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Approved SOPL Study Guide<br />
Lessons In Electric Circuits, Volume 6 – <strong>Experiments</strong>
FirstEdition,lastupdateJanuary18,2010
2
LessonsInElectricCircuits,VolumeVI–<strong>Experiments</strong><br />
ByTonyR.Kuphaldt<br />
FirstEdition,lastupdateJanuary18,2010
i<br />
c○2002-2011,TonyR.Kuphaldt<br />
ThisbookispublishedunderthetermsandconditionsoftheDesignScienceLicense.These<br />
termsandconditionsallowforfreecopying,distribution,and/ormodificationofthisdocument<br />
bythegeneralpublic.ThefullDesignScienceLicensetextisincludedinthelastchapter.<br />
Asanopenandcollaborativelydevelopedtext,thisbookisdistributedinthehopethat<br />
itwillbeuseful,butWITHOUTANYWARRANTY;withouteventheimpliedwarrantyof<br />
MERCHANTABILITYorFITNESSFORAPARTICULARPURPOSE.SeetheDesignScience<br />
Licenseformoredetails.<br />
AvailableinitsentiretyaspartoftheOpen<strong>Book</strong>Projectcollectionat:<br />
openbookproject.net/electricCircuits<br />
PRINTINGHISTORY<br />
• FirstEdition:PrintedinApril2002.SourcefileswritteninSubMLformat.SubMLisa<br />
simplemarkuplanguagedesignedtoeasilyconverttoothermarkupslikeL A TEX,HTML,<br />
orDoc<strong>Book</strong>usingnothingbutsearch-and-replacesubstitutions.
ii
Contents<br />
1 INTRODUCTION 1<br />
1.1 Electronicsasscience . ................................. 1<br />
1.2 Settingupahomelab . ................................. 3<br />
1.3 Contributors........................................ 14<br />
2 BASICCONCEPTSANDTESTEQUIPMENT 15<br />
2.1 Voltmeterusage...................................... 15<br />
2.2 Ohmmeterusage ..................................... 21<br />
2.3 Averysimplecircuit ................................... 28<br />
2.4 Ammeterusage ...................................... 35<br />
2.5 Ohm’sLaw......................................... 42<br />
2.6 Nonlinearresistance ................................... 45<br />
2.7 Powerdissipation..................................... 48<br />
2.8 Circuitwithaswitch................................... 53<br />
2.9 Electromagnetism .................................... 55<br />
2.10 Electromagneticinduction................................ 57<br />
3 DCCIRCUITS 59<br />
3.1 Introduction........................................ 59<br />
3.2 Seriesbatteries ...................................... 60<br />
3.3 Parallelbatteries ..................................... 63<br />
3.4 Voltagedivider ...................................... 67<br />
3.5 Currentdivider ...................................... 78<br />
3.6 Potentiometerasavoltagedivider ........................... 87<br />
3.7 Potentiometerasarheostat............................... 93<br />
3.8 Precisionpotentiometer ................................. 99<br />
3.9 Rheostatrangelimiting ................................. 102<br />
3.10 Thermoelectricity..................................... 109<br />
3.11 Makeyourownmultimeter ............................... 112<br />
3.12 Sensitivevoltagedetector ................................ 117<br />
3.13 Potentiometricvoltmeter ................................ 122<br />
3.14 4-wireresistancemeasurement............................. 127<br />
3.15 Averysimplecomputer ................................. 131<br />
3.16 Potatobattery. ...................................... 136<br />
iii
iv<br />
CONTENTS<br />
3.17 Capacitorcharginganddischarging .......................... 138<br />
3.18 Rate-of-changeindicator................................. 142<br />
4 ACCIRCUITS 145<br />
4.1 Introduction........................................ 145<br />
4.2 Transformer–powersupply .............................. 147<br />
4.3 Buildatransformer ................................... 151<br />
4.4 Variableinductor ..................................... 153<br />
4.5 Sensitiveaudiodetector ................................. 155<br />
4.6 SensingACmagneticfields ............................... 160<br />
4.7 SensingACelectricfields ................................ 162<br />
4.8 Automotivealternator . ................................. 164<br />
4.9 Inductionmotor...................................... 170<br />
4.10 Inductionmotor,large . ................................. 174<br />
4.11 Phaseshift......................................... 177<br />
4.12 Soundcancellation .................................... 180<br />
4.13 Musicalkeyboardasasignalgenerator ........................ 183<br />
4.14 PCOscilloscope ...................................... 186<br />
4.15 Waveformanalysis .................................... 189<br />
4.16 Inductor-capacitor”tank”circuit . ........................... 191<br />
4.17 Signalcoupling ...................................... 194<br />
5 DISCRETESEMICONDUCTORCIRCUITS 201<br />
5.1 Introduction........................................ 202<br />
5.2 Commutatingdiode ................................... 203<br />
5.3 Half-waverectifier .................................... 205<br />
5.4 Full-wavecenter-taprectifier .............................. 213<br />
5.5 Full-wavebridgerectifier ................................ 218<br />
5.6 Rectifier/filtercircuit................................... 221<br />
5.7 Voltageregulator ..................................... 227<br />
5.8 Transistorasaswitch . ................................. 230<br />
5.9 Staticelectricitysensor ................................. 235<br />
5.10 Pulsed-lightsensor .................................... 238<br />
5.11 Voltagefollower...................................... 241<br />
5.12 Common-emitteramplifier ............................... 246<br />
5.13 Multi-stageamplifier................................... 251<br />
5.14 Currentmirror ...................................... 255<br />
5.15 JFETcurrentregulator ................................. 261<br />
5.16 Differentialamplifier................................... 266<br />
5.17 Simpleop-amp ...................................... 269<br />
5.18 Audiooscillator ...................................... 274<br />
5.19 Vacuumtubeaudioamplifier .............................. 277<br />
Bibliography ........................................... 288
CONTENTS<br />
v<br />
6 ANALOGINTEGRATEDCIRCUITS 289<br />
6.1 Introduction........................................ 289<br />
6.2 Voltagecomparator.................................... 291<br />
6.3 Precisionvoltagefollower ................................ 294<br />
6.4 Noninvertingamplifier. ................................. 298<br />
6.5 High-impedancevoltmeter ............................... 301<br />
6.6 Integrator ......................................... 305<br />
6.7 555audiooscillator.................................... 311<br />
6.8 555rampgenerator ................................... 314<br />
6.9 PWMpowercontroller . ................................. 317<br />
6.10 ClassBaudioamplifier ................................. 321<br />
7 DIGITALINTEGRATEDCIRCUITS 331<br />
7.1 Introduction........................................ 331<br />
7.2 Basicgatefunction .................................... 333<br />
7.3 NORgateS-Rlatch.................................... 337<br />
7.4 NANDgateS-Renabledlatch ............................. 341<br />
7.5 NANDgateS-Rflip-flop ................................. 343<br />
7.6 LEDsequencer ...................................... 347<br />
7.7 Simplecombinationlock................................. 356<br />
7.8 3-bitbinarycounter ................................... 359<br />
7.9 7-segmentdisplay .................................... 361<br />
8 555TIMERCIRCUITS 365<br />
8.1 The555IC......................................... 365<br />
8.2 555SchmittTrigger ................................... 366<br />
8.3 555HYSTERETICOSCILLATOR ........................... 370<br />
8.4 555MONOSTABLEMULTIVIBRATOR . ...................... 374<br />
8.5 CMOS555LONGDURATIONMINIMUMPARTSREDLEDFLASHER .... 380<br />
8.6 CMOS555LONGDURATIONBLUELEDFLASHER ............... 385<br />
8.7 CMOS555LONGDURATIONFLYBACKLEDFLASHER . ........... 389<br />
8.8 HOWTOMAKEANINDUCTOR ........................... 392<br />
8.9 CMOS555LONGDURATIONREDLEDFLASHER................ 395<br />
A-1ABOUTTHISBOOK 399<br />
A-2CONTRIBUTORLIST 405<br />
A-3DESIGNSCIENCELICENSE 409<br />
INDEX 412
Chapter1<br />
INTRODUCTION<br />
Contents<br />
1.1 Electronicsasscience . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1<br />
1.2 Settingupahomelab . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3<br />
1.2.1 Workarea . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3<br />
1.2.2 Tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3<br />
1.2.3 Supplies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12<br />
1.3 Contributors...................................... 14<br />
1.1 Electronicsasscience<br />
Electronicsisascience,andaveryaccessiblescienceatthat. Withotherareasofscientific<br />
study,expensiveequipmentisgenerallyrequiredtoperformanynon-trivialexperiments.Not<br />
