisfact. 

PWMcanhavemanyofthecharacteristicsofananalogcontrolsystem,inthatthedigital 

signalcanbefreewheeling.PWMdoesnothavetocapturedata,althoughthereareexceptions 

tothiswithhigherendcontrollers. 

Oneoftheparametersofanysquarewaveisdutycycle.Mostsquarewavesare50%,this 

isthenormwhendiscussingthem,buttheydon’thavetobesymmetrical. TheONtimecan 

bevariedcompletelybetweensignalbeingofftobeingfullyon,0%to100%,andallranges 

between. 

Shownbelowareexamplesofa10%,50%,and90%dutycycle.Whilethefrequencyisthe 

sameforeach,thisisnotarequirement. 

461

462 CHAPTER11. DCMOTORDRIVES 

ThereasonPWMispopularissimple.Manyloads,suchasresistors,integratethepower 

intoanumbermatchingthepercentage.Conversionintoitsanalogequivalentvalueisstraightforward. 

LEDsareverynonlinearintheirresponsetocurrent,giveanLEDhalfitsrated 

currentyouyoustillgetmorethanhalfthelighttheLEDcanproduce.WithPWMthelight 

levelproducedbytheLEDisverylinear. Motors,whichwillbecoveredlater,arealsovery 

responsivetoPWM. 

OneofseveralwaysPWMcanbeproducedisbyusingasawtoothwaveformandacomparator.Asshownbelowthesawtooth(ortrianglewave)neednotbesymmetrical,butlinearityof 

thewaveformisimportant.Thefrequencyofthesawtoothwaveformisthesamplingratefor 

thesignal. 

Ifthereisn’tanycomputationinvolvedPWMcanbefast. Thelimitingfactoristhecomparatorsfrequencyresponse.Thismaynotbeanissuesincequiteafewoftheusesarefairly 

lowspeed. SomemicrocontrollershavePWMbuiltin,andcanrecordorcreatesignalson 

demand. 

UsesforPWMvarywidely. ItistheheartofClassDaudioamplifiers,byincreasingthe 

voltagesyouincreasethemaximumoutput,andbyselectingafrequencybeyondhumanhearing(typically44Khz)PWMcanbeused. 

Thespeakersdonotrespondtothehighfrequency, 

butduplicatesthelowfrequency,whichistheaudiosignal.Highersamplingratescanbeused 

forevenbetterfidelity,and100Khzormuchhigherisnotunheardof. 

Anotherpopularapplicationismotorspeedcontrol. Motorsasaclassrequireveryhigh 

currentstooperate. BeingabletovarytheirspeedwithPWMincreasestheefficiencyofthe

11.1. PULSEWIDTHMODULATION 463 

totalsystembyquiteabit. PWMismoreeffectiveatcontrollingmotorspeedsatlowRPM 

thanlinearmethods. 

PWMisoftenusedinconjunctionwithanH-Bridge. ThisconfigurationissonamedbecauseitresemblestheletterH,andallowstheeffectivevoltageacrosstheloadtobedoubled, 

sincethepowersupplycanbeswitchedacrossbothsidesoftheload.Inthecaseofinductive 

loads,suchasmotors,diodesareusedtosuppressinductivespikes,whichmaydamagethe 

transistors. Theinductanceinamotoralsotendstorejectthehighfrequencycomponentof 

thewaveform.ThisconfigurationcanalsobeusedwithspeakersforClassDaudioamps. 

Whilebasicallyaccurate,thisschematicofanH-Bridgehasoneseriousflaw,itispossible 

whiletransitioningbetweentheMOSFETsthatbothtransistorsontopandbottomwillbe 

onsimultaneously,andwilltakethefullbruntofwhatthepowersupplycanprovide. This 

conditionisreferredtoasshootthrough,andcanhappenwithanytypeoftransistorusedina 

H-Bridge.Ifthepowersupplyispowerfulenoughthetransistorswillnotsurvive.Itishandled 

byusingdriversinfrontofthetransistorsthatallowonetoturnoffbeforeallowingtheother 

toturnon. 

SwitchingModePowerSupplies(SMPS)canalsousePWM,althoughothermethodsalso 

exist.Addingtopologiesthatusethestoredpowerinbothinductorsandcapacitorsafterthe 

mainswitchingcomponentscanboosttheefficienciesforthesedevicesquitehigh,exceeding 

90%insomecases.Belowisanexampleofsuchaconfiguration. 

Efficiencyinthiscaseismeasuredaswattage.IfyouhaveaSMPSwith90%efficiency,and 

itconverts12VDCto5VDCat10Amps,the12Vsidewillbepullingapproximately4.6Amps. 

The10%(5watts)notaccountedforwillshowupaswasteheat.Whilebeingslightlynoisier, 

thistypeofregulatorwillrunmuchcoolerthanitslinearcounterpart. 

Contributors 



BillMarsden(February2010)Authorof“PulseWidthModulation”section.

464 CHAPTER11. DCMOTORDRIVES

Chapter12 

INVERTERSANDACMOTOR 

DRIVES 

Contents 

***PENDING*** 

465

466 CHAPTER12. INVERTERSANDACMOTORDRIVES

Chapter13 

ELECTRONTUBES 

Contents 


13.2 Earlytubehistory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .468 

13.3 Thetriode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .471 

13.4 Thetetrode. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .473 

13.5 Beampowertubes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .474 

13.6 Thepentode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .476 

13.7 Combinationtubes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .476 

13.8 Tubeparameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .479 

13.9 Ionization(gas-filled)tubes . . . . . . . . . . . . . . . . . . . . . . . . . . . .481 

13.10Displaytubes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .485 

13.11Microwavetubes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .488 

13.12TubesversusSemiconductors . . . . . . . . . . . . . . . . . . . . . . . . . . .491 


Anoftenneglectedareaofstudyinmodernelectronicsisthatoftubes,morepreciselyknownas 

vacuumtubesorelectrontubes.Almostcompletelyovershadowedbysemiconductor,or”solidstate”componentsinmostmodernapplications,tubetechnologyoncedominatedelectronic 

circuitdesign. 

Infact,thehistoricaltransitionfrom”electric”to”electronic”circuitsreallybeganwith 

tubes,foritwaswithtubesthatweenteredintoawholenewrealmofcircuitfunction:awayof 

controllingtheflowofelectrons(current)inacircuitbymeansofanotherelectricsignal(inthe 

caseofmosttubes,thecontrollingsignalisasmallvoltage). Thesemiconductorcounterpart 

tothetube,ofcourse,isthetransistor.Transistorsperformmuchthesamefunctionastubes: 

controllingtheflowofelectronsinacircuitbymeansofanotherflowofelectronsinthecaseof 

thebipolartransistor,andcontrollingtheflowofelectronsbymeansofavoltageinthecaseof 

467

468 CHAPTER13. ELECTRONTUBES 

thefield-effecttransistor.Ineithercase,arelativelysmallelectricsignalcontrolsarelatively 

largeelectriccurrent.Thisistheessenceoftheword”electronic,”soastodistinguishitfrom 

”electric,”whichhasmoretodowithhowelectronflowisregulatedbyOhm’sLawandthe 

physicalattributesofwireandcomponents. 

Thoughtubesarenowobsoleteforallbutafewspecializedapplications,theyarestilla 

worthyareaofstudy. Ifnothingelse,itisfascinatingtoexplore”thewaythingsusedtobe 

done”inordertobetterappreciatemoderntechnology. 

13.2 Earlytubehistory 

ThomasEdison,thatprolificAmericaninventor,isoftencreditedwiththeinventionofthe 

incandescentlamp. Moreaccurately,itcouldbesaidthatEdisonwasthemanwhoperfected 

theincandescentlamp.Edison’ssuccessfuldesignof1879wasactuallyprecededby77yearsby 

theBritishscientistSirHumphryDavy,whofirstdemonstratedtheprincipleofusingelectric 

currenttoheatathinstripofmetal(calleda”filament”)tothepointofincandescence(glowing 

whitehot). 

Edisonwasabletoachievehissuccessbyplacinghisfilament(madeofcarbonizedsewing 

thread)insideofaclearglassbulbfromwhichtheairhadbeenforciblyremoved. Inthis 

vacuum,thefilamentcouldglowatwhite-hottemperatureswithoutbeingconsumedbycombustion: 

clear, glass bulb 

air removed 

filament 

Inthecourseofhisexperimentation(sometimearound1883),Edisonplacedastripofmetal 

insideofanevacuated(vacuum)glassbulbalongwiththefilament.Betweenthismetalstrip 

andoneofthefilamentconnectionsheattachedasensitiveammeter.Whathefoundwasthat 

electronswouldflowthroughthemeterwheneverthefilamentwashot,butceasedwhenthe 

filamentcooleddown:

13.2. EARLYTUBEHISTORY 469 

metal strip 

Thewhite-hotfilamentinEdison’slampwasliberatingfreeelectronsintothevacuumof 

thelamp,thoseelectronsfindingtheirwaytothemetalstrip,throughthegalvanometer,and 

backtothefilament.Hiscuriositypiqued,Edisonthenconnectedafairlyhigh-voltagebattery 

inthegalvanometercircuittoaidthesmallcurrent: 

more 

current 

Sureenough,thepresenceofthebatterycreatedamuchlargercurrentfromthefilamentto 

themetalstrip.However,whenthebatterywasturnedaround,therewaslittletonocurrent 

atall! 

no 

current 

Ineffect,whatEdisonhadstumbleduponwasadiode!Unfortunately,hesawnopractical 

useforsuchadeviceandproceededwithfurtherrefinementsinhislampdesign. 

Theone-wayelectronflowofthisdevice(knownastheEdisonEffect)remainedacuriosityuntilJ.A.Flemingexperimentedwithitsusein1895. 

Flemingmarketedhisdeviceasa 

”valve,”initiatingawholenewareaofstudyinelectriccircuits.Vacuumtubediodes–Fleming’s”valves”beingnoexception–arenotabletohandlelargeamountsofcurrent,andso 

Fleming’sinventionwasimpracticalforanyapplicationinACpower,onlyforsmallelectric 

signals. 

! 

- 

A 

+ 

- 

A 

+ 

+ 

A 

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Thenin1906,anotherinventorbythenameofLeeDeForeststartedplayingaroundwith 

the”EdisonEffect,”seeingwhatmorecouldbegainedfromthephenomenon.Indoingso,he 

madeastartlingdiscovery:byplacingametalscreenbetweentheglowingfilamentandthe 

metalstrip(whichbynowhadtakentheformofaplateforgreatersurfacearea),thestreamof 

electronsflowingfromfilamenttoplatecouldberegulatedbytheapplicationofasmallvoltage 

betweenthemetalscreenandthefilament: 

control 

voltage 

The DeForest "Audion" tube 

"plate" 

"grid" 

"filament" 

plate current can be controlled by the 

application of a small control voltage 

between the grid and filament! 

DeForestcalledthismetalscreenbetweenfilamentandplateagrid. Itwasn’tjustthe 

amountofvoltagebetweengridandfilamentthatcontrolledcurrentfromfilamenttoplate,it 

wasthepolarityaswell. Anegativevoltageappliedtothegridwithrespecttothefilament 

wouldtendtochokeoffthenaturalflowofelectrons,whereasapositivevoltagewouldtendto 

enhancetheflow. Althoughtherewassomeamountofcurrentthroughthegrid,itwasvery 

small;muchsmallerthanthecurrentthroughtheplate. 

Perhapsmostimportantlywashisdiscoverythatthesmallamountsofgridvoltageandgrid 

currentwerehavinglargeeffectsontheamountofplatevoltage(withrespecttothefilament) 

andplatecurrent. InaddingthegridtoFleming’s”valve,”DeForesthadmadethevalve 

adjustable:itnowfunctionedasanamplifyingdevice,wherebyasmallelectricalsignalcould 

takecontroloveralargerelectricalquantity. 

TheclosestsemiconductorequivalenttotheAudiontube,andtoallofitsmoremoderntube 

equivalents,isann-channelD-typeMOSFET.Itisavoltage-controlleddevicewithalarge 

currentgain. 

Callinghisinventionthe”Audion,”hevigorouslyappliedittothedevelopmentofcommunicationstechnology. 

In1912hesoldtherightstohisAudiontubeasatelephonesignal 

amplifiertotheAmericanTelephoneandTelegraphCompany(ATandT),whichmadelongdistancetelephonecommunicationpractical.Inthefollowingyearhedemonstratedtheuseof 

anAudiontubeforgeneratingradio-frequencyACsignals. In1915heachievedtheremarkablefeatofbroadcastingvoicesignalsviaradiofromArlington,VirginiatoParis,andin1916 

inauguratedthefirstradionewsbroadcast.SuchaccomplishmentsearnedDeForestthetitle 

”FatherofRadio”inAmerica. 

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A 

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13.3. THETRIODE 471 

13.3 Thetriode 

DeForest’sAudiontubecametobeknownasthetriodetube,becauseithadthreeelements: 

filament,grid,andplate(justasthe”di”inthenamediodereferstotwoelements,filament 

andplate).Laterdevelopmentsindiodetubetechnologyledtotherefinementoftheelectron 

emitter: insteadofusingthefilamentdirectlyastheemissiveelement,anothermetalstrip 

calledthecathodecouldbeheatedbythefilament. 

Thisrefinementwasnecessaryinordertoavoidsomeundesiredeffectsofanincandescent 

filamentasanelectronemitter.First,afilamentexperiencesavoltagedropalongitslength, 

ascurrentovercomestheresistanceofthefilamentmaterialanddissipatesheatenergy.This 

meantthatthevoltagepotentialbetweendifferentpointsalongthelengthofthefilamentwire 

andotherelementsinthetubewouldnotbeconstant.Forthisandsimilarreasons,alternating 

currentusedasapowersourceforheatingthefilamentwirewouldtendtointroduceunwanted 

AC”noise”intherestofthetubecircuit.Furthermore,thesurfaceareaofathinfilamentwas 

limitedatbest,andlimitedsurfaceareaontheelectronemittingelementtendstoplacea 

correspondinglimitonthetube’scurrent-carryingcapacity. 

Thecathodewasathinmetalcylinderfittingsnuglyoverthetwistedwireofthefilament. 

Thecathodecylinderwouldbeheatedbythefilamentwireenoughtofreelyemitelectrons, 

withouttheundesirablesideeffectsofactuallycarryingtheheatingcurrentasthefilament 

wirehadto.Thetubesymbolforatriodewithanindirectly-heatedcathodelookslikethis:


grid 

plate 

cathode filament 

Sincethefilamentisnecessaryforallbutafewtypesofvacuumtubes,itisoftenomittedin 

thesymbolforsimplicity,oritmaybeincludedinthedrawingbutwithnopowerconnections 

drawntoit: 

no filament 

shown at all 

... 

... 

... 

no connections shown 

to filament wires 

Asimpletriodecircuitisshowntoillustrateitsbasicoperationasanamplifier: 

input 

voltage 

Triode amplifier circuit 

R 

output 

voltage 

"plate supply" 

DC power 

source 

Thelow-voltageACsignalconnectedbetweenthegridandcathodealternatelysuppresses, 

thenenhancestheelectronflowbetweencathodeandplate.Thiscausesachangeinvoltageon 

theoutputofthecircuit(betweenplateandcathode).TheACvoltageandcurrentmagnitudes 

onthetube’sgridaregenerallyquitesmallcomparedwiththevariationofvoltageandcurrent 

intheplatecircuit. Thus,thetriodefunctionsasanamplifieroftheincomingACsignal

13.4. THETETRODE 473 

(takinghigh-voltage,high-currentDCpowersuppliedfromthelargeDCsourceontheright 

and”throttling”itbymeansofthetube’scontrolledconductivity). 

Inthetriode,theamountofcurrentfromcathodetoplate(the”controlled”currentisa 

functionbothofgrid-to-cathodevoltage(thecontrollingsignal)andtheplate-to-cathodevoltage(theelectromotiveforceavailabletopushelectronsthroughthevacuum).Unfortunately, 

neitheroftheseindependentvariableshaveapurelylineareffectontheamountofcurrent 

throughthedevice(oftenreferredtosimplyasthe”platecurrent”). Thatis,triodecurrent 

doesnotnecessarilyrespondinadirect,proportionalmannertothevoltagesapplied. 

Inthisparticularamplifiercircuitthenonlinearitiesarecompounded,asplatevoltage(with 

respecttocathode)changesalongwiththegridvoltage(alsowithrespecttocathode)asplate 

currentisthrottledbythetube. Theresultwillbeanoutputvoltagewaveformthatdoesn’t 

preciselyresemblethewaveformoftheinputvoltage. Inotherwords,thequirkinessofthe 

triodetubeandthedynamicsofthisparticularcircuitwilldistortthewaveshape. Ifwereallywantedtogetcomplexabouthowwestatedthis,wecouldsaythatthetubeintroduces 

harmonicsbyfailingtoexactlyreproducetheinputwaveform. 

Anotherproblemwithtriodebehavioristhatofstraycapacitance. Rememberthatany 

timewehavetwoconductivesurfacesseparatedbyaninsulatingmedium,acapacitorwill 

beformed. Anyvoltagebetweenthosetwoconductivesurfaceswillgenerateanelectricfield 

withinthatinsulatingregion,potentiallystoringenergyandintroducingreactanceintoacircuit.Suchisthecasewiththetriode,mostproblematicallybetweenthegridandtheplate.It 

isasifthereweretinycapacitorsconnectedbetweenthepairsofelementsinthetube: 

C grid-plate 

C grid-cathode 

C plate-cathode 

Now,thisstraycapacitanceisquitesmall,andthereactiveimpedancesusuallyhigh.Usually,thatis,unlessradiofrequenciesarebeingdealtwith.AswesawwithDeForest’sAudiontube,radiowasprobablytheprimeapplicationforthisnewtechnology,sothese”tiny”capacitancesbecamemorethanjustapotentialproblem.Anotherrefinementintubetechnologywas 

necessarytoovercomethelimitationsofthetriode. 

13.4 Thetetrode 

Asthenamesuggests,thetetrodetubecontainedfourelements: cathode(withtheimplicit 

filament,or”heater”),grid,plate,andanewelementcalledthescreen.Similarinconstruction 

tothegrid,thescreenwasawiremeshorcoilpositionedbetweenthegridandplate,connected 

toasourceofpositiveDCpotential(withrespecttothecathode,asusual)equaltoafraction 

oftheplatevoltage. Whenconnectedtogroundthroughanexternalcapacitor,thescreen 

hadtheeffectofelectrostaticallyshieldingthegridfromtheplate. Withoutthescreen,the


capacitivelinkingbetweentheplateandthegridcouldcausesignificantsignalfeedbackat 

highfrequencies,resultinginunwantedoscillations. 

Thescreen,beingoflesssurfaceareaandlowerpositivepotentialthantheplate,didn’t 

attractmanyoftheelectronspassingthroughthegridfromthecathode,sothevastmajority 

ofelectronsinthetubestillflewbythescreentobecollectedbytheplate: 

input 

voltage 

Tetrode amplifier circuit 

"screen" 

R 

R 

R C 

"plate supply" 

DC power 

source 

WithaconstantDCscreenvoltage,electronflowfromcathodetoplatebecamealmostexclusivelydependentupongridvoltage,meaningtheplatevoltagecouldvaryoverawiderange 

withlittleeffectonplatecurrent. Thismadeformorestablegainsinamplifiercircuits,and 

betterlinearityformoreaccuratereproductionoftheinputsignalwaveform. 

Despitetheadvantagesrealizedbytheadditionofascreen,thereweresomedisadvantages 

aswell. Themostsignificantdisadvantagewasrelatedtosomethingknownassecondary 

emission. Whenelectronsfromthecathodestriketheplateathighvelocity,theycancause 

freeelectronstobejarredloosefromatomsinthemetaloftheplate.Theseelectrons,knocked 

offtheplatebytheimpactofthecathodeelectrons,aresaidtobe”secondarilyemitted.”Ina 

triodetube,secondaryemissionisnotthatgreataproblem,butinatetrodewithapositivelychargedscreengridincloseproximity,thesesecondaryelectronswillbeattractedtothescreen 

ratherthantheplatefromwhichtheycame,resultinginalossofplatecurrent. Lessplate 

currentmeanslessgainfortheamplifier,whichisnotgood. 

Twodifferentstrategiesweredevelopedtoaddressthisproblemofthetetrodetube:beam 

powertubesandpentodes.Bothsolutionsresultedinnewtubedesignswithapproximatelythe 

sameelectricalcharacteristics. 

13.5 Beampowertubes 

Inthebeampowertube,thebasicfour-elementstructureofthetetrodewasmaintained,but 

thegridandscreenwireswerecarefullyarrangedalongwithapairofauxiliaryplatestocreate 

aninterestingeffect: focusedbeamsor”sheets”ofelectronstravelingfromcathodetoplate. 

Theseelectronbeamsformedastationary”cloud”ofelectronsbetweenthescreenandplate

13.5. BEAMPOWERTUBES 475 

(calleda”spacecharge”)whichactedtorepelsecondaryelectronsemittedfromtheplateback 

totheplate.Asetof”beam-forming”plates,eachconnectedtothecathode,wereaddedtohelp 

maintainproperelectronbeamfocus.Gridandscreenwirecoilswerearrangedinsuchaway 

thateachturnorwrapofthescreenfelldirectlybehindawrapofthegrid,whichplacedthe 

screenwiresinthe”shadow”formedbythegrid.Thisprecisealignmentenabledthescreento 

stillperformitsshieldingfunctionwithminimalinterferencetothepassageofelectronsfrom 

cathodetoplate. 

grid wires 

(cross-sectional view) 

cathode 

screen wires 

(cross-sectional view) 

beam-forming plates 

(2) 

- 

- - 

- - 

-- - 

-- - 

--- 

--- -- 

- 

- 

-- -- - 

-- 

- - 

-- 

- 

- - - 

- 

- - 

"space charge" 

plate 

electron beams 

Thisresultedinlowerscreencurrent(andmoreplatecurrent!) thananordinarytetrode 

tube,withlittleaddedexpensetotheconstructionofthetube. 

Beampowertetrodeswereoftendistinguishedfromtheirnon-beamcounterpartsbyadifferentschematicsymbol,showingthebeam-formingplates: 

The "Beam power" tetrode tube 

grid 

cathode 

plate 

screen


13.6 Thepentode 

Anotherstrategyforaddressingtheproblemofsecondaryelectronsbeingattractedbythe 

screenwastheadditionofafifthwireelementtothetubestructure: asuppressor. These 

five-elementtubeswerenaturallycalledpentodes. 

screen 

The pentode tube 

cathode 

plate 

suppressor 

Thesuppressorwasanotherwirecoilormeshsituatedbetweenthescreenandtheplate, 

usuallyconnecteddirectlytogroundpotential.Insomepentodetubedesigns,thesuppressor 

wasinternallyconnectedtothecathodesoastominimizethenumberofconnectionpinshaving 

topenetratethetubeenvelope: 

screen 

cathode 

plate 

grid 

grid 

(suppressor internally 

connected to cathode) 

Thesuppressor’sjobwastorepelanysecondarilyemittedelectronsbacktotheplate: a 

structuralequivalentofthebeampowertube’sspacecharge. This,ofcourse,increasedplate 

currentanddecreasedscreencurrent,resultinginbettergainandoverallperformance. In 

someinstancesitallowedforgreateroperatingplatevoltageaswell. 

13.7 Combinationtubes 

Similarinthoughttotheideaoftheintegratedcircuit,tubedesignerstriedintegratingdifferenttubefunctionsintosingletubeenvelopestoreducespacerequirementsinmoremodern 

tube-typeelectronicequipment. Acommoncombinationseenwithinasingleglassshellwas 

twoeitherdiodesortwotriodes. Theideaoffittingpairsofdiodesinsideasingleenvelope 

makesalotofsenseinlightofpowersupplyfull-waverectifierdesigns,alwaysrequiringmultiplediodes. 

Ofcourse,itwouldhavebeenquiteimpossibletocombinethousandsoftubeelementsinto 

asingletubeenvelopethewaythatthousandsoftransistorscanbeetchedontoasinglepiece

13.7. COMBINATIONTUBES 477 

ofsilicon,butengineersstilldidtheirbesttopushthelimitsoftubeminiaturizationand 

consolidation.Someofthesetubes,whimsicallycalledcompactrons,heldfourormorecomplete 

tubeelementswithinasingleenvelope. 

Sometimesthefunctionsoftwodifferenttubescouldbeintegratedintoasingle,combinationtubeinawaythatsimplyworkedmoreelegantlythantwotubesevercould.Anexampleofthiswasthepentagridconverter,moregenerallycalledaheptode,usedinsomesuperheterodyneradiodesigns.Thesetubescontainedsevenelements:5gridsplusacathodeandaplate. 

Twoofthegridswerenormallyreservedforsignalinput,theotherthreerelegatedtoscreening 

andsuppression(performance-enhancing)functions. Combiningthesuperheterodynefunctionsofoscillatorandsignalmixertogetherinonetube,thesignalcouplingbetweenthesetwo 

stageswasintrinsic.Ratherthanhavingseparateoscillatorandmixercircuits,theoscillator 

creatinganACvoltageandthemixer”mixing”thatvoltagewithanothersignal,thepentagrid 

converter’soscillatorsectioncreatedanelectronstreamthatoscillatedinintensitywhichthen 

directlypassedthroughanothergridfor”mixing”withanothersignal. 

Thissametubewassometimesusedinadifferentway:byapplyingaDCvoltagetooneof 

thecontrolgrids,thegainofthetubecouldbechangedforasignalimpressedontheothercontrolgrid.Thiswasknownasvariable-muoperation,becausethe”mu”(µ)ofthetube(itsamplificationfactor,measuredasaratioofplate-to-cathodevoltagechangeovergrid-to-cathode 

voltagechangewithaconstantplatecurrent)couldbealteredatwillbyaDCcontrolvoltage 

signal. 