sowithelectronics. Manyadvancedconceptsmaybeexploredusingpartsandequipment<br />
totalingunderafewhundredUSdollars. Thisisgood,becausehands-onexperimentationis<br />
vitaltogainingscientificknowledgeaboutanysubject.<br />
WhenIstartedwritingLessonsInElectricCircuits,myintentwastocreateatextbook<br />
suitableforintroductorycollegeuse.However,beingmostlyself-taughtinelectronicsmyself,<br />
Iknewthevalueofagoodtextbooktohobbyistsandexperimentersnotenrolledinanyformal<br />
electronicscourse.Manypeopleselflesslyvolunteeredtheirtimeandexpertiseinhelpingme<br />
learnelectronicswhenIwasyounger,andmyintentistohonortheirserviceandlovebygiving<br />
backtotheworldwhattheygavetome.<br />
Inorderforsomeonetoteachthemselvesasciencesuchaselectronics,theymustengagein<br />
hands-onexperimentation.Knowledgegleanedfrombooksalonehaslimiteduse,especiallyin<br />
scientificendeavors.Ifmycontributiontosocietyistobecomplete,Imustincludeaguideto<br />
experimentationalongwiththetext(s)ontheory,sothattheindividuallearningontheirown<br />
hasaresourcetoguidetheirexperimentaladventures.<br />
Aformallaboratorycourseforcollegeelectronicsstudyrequiresanenormousamountof<br />
worktoprepare,andusuallymustbebasedaroundspecificpartsandequipmentsothatthe<br />
1
2 CHAPTER1. INTRODUCTION<br />
experimentswillbesufficientdetailed,withresultssufficientlyprecisetoallowforrigorous<br />
comparisonbetweenexperimentalandtheoreticaldata.Aprocessofassessment,articulated<br />
throughaqualifiedinstructor,isalsovitaltoguaranteethatacertainleveloflearninghas<br />
takenplace. Peerreview(comparisonofexperimentalresultswiththeworkofothers)isanotherimportantcomponentofcollege-levellaboratorystudy,andhelpstoimprovethequality<br />
oflearning.SinceIcannotmeetthesecriteriathroughthemediumofabook,itisimpractical<br />
formetopresentacompletelaboratorycoursehere.Intheinterestofkeepingthisexperiment<br />
guidereasonablylow-costforpeopletofollow,andpracticalfordeploymentovertheinternet,I<br />
amforcedtodesigntheexperimentsatalowerlevelthanwhatwouldbeexpectedforacollege<br />
labcourse.<br />
Theexperimentsinthisvolumebeginatalevelappropriateforsomeonewithnoelectronics<br />
knowledge,andprogresstohigherlevels.Theystressqualitativeknowledgeoverquantitative<br />
knowledge,althoughtheycouldserveastemplatesformorerigorouscoursework. Ifthere<br />
isanyportionofLessonsInElectricCircuitsthatwillremain”incomplete,”itisthisone: I<br />
fullyintendtocontinueaddingexperimentsadinfinitumsoastoprovidetheexperimenteror<br />
hobbyistwithawealthofideastoexplorethescienceofelectronics. Thisvolumeofthebook<br />
seriesisalsotheeasiesttocontributeto,forthosewhowouldliketohelpmeinprovidingfree<br />
informationtopeoplelearningelectronics. Itdoesn’ttakeatremendousefforttodescribean<br />
experimentortwo,andIwillgladlyincludeitifyouemailittome,givingyoufullcreditfor<br />
thework.RefertoAppendix2fordetailsoncontributingtothisbook.<br />
Whenperformingtheseexperiments,feelfreetoexplorebytryingdifferentcircuitconstructionandmeasurementtechniques.Ifsomethingisn’tworkingasthetextdescribesitshould,<br />
don’tgiveup! It’sprobablyduetoasimpleprobleminconstruction(loosewire,wrongcomponentvalue)ortestequipmentsetup.Itcanbefrustratingworkingthroughtheseproblems<br />
onyourown,buttheknowledgegainedby”troubleshooting”acircuityourselfisatleastas<br />
importantastheknowledgegainedbyaproperlyfunctioningexperiment. Thisisoneofthe<br />
mostimportantreasonswhyexperimentationissovitaltoyourscientificeducation:thereal<br />
problemsyouwillinvariablyencounterinexperimentationchallengeyoutodeveloppractical<br />
problem-solvingskills.<br />
Inmanyoftheseexperiments,IofferpartnumbersforRadioShackbrandcomponents.This<br />
isnotanendorsementofRadioShack,butsimplyaconvenientreferencetoanelectronicsupply<br />
companywell-knowninNorthAmerica.Oftentimes,componentsofbetterqualityandlower<br />
pricemaybeobtainedthroughmail-ordercompaniesandother,lesser-knownsupplyhouses.I<br />
stronglyrecommendthatexperimentersobtainsomeofthemoreexpensivecomponentssuch<br />
astransformers(seetheACchapter)bysalvagingthemfromdiscardedelectricalappliances,<br />
bothforeconomicandecologicalreasons.<br />
Allexperimentsshowninthisbookaredesignedwithsafetyinmind.Itisnearlyimpossible<br />
toshockorotherwisehurtyourselfbybattery-poweredexperimentsorothercircuitsoflow<br />
voltage.However,hazardsdoexistbuildinganythingwithyourowntwohands.Wherethere<br />
isagreater-than-normallevelofdangerinanexperiment,Itakeeffortstodirectthereader’s<br />
attentiontowardit.However,itisunfortunatelynecessaryinthislitigioussocietytodisclaim<br />
anyandallliabilityfortheoutcomeofanyexperimentpresentedhere. Neithermyselfnor<br />
anycontributorsbearresponsibilityforinjuriesresultingfromtheconstructionoruseofany<br />
oftheseprojects,fromthemis-handlingofelectricitybytheexperimenter,orfromanyother<br />
unsafepracticesleadingtoinjury.Performtheseexperimentsatyourownrisk!
1.2. SETTINGUPAHOMELAB 3<br />
1.2 Settingupahomelab<br />
Inordertobuildthecircuitsdescribedinthisvolume,youwillneedasmallworkarea,as<br />
wellasafewtoolsandcriticalsupplies.Thissectiondescribesthesetupofahomeelectronics<br />
laboratory.<br />
1.2.1 Workarea<br />
Aworkareashouldconsistofalargeworkbench,desk,ortable(preferablywooden)forperformingcircuitassembly,withhouseholdelectricalpower(120voltsAC)readilyaccessibleto<br />
powersolderingequipment,powersupplies,andanytestequipment. Inexpensivedesksintendedforcomputerusefunctionverywellforthispurpose.Avoidametal-surfacedesk,asthe<br />
electricalconductivityofametalsurfacecreatesbothashockhazardandtheverydistinctpossibilityofunintentional”shortcircuits”developingfromcircuitcomponentstouchingthemetal<br />
tabletop. Vinylandplasticbenchsurfacesaretobeavoidedfortheirabilitytogenerateand<br />
storelargestatic-electriccharges,whichmaydamagesensitiveelectroniccomponents. Also,<br />
thesematerialsmelteasilywhenexposedtohotsolderingironsandmoltensolderdroplets.<br />
Ifyoucannotobtainawooden-surfaceworkbench,youmayturnanyformoftableordesk<br />
intoonebylayingapieceofplywoodontop.Ifyouarereasonablyskilledwithwoodworking<br />
tools,youmayconstructyourowndeskusingplywoodand2x4boards.<br />
Theworkareashouldbewell-litandcomfortable. Ihaveasmallradiosetuponmyown<br />
workbenchforlisteningtomusicornewsasIexperiment. Myownworkbenchhasa”power<br />
strip”receptacleandswitchassemblymountedtotheunderside,intowhichIplugall120<br />
voltdevices. Itisconvenienttohaveasingleswitchforshuttingoffallpowerincaseofan<br />
accidentalshort-circuit!<br />
1.2.2 Tools<br />
Afewtoolsarerequiredforbasicelectronicswork.Mostofthesetoolsareinexpensiveandeasy<br />
toobtain.Ifyoudesiretokeepthecostaslowaspossible,youmightwanttosearchforthem<br />
atthriftstoresandpawnshopsbeforebuyingthemnew.Asyoucantellfromthephotographs,<br />
someofmyowntoolsareratheroldbutfunctionwellnonetheless.<br />
Firstandforemostinyourtoolcollectionisamultimeter.Thisisanelectricalinstrument<br />
designedtomeasurevoltage,current,resistance,andoftenothervariablesaswell.Multimetersaremanufacturedinbothdigitalandanalogform.<br />
Adigitalmultimeterispreferredfor<br />
precisionwork,butanalogmetersarealsousefulforgaininganintuitiveunderstandingof<br />
instrumentsensitivityandrange.<br />
MyowndigitalmultimeterisaFlukemodel27,purchasedin1987:<br />
Digitalmultimeter
4 CHAPTER1. INTRODUCTION<br />
======================================<br />
Mostanalogmultimeterssoldtodayarequiteinexpensive,andnotnecessarilyprecision<br />
testinstruments.Irecommendhavingbothdigitalandanalogmetertypesinyourtoolcollection,spendingaslittlemoneyaspossibleontheanalogmultimeterandinvestinginagoodqualitydigitalmultimeter(IhighlyrecommendtheFlukebrand).<br />
AtestinstrumentIhavefoundindispensableinmyhomeworkisasensitivevoltagedetector,orsensitiveaudiodetector,describedinnearlyidenticalexperimentsintwochapters<br />
ofthisbookvolume. Itisnothingmorethanasensitizedsetofaudioheadphones,equipped<br />
withanattenuator(volumecontrol)andlimitingdiodestolimitsoundintensityfromstrong<br />
signals.Itspurposeistoaudiblyindicatethepresenceoflow-intensityvoltagesignals,DCor<br />
AC.Intheabsenceofanoscilloscope,thisisamostvaluabletool,becauseitallowsyoutolistentoanelectronicsignal,andtherebydeterminesomethingofitsnature.Fewtoolsengender<br />
anintuitivecomprehensionoffrequencyandamplitudeasthis! Iciteitsuseinmanyofthe<br />
experimentsshowninthisvolume,soIstronglyencouragethatyoubuildyourown. Second<br />
onlytoamultimeter,itisthemostusefulpieceoftestequipmentinthecollectionofthebudget<br />
electronicsexperimenter.<br />
Sensitivevoltage/audiodetector
1.2. SETTINGUPAHOMELAB 5<br />
Asyoucansee,Ibuiltmydetectorusingscrapparts(householdelectricalswitch/receptacle<br />
boxfortheenclosure,sectionofbrownlampcordforthetestleads).Evensomeoftheinternal<br />
componentsweresalvagedfromscrap(thestep-downtransformerandheadphonejackwere<br />