Enterprisingelectronicsengineersalsodiscoveredwaystoexploitsuchmulti-variablecapabilitiesof”lesser”tubessuchastetrodesandpentodes.Onesuchwaywastheso-calledultralinearaudiopoweramplifier,inventedbyapairofengineersnamedHaflerandKeroes,utilizingatetrodetubeincombinationwitha”tapped”outputtransformertoprovidesubstantial 

improvementsinamplifierlinearity(decreasesindistortionlevels).Considera”single-ended” 

triodetubeamplifierwithanoutputtransformercouplingpowertothespeaker: 

input 

voltage 

Speaker 

Ifwesubstituteatetrodeforatriodeinthiscircuit,wewillseeimprovementsincircuitgain


resultingfromtheelectrostaticshieldingofferedbythescreen,preventingunwantedfeedback 

betweentheplateandcontrolgrid: 

input 

voltage 

Standard 

configuration 

of tetrode tube 

in a single-ended 

audio amplifier 

Speaker 

However,thetetrode’sscreenmaybeusedforfunctionsotherthanmerelyshieldingthe 

gridfromtheplate. Itcanalsobeusedasanothercontrolelement,likethegriditself. If 

a”tap”ismadeonthetransformer’sprimarywinding,andthistapconnectedtothescreen, 

thescreenwillreceiveavoltagethatvarieswiththesignalbeingamplified(feedback).More 

specifically,thefeedbacksignalisproportionaltotherate-of-changeofmagneticfluxinthe 

transformercore(dΦ/dt),thusimprovingtheamplifier’sabilitytoreproducetheinputsignal 

waveformatthespeakerterminalsandnotjustintheprimarywindingofthetransformer: 

input 

voltage 

"Ultralinear" 

configuration 

of tetrode tube 

in a single-ended 

audio amplifier 

Speaker

13.8. TUBEPARAMETERS 479 

Thissignalfeedbackresultsinsignificantimprovementsinamplifierlinearity(andconsequently,distortion),solongasprecautionsaretakenagainst”overpowering”thescreenwithtoogreatapositivevoltagewithrespecttothecathode.Asaconcept,theultralinear(screenfeedback)designdemonstratestheflexibilityofoperationgrantedbymultiplegrid-elements 

insideasingletube:acapabilityrarelymatchedbysemiconductorcomponents. 

Sometubedesignscombinedmultipletubefunctionsinamosteconomicway:dualplates 

withasinglecathode,thecurrentsforeachoftheplatescontrolledbyseparatesetsofcontrol 

grids.Commonexamplesofthesetubesweretriode-heptodeandtriode-hexodetubes(ahexode 

tubeisatubewithfourgrids,onecathode,andoneplate). 

Othertubedesignssimplyincorporatedseparatetubestructuresinsideasingleglassenvelopeforgreatereconomy.Dualdiode(rectifier)tubeswerequitecommon,asweredualtriode 

tubes,especiallywhenthepowerdissipationofeachtubewasrelativelylow. 

Dual triode tube 

The12AX7and12AU7modelsarecommonexamplesofdual-triodetubes,bothoflow-power 

rating. The12AX7isespeciallycommonasapreamplifiertubeinelectricguitaramplifier 

circuits. 

13.8 Tubeparameters 

Forbipolarjunctiontransistors,thefundamentalmeasureofamplificationistheBetaratio 

(β),definedastheratioofcollectorcurrenttobasecurrent(IC/IB). Othertransistorcharacteristicssuchasjunctionresistance,whichinsomeamplifiercircuitsmayimpactperformance 

asmuchas β,arequantifiedforthebenefitofcircuitanalysis.Electrontubesarenodifferent, 

theirperformancecharacteristicshavingbeenexploredandquantifiedlongagobyelectrical 

engineers. 

Beforewecanspeakmeaningfullyonthesecharacteristics,wemustdefineseveralmathematicalvariablesusedforexpressingcommonvoltage,current,andresistancemeasurements 

aswellassomeofthemorecomplexquantities:


µ = amplification factor, pronounced "mu" 

(unitless) 

gm = mutual conductance, in siemens 

E p = plate-to-cathode voltage 

E g = grid-to-cathode voltage 

I p = plate current 

I k = cathode current 

E s = input signal voltage 

r p = dynamic plate resistance, in ohms 

∆ = delta, the Greek symbol for change 

Thetwomostbasicmeasuresofanamplifyingtube’scharacteristicsareitsamplification 

factor(µ)anditsmutualconductance(gm),alsoknownastransconductance. Transconductanceisdefinedherejustthesameasitisforfield-effecttransistors,anothercategoryof 

voltage-controlleddevices. Herearethetwoequationsdefiningeachoftheseperformance 

characteristics: 

µ = ∆E p 

∆E g 

g m = ∆I p 

∆E g 

with constant I p (plate current) 

with constant E p (plate voltage) 

Anotherimportant,thoughmoreabstract,measureoftubeperformanceisitsplateresistance.Thisisthemeasurementofplatevoltagechangeoverplatecurrentchangeforaconstant 

valueofgridvoltage. Inotherwords,thisisanexpressionofhowmuchthetubeactslikea 

resistorforanygivenamountofgridvoltage,analogoustotheoperationofaJFETinitsohmic 

mode: 

∆E p 

r p = ∆Ip 

with constant E g (grid voltage) 

Theastutereaderwillnoticethatplateresistancemaybedeterminedbydividingtheamplificationfactorbythetransconductance:

13.9. IONIZATION(GAS-FILLED)TUBES 481 

µ = ∆E p 

∆E g 

∆E p 

r p = ∆Ip 

∆I p 

g m = ∆Eg 

. . . dividing µ by g m . . . 

r p = 

r p = ∆E p 

∆E g 

∆E p 

∆E g 

∆I p 

∆E g 

∆E g 

∆I p 

Thesethreeperformancemeasuresoftubesaresubjecttochangefromtubetotube(justas 

βratiosbetweentwo”identical”bipolartransistorsareneverpreciselythesame)andbetween 

differentoperatingconditions.Thisvariabilityisduepartlytotheunavoidablenonlinearities 

ofelectrontubesandpartlyduetohowtheyaredefined. Evensupposingtheexistenceofa 

perfectlylineartube,itwillbeimpossibleforallthreeofthesemeasurestobeconstantover 

theallowablerangesofoperation. Consideratubethatperfectlyregulatescurrentatany 

givenamountofgridvoltage(likeabipolartransistorwithanabsolutelyconstant β): that 

tube’splateresistancemustvarywithplatevoltage,becauseplatecurrentwillnotchange 

eventhoughplatevoltagedoes. 

Nevertheless,tubeswere(andare)ratedbythesevaluesatgivenoperatingconditions,and 

mayhavetheircharacteristiccurvespublishedjustliketransistors. 

13.9 Ionization(gas-filled)tubes 

Sofar,we’veexploredtubeswhicharetotally”evacuated”ofallgasandvaporinsidetheirglass 

envelopes,properlyknownasvacuumtubes. Withtheadditionofcertaingasesorvapors, 

however,tubestakeonsignificantlydifferentcharacteristics,andareabletofulfillcertain 

specialrolesinelectroniccircuits. 

Whenahighenoughvoltageisappliedacrossadistanceoccupiedbyagasorvapor,orwhen 

thatgasorvaporisheatedsufficiently,theelectronsofthosegasmoleculeswillbestripped 

awayfromtheirrespectivenuclei,creatingaconditionofionization.Havingfreedtheelectrons 

fromtheirelectrostaticbondstotheatoms’nuclei,theyarefreetomigrateintheformofa 

current,makingtheionizedgasarelativelygoodconductorofelectricity.Inthisstate,thegas 

ismoreproperlyreferredtoasaplasma. 

Ionizedgasisnotaperfectconductor. Assuch,theflowofelectronsthroughionizedgas 

willtendtodissipateenergyintheformofheat,therebyhelpingtokeepthegasinastate


ofionization. Theresultofthisisatubethatwillbegintoconductundercertainconditions, 

thentendtostayinastateofconductionuntiltheappliedvoltageacrossthegasand/orthe 

heat-generatingcurrentdropstoaminimumlevel. 

Theastuteobserverwillnotethatthisispreciselythekindofbehaviorexhibitedbyaclass 

ofsemiconductordevicescalled”thyristors,”whichtendtostay”on”onceturned”on”andtend 

tostay”off”onceturned”off.”Gas-filledtubes,itcanbesaid,manifestthissamepropertyof 

hysteresis. 

Unliketheirvacuumcounterparts,ionizationtubeswereoftenmanufacturedwithnofilament(heater)atall.Thesewerecalledcold-cathodetubes,withtheheatedversionsdesignated 

ashot-cathodetubes.Whetherornotthetubecontainedasourceofheatobviouslyimpacted 

thecharacteristicsofagas-filledtube,butnottotheextentthatlackofheatwouldimpactthe 

performanceofahard-vacuumtube. 

Thesimplesttypeofionizationdeviceisnotnecessarilyatubeatall;rather,itisconstructed 

oftwoelectrodesseparatedbyagas-filledgap.Simplycalledasparkgap,thegapbetweenthe 

electrodesmaybeoccupiedbyambientair,othertimesaspecialgas,inwhichcasethedevice 

musthaveasealedenvelopeofsomekind. 

Spark gap 

electrodes 

enclosure (optional) 

Aprimeapplicationforsparkgapsisinovervoltageprotection. Engineerednottoionize, 

or”breakdown”(beginconducting),withnormalsystemvoltageappliedacrosstheelectrodes, 

thesparkgap’sfunctionistoconductintheeventofasignificantincreaseinvoltage. Once 

conducting,itwillactasaheavyload,holdingthesystemvoltagedownthroughitslarge 

currentdrawandsubsequentvoltagedropalongconductorsandotherseriesimpedances.Ina 

properlyengineeredsystem,thesparkgapwillstopconducting(”extinguish”)whenthesystem 

voltagedecreasestoanormallevel,wellbelowthevoltagerequiredtoinitiateconduction. 

Onemajorcaveatofsparkgapsistheirsignificantlyfinitelife. Thedischargegenerated 

bysuchadevicecanbequiteviolent,andassuchwilltendtodeterioratethesurfacesofthe 

electrodesthroughpittingand/ormelting. 

Sparkgapscanbemadetoconductoncommandbyplacingathirdelectrode(usuallywith 

asharpedgeorpoint)betweentheothertwoandapplyingahighvoltagepulsebetweenthat 

electrodeandoneoftheotherelectrodes. Thepulsewillcreateasmallsparkbetweenthe 

twoelectrodes,ionizingpartofthepathwaybetweenthetwolargeelectrodes,andenabling 

conductionbetweenthemiftheappliedvoltageishighenough:

13.9. IONIZATION(GAS-FILLED)TUBES 483 

main 

voltage 

source 

Triggered spark gap 

(high voltage, 

high current) 

spark gap 

triggering voltage source 

(high voltage, low current) 

Load 

third electrode 

Sparkgapsofboththetriggeredanduntriggeredvarietycanbebuilttohandlehuge 

amountsofcurrent,someevenintotherangeofmega-amps(millionsofamps)!Physicalsize 

istheprimarylimitingfactortotheamountofcurrentasparkgapcansafelyandreliably 

handle. 

Whenthetwomainelectrodesareplacedinasealedtubefilledwithaspecialgas,adischargetubeisformed.Themostcommontypeofdischargetubeistheneonlight,usedpopularlyasasourceofcolorfulillumination,thecolorofthelightemittedbeingdependentonthe 

typeofgasfillingthetube. 

Constructionofneonlampscloselyresemblesthatofsparkgaps,buttheoperationalcharacteristicsarequitedifferent:


electrode 

NEON LAMP 

electrode 

current through the tube 

causes the neon gas to glow 

high voltage power supply (AC or DC) 

small neon 

indicator lamp 

glass tube 

Neon lamp schematic symbol 

Bycontrollingthespacingoftheelectrodesandthetypeofgasinthetube,neonlights 

canbemadetoconductwithoutdrawingtheexcessivecurrentsthatsparkgapsdo. They 

stillexhibithysteresisinthatittakesahighervoltagetoinitiateconductionthanitdoesto 

makethem”extinguish,”andtheirresistanceisdefinitelynonlinear(themorevoltageapplied 

acrossthetube,themorecurrent,thusmoreheat,thuslowerresistance).Giventhisnonlinear 

tendency,thevoltageacrossaneontubemustnotbeallowedtoexceedacertainlimit,lestthe 

tubebedamagedbyexcessivetemperatures. 

Thisnonlineartendencygivestheneontubeanapplicationotherthancolorfulillumination: 

itcanactsomewhatlikeazenerdiode,”clamping”thevoltageacrossitbydrawingmoreand 

morecurrentifthevoltagedecreases.Whenusedinthisfashion,thetubeisknownasaglow 

tube,orvoltage-regulatortube,andwasapopularmeansofvoltageregulationinthedaysof 

electrontubecircuitdesign. 

R series 

glow-discharge 

voltage regulator 

tube 

R load 

voltage across load 

held relative constant 

with variations of voltage 

source and load resistance 

Pleasetakenoteoftheblackdotfoundinthetubesymbolshownabove(andintheneon 

lampsymbolshownbeforethat).Thatmarkerindicatesthetubeisgas-filled.Itisacommon 

markerusedinallgas-filledtubesymbols. 

OneexampleofaglowtubedesignedforvoltageregulationwastheVR-150,withanominal 

regulatingvoltageof150volts.Itsresistancethroughouttheallowablelimitsofcurrentcould

13.10. DISPLAYTUBES 485 

varyfrom5kΩto30kΩ,a6:1span. Likezenerdioderegulatorcircuitsoftoday,glowtube 

regulatorscouldbecoupledtoamplifyingtubesforbettervoltageregulationandhigherload 

currentranges. 

Ifaregulartriodewasfilledwithgasinsteadofahardvacuum,itwouldmanifestallthe 

hysteresisandnonlinearityofothergastubeswithonemajoradvantage:theamountofvoltageappliedbetweengridandcathodewoulddeterminetheminimumplate-tocathodevoltage 

necessarytoinitiateconduction.Inessence,thistubewastheequivalentofthesemiconductor 

SCR(Silicon-ControlledRectifier),andwascalledthethyratron. 

control 

voltage 

+ 

- 

R load 

Thyratron 

Tube 

high voltage 

AC source 

Itshouldbenotedthattheschematicshownaboveisgreatlysimplifiedformostpurposes 

andthyratrontubedesigns. Somethyratrons,forinstance,requiredthatthegridvoltage 

switchpolaritybetweentheir”on”and”off”statesinordertoproperlywork.Also,somethyratronshadmorethanonegrid! 

ThyratronsfounduseinmuchthesamewayasSCR’sfindusetoday:controllingrectified 

ACtolargeloadssuchasmotors. Thyratrontubeshavebeenmanufacturedwithdifferent 

typesofgasfillingsfordifferentcharacteristics:inert(chemicallynon-reactive)gas,hydrogen 

gas,andmercury(vaporizedintoagasformwhenactivated). Deuterium,arareisotopeof 

hydrogen,wasusedinsomespecialapplicationsrequiringtheswitchingofhighvoltages. 

13.10 Displaytubes 

Inadditiontoperformingtasksofamplificationandswitching,tubescanbedesignedtoserve 

asdisplaydevices. 

Perhapsthebest-knowndisplaytubeisthecathoderaytube,orCRT.Originallyinvented 

asaninstrumenttostudythebehaviorof”cathoderays”(electrons)inavacuum,thesetubes 

developedintoinstrumentsusefulindetectingvoltage,thenlaterasvideoprojectiondevices 

withtheadventoftelevision. ThemaindifferencebetweenCRTsusedinoscilloscopesand 

CRTsusedintelevisionsisthattheoscilloscopevarietyexclusivelyuseelectrostatic(plate) 

deflection,whiletelevisionsuseelectromagnetic(coil)deflection.Platesfunctionmuchbetter 

thancoilsoverawiderrangeofsignalfrequencies,whichisgreatforoscilloscopesbutirrelevantfortelevisions,sinceatelevisionelectronbeamsweepsverticallyandhorizontallyatfixed 

frequencies. ElectromagneticdeflectioncoilsaremuchpreferredintelevisionCRTconstructionbecausetheydonothavetopenetratetheglassenvelopeofthetube,thusdecreasingthe


productioncostsandincreasingtubereliability. 

Aninteresting”cousin”totheCRTistheCat-EyeorMagic-Eyeindicatortube. Essentially,thistubeisavoltage-measuringdevicewithadisplayresemblingaglowinggreenring. 

Electronsemittedbythecathodeofthistubeimpingeonafluorescentscreen,causingthe 

green-coloredlighttobeemitted. Theshapeoftheglowproducedbythefluorescentscreen 

variesastheamountofvoltageappliedtoagridchanges: 

large shadow 

"Cat-Eye" indicator tube displays 

slight shadow 

minimal shadow 

Thewidthoftheshadowisdirectlydeterminedbythepotentialdifferencebetweenthecontrolelectrodeandthefluorescentscreen.Thecontrolelectrodeisanarrowrodplacedbetweenthecathodeandthefluorescentscreen.Ifthatcontrolelectrode(rod)issignificantlymorenegativethanthefluorescentscreen,itwilldeflectsomeelectronsawayfromthethatareaofthe 

screen. Theareaofthescreen”shadowed”bythecontrolelectrodewillappeardarkerwhen 

thereisasignificantvoltagedifferencebetweenthetwo.Whenthecontrolelectrodeandfluorescentscreenareatequalpotential(zerovoltagebetweenthem),theshadowingeffectwillbe 

minimalandthescreenwillbeequallyilluminated. 

Theschematicsymbolfora”cat-eye”tubelookssomethinglikethis: 

"Cat-Eye" or "Magic-Eye" 

indicator tube 

plate 

amplifier 

grid 

cathode 

fluorescent 

screen 

control 

electrode 

Hereisaphotographofacat-eyetube,showingthecirculardisplayregionaswellasthe 

glassenvelope,socket(black,atfarendoftube),andsomeofitsinternalstructure:

13.10. DISPLAYTUBES 487 

Normally,onlytheendofthetubewouldprotrudefromaholeinaninstrumentpanel,so 

theusercouldviewthecircular,fluorescentscreen. 

Initssimplestusage,a”cat-eye”tubecouldbeoperatedwithouttheuseoftheamplifier 

grid.However,inordertomakeitmoresensitive,theamplifiergridisused,anditisusedlike 

this: 

signal 

"Cat-Eye" indicator tube circuit 

R 

As the signal voltage increases, current through 

the tube is choked off. This decreases the voltage 

between the plate and the fluorescent screen, 

lessening the shadow effect (shadow narrows). 

Thecathode,amplifiergrid,andplateactasatriodetocreatelargechangesinplate-tocathodevoltageforsmallchangesingrid-to-cathodevoltage. 

Becausethecontrolelectrode 

isinternallyconnectedtotheplate,itiselectricallycommontoitandthereforepossessesthe 

sameamountofvoltagewithrespecttothecathodethattheplatedoes.Thus,thelargevoltage 

changesinducedontheplateduetosmallvoltagechangesontheamplifiergridendupcausing 

largechangesinthewidthoftheshadowseenbywhoeverisviewingthetube.


Control electrode negative with 

respect to the fluorescent screen. 

This is caused by a positive 

amplifier grid voltage (with 

respect to the cathode). 

No voltage between control 

electrode and flourescent screen. 

This is caused by a negative 

amplifier grid voltage (with 

respect to the cathode). 

”Cat-eye”tubeswereneveraccurateenoughtobeequippedwithagraduatedscaleasis 

thecasewithCRT’sandelectromechanicalmetermovements,buttheyservedwellasnull 

detectorsinbridgecircuits,andassignalstrengthindicatorsinradiotuningcircuits. An 

unfortunatelimitationtothe”cat-eye”tubeasanulldetectorwasthefactthatitwasnot 

directlycapableofvoltageindicationinbothpolarities. 

13.11 Microwavetubes 

Forextremelyhigh-frequencyapplications(above1GHz),theinterelectrodecapacitancesand 

transit-timedelaysofstandardelectrontubeconstructionbecomeprohibitive.However,there 

seemstobenoendtothecreativewaysinwhichtubesmaybeconstructed,andseveralhighfrequencyelectrontubedesignshavebeenmadetoovercomethesechallenges. 

Itwasdiscoveredin1939thatatoroidalcavitymadeofconductivematerialcalledacavity 

resonatorsurroundinganelectronbeamofoscillatingintensitycouldextractpowerfromthe 

beamwithoutactuallyinterceptingthebeamitself.Theoscillatingelectricandmagneticfields 

associatedwiththebeam”echoed”insidethecavity,inamannersimilartothesoundsof 

travelingautomobilesechoinginaroadsidecanyon,allowingradio-frequencyenergytobe 

transferredfromthebeamtoawaveguideorcoaxialcableconnectedtotheresonatorwitha 

couplingloop.Thetubewascalledaninductiveoutputtube,orIOT: 

RF 

signal 

input 

The inductive output tube (IOT) 

coaxial 

output 

cable 

electron beam 

DC supply 

RF power 

output 

toroidal 

cavity

13.11. MICROWAVETUBES 489 

TwooftheresearchersinstrumentalintheinitialdevelopmentoftheIOT,apairofbrothers 

namedSigurdandRussellVarian,addedasecondcavityresonatorforsignalinputtothe 

inductiveoutputtube. Thisinputresonatoractedasapairofinductivegridstoalternately 

”bunch”andreleasepacketsofelectronsdownthedriftspaceofthetube,sotheelectronbeam 

wouldbecomposedofelectronstravelingatdifferentvelocities.This”velocitymodulation”of 

thebeamtranslatedintothesamesortofamplitudevariationattheoutputresonator,where 

energywasextractedfromthebeam.TheVarianbrotherscalledtheirinventionaklystron. 

Beam 

control 

RF 

signal 

input 

The klystron tube 

electron beam 

DC supply 

coaxial 

output 

cable 

RF power 

output 

AnotherinventionoftheVarianbrotherswasthereflexklystrontube.Inthistube,electrons 

emittedfromtheheatedcathodetravelthroughthecavitygridstowardtherepellerplate,then 

arerepelledandreturnedbackthewaytheycame(hencethenamereflex)throughthecavity 

grids.Self-sustainingoscillationswoulddevelopinthistube,thefrequencyofwhichcouldbe 

changedbyadjustingtherepellervoltage. Hence,thistubeoperatedasavoltage-controlled 

oscillator. 

RF output 

The reflex klystron tube 

cavity 

grids 

control grid 

cathode 

repeller 

cavity


Asavoltage-controlledoscillator,reflexklystrontubesservedcommonlyas”localoscillators”forradarequipmentandmicrowavereceivers: 

Reflex klystron tube used as 

a voltage-controlled oscillator 

Initiallydevelopedaslow-powerdeviceswhoseoutputrequiredfurtheramplificationfor 

radiotransmitteruse,reflexklystrondesignwasrefinedtothepointwherethetubescould 

serveaspowerdevicesintheirownright. Reflexklystronshavesincebeensupersededby 

semiconductordevicesintheapplicationoflocaloscillators,butamplificationklystronscontinuetofinduseinhigh-power,high-frequencyradiotransmittersandinscientificresearch 

applications. 

Onemicrowavetubeperformsitstasksowellandsocost-effectivelythatitcontinuesto 

reignsupremeinthecompetitiverealmofconsumerelectronics:themagnetrontube.Thisdeviceformstheheartofeverymicrowaveoven,generatingseveralhundredwattsofmicrowave 

RFenergyusedtoheatfoodandbeverages,anddoingsounderthemostgruelingconditions 

foratube:poweredonandoffatrandomtimesandforrandomdurations. 

MagnetrontubesarerepresentativeofanentirelydifferentkindoftubethantheIOTand 

klystron.Whereasthelattertubesusealinearelectronbeam,themagnetrondirectsitselectronbeaminacircularpatternbymeansofastrongmagneticfield:

13.12. TUBESVERSUSSEMICONDUCTORS 491 

cavity 

resonators 

The magnetron tube 

electron 

cathode 

beam 

RF output 

Onceagain,cavityresonatorsareusedasmicrowave-frequency”tankcircuits,”extracting 

energyfromthepassingelectronbeaminductively.Likeallmicrowave-frequencydevicesusing 

acavityresonator,atleastoneoftheresonatorcavitiesistappedwithacouplingloop:aloop 

ofwiremagneticallycouplingthecoaxialcabletotheresonantstructureofthecavity,allowing 

RFpowertobedirectedoutofthetubetoaload.Inthecaseofthemicrowaveoven,theoutput 

powerisdirectedthroughawaveguidetothefoodordrinktobeheated,thewatermolecules 

withinactingastinyloadresistors,dissipatingtheelectricalenergyintheformofheat. 

Themagnetrequiredformagnetronoperationisnotshowninthediagram.Magneticflux 

runsperpendiculartotheplaneofthecircularelectronpath.Inotherwords,fromtheviewof 

thetubeshowninthediagram,youarelookingstraightatoneofthemagneticpoles. 

13.12 TubesversusSemiconductors 

Devotingawholechapterinamodernelectronicstexttothedesignandfunctionofelectron 

tubesmayseemabitstrange,seeingashowsemiconductortechnologyhasallbutobsoleted 

tubesinalmosteveryapplication. However,thereismeritinexploringtubesnotjustfor 

historicalpurposes,butalsoforthosenicheapplicationsthatnecessitatethequalifyingphrase 

”almosteveryapplication”inregardtosemiconductorsupremacy. 

Insomeapplications,electrontubesnotonlycontinuetoseepracticaluse,butperformtheir 

respectivetasksbetterthananysolid-statedeviceyetinvented.Insomecasestheperformance 

andreliabilityofelectrontubetechnologyisfarsuperior. 

Inthefieldsofhigh-power,high-speedcircuitswitching,specializedtubessuchashydrogen 

thyratronsandkrytronsareabletoswitchfarlargeramountsofcurrent,farfasterthanany 

semiconductordevicedesignedtodate. Thethermalandtemporallimitsofsemiconductor 

physicsplacelimitationsonswitchingabilitythattubes–whichdonotoperateonthesame 

principles–areexemptfrom. 

Inhigh-powermicrowavetransmitterapplications,theexcellentthermaltoleranceoftubes 

alonesecurestheirdominanceoversemiconductors. Electronconductionthroughsemiconductingmaterialsisgreatlyimpactedbytemperature.Electronconductionthroughavacuum


isnot. Asaconsequence,thepracticalthermallimitsofsemiconductordevicesarerather 

lowcomparedtothatoftubes. Beingabletooperatetubesatfargreatertemperaturesthan 

equivalentsemiconductordevicesallowstubestodissipatemorethermalenergyforagiven 

amountofdissipationarea,whichmakesthemsmallerandlighterincontinuoushighpower 

applications. 

Anotherdecidedadvantageoftubesoversemiconductorcomponentsinhigh-powerapplicationsistheirrebuildability.Whenalargetubefails,itmaybedisassembledandrepairedat 

farlowercostthanthepurchasepriceofanewtube.Whenasemiconductorcomponentfails, 

largeorsmall,thereisgenerallynomeansofrepair. 