takenfromanoldradio,purchasedinnon-workingconditionfromathriftstore). Theentirething,includingtheheadphonespurchasedsecond-hand,costnomorethan$15tobuild.<br />
Ofcourse,onecouldtakemuchgreatercareinchoosingconstructionmaterials(metalbox,<br />
shieldedtestprobecable),butitprobablywouldn’timproveitsperformancesignificantly.<br />
Thesinglemostinfluentialcomponentwithregardtodetectorsensitivityistheheadphone<br />
assembly:generallyspeaking,thegreaterthe”dB”ratingoftheheadphones,thebetterthey<br />
willfunctionforthispurpose.Sincetheheadphonesneednotbemodifiedforuseinthedetector<br />
circuit,andtheycanbeunpluggedfromit,youmightjustifythepurchaseofmoreexpensive,<br />
high-qualityheadphonesbyusingthemaspartofahomeentertainment(audio/video)system.<br />
======================================<br />
Alsoessentialisasolderlessbreadboard,sometimescalledaprototypingboard,orprotoboard.<br />
Thisdeviceallowsyoutoquicklyjoinelectroniccomponentstooneanotherwithout<br />
havingtosoldercomponentterminalsandwirestogether.<br />
Solderlessbreadboard
6 CHAPTER1. INTRODUCTION<br />
======================================<br />
Whenworkingwithwire,youneedatoolto”strip”theplasticinsulationofftheendsso<br />
thatbarecoppermetalisexposed. Thistooliscalledawirestripper,anditisaspecialform<br />
ofplierwithseveralknife-edgedholesinthejawareasizedjustrightforcuttingthroughthe<br />
plasticinsulationandnotthecopper,foramultitudeofwiresizes,orgauges.Shownhereare<br />
twodifferentsizesofwirestrippingpliers:<br />
Wirestrippingpliers<br />
======================================<br />
Inordertomakequick,temporaryconnectionsbetweensomeelectroniccomponents,you<br />
needjumperwireswithsmall”alligator-jaw”clipsateachend.Thesemaybepurchasedcomplete,orassembledfromclipsandwires.<br />
Jumperwires(assoldbyRadioShack)
1.2. SETTINGUPAHOMELAB 7<br />
Jumperwires(home-made)<br />
Thehome-madejumperwireswithlarge,uninsulated(baremetal)alligatorclipsareokay<br />
tousesolongascareistakentoavoidanyunintentionalcontactbetweenthebareclipsand<br />
anyotherwiresorcomponents. Foruseincrowdedbreadboardcircuits,jumperwireswith<br />
insulated(rubber-covered)clipslikethejumpershownfromRadioShackaremuchpreferred.<br />
======================================<br />
Needle-nosepliersaredesignedtograspsmallobjects,andareespeciallyusefulforpushing<br />
wiresintostubbornbreadboardholes.<br />
Needle-nosepliers
8 CHAPTER1. INTRODUCTION<br />
======================================<br />
Notoolsetwouldbecompletewithoutscrewdrivers,andIrecommendacomplementary<br />
pair(3/16inchslottedand#2Phillips)asthestartingpointforyourcollection.Youmaylater<br />
finditusefultoinvestinasetofjeweler’sscrewdriversforworkwithverysmallscrewsand<br />
screw-headadjustments.<br />
Screwdrivers<br />
======================================<br />
Forprojectsinvolvingprinted-circuitboardassemblyorrepair,asmallsolderingironanda<br />
spoolof”rosin-core”solderareessentialtools.Irecommenda25wattsolderingiron,nolarger<br />
forprintedcircuitboardwork,andthethinnestsolderyoucanfind. Donotuse”acid-core”<br />
solder!Acid-coresolderisintendedforthesolderingofcoppertubes(plumbing),whereasmall<br />
amountofacidhelpstocleanthecopperofsurfaceimpuritiesandprovideastrongerbond.If<br />
usedforelectricalwork,theresidualacidwillcausewirestocorrode. Also,youshouldavoid<br />
soldercontainingthemetallead,optinginsteadforsilver-alloysolder. Ifyoudonotalready<br />
wearglasses,apairofsafetyglassesishighlyrecommendedwhilesoldering,topreventbitsof
1.2. SETTINGUPAHOMELAB 9<br />
moltensolderfromaccidentlylandinginyoureyeshouldawirereleasefromthejointduring<br />
thesolderingprocessandflingbitsofsoldertowardyou.<br />
Solderingironandsolder(”rosincore”)<br />
======================================<br />
Projectsrequiringthejoiningoflargewiresbysolderingwillnecessitateamorepowerful<br />
heatsourcethana25wattsolderingiron.Asolderinggunisapracticaloption.<br />
Solderinggun<br />
======================================<br />
Knives,likescrewdrivers,areessentialtoolsforallkindsofwork. Forsafety’ssake,I<br />
recommenda”utility”knifewithretractingblade.Theseknivesarealsoadvantageoustohave<br />
fortheirabilitytoacceptreplacementblades.<br />
Utilityknife
10 CHAPTER1. INTRODUCTION<br />
======================================<br />
Pliersotherthantheneedle-nosetypeareusefulfortheassemblyanddisassemblyofelectronicdevicechassis.<br />
TwotypesIrecommendareslip-jointandadjustable-joint(”Channellock”).<br />
Slip-jointpliers<br />
Adjustable-jointpliers
1.2. SETTINGUPAHOMELAB 11<br />
======================================<br />
Drillingmayberequiredfortheassemblyoflargeprojects. Althoughpowerdrillswork<br />
well,Ihavefoundthatasimplehand-crankdrilldoesaremarkablejobdrillingthroughplastic,<br />
wood,andmostmetals.Itiscertainlysaferandquieterthanapowerdrill,andcostsquitea<br />
bitless.<br />
Handdrill<br />
Asthewearonmydrillindicates,itisanoften-usedtoolaroundmyhome!<br />
======================================<br />
Someexperimentswillrequireasourceofaudio-frequencyvoltagesignals.Normally,this<br />
typeofsignalisgeneratedinanelectronicslaboratorybyadevicecalledasignalgenerator<br />
orfunctiongenerator. Whilebuildingsuchadeviceisnotimpossible(nordifficult!),itoften<br />
requirestheuseofanoscilloscopetofine-tune,andoscilloscopesareusuallyoutsidethebudgetaryrangeofthehomeexperimenter.Arelativelyinexpensivealternativetoacommercial<br />
signalgeneratorisanelectronickeyboardofthemusicaltype.Youneednotbeamusicianto<br />
operateoneforthepurposesofgeneratinganaudiosignal(justpressanykeyontheboard!),
12 CHAPTER1. INTRODUCTION<br />
andtheymaybeobtainedquitereadilyatsecond-handstoresforsubstantiallylessthannew<br />
price.Theelectronicsignalgeneratedbythekeyboardisconductedtoyourcircuitviaaheadphonecablepluggedintothe”headphones”jack.Moredetailsregardingtheuseofa”Musical<br />
KeyboardasaSignalGenerator”maybefoundintheexperimentofthatnameinchapter4<br />
(AC).<br />
1.2.3 Supplies<br />
Wireusedinsolderlessbreadboardsmustbe22-gauge,solidcopper. Spoolsofthiswireare<br />
availablefromelectronicsupplystoresandsomehardwarestores,indifferentinsulationcolors.<br />
Insulationcolorhasnobearingonthewire’sperformance,butdifferentcolorsaresometimes<br />
usefulfor”color-coding”wirefunctionsinacomplexcircuit.<br />
Spoolof22-gauge,solidcopperwire<br />
Notehowthelast1/4inchorsoofthecopperwireprotrudingfromthespoolhasbeen<br />
”stripped”ofitsplasticinsulation.<br />
======================================<br />
Analternativetosolderlessbreadboardcircuitconstructioniswire-wrap,where30-gauge<br />
(verythin!)solidcopperwireistightlywrappedaroundtheterminalsofcomponentsinserted<br />
throughtheholesofafiberglassboard.Nosolderingisrequired,andtheconnectionsmadeare<br />
atleastasdurableassolderedconnections,perhapsmore.Wire-wrappingrequiresaspoolof<br />
thisverythinwire,andaspecialwrappingtool,thesimplestkindresemblingasmallscrewdriver.<br />
Wire-wrapwireandwrappingtool
1.2. SETTINGUPAHOMELAB 13<br />
======================================<br />
Largewire(14gaugeandbigger)maybeneededforbuildingcircuitsthatcarrysignificant<br />
levelsofcurrent.Thoughelectricalwireofpracticallyanygaugemaybepurchasedonspools,<br />
Ihavefoundaveryinexpensivesourceofstranded(flexible),copperwire,availableatany<br />
hardwarestore:cheapextensioncords.Typicallycomprisedofthreewirescoloredwhite,black,<br />
andgreen,extensioncordsareoftensoldatpriceslessthantheretailcostoftheconstituent<br />
wirealone. Thisisespeciallytrueifthecordispurchasedonsale! Also,anextensioncord<br />
providesyouwithapairof120voltconnectors:male(plug)andfemale(receptacle)thatmay<br />
beusedforprojectspoweredby120volts.<br />
Extensioncord,inpackage<br />
Toextractthewires,carefullycuttheouterlayerofplasticinsulationawayusingautility<br />
knife.Withpractice,youmayfindyoucanpeelawaytheouterinsulationbymakingashort<br />
cutinitatoneendofthecable,thengraspingthewireswithonehandandtheinsulation<br />
withtheotherandpullingthemapart.Thisis,ofcourse,muchpreferabletoslicingtheentire<br />
lengthoftheinsulationwithaknife,bothforsafety’ssakeandforthesakeofavoidingcutsin
14 CHAPTER1. INTRODUCTION<br />
theindividualwires’insulation.<br />
======================================<br />
Duringthecourseofbuildingmanycircuits,youwillaccumulatealargenumberofsmall<br />
components. Onetechniqueforkeepingthesecomponentsorganizedistokeepthemina<br />
plastic”organizer”boxlikethetypeusedforfishingtackle.<br />
Componentbox<br />
Inthisviewofoneofmycomponentboxes,youcanseeplentyof1/8wattresistors,transistors,diodes,andevenafew8-pinintegratedcircuits(”chips”).<br />
Labelsforeachcompartment<br />
weremadewithapermanentinkmarker.<br />
1.3 Contributors<br />
Contributorstothischapterarelistedinchronologicalorderoftheircontributions,frommost<br />
recenttofirst.SeeAppendix2(ContributorList)fordatesandcontactinformation.<br />
MichaelWarner(April9,2002): Suggestionsforasectiondescribinghomelaboratory<br />
setup.