Thefollowingphotographshowsthefrontpanelofa1960’svintage5kWAMradiotransmitter. 

Oneoftwo”Eimac”brandpowertubescanbeseeninarecessedarea,behindthe 

glassdoor. Accordingtothestationengineerwhogavethefacilitytour,therebuildcostfor 

suchatubeisonly$800:quiteinexpensivecomparedtothecostofanewtube,andstillquite 

reasonableincontrasttothepriceofanew,comparablesemiconductorcomponent! 

Tubes,beinglesscomplexintheirmanufacturethansemiconductorcomponents,arepotentiallycheapertoproduceaswell,althoughthehugevolumeofsemiconductordeviceproductionintheworldgreatlyoffsetsthistheoreticaladvantage.Semiconductormanufactureis 

quitecomplex,involvingmanydangerouschemicalsubstancesandnecessitatingsuper-clean 

assemblyenvironments.Tubesareessentiallynothingmorethanglassandmetal,withavacuumseal. 

Physicaltolerancesare”loose”enoughtopermithand-assemblyofvacuumtubes, 

andtheassemblyworkneednotbedoneina”cleanroom”environmentasisnecessaryfor 

semiconductormanufacture. 

Onemodernareawhereelectrontubesenjoysupremacyoversemiconductorcomponents 

isintheprofessionalandhigh-endaudioamplifiermarkets,althoughthisispartiallydueto 

musicalculture. Manyprofessionalguitarplayers,forexample,prefertubeamplifiersover 

transistoramplifiersbecauseofthespecificdistortionproducedbytubecircuits. Anelectric 

guitaramplifierisdesignedtoproducedistortionratherthanavoiddistortionasisthecase 

withaudio-reproductionamplifiers(thisiswhyanelectricguitarsoundssomuchdifferent 

thananacousticalguitar),andthetypeofdistortionproducedbyanamplifierisasmucha 

matterofpersonaltasteasitistechnicalmeasurement. Sincerockmusicinparticularwas

13.12. TUBESVERSUSSEMICONDUCTORS 493 

bornwithguitaristsplayingtube-amplifierequipment,thereisasignificantlevelof”tube 

appeal”inherenttothegenreitself,andthisappealshowsitselfinthecontinuingdemandfor 

”tubed”guitaramplifiersamongrockguitarists. 

Asanillustrationoftheattitudeamongsomeguitarists,considerthefollowingquotetaken 

fromthetechnicalglossarypageofatube-amplifierwebsitewhichwillremainnameless: 

SolidState:Acomponentthathasbeenspecificallydesignedtomakeaguitar 

amplifiersoundbad.Comparedtotubes,thesedevicescanhaveaverylonglifespan, 

whichguaranteesthatyouramplifierwillretainitsthin,lifeless,andbuzzysound 

foralongtimetocome. 

Intheareaofaudioreproductionamplifiers(musicstudioamplifiersandhomeentertainmentamplifiers),itisbestforanamplifiertoreproducethemusicalsignalwithaslittledistortionaspossible.Paradoxically,incontrasttotheguitaramplifiermarketwheredistortionisa 

designgoal,high-endaudioisanotherareawheretubeamplifiersenjoycontinuingconsumer 

demand. Thoughonemightsupposetheobjective,technicalrequirementoflowdistortion 

wouldeliminateanysubjectivebiasonthepartofaudiophiles,onewouldbeverywrong.The 

marketforhigh-end”tubed”amplifierequipmentisquitevolatile,changingrapidlywithtrends 

andfads,drivenbyhighlysubjectiveclaimsof”magical”soundfromaudiosystemreviewers 

andsalespeople.Asintheelectricguitarworld,thereisnosmallmeasureofcult-likedevotion 

totubeamplifiersamongsomequartersoftheaudiophileworld. Asanexampleofthisirrationality,considerthedesignofmanyultra-high-endamplifiers,withchassisbuilttodisplay 

theworkingtubesopenly,eventhoughthisphysicalexposureofthetubesobviouslyenhances 

theundesirableeffectofmicrophonics(changesintubeperformanceasaresultofsoundwaves 

vibratingthetubestructure). 

Havingsaidthis,though,thereisawealthoftechnicalliteraturecontrastingtubesagainst 

semiconductorsforaudiopoweramplifieruse,especiallyintheareaofdistortionanalysis. 

Morethanafewcompetentelectricalengineersprefertubeamplifierdesignsovertransistors, 

andareabletoproduceexperimentalevidenceinsupportoftheirchoice. Theprimarydifficultyinquantifyingaudiosystemperformanceistheuncertainresponseofhumanhearing. 

Allamplifiersdistorttheirinputsignaltosomedegree,especiallywhenoverloaded,sothe 

questioniswhichtypeofamplifierdesigndistortstheleast.However,sincehumanhearingis 

verynonlinear,peopledonotinterpretalltypesofacousticdistortionequally,andsosomeamplifierswillsound”better”thanothersevenifaquantitativedistortionanalysiswithelectronic 

instrumentsindicatessimilardistortionlevels.Todeterminewhattypeofaudioamplifierwill 

distortamusicalsignal”theleast,”wemustregardthehumanearandbrainaspartofthe 

wholeacousticalsystem. Sincenocompletemodelyetexistsforhumanauditoryresponse, 

objectiveassessmentisdifficultatbest.However,someresearchindicatesthatthecharacteristicdistortionoftubeamplifiercircuits(especiallywhenoverloaded)islessobjectionablethan 

distortionproducedbytransistors. 

Tubesalsopossessthedistinctadvantageoflow”drift”overawiderangeofoperating 

conditions. Unlikesemiconductorcomponents,whosebarriervoltages, βratios,bulkresistances,andjunctioncapacitancesmaychangesubstantiallywithchangesindevicetemperatureand/orotheroperatingconditions,thefundamentalcharacteristicsofavacuumtuberemainnearlyconstantoverawiderangeinoperatingconditions,becausethosecharacteristicsaredeterminedprimarilybythephysicaldimensionsofthetube’sstructuralelements


(cathode,grid(s),andplate)ratherthantheinteractionsofsubatomicparticlesinacrystalline 

lattice. 

Thisisoneofthemajorreasonssolid-stateamplifierdesignerstypicallyengineertheircircuitstomaximizepower-efficiencyevenwhenitcompromisesdistortionperformance,because 

apower-inefficientamplifierdissipatesalotofenergyintheformofwasteheat,andtransistor 

characteristicstendtochangesubstantiallywithtemperature. Temperature-induced”drift” 

makesitdifficulttostabilize”Q”pointsandotherimportantperformance-relatedmeasuresin 

anamplifiercircuit. Unfortunately,powerefficiencyandlowdistortionseemtobemutually 

exclusivedesigngoals. 

Forexample,classAaudioamplifiercircuitstypicallyexhibitverylowdistortionlevels,but 

areverywastefulofpower,meaningthatitwouldbedifficulttoengineerasolid-stateclassA 

amplifierofanysubstantialpowerratingduetotheconsequentdriftoftransistorcharacteristics.Thus,mostsolid-stateaudioamplifierdesignerschooseclassBcircuitconfigurationsfor 

greaterefficiency,eventhoughclassBdesignsarenotoriousforproducingatypeofdistortion 

knownascrossoverdistortion.However,withtubesitiseasytodesignastableclassAaudio 

amplifiercircuitbecausetubesarenotasadverselyaffectedbythechangesintemperature 

experiencedinasuchapower-inefficientcircuitconfiguration. 

Tubeperformanceparameters,though,tendto”drift”morethansemiconductordevices 

whenmeasuredoverlongperiodsoftime(years). Onemajormechanismoftube”aging”appearstobevacuumleaks:whenairenterstheinsideofavacuumtube,itselectricalcharacteristicsbecomeirreversiblyaltered.Thissamephenomenonisamajorcauseoftubemortality, 

orwhytubestypicallydonotlastaslongastheirrespectivesolid-statecounterparts. When 

tubevacuumismaintainedatahighlevel,though,excellentperformanceandlifeispossible. 

Anexampleofthisisaklystrontube(usedtoproducethehigh-frequencyradiowavesusedin 

aradarsystem)thatlastedfor240,000hoursofoperation(citedbyRobertS.SymonsofLitton 

ElectronDevicesDivisioninhisinformativepaper,”Tubes: Stillvitalafteralltheseyears,” 

printedintheApril1998issueofIEEESpectrummagazine). 

Ifnothingelse, thetensionbetweenaudiophilesovertubesversussemiconductorshas 

spurredaremarkabledegreeofexperimentationandtechnicalinnovation,servingasanexcellentresourceforthosewishingtoeducatethemselvesonamplifiertheory. 

Takingawider 

view,theversatilityofelectrontubetechnology(differentphysicalconfigurations,multiple 

controlgrids)hintsatthepotentialforcircuitdesignsoffargreatervarietythanispossible 

usingsemiconductors.Forthisandotherreasons,electrontubeswillneverbe”obsolete,”but 

willcontinuetoserveinnicheroles,andtofosterinnovationforthoseelectronicsengineers, 

inventors,andhobbyistswhoareunwillingtolettheirmindsbystifledbyconvention.

AppendixA-1 

ABOUTTHISBOOK 

A-1.1 Purpose 

Theysaythatnecessityisthemotherofinvention.Atleastinthecaseofthisbook,thatadage 

istrue. Asanindustrialelectronicsinstructor,Iwasforcedtouseasub-standardtextbook 

duringmyfirstyearofteaching.Mystudentsweredailyfrustratedwiththemanytypographicalerrorsandobscureexplanationsinthisbook,havingspentmuchtimeathomestruggling 

tocomprehendthematerialwithin.Worseyetwerethemanyincorrectanswersinthebackof 

thebooktoselectedproblems.Addinginsulttoinjurywasthe$100+price. 

Contactingthepublisherprovedtobeanexerciseinfutility. Eventhoughtheparticular 

textIwasusinghadbeeninprintandinpopularuseforacoupleofyears,theyclaimedmy 

complaintwasthefirstthey’deverheard.Myrequesttoreviewthedraftforthenextedition 

oftheirbookwasmetwithdisinterestontheirpart,andIresolvedtofindanalternativetext. 

FindingasuitablealternativewasmoredifficultthanIhadimagined. Sure,therewere 

plentyoftextsinprint,butthereallygoodbooksseemedabittooheavyonthemathandthe 

lessintimidatingbooksomittedalotofinformationIfeltwasimportant. Someofthebest 

bookswereoutofprint,andthosethatwerestillbeingprintedwerequiteexpensive. 

ItwasoutoffrustrationthatIcompiledLessonsinElectricCircuitsfromnotesandideasI 

hadbeencollectingforyears.Myprimarygoalwastoputreadable,high-qualityinformation 

intothehandsofmystudents,butasecondarygoalwastomakethebookasaffordableas 

possible.Overtheyears,Ihadexperiencedthebenefitofreceivingfreeinstructionandencouragementinmypursuitoflearningelectronicsfrommanypeople,includingseveralteachers 

ofmineinelementaryandhighschool.Theirselflessassistanceplayedakeyroleinmyown 

studies,pavingthewayforarewardingcareerandfascinatinghobby. IfonlyIcouldextend 

thegiftoftheirhelpbygivingtootherpeoplewhattheygavetome... 

So,Idecidedtomakethebookfreelyavailable.Morethanthat,Idecidedtomakeit”open,” 

followingthesamedevelopmentmodelusedinthemakingoffreesoftware(mostnotablythe 

variousUNIXutilitiesreleasedbytheFreeSoftwareFoundation,andtheLinuxoperating 

495

496 APPENDIXA-1. ABOUTTHISBOOK 

system,whosefameisgrowingevenasIwrite).Thegoalwastocopyrightthetext–soasto 

protectmyauthorship–butexpresslyallowanyonetodistributeand/ormodifythetexttosuit 

theirownneedswithaminimumoflegalencumbrance. Thiswillfulandformalrevokingof 

standarddistributionlimitationsundercopyrightiswhimsicallytermedcopyleft.Anyonecan 

”copyleft”theircreativeworksimplybyappendinganoticetothateffectontheirwork,but 

severalLicensesalreadyexist,coveringthefinelegalpointsingreatdetail. 

ThefirstsuchLicenseIappliedtomyworkwastheGPL–GeneralPublicLicense–ofthe 

FreeSoftwareFoundation(GNU).TheGPL,however,isintendedtocopyleftworksofcomputer 

software,andalthoughitsintroductorylanguageisbroadenoughtocoverworksoftext,its 

wordingisnotasclearasitcouldbeforthatapplication. Whenother,lessspecificcopyleft 

Licensesbeganappearingwithinthefreesoftwarecommunity,Ichoseoneofthem(theDesign 

ScienceLicense,orDSL)astheofficialnoticeformyproject. 

In”copylefting”thistext,Iguaranteedthatnoinstructorwouldbelimitedbyatextinsufficientfortheirneeds,asIhadbeenwitherror-riddentextbooksfrommajorpublishers.I’msure 

thisbookinitsinitialformwillnotsatisfyeveryone,butanyonehasthefreedomtochangeit, 

leveragingmyeffortstosuitvariantandindividualrequirements.Forthebeginningstudent 

ofelectronics,learnwhatyoucanfromthisbook,editingitasyoufeelnecessaryifyoucome 

acrossausefulpieceofinformation.Then,ifyoupassitontosomeoneelse,youwillbegiving 

themsomethingbetterthanwhatyoureceived.Fortheinstructororelectronicsprofessional, 

feelfreetousethisasareferencemanual,addingoreditingtoyourheart’scontent. The 

only”catch”isthis:ifyouplantodistributeyourmodifiedversionofthistext,youmustgive 

creditwherecreditisdue(tome,theoriginalauthor,andanyoneelsewhosemodificationsare 

containedinyourversion),andyoumustensurethatwhoeveryougivethetexttoisawareof 

theirfreedomtosimilarlyshareandeditthetext.Thenextchaptercoversthisprocessinmore 

detail. 

ItmustbementionedthatalthoughIstrivetomaintaintechnicalaccuracyinallofthis 

book’scontent,thesubjectmatterisbroadandharborsmanypotentialdangers. Electricity 

maimsandkillswithoutprovocation,anddeservestheutmostrespect. Istronglyencourage 

experimentationonthepartofthereader,butonlywithcircuitspoweredbysmallbatteries 

wherethereisnoriskofelectricshock,fire,explosion,etc.High-powerelectriccircuitsshould 

belefttothecareoftrainedprofessionals! TheDesignScienceLicenseclearlystatesthat 

neitherInoranycontributorstothisbookbearanyliabilityforwhatisdonewithitscontents. 

A-1.2 TheuseofSPICE 

Oneofthebestwaystolearnhowthingsworkistofollowtheinductiveapproach:toobserve 

specificinstancesofthingsworkingandderivegeneralconclusionsfromthoseobservations. 

Inscienceeducation,labworkisthetraditionallyacceptedvenueforthistypeoflearning,althoughinmanycaseslabsaredesignedbyeducatorstoreinforceprinciplespreviouslylearned 

throughlectureortextbookreading,ratherthantoallowthestudenttolearnontheirown 

throughatrulyexploratoryprocess. 

HavingtaughtmyselfmostoftheelectronicsthatIknow,Iappreciatethesenseoffrustrationstudentsmayhaveinteachingthemselvesfrombooks. 

Althoughelectroniccomponents 

aretypicallyinexpensive,noteveryonehasthemeansoropportunitytosetupalaboratory 

intheirownhomes,andwhenthingsgowrongthere’snoonetoaskforhelp.Mosttextbooks

A-1.3. ACKNOWLEDGEMENTS 497 

seemtoapproachthetaskofeducationfromadeductiveperspective: tellthestudenthow 

thingsaresupposedtowork,thenapplythoseprinciplestospecificinstancesthatthestudent 

mayormaynotbeabletoexplorebythemselves.Theinductiveapproach,asusefulasitis,is 

hardtofindinthepagesofabook. 

However,textbooksdon’thavetobethisway. IdiscoveredthiswhenIstartedtolearna 

computerprogramcalledSPICE.Itisatext-basedpieceofsoftwareintendedtomodelcircuits 

andprovideanalysesofvoltage,current,frequency,etc.Althoughnothingisquiteasgoodas 

buildingrealcircuitstogainknowledgeinelectronics,computersimulationisanexcellentalternative.Inlearninghowtousethispowerfultool,Imadeadiscovery:SPICEcouldbeused 

withinatextbooktopresentcircuitsimulationstoallowstudentsto”observe”thephenomena 

forthemselves. Thisway,thereaderscouldlearntheconceptsinductively(byinterpreting 

SPICE’soutput)aswellasdeductively(byinterpretingmyexplanations). Furthermore,in 

seeingSPICEusedoverandoveragain,theyshouldbeabletounderstandhowtouseitthemselves,providingaperfectlysafemeansofexperimentationontheirowncomputerswithcircuit 

simulationsoftheirowndesign. 

Anotheradvantagetoincludingcomputeranalysesinatextbookistheempiricalverificationitaddstotheconceptspresented. 

Withoutdemonstrations,thereaderislefttotake 

theauthor’sstatementsonfaith,trustingthatwhathasbeenwrittenisindeedaccurate.The 

problemwithfaith,ofcourse,isthatitisonlyasgoodastheauthorityinwhichitisplacedand 

theaccuracyofinterpretationthroughwhichitisunderstood.Authors,likeallhumanbeings, 

areliabletoerrand/orcommunicatepoorly. Withdemonstrations,however,thereadercan 

immediatelyseeforthemselvesthatwhattheauthordescribesisindeedtrue.Demonstrations 

alsoservetoclarifythemeaningofthetextwithconcreteexamples. 

SPICEisintroducedearlyinvolumeI(DC)ofthisbookseries,andhopefullyinagentle 

enoughwaythatitdoesn’tcreateconfusion. Forthosewishingtolearnmore,achapterin 

theReferencevolume(volumeV)containsanoverviewofSPICEwithmanyexamplecircuits. 

Theremaybemoreflashy(graphic)circuitsimulationprogramsinexistence,butSPICEis 

free,avirtuecomplementingthecharitablephilosophyofthisbookverynicely. 

A-1.3 Acknowledgements 

First,Iwishtothankmywife,whosepatienceduringthosemanyandlongevenings(and 

weekends!)oftypinghasbeenextraordinary. 

Ialsowishtothankthosewhoseopen-sourcesoftwaredevelopmenteffortshavemadethis 

endeavorallthemoreaffordableandpleasurable.Thefollowingisalistofvariousfreecomputersoftwareusedtomakethisbook,andtherespectiveprogrammers: 

• GNU/LinuxOperatingSystem–LinusTorvalds,RichardStallman,andahostofothers 

toonumeroustomention. 

• Vimtexteditor–BramMoolenaarandothers. 

• Xcircuitdraftingprogram–TimEdwards. 

• SPICEcircuitsimulationprogram–toomanycontributorstomention. 

• TEXtextprocessingsystem–DonaldKnuthandothers.

498 APPENDIXA-1. ABOUTTHISBOOK 

• Texinfodocumentformattingsystem–FreeSoftwareFoundation. 

• L ATEXdocumentformattingsystem–LeslieLamportandothers. 

• Gimpimagemanipulationprogram–toomanycontributorstomention. 

AppreciationisalsoextendedtoRobertL.Boylestad,whosefirsteditionofIntroductory 

CircuitAnalysistaughtmemoreaboutelectriccircuitsthananyotherbook.Otherimportant 

textsinmyelectronicsstudiesincludethe1939editionofThe”Radio”Handbook,Bernard 

Grob’ssecondeditionofIntroductiontoElectronicsI,andForrestMims’originalEngineer’s 

Notebook. 

ThankstothestaffoftheBellinghamAntiqueRadioMuseum,whoweregenerousenough 

toletmeterrorizetheirestablishmentwithmycameraandflashunit. 

IwishtospecificallythankJeffreyElknerandallthoseatYorktownHighSchoolforbeing 

willingtohostmybookaspartoftheirOpenBookProject,andtomakethefirsteffortincontributingtoitsformandcontent.ThanksalsotoDavidSweet(website: 

(http://www.andamooka.org)) 

andBenCrowell(website: (http://www.lightandmatter.com))forprovidingencouragement,constructivecriticism,andawideraudiencefortheonlineversionofthisbook. 

ThankstoMichaelStutzfordraftinghisDesignScienceLicense,andtoRichardStallman 

forpioneeringtheconceptofcopyleft. 

Lastbutcertainlynotleast,manythankstomyparentsandthoseteachersofminewho 

sawinmeadesiretolearnaboutelectricity,andwhokindledthatflameintoapassionfor 

discoveryandintellectualadventure.Ihonoryoubyhelpingothersasyouhavehelpedme. 

TonyKuphaldt,July2001 

”Acandlelosesnothingofitslightwhenlightinganother” 

KahlilGibran

AppendixA-2 

CONTRIBUTORLIST 

A-2.1 Howtocontributetothisbook 

Asacopyleftedwork,thisbookisopentorevisionandexpansionbyanyinterestedparties. 

Theonly”catch”isthatcreditmustbegivenwherecreditisdue.Thisisacopyrightedwork: 

itisnotinthepublicdomain! 

Ifyouwishtociteportionsofthisbookinaworkofyourown,youmustfollowthesame 

guidelinesasforanyothercopyrightedwork. HereisasamplefromtheDesignScienceLicense: 

The Work is copyright the Author. All rights to the Work are reserved 

by the Author, except as specifically described below. This License 

describes the terms and conditions under which the Author permits you 

to copy, distribute and modify copies of the Work. 

In addition, you may refer to the Work, talk about it, and (as 

dictated by "fair use") quote from it, just as you would any 

copyrighted material under copyright law. 

Your right to operate, perform, read or otherwise interpret and/or 

execute the Work is unrestricted; however, you do so at your own risk, 

because the Work comes WITHOUT ANY WARRANTY -- see Section 7 ("NO 

WARRANTY") below. 

Ifyouwishtomodifythisbookinanyway,youmustdocumentthenatureofthosemodificationsinthe”Credits”sectionalongwithyourname,andideally,informationconcerninghow 

youmaybecontacted.Again,theDesignScienceLicense: 

Permission is granted to modify or sample from a copy of the Work, 

499

500 APPENDIXA-2. CONTRIBUTORLIST 

producing a derivative work, and to distribute the derivative work 

under the terms described in the section for distribution above, 

provided that the following terms are met: 

(a) The new, derivative work is published under the terms of this 

License. 

(b) The derivative work is given a new name, so that its name or 

title can not be confused with the Work, or with a version of 

the Work, in any way. 

(c) Appropriate authorship credit is given: for the differences 

between the Work and the new derivative work, authorship is 

attributed to you, while the material sampled or used from 

the Work remains attributed to the original Author; appropriate 

notice must be included with the new work indicating the nature 

and the dates of any modifications of the Work made by you. 

Giventhecomplexitiesandsecurityissuessurroundingthemaintenanceoffilescomprising 

thisbook,itisrecommendedthatyousubmitanyrevisionsorexpansionstotheoriginalauthor 

(TonyR.Kuphaldt). Youare,ofcourse,welcometomodifythisbookdirectlybyeditingyour 

ownpersonalcopy,butwewouldallstandtobenefitfromyourcontributionsifyourideaswere 

incorporatedintotheonline“mastercopy”wherealltheworldcanseeit. 

A-2.2 Credits 

Allentriesarrangedinalphabeticalorderofsurname.Majorcontributionsarelistedbyindividualnamewithsomedetailonthenatureofthecontribution(s),date,contactinfo,etc.Minorcontributions(typocorrections,etc.)arelistedbynameonlyforreasonsofbrevity.PleaseunderstandthatwhenIclassifyacontributionas“minor,”itisinnowayinferiortotheeffort 

orvalueofa“major”contribution,justsmallerinthesenseoflesstextchanged.Anyandall 

contributionsaregratefullyaccepted.Iamindebtedtoallthosewhohavegivenfreelyoftheir 

ownknowledge,time,andresourcestomakethisabetterbook! 

A-2.2.1 TonyR.Kuphaldt 

• Date(s)ofcontribution(s):1996topresent 

• Natureofcontribution:Originalauthor. 

• Contactat: liec0@lycos.com

A-2.2. CREDITS 501 

A-2.2.2 DennisCrunkilton 

• Date(s)ofcontribution(s):July2004topresent 

• Natureofcontribution: Minitableofcontents,allchaptersexceptappendicies;html, 

latex,ps,pdf;SeeDevel/tutorial.html;01/2006. 

• Natureofcontribution:CompletedCh4Bipolarjunctiontransistors,CH7Thyristors; 

Ch9Practicalanlogckts,afewadditions;Ch8Opamps,minor;04/2009 

• Contactat: dcrunkilton(at)att(dot)net 

A-2.2.3 BillMarsden 

• Date(s)ofcontribution(s):May2003-present 

• Natureofcontribution:UpdatetoLEDsubsection,DiodesCh3,Nov2003. 

• Natureofcontribution:Originalauthor:“ElectroStaticDischarge”Section,Chapter 

9,May2008. 

• Natureofcontribution:Chapter3,LED’supdate,photodiodeupdate,Feburary2009. 

• Natureofcontribution:Chapter11,Sectionauthor:”PulseWidthModulation”,Feburary2010. 

• Contactat: bill marsden2(at)hotmail(dot)com 

A-2.2.4 JohnAnhalt 

• Date(s)ofcontribution(s):June2011 

• Natureofcontribution:UpdatedSiSP3electronhybridization,Ch2 

• Contactat: jpa@anhalt.org 

A-2.2.5 Yournamehere 

• Date(s)ofcontribution(s):Monthandyearofcontribution 

• Natureofcontribution:Inserttexthere,describinghowyoucontributedtothebook. 

• Contactat: my email@provider.net


A-2.2.6 Typocorrectionsandother“minor”contributions 

• line-allaboutcircuits.com(June2005)TypographicalerrorcorrectioninVolumes1,2,3,5, 

variouschapters,(:s/visa-versa/viceversa/). 

• ColinCreitz(May2007)Chapters:several,s/it’s/its. 

• DennisCrunkilton(October2005)Typographicalcapitlizationcorrectiontosectiontitles,chapter9. 

• JeffDeFreitas(March2006)Improveappearance:replace“/”and”/”Chapters:A1,A2. 

• PaulStokes,ProgramChair,ComputerandElectronicsEngineeringTechnology,ITT 

TechnicalInstitute,Houston,Tx(October2004)Change(10012=-810+710=-110)to 

(10012=-810+110=-110),CH2,BinaryArithmetic 

• PaulStokes,ProgramChairComputerandElectronicsEngineeringTechnology,ITT 

TechnicalInstitute,Houston,Tx(October2004)Near”Foldupthecorners”changeOut=B’C’ 

toOut=B’D’,14118.epssamechange,KarnaughMapping 

• ThestudentsofBellinghamTechnicalCollege’sInstrumentationprogram,. 