Chapter2<br />
BASICCONCEPTSANDTEST<br />
EQUIPMENT<br />
Contents<br />
2.1 Voltmeterusage. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15<br />
2.2 Ohmmeterusage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21<br />
2.3 Averysimplecircuit. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28<br />
2.4 Ammeterusage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35<br />
2.5 Ohm’sLaw . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42<br />
2.6 Nonlinearresistance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45<br />
2.7 Powerdissipation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48<br />
2.8 Circuitwithaswitch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53<br />
2.9 Electromagnetism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55<br />
2.10 Electromagneticinduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57<br />
2.1 Voltmeterusage<br />
PARTSANDMATERIALS<br />
• Multimeter,digitaloranalog<br />
• Assortedbatteries<br />
• Onelight-emittingdiode(RadioShackcatalog#276-026orequivalent)<br />
• Small”hobby”motor,permanent-magnettype(RadioShackcatalog#273-223orequivalent)<br />
15
16 CHAPTER2. BASICCONCEPTSANDTESTEQUIPMENT<br />
• Twojumperwireswith”alligatorclip”ends(RadioShackcatalog#278-1156,278-1157,<br />
orequivalent)<br />
Amultimeterisanelectricalinstrumentcapableofmeasuringvoltage,current,andresistance.<br />
Digitalmultimetershavenumericaldisplays,likedigitalclocks,forindicatingthe<br />
quantityofvoltage,current,orresistance. Analogmultimetersindicatethesequantitiesby<br />
meansofamovingpointeroveraprintedscale.<br />
Analogmultimeterstendtobelessexpensivethandigitalmultimeters,andmorebeneficial<br />
aslearningtoolsforthefirst-timestudentofelectricity.Istronglyrecommendpurchasingan<br />
analogmultimeterbeforepurchasingadigitalmultimeter,buttoeventuallyhavebothinyour<br />
toolkitfortheseexperiments.<br />
CROSS-REFERENCES<br />
LessonsInElectricCircuits,Volume1,chapter1:”BasicConceptsofElectricity”<br />
LessonsInElectricCircuits,Volume1,chapter8:”DCMeteringCircuits”<br />
LEARNINGOBJECTIVES<br />
• Howtomeasurevoltage<br />
• Characteristicsofvoltage:existingbetweentwopoints<br />
• Selectionofpropermeterrange<br />
ILLUSTRATION
2.1. VOLTMETERUSAGE 17<br />
Digital<br />
multimeter<br />
V<br />
V<br />
OFF<br />
A<br />
A<br />
Analog<br />
multimeter<br />
A<br />
COM<br />
- +<br />
Test leads<br />
Test leads<br />
Test probes<br />
Test probes<br />
+ -<br />
6-volt "lantern"<br />
battery<br />
Light-emitting<br />
diode ("LED")<br />
1.5-volt "D-cell"<br />
battery<br />
Permanentmagnet<br />
motor<br />
INSTRUCTIONS
18 CHAPTER2. BASICCONCEPTSANDTESTEQUIPMENT<br />
Inalltheexperimentsinthisbook,youwillbeusingsomesortoftestequipmenttomeasure<br />
aspectsofelectricityyoucannotdirectlysee,feel,hear,taste,orsmell.Electricity–atleastin<br />
small,safequantities–isinsensiblebyourhumanbodies.Yourmostfundamental”eyes”inthe<br />
worldofelectricityandelectronicswillbeadevicecalledamultimeter.Multimetersindicate<br />
thepresenceof,andmeasurethequantityof,electricalpropertiessuchasvoltage,current,and<br />
resistance.Inthisexperiment,youwillfamiliarizeyourselfwiththemeasurementofvoltage.<br />
Voltageisthemeasureofelectrical”push”readytomotivateelectronstomovethrougha<br />
conductor.Inscientificterms,itisthespecificenergyperunitcharge,mathematicallydefined<br />
asjoulespercoulomb.Itisanalogoustopressureinafluidsystem:theforcethatmovesfluid<br />
throughapipe,andismeasuredintheunitoftheVolt(V).<br />
Yourmultimetershouldcomewithsomebasicinstructions.Readthemwell!Ifyourmultimeterisdigital,itwillrequireasmallbatterytooperate.<br />
Ifitisanalog,itdoesnotneeda<br />
batterytomeasurevoltage.<br />
Somedigitalmultimetersareautoranging. Anautorangingmeterhasonlyafewselectorswitch(dial)positions.<br />
Manual-rangingmetershaveseveraldifferentselectorpositions<br />
foreachbasicquantity: severalforvoltage,severalforcurrent,andseveralforresistance.<br />
Autorangingisusuallyfoundononlythemoreexpensivedigitalmeters,andistomanual<br />
rangingasanautomatictransmissionistoamanualtransmissioninacar. Anautoranging<br />
meter”shiftsgears”automaticallytofindthebestmeasurementrangetodisplaytheparticular<br />
quantitybeingmeasured.<br />
Setyourmultimeter’sselectorswitchtothehighest-value”DCvolt”positionavailable.AutorangingmultimetersmayonlyhaveasinglepositionforDCvoltage,inwhichcaseyouneed<br />
tosettheswitchtothatoneposition. Touchtheredtestprobetothepositive(+)sideofa<br />
battery,andtheblacktestprobetothenegative(-)sideofthesamebattery.Themetershould<br />
nowprovideyouwithsomesortofindication.Reversethetestprobeconnectionstothebattery<br />
ifthemeter’sindicationisnegative(onananalogmeter,anegativevalueisindicatedbythe<br />
pointerdeflectingleftinsteadofright).<br />
Ifyourmeterisamanual-rangetype,andtheselectorswitchhasbeensettoahigh-range<br />
position,theindicationwillbesmall. MovetheselectorswitchtothenextlowerDCvoltage<br />
rangesettingandreconnecttothebattery.Theindicationshouldbestrongernow,asindicated<br />
byagreaterdeflectionoftheanalogmeterpointer(needle),ormoreactivedigitsonthedigital<br />
meterdisplay. Forthebestresults,movetheselectorswitchtothelowest-rangesettingthat<br />
doesnot”over-range”themeter. Anover-rangedanalogmeterissaidtobe”pegged,”asthe<br />
needlewillbeforcedallthewaytotheright-handsideofthescale,pastthefull-rangescale<br />
value.Anover-rangeddigitalmetersometimesdisplaystheletters”OL”,oraseriesofdashed<br />
lines.Thisindicationismanufacturer-specific.<br />
Whathappensifyouonlytouchonemetertestprobetooneendofabattery?Howdoesthe<br />
meterhavetoconnecttothebatteryinordertoprovideanindication?Whatdoesthistellus<br />
aboutvoltmeteruseandthenatureofvoltage? Istheresuchathingasvoltage”at”asingle<br />
point?<br />
Besuretomeasuremorethanonesizeofbattery,andlearnhowtoselectthebestvoltage<br />
rangeonthemultimetertogiveyoumaximumindicationwithoutover-ranging.<br />
NowswitchyourmultimetertothelowestDCvoltagerangeavailable,andtouchthemeter’s<br />
testprobestotheterminals(wireleads)ofthelight-emittingdiode(LED).AnLEDisdesigned<br />
toproducelightwhenpoweredbyasmallamountofelectricity,butLEDsalsohappento<br />
generateDCvoltagewhenexposedtolight,somewhatlikeasolarcell.PointtheLEDtoward
2.1. VOLTMETERUSAGE 19<br />
abrightsourceoflightwithyourmultimeterconnectedtoit,andnotethemeter’sindication:<br />
Light source<br />
LED<br />
- +<br />
Batteriesdevelopelectricalvoltagethroughchemicalreactions. Whenabattery”dies,”it<br />
hasexhausteditsoriginalstoreofchemical”fuel.”TheLED,however,doesnotrelyonan<br />
internal”fuel”togeneratevoltage;rather,itconvertsopticalenergyintoelectricalenergy.So<br />
longasthereislighttoilluminatetheLED,itwillproducevoltage.<br />
Anothersourceofvoltagethroughenergyconversionagenerator. Thesmallelectricmotorspecifiedinthe”PartsandMaterials”listfunctionsasanelectricalgeneratorifitsshaft<br />
isturnedbyamechanicalforce. Connectyourvoltmeter(yourmultimeter,settothe”volt”<br />
function)tothemotor’sterminalsjustasyouconnectedittotheLED’sterminals,andspin<br />
theshaftwithyourfingers. Themetershouldindicatevoltagebymeansofneedledeflection<br />
(analog)ornumericalreadout(digital).<br />
Ifyoufinditdifficulttomaintainbothmetertestprobesinconnectionwiththemotor’s<br />
terminalswhilesimultaneouslyspinningtheshaftwithyourfingers,youmayusealligator<br />
clip”jumper”wireslikethis:<br />
Jumper<br />
wire<br />
Alligator<br />
clip<br />
- +<br />
Motor
20 CHAPTER2. BASICCONCEPTSANDTESTEQUIPMENT<br />
Determinetherelationshipbetweenvoltageandgeneratorshaftspeed? Reversethegenerator’sdirectionofrotationandnotethechangeinmeterindication.Whenyoureverseshaft<br />
rotation,youchangethepolarityofthevoltagecreatedbythegenerator.Thevoltmeterindicatespolaritybydirectionofneedledirection(analog)orsignofnumericalindication(digital).<br />
Whentheredtestleadispositive(+)andtheblacktestleadnegative(-),themeterwillregister<br />
voltageinthenormaldirection. Iftheappliedvoltageisofthereversepolarity(negativeon<br />
redandpositiveonblack),themeterwillindicate”backwards.”
2.2. OHMMETERUSAGE 21<br />
2.2 Ohmmeterusage<br />
PARTSANDMATERIALS<br />
• Multimeter,digitaloranalog<br />
• Assortedresistors(RadioShackcatalog#271-312isa500-pieceassortment)<br />
• Rectifyingdiode(1N4001orequivalent;RadioShackcatalog#276-1101)<br />
• CadmiumSulphidephotocell(RadioShackcatalog#276-1657)<br />
• Breadboard(RadioShackcatalog#276-174orequivalent)<br />
• Jumperwires<br />
• Paper<br />
• Pencil<br />
• Glassofwater<br />
• Tablesalt<br />
Thisexperimentdescribeshowtomeasuretheelectricalresistanceofseveralobjects.You<br />
neednotpossessallitemslistedaboveinordertoeffectivelylearnaboutresistance. Conversely,youneednotlimityourexperimentstotheseitems.However,besuretonevermeasuretheresistanceofanyelectrically”live”objectorcircuit.Inotherwords,donotattemptto<br />
measuretheresistanceofabatteryoranyothersourceofsubstantialvoltageusingamultimetersettotheresistance(”ohms”)function.Failingtoheedthiswarningwilllikelyresultin<br />
meterdamageandevenpersonalinjury.<br />
CROSS-REFERENCES<br />
LessonsInElectricCircuits,Volume1,chapter1:”BasicConceptsofElectricity”<br />
LessonsInElectricCircuits,Volume1,chapter8:”DCMeteringCircuits”<br />
LEARNINGOBJECTIVES<br />
• Determinationandcomprehensionof”electricalcontinuity”<br />
• Determinationandcomprehensionof”electricallycommonpoints”<br />
• Howtomeasureresistance<br />
• Characteristicsofresistance:existingbetweentwopoints<br />
• Selectionofpropermeterrange<br />
• Relativeconductivityofvariouscomponentsandmaterials
22 CHAPTER2. BASICCONCEPTSANDTESTEQUIPMENT<br />
ILLUSTRATION<br />
Incandescent<br />
lamp<br />
Photocell<br />
Diode<br />
Resistor<br />
Resistor<br />
INSTRUCTIONS<br />
Resistanceisthemeasureofelectrical”friction”aselectronsmovethroughaconductor.It<br />
ismeasuredintheunitofthe”Ohm,”thatunitsymbolizedbythecapitalGreekletteromega<br />
(Ω).<br />
Setyourmultimetertothehighestresistancerangeavailable. Theresistancefunctionis<br />
usuallydenotedbytheunitsymbolforresistance:theGreekletteromega(Ω),orsometimes<br />
bytheword”ohms.”Touchthetwotestprobesofyourmetertogether. Whenyoudo,the<br />
metershouldregister0ohmsofresistance. Ifyouareusingananalogmeter,youwillnotice<br />
theneedledeflectfull-scalewhentheprobesaretouchedtogether,andreturntoitsresting<br />
positionwhentheprobesarepulledapart. Theresistancescaleonananalogmultimeteris<br />
reverse-printedfromtheotherscales:zeroresistanceinindicatedatthefarright-handsideof<br />
thescale,andinfiniteresistanceisindicatedatthefarleft-handside.Thereshouldalsobea<br />
smalladjustmentknobor”wheel”ontheanalogmultimetertocalibrateitfor”zero”ohmsof<br />
resistance.Touchthetestprobestogetherandmovethisadjustmentuntiltheneedleexactly<br />
pointstozeroattheright-handendofthescale.<br />
Althoughyourmultimeteriscapableofprovidingquantitativevaluesofmeasuredresistance,itisalsousefulforqualitativetestsofcontinuity:whetherornotthereisacontinuous<br />
electricalconnectionfromonepointtoanother. Youcan,forinstance,testthecontinuityof<br />
apieceofwirebyconnectingthemeterprobestooppositeendsofthewireandcheckingto<br />
seethetheneedlemovesfull-scale.Whatwouldwesayaboutapieceofwireiftheohmmeter<br />
needledidn’tmoveatallwhentheprobeswereconnectedtooppositeends?<br />
Digitalmultimeterssettothe”resistance”modeindicatenon-continuitybydisplayingsome<br />
non-numericalindicationonthedisplay. Somemodelssay”OL”(Open-Loop),whileothers<br />
displaydashedlines.<br />
Useyourmetertodeterminecontinuitybetweentheholesonabreadboard:adeviceused<br />
fortemporaryconstructionofcircuits,wherecomponentterminalsareinsertedintoholesona<br />
plasticgrid,metalspringclipsunderneatheachholeconnectingcertainholestoothers. Use<br />
smallpiecesof22-gaugesolidcopperwire,insertedintotheholesofthebreadboard,toconnect<br />
themetertothesespringclipssothatyoucantestforcontinuity:
2.2. OHMMETERUSAGE 23<br />
Continuity!<br />
Analog<br />
meter<br />
- +<br />
22-gauge wire<br />
22-gauge wire<br />
Breadboard
24 CHAPTER2. BASICCONCEPTSANDTESTEQUIPMENT<br />
No continuity<br />
Analog<br />
meter<br />
- +<br />
22-gauge wire<br />
22-gauge wire<br />
Breadboard<br />
Animportantconceptinelectricity,closelyrelatedtoelectricalcontinuity,isthatofpoints<br />
beingelectricallycommontoeachother.<strong>Electrical</strong>lycommonpointsarepointsofcontactona<br />
deviceorinacircuitthathavenegligible(extremelysmall)resistancebetweenthem.Wecould<br />
say,then,thatpointswithinabreadboardcolumn(verticalintheillustrations)areelectrically<br />
commontoeachother,becausethereiselectricalcontinuitybetweenthem.Conversely,breadboardpointswithinarow(horizontalintheillustrations)arenotelectricallycommon,because<br />
thereisnocontinuitybetweenthem.Continuitydescribeswhatisbetweenpointsofcontact,<br />
whilecommonalitydescribeshowthepointsthemselvesrelatetoeachother.<br />
Likecontinuity,commonalityisaqualitativeassessment,basedonarelativecomparisonof<br />
resistancebetweenotherpointsinacircuit.Itisanimportantconcepttograsp,becausethere<br />
arecertainfactsregardingvoltageinrelationtoelectricallycommonpointsthatarevaluable<br />
incircuitanalysisandtroubleshooting,thefirstonebeingthattherewillneverbesubstantial<br />
voltagedroppedbetweenpointsthatareelectricallycommontoeachother.<br />
Selecta10,000ohm(10kΩ)resistorfromyourpartsassortment.Thisresistancevalueis<br />
indicatedbyaseriesofcolorbands:Brown,Black,Orange,andthenanothercolorrepresenting<br />
theprecisionoftheresistor,Gold(+/-5%)orSilver(+/-10%).Someresistorshavenocolorfor<br />
precision,whichmarksthemas+/-20%. Otherresistorsusefivecolorbandstodenotetheir<br />
valueandprecision,inwhichcasethecolorsfora10kΩresistorwillbeBrown,Black,Black,
2.2. OHMMETERUSAGE 25<br />
Red,andafifthcolorforprecision.<br />
Connectthemeter’stestprobesacrosstheresistorassuch,andnoteitsindicationonthe<br />
resistancescale:<br />
Analog<br />
meter<br />
Resistor<br />
- +<br />
Iftheneedlepointsveryclosetozero,youneedtoselectalowerresistancerangeonthe<br />
meter,justasyouneededtoselectanappropriatevoltagerangewhenreadingthevoltageofa<br />
battery.<br />
Ifyouareusingadigitalmultimeter,youshouldseeanumericalfigurecloseto10shown<br />
onthedisplay,withasmall”k”symbolontheright-handsidedenotingthemetricprefixfor<br />
”kilo”(thousand). Somedigitalmetersaremanually-ranged,andrequireappropriaterange<br />
selectionjustastheanalogmeter.Ifyoursislikethis,experimentwithdifferentrangeswitch<br />
positionsandseewhichonegivesyouthebestindication.<br />
Tryreversingthetestprobeconnectionsontheresistor.Doesthischangethemeter’sindicationatall?Whatdoesthistellusabouttheresistanceofaresistor?Whathappenswhenyou<br />
onlytouchoneprobetotheresistor?Whatdoesthistellusaboutthenatureofresistance,and<br />
howitismeasured? Howdoesthiscomparewithvoltagemeasurement,andwhathappened<br />
whenwetriedtomeasurebatteryvoltagebytouchingonlyoneprobetothebattery?<br />
Whenyoutouchthemeterprobestotheresistorterminals,trynottotouchbothprobe<br />
tipstoyourfingers. Ifyoudo,youwillbemeasuringtheparallelcombinationoftheresistor<br />
andyourownbody,whichwilltendtomakethemeterindicationlowerthanitshouldbe!<br />
Whenmeasuringa10kΩresistor,thiserrorwillbeminimal,butitmaybemoreseverewhen<br />
measuringothervaluesofresistor.<br />
Youmaysafelymeasuretheresistanceofyourownbodybyholdingoneprobetipwiththe<br />
fingersofonehand,andtheotherprobetipwiththefingersoftheotherhand. Note: be<br />
verycarefulwiththeprobes,astheyareoftensharpenedtoaneedle-point. Holdtheprobe<br />
tipsalongtheirlength,notattheverypoints!Youmayneedtoadjustthemeterrangeagain<br />
aftermeasuringthe10kΩresistor,asyourbodyresistancetendstobegreaterthan10,000
26 CHAPTER2. BASICCONCEPTSANDTESTEQUIPMENT<br />
ohmshand-to-hand.Trywettingyourfingerswithwaterandre-measuringresistancewiththe<br />
meter.Whatimpactdoesthishaveontheindication?Trywettingyourfingerswithsaltwater<br />
preparedusingtheglassofwaterandtablesalt,andre-measuringresistance. Whatimpact<br />
doesthishaveonyourbody’sresistanceasmeasuredbythemeter?<br />
Resistanceisthemeasureoffrictiontoelectronflowthroughanobject.Thelessresistance<br />
thereisbetweentwopoints,theharderitisforelectronstomove(flow)betweenthosetwo<br />
points.Giventhatelectricshockiscausedbyalargeflowofelectronsthroughaperson’sbody,<br />
andincreasedbodyresistanceactsasasafeguardbymakingitmoredifficultforelectronsto<br />
flowthroughus,whatcanweascertainaboutelectricalsafetyfromtheresistancereadings<br />
obtainedwithwetfingers?Doeswaterincreaseordecreaseshockhazardtopeople?<br />
Measuretheresistanceofarectifyingdiodewithananalogmeter. Tryreversingthetest<br />
probeconnectionstothediodeandre-measureresistance.Whatstrikesyouasbeingremarkableaboutthediode,especiallyincontrasttotheresistor?<br />
Takeapieceofpaperanddrawaveryheavyblackmarkonitwithapencil(notapen!).<br />
Measureresistanceontheblackstripwithyourmeter,placingtheprobetipsateachendof<br />
themarklikethis:<br />
- +<br />
Paper<br />
Mark made with pencil<br />
Movetheprobetipsclosertogetherontheblackmarkandnotethechangeinresistance<br />
value.Doesitincreaseordecreasewithdecreasedprobespacing?Iftheresultsareinconsistent,youneedtoredrawthemarkwithmoreandheavierpencilstrokes,sothatitisconsistent
2.2. OHMMETERUSAGE 27<br />
initsdensity.Whatdoesthisteachyouaboutresistanceversuslengthofaconductivematerial?<br />
Connectyourmetertotheterminalsofacadmium-sulphide(CdS)photocellandmeasure<br />
thechangeinresistancecreatedbydifferencesinlightexposure. Justaswiththelightemittingdiode(LED)ofthevoltmeterexperiment,youmaywanttousealligator-clipjumper<br />
wirestomakeconnectionwiththecomponent,leavingyourhandsfreetoholdthephotocellto<br />
alightsourceand/orchangemeterranges:<br />
Light source<br />
Photocell<br />
- +<br />
Experimentwithmeasuringtheresistanceofseveraldifferenttypesofmaterials,justbe<br />
surenottotrymeasureanythingthatproducessubstantialvoltage,likeabattery.Suggestions<br />
formaterialstomeasureare:fabric,plastic,wood,metal,cleanwater,dirtywater,saltwater,<br />
glass,diamond(onadiamondringorotherpieceofjewelry),paper,rubber,andoil.