• RogerHollingsworth(May2003)SuggestedawaytomakethePLCmotorcontrol 

systemfail-safe. 

• Jan-WillemRensman(May2002)SuggestedtheinclusionofSchmitttriggersandgate 

hysteresistothe”LogicGates”chapter. 

• DonStalkowski(June2002)TechnicalhelpwithPostScript-to-PDFfileformatconversion. 

• JosephTeichman(June2002)SuggestionandtechnicalhelpregardinguseofPNG 

imagesinsteadofJPEG. 

• Unregistered@allaboutcircuits.com(November2007)“Booleanalgebra”,images14019.pes 

14021.epsoutputofgatesincorrects/0/As/1/A. 

• DanSimon(February2008)“NumerationSystems”,AfterBINARYTOOCTALCON- 

VERSION,positionofdecimalpoint—. 

• TimothyKingman(March2008)Changeddefaultromanfonttonewcent. 

• ImranullahSyed(March2008)Suggestedcenteringofuncaptionedschematics. 

• Chris01720@allaboutcircuits.com(March2008)Ch15,InaccuracyinvolvingCD-ROM 

production. 

• studiot@allaboutcircuits.com(March2008)Ch15,s/disk/disc/inCDROM. 

• Keith@allaboutcircuits.com(April2008)Ch12,s/laralel-out/parallel-out/. 

• KenBraswell(May2008)Ch3,s/drips/drops/.


• Guest@allaboutcircuits.com(Oct2008)Ch2,s/areinclose/areclose/. 

• Radoslav@allaboutcircuits.com(Oct2008)Ch8,s/that1mAof/that6mA/. 

• Scanman@allaboutcircuits.com(Dec2008)Ch2,s/shellsarehold/shellshold/. 

• dgeorge@allaboutcircuits.com(Dec2008)Ch7,image03320.png,swappedanodeand 

anodegate.leftdiagram. 

• UnregisteredGuest@allaboutcircuits.com(Feb2009)Ch2s/thanFET’s/thanJFET’s. 

• UnregisteredGuest@allaboutcircuits.com(March2009)Ch8,13061.png,change 

formulaforinvertinggaintoinclude”-”. 

• dezurtrat@allaboutcircuits.com(March2009)Ch3,03443.png,s/p-p/peak. 

• BillMarsden@allaboutcircuits.com(April2009)Ch3,s/Iwould/Itwould/ 

• PeterO@allaboutcircuits.com(April2009)Ch1,closingparenthesis,abovereplaced 

withreferencetofigure. 

• Nanophotonics@allaboutcircuits.com(April2009)Ch9,image53009.jpgs/courtisy/courtesy. 

• BillMarsden@allaboutcircuits.com(April2009)Ch8,images2001.png,2002.png 

appearance. 

• DCrunkilton(April2009)Ch4,images23006.png,23007.pngupdated. 

• UnregisteredGuest@allaboutcircuits.com(June2009)Ch7,s/SCRschematicsymbol/TRIACschematicsymbol. 

• PeterO’Dette(June2009)Ch1,s/is1watts/is1Watt,s/10watt/10Watts,s/watt/Watt 

. 

• UnregisteredGuest@allaboutcircuits.com(June2009)Ch3, s/being/begin,near 

”voltageatwhichthey”.s/is/innear”Thediodesmustbe”. 

• regrehan@allaboutcircuits.com(June2009)Ch4,s/r1121/r1121kincommonemitteramplifierSPICElist. 

• UnregisteredGuest@allaboutcircuits.com(July2009)Ch3,s/Notepolaritychange 

oncoilchanged/Notepolaritychangeoncoil. 

• UnregisteredGuest@allaboutcircuits.com(August2009)Ch4,SwapPNP&NPNat 

(b)&(c),captionof03075.png. 

• UnregisteredGuest@allaboutcircuits.com(August2009)equationtypos03077.png 

03479.png. 

• PeterO’Dette@allaboutcircuits.com(August2009)Ch2, Numerouschanges, and 

03409.png.


• BillMarsden@allaboutcircuits.com(November2009)Ch4,Betaformula,”Transistor 

atingsandPackages”. 

• UnregisteredGuest@allaboutcircuits.com(November2009)Ch3,Image03288.eps 

changedpolarizedcapacitortonon-polarized. 

• UnregisteredGuest@allaboutcircuits.com(November2009)Ch4s/hasre/share/s/common=emitter/commonemitter/. 

• Uisge@allaboutcircuits.com(November2009)Ch3,s/onceeveryhalf-cycle/onehalfof 

everyfullcycle/,s/much/half/. 

• UnregisteredGuest@allaboutcircuits.com(November2009)Ch4s/Tomaintaining/To 

maintain. 

• UnregisteredGuest@allaboutcircuits.com(November2009)Ch3s/[model]/[modelname]/ 

. 

• gareththegeek@allaboutcircuits.com(November2009)Ch2numeroustypos,omissions. 

• Dcrunkilton@allaboutcircuits.com(November2009)Ch2minorchagestotextand 

image03392.eps. 

• waynerr@allaboutcircuits.com(December2009)Ch4equations4and7ofimage 

03488.eps. 

• jkenny@allaboutcircuits.com(January2010)Ch7s/willwill/will/. 

• BHijazi@allaboutcircuits.com(February2010)Ch1,Clarificationoftextbetweenimages03378.pngand03379.png. 

• SgtWookiei@allaboutcircuits.com(March2010)Ch4,image03375.png,flippedpnp 

andbattery. 

• BillMarsden@allaboutcircuits.com(March2010)Ch9,ChangestoESDsection. 

• SgtWookiei@allaboutcircuits.com(April2010)Ch4,image03078.png,addedresistors. 

• silv3rmOOn@allaboutcircuits.com(April2010)Ch4,typoinSPICElistingnearimage20004.png. 

• optomist1@allaboutcircuits.com(July2010)Ch2,typos/campared/compared/. 

• BillMarsden@allaboutcircuits.com(July2010)Ch11,change[I]toitalictagsindcdrive.sml. 

• Unregisteredguest@allaboutcircuits.com(August2010)Ch2,s/Thebopolartransistor/Thebipolarjunctiontransistor/. 

• Unregisteredguest@allaboutcircuits.com(August2010)Ch4,


• DCrunkilton(Sept2010)Ch2s/minuscule/minuscule;Ch3,4,5,7,s/useable/usable. 

• beenthere@allaboutcircuits.com(Oct2010)Ch3,AClinepoweredLEDmaterialremoved. 

• mulebones@allaboutcircuits.com(Feb2011)Ch3,s/5Vptp/10Vptp/ 

• Skfir@allaboutcircuits.com(Feb2011)Ch1,s/ource/source/ 

• Skfir@allaboutcircuits.com(Feb2011)Ch2,4,A3s/thethe/the/ 

• Skfir@allaboutcircuits.com(Feb2011)Ch2,s/insulatorinsulator/insulator/ 

• Skfir@allaboutcircuits.com(Feb2011)Ch3, s/aapproximately/atapproximately/, 

s/frequencymy/frequencymay/,s/applicationa/appliationisas/,s/beenproduce/been 

produced/;Ch4s/approximage/approximate/s/resistorisashort/capacitorisashort/; 

s/Iisit/Isit/s/Thethe/The/s/thethese/these/,s/distortiondistortion/distortion/ 

• D.Crunkilton(June2011)hi.latex,headerfile;updatedlinktoopenbookproject.net. 

• SamAtOz@allaboutcircuits.com(May2012)Ch2s/occurr/occurs/repells/repels/,s/is 

increases/increases,at(c)changedtofullreference,. 

• john207@allaboutcircuits.com(May2012)Ch4,various 

• BillMarsden@allaboutcircuits.com(May2012)Ch4,Clarificationoftextnear:Bipolartransistorsarecontructed.... 

• kintzlr@allaboutcircuits.com(January2013)Ch4,image03495.epscorrected.Added 

Ohmsymbolto0.26,above2600Ohm. 

• sby64@allaboutcircuits.com(January2013)Ch4,captionimage03495.pngs/resistance 

Vth/resistanceRth. 

• keithostertag@allaboutcircuits.com(January2013)Ch4,captionimage03495.png 

s/resistanceVth/resistanceRth. 

• EugeneSmirnoff(January2013)Ch2,near”ASQUID’”s/isan/isa/s/Superconduction/Superconducting

506 APPENDIXA-2. CONTRIBUTORLIST

AppendixA-3 

DESIGNSCIENCELICENSE 

Copyright c○1999-2000MichaelStutz stutz@dsl.org 

Verbatimcopyingofthisdocumentispermitted,inanymedium. 

A-3.1 0.Preamble 

Copyrightlawgivescertainexclusiverightstotheauthorofawork, includingtherights 

tocopy,modifyanddistributethework(the”reproductive,””adaptative,”and”distribution” 

rights). 

Theideaof”copyleft”istowillfullyrevoketheexclusivityofthoserightsundercertain 

termsandconditions,sothatanyonecancopyanddistributetheworkorproperlyattributed 

derivativeworks,whileallcopiesremainunderthesametermsandconditionsastheoriginal. 

Theintentofthislicenseistobeageneral”copyleft”thatcanbeappliedtoanykindofwork 

thathasprotectionundercopyright.Thislicensestatesthosecertainconditionsunderwhich 

aworkpublishedunderitstermsmaybecopied,distributed,andmodified. 

Whereas”designscience”isastrategyforthedevelopmentofartifactsasawaytoreform 

theenvironment(notpeople)andsubsequentlyimprovetheuniversalstandardofliving,this 

DesignScienceLicensewaswrittenanddeployedasastrategyforpromotingtheprogressof 

scienceandartthroughreformoftheenvironment. 

A-3.2 1.Definitions 

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termsofthisDesignScienceLicense. 

”Work”shallmeansuchanaforementionedwork.TheLicensealsoappliestotheoutputof 

theWork,onlyifsaidoutputconstitutesa”derivativework”ofthelicensedWorkasdefinedby 

copyrightlaw. 

507

508 APPENDIXA-3. DESIGNSCIENCELICENSE 

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510 APPENDIXA-3. DESIGNSCIENCELICENSE 

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EXPRESSORIMPLIED,TOTHEEXTENTPERMITTEDBYAPPLICABLELAW,INCLUD- 

INGBUTNOTLIMITEDTOTHEIMPLIEDWARRANTIESOFMERCHANTABILITYOR 

FITNESSFORAPARTICULARPURPOSE. 

A-3.9 8.Disclaimerofliability 

INNOEVENTSHALLTHEAUTHORORCONTRIBUTORSBELIABLEFORANYDI- 

RECT,INDIRECT,INCIDENTAL,SPECIAL,EXEMPLARY,ORCONSEQUENTIALDAM- 

AGES(INCLUDING,BUTNOTLIMITEDTO,PROCUREMENTOFSUBSTITUTEGOODS 

ORSERVICES;LOSSOFUSE,DATA,ORPROFITS;ORBUSINESSINTERRUPTION) 

HOWEVERCAUSEDANDONANYTHEORYOFLIABILITY,WHETHERINCONTRACT, 

STRICTLIABILITY,ORTORT(INCLUDINGNEGLIGENCEOROTHERWISE)ARISINGIN 

ANYWAYOUTOFTHEUSEOFTHISWORK,EVENIFADVISEDOFTHEPOSSIBILITY 

OFSUCHDAMAGE. 