28 CHAPTER2. BASICCONCEPTSANDTESTEQUIPMENT<br />
2.3 Averysimplecircuit<br />
PARTSANDMATERIALS<br />
• 6-voltbattery<br />
• 6-voltincandescentlamp<br />
• Jumperwires<br />
• Breadboard<br />
• Terminalstrip<br />
Fromthisexperimenton,amultimeterisassumedtobenecessaryandwillnotbeincluded<br />
intherequiredlistofpartsandmaterials.Inallsubsequentillustrations,adigitalmultimeter<br />
willbeshowninsteadofananalogmeterunlessthereissomeparticularreasontousean<br />
analogmeter. Youareencouragedtousebothtypesofmeterstogainfamiliaritywiththe<br />
operationofeachintheseexperiments.<br />
CROSS-REFERENCES<br />
LessonsInElectricCircuits,Volume1,chapter1:”BasicConceptsofElectricity”<br />
LEARNINGOBJECTIVES<br />
• Essentialconfigurationneededtomakeacircuit<br />
• Normalvoltagedropsinanoperatingcircuit<br />
• Importanceofcontinuitytoacircuit<br />
• Workingdefinitionsof”open”and”short”circuits<br />
• Breadboardusage<br />
• Terminalstripusage<br />
SCHEMATICDIAGRAM<br />
Battery<br />
Lamp<br />
ILLUSTRATION
2.3. AVERYSIMPLECIRCUIT 29<br />
Battery<br />
+ -<br />
Lamp<br />
INSTRUCTIONS<br />
Thisisthesimplestcompletecircuitinthiscollectionofexperiments: abatteryandan<br />
incandescentlamp.Connectthelamptothebatteryasshownintheillustration,andthelamp<br />
shouldlight,assumingthebatteryandlamparebothingoodconditionandtheyarematched<br />
tooneanotherintermsofvoltage.<br />
Ifthereisa”break”(discontinuity)anywhereinthecircuit,thelampwillfailtolight.Itdoes<br />
notmatterwheresuchabreakoccurs!Manystudentsassumethatbecauseelectronsleavethe<br />
negative(-)sideofthebatteryandcontinuethroughthecircuittothepositive(+)side,thatthe<br />
wireconnectingthenegativeterminalofthebatterytothelampismoreimportanttocircuit<br />
operationthantheotherwireprovidingareturnpathforelectronsbacktothebattery.Thisis<br />
nottrue!<br />
Battery<br />
+ - No light!<br />
Lamp<br />
break in circuit<br />
Battery<br />
+ - break in circuit<br />
No light!<br />
Lamp
30 CHAPTER2. BASICCONCEPTSANDTESTEQUIPMENT<br />
break in circuit<br />
Battery<br />
+ - No light!<br />
Lamp<br />
break in circuit<br />
Battery<br />
+ - No light!<br />
Lamp<br />
Usingyourmultimetersettotheappropriate”DCvolt”range,measurevoltageacrossthe<br />
battery,acrossthelamp,andacrosseachjumperwire. Familiarizeyourselfwiththenormal<br />
voltagesinafunctioningcircuit.<br />
Now,”break”thecircuitatonepointandre-measurevoltagebetweenthesamesetsof<br />
points,additionallymeasuringvoltageacrossthebreaklikethis:
2.3. AVERYSIMPLECIRCUIT 31<br />
V<br />
A<br />
V<br />
OFF<br />
A<br />
A<br />
COM<br />
Battery<br />
+ - No light!<br />
Lamp<br />
Whatvoltagesmeasurethesameasbefore?Whatvoltagesaredifferentsinceintroducing<br />
thebreak?Howmuchvoltageismanifest,ordroppedacrossthebreak?Whatisthepolarity<br />
ofthevoltagedropacrossthebreak,asindicatedbythemeter?<br />
Re-connectthejumperwiretothelamp,andbreakthecircuitinanotherplace. Measure<br />
allvoltage”drops”again,familiarizingyourselfwiththevoltagesofan”open”circuit.<br />
Constructthesamecircuitonabreadboard,takingcaretoplacethelampandwiresinto<br />
thebreadboardinsuchawaythatcontinuitywillbemaintained.Theexampleshownhereis<br />
onlythat:anexample,nottheonlywaytobuildacircuitonabreadboard:
32 CHAPTER2. BASICCONCEPTSANDTESTEQUIPMENT<br />
+ - Breadboard<br />
Experimentwithdifferentconfigurationsonthebreadboard,pluggingthelampintodifferentholes.Ifyouencounterasituationwherethelamprefusestolightupandtheconnecting<br />
wiresaregettingwarm,youprobablyhaveasituationknownasashortcircuit,wherealowerresistancepaththanthelampbypassescurrentaroundthelamp,preventingenoughvoltage<br />
frombeingdroppedacrossthelamptolightitup.Hereisanexampleofashortcircuitmade<br />
onabreadboard:
2.3. AVERYSIMPLECIRCUIT 33<br />
+ - Breadboard<br />
No light!<br />
"shorting"<br />
wire<br />
Hereisanexampleofanaccidentalshortcircuitofthetypetypicallymadebystudents<br />
unfamiliarwithbreadboardusage:<br />
+ - Breadboard<br />
No light!
34 CHAPTER2. BASICCONCEPTSANDTESTEQUIPMENT<br />
Herethereisno”shorting”wirepresentonthebreadboard,yetthereisashortcircuit,and<br />
thelamprefusestolight. Basedonyourunderstandingofbreadboardholeconnections,can<br />
youdeterminewherethe”short”isinthiscircuit?<br />
Shortcircuitsaregenerallytobeavoided,astheyresultinveryhighratesofelectron<br />
flow,causingwirestoheatupandbatterypowersourcestodeplete. Ifthepowersourceis<br />
substantialenough,ashortcircuitmaycauseheatofexplosiveproportionstomanifest,causing<br />
equipmentdamageandhazardtonearbypersonnel. Thisiswhathappenswhenatreelimb<br />
”shorts”acrosswiresonapowerline: thelimb–beingcomposedofwetwood–actsasa<br />
low-resistancepathtoelectriccurrent,resultinginheatandsparks.<br />
Youmayalsobuildthebattery/lampcircuitonaterminalstrip: alengthofinsulating<br />
materialwithmetalbarsandscrewstoattachwiresandcomponentterminalsto.Hereisan<br />
exampleofhowthiscircuitmightbeconstructedonaterminalstrip:<br />
+ -<br />
Terminal<br />
strip
2.4. AMMETERUSAGE 35<br />
2.4 Ammeterusage<br />
PARTSANDMATERIALS<br />
• 6-voltbattery<br />
• 6-voltincandescentlamp<br />
Basiccircuitconstructioncomponentssuchasbreadboard,terminalstrip,andjumperwires<br />
arealsoassumedtobeavailablefromnowon,leavingonlycomponentsandmaterialsunique<br />
totheprojectlistedunder”PartsandMaterials.”<br />
CROSS-REFERENCES<br />
LessonsInElectricCircuits,Volume1,chapter1:”BasicConceptsofElectricity”<br />
LessonsInElectricCircuits,Volume1,chapter8:”DCMeteringCircuits”<br />
LEARNINGOBJECTIVES<br />
• Howtomeasurecurrentwithamultimeter<br />
• Howtocheckamultimeter’sinternalfuse<br />
• Selectionofpropermeterrange<br />
SCHEMATICDIAGRAM<br />
Ammeter<br />
A<br />
Battery<br />
Lamp<br />
ILLUSTRATION
36 CHAPTER2. BASICCONCEPTSANDTESTEQUIPMENT<br />
V<br />
A<br />
V<br />
OFF<br />
A<br />
Battery<br />
A COM<br />
+ -<br />
Lamp<br />
INSTRUCTIONS<br />
Currentisthemeasureoftherateofelectron”flow”inacircuit.Itismeasuredintheunit<br />
oftheAmpere,simplycalled”Amp,”(A).<br />
Themostcommonwaytomeasurecurrentinacircuitistobreakthecircuitopenandinsert<br />
an”ammeter”inseries(in-line)withthecircuitsothatallelectronsflowingthroughthecircuit<br />
alsohavetogothroughthemeter. Becausemeasuringcurrentinthismannerrequiresthe<br />
meterbemadepartofthecircuit,itisamoredifficulttypeofmeasurementtomakethan<br />
eithervoltageorresistance.<br />
Somedigitalmeters,liketheunitshownintheillustration,haveaseparatejacktoinsert<br />
theredtestleadplugwhenmeasuringcurrent. Othermeters,likemostinexpensiveanalogmeters,usethesamejacksformeasuringvoltage,resistance,andcurrent.<br />
Consultyour<br />
owner’smanualontheparticularmodelofmeteryouownfordetailsonmeasuringcurrent.<br />
Whenanammeterisplacedinserieswithacircuit,itideallydropsnovoltageascurrent<br />
goesthroughit.Inotherwords,itactsverymuchlikeapieceofwire,withverylittleresistance<br />
fromonetestprobetotheother.Consequently,anammeterwillactasashortcircuitifplaced<br />
inparallel(acrosstheterminalsof)asubstantialsourceofvoltage.Ifthisisdone,asurgein<br />
currentwillresult,potentiallydamagingthemeter:
2.4. AMMETERUSAGE 37<br />
V<br />
A<br />
V<br />
OFF<br />
A<br />
Battery<br />
COM<br />
current<br />
surge<br />
+ -<br />
current<br />
surge<br />
SHORT CIRCUIT !<br />
A<br />
Ammetersaregenerallyprotectedfromexcessivecurrentbymeansofasmallfuselocated<br />
insidethemeterhousing.Iftheammeterisaccidentlyconnectedacrossasubstantialvoltage<br />
source,theresultantsurgeincurrentwill”blow”thefuseandrenderthemeterincapableof<br />
measuringcurrentuntilthefuseisreplaced.Beverycarefultoavoidthisscenario!<br />
Youmaytesttheconditionofamultimeter’sfusebyswitchingittotheresistancemodeand<br />
measuringcontinuitythroughthetestleads(andthroughthefuse). Onameterwherethe<br />
sametestleadjacksareusedforbothresistanceandcurrentmeasurement,simplyleavethe<br />
testleadplugswheretheyareandtouchthetwoprobestogether.Onameterwheredifferent<br />
jacksareused,thisishowyouinsertthetestleadplugstocheckthefuse:
38 CHAPTER2. BASICCONCEPTSANDTESTEQUIPMENT<br />
Low resistance<br />
indication = good fuse<br />
High resistance<br />
indication = "blown" fuse<br />
V<br />
A<br />
V<br />
OFF<br />
A<br />
A<br />
COM<br />
Internal<br />
location of<br />
fuse<br />
touch probes together<br />
Buildtheone-battery,one-lampcircuitusingjumperwirestoconnectthebatterytothe<br />
lamp,andverifythatthelamplightsupbeforeconnectingthemeterinserieswithit.Then,<br />
breakthecircuitopenatanypointandconnectthemeter’stestprobestothetwopointsof<br />
thebreaktomeasurecurrent.Asusual,ifyourmeterismanually-ranged,beginbyselecting<br />
thehighestrangeforcurrent,thenmovetheselectorswitchtolowerrangepositionsuntilthe<br />
strongestindicationisobtainedonthemeterdisplaywithoutover-rangingit.Ifthemeterindicationis”backwards,”(leftmotiononanalogneedle,ornegativereadingonadigitaldisplay),<br />
thenreversethetestprobeconnectionsandtryagain.Whentheammeterindicatesanormal<br />
reading(not”backwards”),electronsareenteringtheblacktestleadandexitingthered.This<br />
ishowyoudeterminedirectionofcurrentusingameter.<br />
Fora6-voltbatteryandasmalllamp,thecircuitcurrentwillbeintherangeofthousandths<br />
ofanamp,ormilliamps.Digitalmetersoftenshowasmallletter”m”intheright-handsideof<br />
thedisplaytoindicatethismetricprefix.<br />
Trybreakingthecircuitatsomeotherpointandinsertingthemeterthereinstead.What<br />
doyounoticeabouttheamountofcurrentmeasured?Whydoyouthinkthisis?<br />
Re-constructthecircuitonabreadboardlikethis:
2.4. AMMETERUSAGE 39<br />
+ - Breadboard<br />
Studentsoftengetconfusedwhenconnectinganammetertoabreadboardcircuit.Howcan<br />
themeterbeconnectedsoastointerceptallthecircuit’scurrentandnotcreateashortcircuit?<br />
Oneeasymethodthatguaranteessuccessisthis:<br />
• Identifywhatwireorcomponentterminalyouwishtomeasurecurrentthrough.<br />
• Pullthatwireorterminaloutofthebreadboardhole.Leaveithanginginmid-air.<br />
• Insertasparepieceofwireintotheholeyoujustpulledtheotherwireorterminaloutof.<br />
Leavetheotherendofthiswirehanginginmid-air.<br />
• Connecttheammeterbetweenthetwounconnectedwireends(thetwothatwerehanging<br />
inmid-air). Youarenowassuredofmeasuringcurrentthroughthewireorterminal<br />
initiallyidentified.
40 CHAPTER2. BASICCONCEPTSANDTESTEQUIPMENT<br />
m<br />
wire pulled<br />
out of<br />
breadboard<br />
V<br />
V<br />
OFF<br />
A<br />
A<br />
+ - A COM<br />
spare wire<br />
Again,measurecurrentthroughdifferentwiresinthiscircuit,followingthesameconnectionprocedureoutlinedabove.<br />
Whatdoyounoticeaboutthesecurrentmeasurements? The<br />
resultsinthebreadboardcircuitshouldbethesameastheresultsinthefree-form(nobreadboard)circuit.<br />
Buildingthesamecircuitonaterminalstripshouldalsoyieldsimilarresults:
2.4. AMMETERUSAGE 41<br />
m<br />
V<br />
A<br />
+ -<br />
V<br />
OFF<br />
A<br />
A<br />
COM<br />
Terminal<br />
strip<br />
Thecurrentfigureof24.70milliamps(24.70mA)shownintheillustrationsisanarbitrary<br />
quantity,reasonableforasmallincandescentlamp.Ifthecurrentforyourcircuitisadifferent<br />
value,thatisokay,solongasthelampisfunctioningwhenthemeterisconnected. Ifthe<br />
lamprefusestolightwhenthemeterisconnectedtothecircuit,andthemeterregistersa<br />
muchgreaterreading,youprobablyhaveashort-circuitconditionthroughthemeter.Ifyour<br />
lamprefusestolightwhenthemeterisconnectedinthecircuit,andthemeterregisterszero<br />
current,you’veprobablyblownthefuseinsidethemeter.Checktheconditionofyourmeter’s<br />
fuseasdescribedpreviouslyinthissectionandreplacethefuseifnecessary.
42 CHAPTER2. BASICCONCEPTSANDTESTEQUIPMENT<br />
2.5 Ohm’sLaw<br />
PARTSANDMATERIALS<br />
• Calculator(orpencilandpaperfordoingarithmetic)<br />
• 6-voltbattery<br />
• Assortmentofresistorsbetween1KΩand100kΩinvalue<br />
I’mpurposelyrestrictingtheresistancevaluesbetween1kΩand100kΩforthesakeof<br />
obtainingaccuratevoltageandcurrentreadingswithyourmeter. Withverylowresistance<br />
values,theinternalresistanceoftheammeterhasasignificantimpactonmeasurementaccuracy.<br />
Veryhighresistancevaluescancauseproblemsforvoltagemeasurement,theinternal<br />
resistanceofthevoltmetersubstantiallychangingcircuitresistancewhenitisconnectedin<br />
parallelwithahigh-valueresistor.<br />
Attherecommendedresistancevalues,therewillstillbeasmallamountofmeasurement<br />
errorduetothe”impact”ofthemeter,butnotenoughtocauseseriousdisagreementwith<br />
calculatedvalues.<br />
CROSS-REFERENCES<br />
LessonsInElectricCircuits,Volume1,chapter2:”Ohm’sLaw”<br />
LEARNINGOBJECTIVES<br />
• Voltmeteruse<br />
• Ammeteruse<br />
• Ohmmeteruse<br />
• UseofOhm’sLaw<br />
SCHEMATICDIAGRAM<br />
Ammeter<br />
A<br />
Battery<br />
Resistor V Voltmeter<br />
ILLUSTRATION
2.5. OHM’SLAW 43<br />
Ammeter<br />
V<br />
A<br />
+ -<br />
V<br />
OFF<br />
A<br />
A<br />
COM<br />
Terminal<br />
strip<br />
Resistor<br />
V<br />
A<br />
Voltmeter<br />
V<br />
OFF<br />
A<br />
A<br />
COM<br />
INSTRUCTIONS<br />
Selectaresistorfromtheassortment,andmeasureitsresistancewithyourmultimeterset<br />
totheappropriateresistancerange.Besurenottoholdtheresistorterminalswhenmeasuring<br />
resistance,orelseyourhand-to-handbodyresistancewillinfluencethemeasurement!Record<br />
thisresistancevalueforfutureuse.<br />
Buildaone-battery,one-resistorcircuit.Aterminalstripisshownintheillustration,but<br />
anyformofcircuitconstructionisokay.Setyourmultimetertotheappropriatevoltagerange<br />
andmeasurevoltageacrosstheresistorasitisbeingpoweredbythebattery. Recordthis<br />
voltagevaluealongwiththeresistancevaluepreviouslymeasured.<br />
Setyourmultimetertothehighestcurrentrangeavailable.Breakthecircuitandconnect<br />
theammeterwithinthatbreak,soitbecomesapartofthecircuit,inserieswiththebattery<br />
andresistor.Selectthebestcurrentrange:whicheveronegivesthestrongestmeterindication
44 CHAPTER2. BASICCONCEPTSANDTESTEQUIPMENT<br />
withoutover-rangingthemeter. Ifyourmultimeterisautoranging,ofcourse,youneednot<br />
botherwithsettingranges. Recordthiscurrentvaluealongwiththeresistanceandvoltage<br />
valuespreviouslyrecorded.<br />
Takingthemeasuredfiguresforvoltageandresistance,usetheOhm’sLawequationto<br />
calculatecircuitcurrent.Comparethiscalculatedfigurewiththemeasuredfigureforcircuit<br />
current:<br />
Ohm’s Law<br />
(solving for current)<br />
I = E R<br />
Where,<br />
E = Voltage in volts<br />
I = Current in amps<br />
R = Resistance in ohms<br />
Takingthemeasuredfiguresforvoltageandcurrent,usetheOhm’sLawequationtocalculatecircuitresistance.<br />
Comparethiscalculatedfigurewiththemeasuredfigureforcircuit<br />
resistance:<br />
Ohm’s Law<br />
(solving for resistance)<br />
R =<br />
E<br />
I<br />
Finally,takingthemeasuredfiguresforresistanceandcurrent,usetheOhm’sLawequationtocalculatecircuitvoltage.<br />
Comparethiscalculatedfigurewiththemeasuredfigurefor<br />
circuitvoltage:<br />
Ohm’s Law<br />
(solving for voltage)<br />
E = IR<br />
Thereshouldbecloseagreementbetweenallmeasuredandallcalculatedfigures. Any<br />
differencesinrespectivequantitiesofvoltage,current,orresistancearemostlikelydueto<br />
meterinaccuracies. Thesedifferencesshouldberathersmall,nomorethanseveralpercent.<br />
Somemeters,ofcourse,aremoreaccuratethanothers!<br />
Substitutedifferentresistorsinthecircuitandre-takeallresistance,voltage,andcurrent<br />
measurements.Re-calculatethesefiguresandcheckforagreementwiththeexperimentaldata<br />
(measuredquantities). Alsonotethesimplemathematicalrelationshipbetweenchangesin<br />
resistorvalueandchangesincircuitcurrent.Voltageshouldremainapproximatelythesame<br />
foranyresistorsizeinsertedintothecircuit,becauseitisthenatureofabatterytomaintain<br />
voltageataconstantlevel.