ENDOFTERMSANDCONDITIONS 

[$Id: dsl.txt,v 1.25 2000/03/14 13:14:14 m Exp m $]

Index 

αratio,210,264 

βratio,186,264 

10-50milliampsignal,379 

4-20milliampsignal,379 

4-layerdiode,322 

741operationalamplifier,361 

A-weighteddBscale,14 

A/Dconverter,365 

AC-DCpowersupplyschematic,333 

Activedevice,3 

Activemode,transistor,183 

Alpharatio,210,264 

Amplification,definition,3 

Amplifier,differential,357 

Amplifier,inverting,371 

Amplifier,noninverting,371 

Amplifier,single-ended,357 

Analog-to-digitalconverter,365 

AngularMomentumquantumnumber,33 

Anti-staticfoam,287 

Antilogarithm,10 

Artifact,measurement,450 

Astable,391 

Attenuator,16 

Attenuator,bridgedT,21 

Attenuator,coaxial,23 

Attenuator,L,21 

Attenuator,PI,20 

Attenuator,rf,23 

Attenuator,T,19 

Avalanchephotodiode,153 

Averager,380 

Band,electron,47 

Bandwidth,amplifier,256 

Bardeen,John,60,65 

Beampowertube,474 

Bel,8 

Betaratio,186,264 

Betaratio,bipolartransistor,479 

Betavariations,187 

Biascurrent,op-amp,398 

Bias,BJT,base,235 

Bias,BJT,calculations,235 

Bias,BJT,collector-feedback,236 

Bias,BJT,emitter,237 

Bias,BJT,voltagedivider,243 

Bias,diode,98 

Bias,transistor,195,222 

Bilateral,294 

Bipolar-modeMOSFET,314 

Bistable,389 

Brattain,Walter,60,65 

Breakdown,diode,102 

Breakdown,transistor,327 

Breakover,thyristor,327 

Bridgerectifiercircuit,111 

Bridgerectifiercircuit,polyphase,111 

Bypasscapacitor,261 

Calculus,360,386,438 

Capacitance,diode,108 

Capacitor,bypass,261 

Capacitor,coupling,231 

Capacitor,op-ampcompensation,404 

Cascodeamplifier,218 

Cat-Eyetube,486 

Cathode,471 

CathodeRayTube,485 

Center-taprectifiercircuit,109 

Characteristiccurves,transistor,186,293 

Checkvalve,98 

Clampercircuit,121 

511

512 INDEX 

ClassAamplifieroperation,223 

ClassABamplifieroperation,224 

ClassBamplifieroperation,223 

ClassCamplifieroperation,225 

ClassDamplifieroperation,225 

Class,amplifieroperation,222 

Clippercircuit,117 

clipper,zenerdiode,142 

CMRR,393 

Cockcroft-Walton,voltagemultiplier,128 

Coherentlight,151 

Cold-cathodetube,482 

COMFET,314 

Common-baseamplifier,210 

Common-collectoramplifier,202 

Common-emitteramplifier,189 

Common-moderejectionratio,393 

Common-modevoltage,393 

Commutatingdiode,130,131 

Commutation,131 

Commutationtime,diode,108 

Commutation,forced,350,351 

Commutation,natural,333,351 

Comparator,363 

Compensationcapacitor,op-amp,404 

Conductionband,48 

Conductivity-ModulatedField-EffectTransis- 

tor,314 

Constant-currentdiode,162 

Controlledrectifier,338 

Conventionalflow,98 

Cooperpair,80 

Couplingcapacitor,231 

Couplingloop,resonator,488,491 

Criticalrateofvoltagerise,328,330 

Crossoverdistortion,494 

Crowbar,333 

CRT,485 

Crystalradio,424 

Currentmirror,264 

Currentsource,184,378 

Currentsourcingvs.sinking,267 

Current,diodeleakage,108 

Current-limitingdiode,162 

Current-regulatingdiode,162 

Curve,characteristic,186,293 

Cutoffvoltage,285 

Cutoff,transistor,177,183 

Czochralskiprocess,silicon,75 

Darlingtonpair,209 

Datasheet,component,107 

dB,8 

dB,absolutepowermeasurements,15,16 

dB,soundmeasurements,14 

dBA,14 

dBk,16 

dBm,15 

dBW,16 

DCrestorercircuit,121 

Decibel,8 

Decibels,attenuator,17 

Decineper,13 

Degenerativefeedback,256 

Derivative,calculus,439 

DIAC,329 

Differentialamplifier,357 

Differentialpair,408,409 

Differentiation,360 

Differentiation,calculus,386,438 

Diode,98 

Diodecheck,meterfunction,104,180 

Diodeequation,the,101 

Diodejunctioncapacitance,108 

Diodeleakagecurrent,108 

DiodePIVrating,102 

Diodetube,471 

Diode,4-layer,73 

Diode,constant-current,162 

Diode,Esaki,144 

Diode,four-layer,322 

Diode,hotcarrier,143,158 

Diode,IMPATT,160 

Diode,laser,150 

Diode,light-activated,152 

Diode,light-emitting,146 

diode,MIIM,85 

diode,MIM,163 

Diode,pin,159 

Diode,PNPN,322 

Diode,schottky,143 

Diode,Shockley,322

INDEX 513 

Diode,snap,159 

Diode,SPICE,163 

Diode,tunnel,144 

Diode,varactor,158 

Diode,varicap,158 

Diode,zener,136 

DIP,361 

Dischargetube,483 

Distortion,amplifier,256 

Distortion,crossover,494 

dn,13 

Double-layertunnelingtransistor,84 

Drift,op-amp,404 

Dropout,thyristor,327 

DualInlinePackage,361 

Dualpowersupply,357 

Dutycycle,squarewave,364 

Dutycycle,squarewave,225 

Edisoneffect,469 

Effect,Edison,469 

Electrode,cathode,471 

Electrode,grid,470 

Electrode,screen,473 

Electrode,suppressor,476 

Electron,28 

Electronflow,98 

Emitterfollower,205 

Emitter-followeramplifier,202 

Equation,diode,101 

Equilibrium,366 

Esakidiode,144 

Exclusionprinciple,36 

Failuremode,zenerdiode,136 

Faraday’sLaw,130,131 

Feedback,amplifier,256 

Feedback,negative,366 

Feedback,positive,388 

FET,fieldeffecttransistor,65 

Fieldeffecttransistor,65 

Firing,thyristor,327 

Flashconverter,365 

Floating,177,330 

Flow,electronvs.conventional,98 

Foam,anti-static,287 

Forcedcommutation,350,351 

Forwardbias,98 

Forwardvoltage,diode,100 

Four-layerdiode,322 

Frequencyresponse,op-amp,404 

Full-waverectifiercircuit,109,111 

Gain,6 

Gain,ACversusDC,7 

Gateturnoffswitch,73 

Gate-ControlledSwitch,330 

Gate-Turn-Offthyristor,330 

GCS,330 

Glowtube,484 

Grid,470 

Ground,356 

Ground,virtual,371 

GTO,330 

GTO,gateturnoffswitch,73 

Half-waverectifiercircuit,108 

Harmonic,342 

Harmonic,evenvs.odd,342 

Harmonicsandwaveformsymmetry,342 

Heptode,477 

hfe,187 

Hightemperaturesuperconductors:,82 

Holdingcurrent,SCR,332 

hotcarrierdiode,143 

Hot-cathodetube,482 

Hybridparameters,187 

Hysteresis,389,482 

IC,267 

IGBT,314,353 

IGFET,insulatedgatefieldeffecttransistor, 

70 

IGT,314,353 

IMPATTdiode,160 

Inductiveoutputtube,488 

Inertelements,38 

Input,inverting,358 

Input,noninverting,358 

Insulatedgatefieldeffecttransistor,70 

Insulated-GateBipolarTransistor,314,353 

Insulated-GateTransistor,314,353

514 INDEX 

Integratedcircuit,267 

Integration,calculus,386,438 

Invertingamplifier,192,371 

Invertingsummer,381 

Ionization,318,481 

JFET,junctionfieldeffecttransistor,65 

Josephsonjunctions,80 

Josephsontransistor,81 

Joule’sLaw,11,136 

Junctioncapacitance,diode,108 

Kickback,inductive,130 

Kirchhoff’sCurrentLaw,175 

Kirchhoff’sVoltageLaw,205 

Klystron,488 

Laserdiode,150 

Laserlight,151 

Latch-up,396 

Latching,thyristor,327 

Leakagecurrent,diode,102,108 

LED,146 

Light-emittingdiode,146 

Lilienfeld,Julius,65 

Loadline,226 

Logarithm,10 

Magic-Eyetube,486 

Magneticquantumnumber,33 

Magnetictunneljunction,88 

Mechanics,quantum,32 

MESFET,metalsemiconductorfieldeffecttran- 

sistor,68 

Metaloxidefieldeffecttransistor,70 

Mho,296 

Microphonics,electrontube,493 

MIIM,diode,85 

Millereffect,277 

MIMdiode,163 

Monochromaticlight,151 

MOSControlledThyristor,352 

MOS-gatedthyristor,352 

MOSFET,metaloxidefieldeffecttransistor, 

70 

MTJ,magnetictunneljunction,88 

Mu,tubeamplificationfactor,477 

Multipliercircuit,diode,123 

Multiplier,frequency,varactor,422 

Naturalcommutation,333,351 

Negativefeedback,256,366 

Negativeresistance,144 

Neper,13 

Neutron,28 

Nobleelements,38 

Noninvertingamplifier,371 

Noninvertingsummer,381 

Number,quantum,33 

Offsetnull,op-amp,397 

Offsetvoltage,op-amp,396 

Ohmicregion,JFET,295 

Op-amp,262,361 

Operationalamplifier,262,361 

Orbital,electron,35 

Oscillator,256 

Oscillator,op-amp,391 

oscillator,phaseshift,422 

Oscillator,relaxation,319 

Oscillator,voltage-controlled,489 

Over-unitymachine,5 

Passiveaverager,380 

Passivedevice,3 

Pauli,exclusionprinciple,36 

PCB,106 

Peakdetector,115 

Pentagridtube,477 

Pentodetube,306 

Perpetualmotionmachine,3 

Phaseshift,op-amp,405 

Photodiode,152 

Photodiodeamplifier,455 

Photodiode,APD,153 

Photodiode,PIN,153 

PI-network,16 

PINdiode,159 

PIN,photodiode,153 

Pinch-offvoltage,285 

PIVrating,diode,102 

Plasma,318,481

INDEX 515 

PNPNdiode,322 

Polyphasebridgerectifiercircuit,111 

Positivefeedback,256,318,388 

Powersupplyschematic,AC-DC,333 

Principalquantumnumber,33 

Printedcircuitboard,106 

Processvariable,359 

Programmableunijunctiontransistor,347 

Proton,28 

Pulse-widthmodulation,364 

Push-pullamplifier,223 

PWM,364 

Quantumdot,86 

Quantumdottransistor,86 

Quantummechanics,32 

Quantumnumber,33 

Quantumphysics,28 

quantumtunneling,83 

Quiescent,226 

Radio,crystal,424 

Railvoltage,368 

Rectifier,98 

Rectifiercircuit,108 

Rectifiercircuit,full-wave,109,111 

Rectifiercircuit,half-wave,108 

Rectifier,controlled,338 

Referencejunction,thermocouple,398 

Reflexklystron,489 

Regenerativefeedback,256,318 

Regulator,voltage,207 

Relaxationoscillator,319 

Resistance,negative,144 

Resonanttunnelingdiode,84 

Restorercircuit,121 

Reversebias,98 

Reverserecoverytime,diode,108 

Reversevoltagerating,diode,102 

Rheostat,188,296 

Richterscale,9 

Ripplevoltage,113 

Runaway,thermal,259 

s,p,d,fsubshellnotation,34 

Saturablereactor,3 

Saturationvoltage,368 

Saturation,transistor,177,183 

Schottkydiode,143 

SCR,329,485 

SCRbridgerectifier,338 

SCR,siliconcontrolledrectifier,73 

Screen,473 

SCS,350 

Secondaryemission,474 

Semiconductor,defined,48 

Sensitivegate,SCR,332 

Setpoint,359 

Shell,electron,33 

Shockleydiode,322 

Shockley,William,60,65,73 

Siemens,296,379 

Signal,10-50milliamp,379 

Signal,4-20milliamp,379 

Siliconcontrolledrectifier,73 

Silicon-controlledrectifier,329,485 

Silicon-controlledswitch,350 

Single-endedamplifier,357 

Sink,current,267 

Slicercircuit,117 

Sliderule,10 

Small-scaleintegration,409 

Snapdiode,159 

Snubber,131 

Solarcell,154 

Solid-state,2 

Soundintensitymeasurement,14 

Sparkgap,482 

SPICE,diode,163 

Spinquantumnumber,33 

Spintronics,88 

Splitpowersupply,357 

SQUID:,81 

SSI,409 

Steprecoverydiode,159 

Subshellnotation,34 

Subshell,electron,34 

Superconductionquantuminterferencedevice, 

81 

Superconductivity,79 

Superpositiontheorem,231 

Suppressor,476

516 INDEX 

Switchingtime,diode,108 

T-network,16 

Tetrodetube,306,473 

Theorem,Superposition,231 

Thermalrunaway,BJT,259 

Thermalvoltage,diode,101 

Thermocouple,398 

Three-phasebridgerectifiercircuit,111 

Thyratron,485 

Thyratrontube,320 

Thyristor,73,482 

Time,diodeswitching,108 

Totalizer,387 

Transconductance,296,379 

Transconductanceamplifier,379 

Transistor,fieldeffect,65 

Transistor,insulatedgatefieldeffect,70 

Transistor,Josephson,81 

Transistor,metaloxidefieldeffect,70 

Transistor,programmableunijunction,347 

Transistor,singleelectron,86 

Transistor,unijunction,344 

Triodetube,306,320,471 

Tube,discharge,483 

Tunneldiode,144 

Tunneljunction,magnetic,88 

tunneling,quantum,83 

Unijunctiontransistor,344 

Unipolar,conduction,65 

Unit,bel,8 

Unit,decineper,13 

Unit,mho,296 

Unit,neper,13 

Unit,siemens,296,379 

Valenceband,48 

Valenceshell,34 

Valve,“check”,98 

Varactordiode,158 

Varicapdiode,158 

VCO,321 

Virtualground,371 

VMOStransistor,314 

Voltagebuffer,368 

Voltagedoublercircuit,123 

Voltagefollower,205,368 

Voltagemultipliercircuit,123 

Voltagemultiplier,Cockcroft-Walton,128 

Voltageregulator,207 

Voltageregulatortube,484 

Voltagerise,criticalrateof,328,330 

Voltage,bias,195,222 

Voltage,common-mode,393 

Voltage,forward,100 

Voltage,op-ampoutputsaturation,368 

Voltage,ripple,113 

Voltage-controlledoscillator,321,489 

Volumeunits,15 

VUscale,15 

Waveformsymmetryandharmonics,342 

Zenerdiode,136 

Zenerdiodefailuremode,136 

Zenerdiode,clipper,142

INDEX 517 

.

"Lessons In Electric Circuits, Volume III -- Semiconductors"

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