2.6. NONLINEARRESISTANCE 45<br />
2.6 Nonlinearresistance<br />
PARTSANDMATERIALS<br />
• Calculator(orpencilandpaperfordoingarithmetic)<br />
• 6-voltbattery<br />
• Low-voltageincandescentlamp(RadioShackcatalog#272-1130orequivalent)<br />
CROSS-REFERENCES<br />
LessonsInElectricCircuits,Volume1,chapter2:”Ohm’sLaw”<br />
LEARNINGOBJECTIVES<br />
• Voltmeteruse<br />
• Ammeteruse<br />
• Ohmmeteruse<br />
• UseofOhm’sLaw<br />
• Realizationthatsomeresistancesareunstable!<br />
• Scientificmethod<br />
SCHEMATICDIAGRAM<br />
Ammeter<br />
A<br />
Battery<br />
Lamp<br />
V<br />
Voltmeter<br />
ILLUSTRATION
46 CHAPTER2. BASICCONCEPTSANDTESTEQUIPMENT<br />
Ammeter<br />
V<br />
A<br />
+ -<br />
V<br />
OFF<br />
A<br />
A<br />
COM<br />
Terminal<br />
strip<br />
Lamp<br />
V<br />
A<br />
Voltmeter<br />
V<br />
OFF<br />
A<br />
A<br />
COM<br />
INSTRUCTIONS<br />
Measuretheresistanceofthelampwithyourmultimeter.Thisresistancefigureisdueto<br />
thethinmetal”filament”insidethelamp.Ithassubstantiallymoreresistancethanajumper<br />
wire,butlessthananyoftheresistorsfromthelastexperiment.Recordthisresistancevalue<br />
forfutureuse.<br />
Buildaone-battery,one-lampcircuit.Setyourmultimetertotheappropriatevoltagerange<br />
andmeasurevoltageacrossthelampasitisenergized(lit). Recordthisvoltagevaluealong<br />
withtheresistancevaluepreviouslymeasured.<br />
Setyourmultimetertothehighestcurrentrangeavailable.Breakthecircuitandconnect<br />
theammeterwithinthatbreak,soitbecomesapartofthecircuit,inserieswiththebattery<br />
andlamp. Selectthebestcurrentrange:whicheveronegivesthestrongestmeterindication<br />
withoutover-rangingthemeter. Ifyourmultimeterisautoranging,ofcourse,youneednot
2.6. NONLINEARRESISTANCE 47<br />
botherwithsettingranges. Recordthiscurrentvaluealongwiththeresistanceandvoltage<br />
valuespreviouslyrecorded.<br />
Takingthemeasuredfiguresforvoltageandresistance,usetheOhm’sLawequationto<br />
calculatecircuitcurrent.Comparethiscalculatedfigurewiththemeasuredfigureforcircuit<br />
current:<br />
Ohm’s Law<br />
(solving for current)<br />
I = E R<br />
Where,<br />
E = Voltage in volts<br />
I = Current in amps<br />
R = Resistance in ohms<br />
Whatyoushouldfindisamarkeddifferencebetweenmeasuredcurrentandcalculated<br />
current:thecalculatedfigureismuchgreater.Whyisthis?<br />
Tomakethingsmoreinteresting,trymeasuringthelamp’sresistanceagain,thistimeusingadifferentmodelofmeter.Youwillneedtodisconnectthelampfromthebatterycircuitin<br />
ordertoobtainaresistancereading,becausevoltagesoutsideofthemeterinterferewithresistancemeasurement.Thisisageneralrulethatshouldberemembered:measureresistance<br />
onlyonanunpoweredcomponent!<br />
Usingadifferentohmmeter,thelampwillprobablyregisterasadifferentvalueofresistance.Usually,analogmetersgivehigherlampresistancereadingsthandigitalmeters.<br />
Thisbehaviorisverydifferentfromthatoftheresistorsinthelastexperiment.Why?What<br />
factor(s)mightinfluencetheresistanceofthelampfilament,andhowmightthosefactorsbe<br />
differentbetweenconditionsoflitandunlit,orbetweenresistancemeasurementstakenwith<br />
differenttypesofmeters?<br />
Thisproblemisagoodtestcasefortheapplicationofscientificmethod.Onceyou’vethought<br />
ofapossiblereasonforthelamp’sresistancechangingbetweenlitandunlitconditions,tryto<br />
duplicatethatcausebysomeothermeans. Forexample,ifyouthinkthelampresistance<br />
mightchangeasitisexposedtolight(itsownlight,whenlit),andthatthisaccountsforthe<br />
differencebetweenthemeasuredandcalculatedcircuitcurrents,tryexposingthelamptoan<br />
externalsourceoflightwhilemeasuringitsresistance.Ifyoumeasuresubstantialresistance<br />
changeasaresultoflightexposure,thenyourhypothesishassomeevidentialsupport.Ifnot,<br />
thenyourhypothesishasbeenfalsified,andanothercausemustberesponsibleforthechange<br />
incircuitcurrent.
48 CHAPTER2. BASICCONCEPTSANDTESTEQUIPMENT<br />
2.7 Powerdissipation<br />
PARTSANDMATERIALS<br />
• Calculator(orpencilandpaperfordoingarithmetic)<br />
• 6voltbattery<br />
• Two1/4wattresistors:10 Ωand330 Ω.<br />
• Smallthermometer<br />
Theresistorvaluesneednotbeexact,butwithinfivepercentofthefiguresspecified(+/-0.5<br />
Ωforthe10 Ωresistor;+/-16.5 Ωforthe330 Ωresistor).Colorcodesfor5%tolerance10 Ωand<br />
330 Ωresistorsareasfollows: Brown,Black,Black,Gold(10,+/-5%),andOrange,Orange,<br />
Brown,Gold(330,+/-5%).<br />
Donotuseanybatterysizeotherthan6voltsforthisexperiment.<br />
Thethermometershouldbeassmallaspossible,tofacilitaterapiddetectionofheatproducedbytheresistor.Irecommendamedicalthermometer,thetypeusedtotakebodytemperature.<br />
CROSS-REFERENCES<br />
LessonsInElectricCircuits,Volume1,chapter2:”Ohm’sLaw”<br />
LEARNINGOBJECTIVES<br />
• Voltmeteruse<br />
• Ammeteruse<br />
• Ohmmeteruse<br />
• UseofJoule’sLaw<br />
• Importanceofcomponentpowerratings<br />
• Significanceofelectricallycommonpoints<br />
SCHEMATICDIAGRAM<br />
ILLUSTRATION
2.7. POWERDISSIPATION 49<br />
Thermometer<br />
+ - Caution: do not hold resistor with<br />
your fingers while powered!<br />
INSTRUCTIONS<br />
Measureeachresistor’sresistancewithyourohmmeter,notingtheexactvaluesonapiece<br />
ofpaperforlaterreference.<br />
Connectthe330 Ωresistortothe6voltbatteryusingapairofjumperwiresasshownin<br />
theillustration.Connectthejumperwirestotheresistorterminalsbeforeconnectingtheother<br />
endstothebattery. Thiswillensureyourfingersarenottouchingtheresistorwhenbattery<br />
powerisapplied.<br />
YoumightbewonderingwhyIadvisenobodilycontactwiththepoweredresistor. This<br />
isbecauseitwillbecomehotwhenpoweredbythebattery. Youwillusethethermometerto<br />
measurethetemperatureofeachresistorwhenpowered.<br />
Withthe330 Ωresistorconnectedtothebattery,measurevoltagewithavoltmeter. In<br />
measuringvoltage,thereismorethanonewaytoobtainaproperreading. Voltagemaybe<br />
measureddirectlyacrossthebattery,ordirectlyacrosstheresistor.Batteryvoltageisthesame<br />
asresistorvoltageinthiscircuit,sincethosetwocomponentssharethesamesetofelectrically<br />
commonpoints:onesideoftheresistorisdirectlyconnectedtoonesideofthebattery,andthe<br />
othersideoftheresistorisdirectlyconnectedtotheothersideofthebattery.
50 CHAPTER2. BASICCONCEPTSANDTESTEQUIPMENT<br />
V<br />
A<br />
V<br />
OFF<br />
A<br />
COM<br />
common<br />
+ -<br />
electrically<br />
A<br />
points<br />
electrically common<br />
points<br />
Allpointsofcontactalongtheupperwireintheillustration(coloredred)areelectrically<br />
commontoeachother. Allpointsofcontactalongthelowerwire(coloredblack)arelikewise<br />
electricallycommontoeachother.Voltagemeasuredbetweenanypointontheupperwireand<br />
anypointonthelowerwireshouldbethesame.Voltagemeasuredbetweenanytwocommon<br />
points,however,shouldbezero.<br />
Usinganammeter,measurecurrentthroughthecircuit. Again,thereisnoone”correct”<br />
waytomeasurecurrent,solongastheammeterisplacedwithintheflow-pathofelectrons<br />
throughtheresistorandnotacrossasourceofvoltage.Todothis,makeabreakinthecircuit,<br />
andplacetheammeterwithinthatbreak: connectthetwotestprobestothetwowireor<br />
terminalendsleftopenfromthebreak.Oneviableoptionisshowninthefollowingillustration:
2.7. POWERDISSIPATION 51<br />
V<br />
A<br />
V<br />
OFF<br />
A<br />
+ - COM<br />
A<br />
Nowthatyou’vemeasuredandrecordedresistorresistance,circuitvoltage,andcircuitcurrent,youarereadytocalculatepowerdissipation.Whereasvoltageisthemeasureofelectrical<br />
”push”motivatingelectronstomovethroughacircuit,andcurrentisthemeasureofelectron<br />
flowrate,poweristhemeasureofwork-rate:howfastworkisbeingdoneinthecircuit.Ittakes<br />
acertainamountofworktopushelectronsthrougharesistance,andpowerisadescriptionof<br />
howrapidlythatworkistakingplace.Inmathematicalequations,powerissymbolizedbythe<br />
letter”P”andmeasuredintheunitoftheWatt(W).<br />
Powermaybecalculatedbyanyoneofthreeequations–collectivelyreferredtoasJoule’s<br />
Law–givenanytwooutofthreequantitiesofvoltage,current,andresistance:<br />
Joule’s Law<br />
(solving for power)<br />
P = IE<br />
P = I 2 R<br />
P = E2<br />
R<br />
Trycalculatingpowerinthiscircuit,usingthethreemeasuredvaluesofvoltage,current,<br />
andresistance. Anywayyoucalculateit,thepowerdissipationfigureshouldberoughlythe<br />
same. Assumingabatterywith6.000voltsandaresistorofexactly330 Ω,thepowerdissi-
52 CHAPTER2. BASICCONCEPTSANDTESTEQUIPMENT<br />
pationwillbe0.1090909watts,or109.0909milli-watts(mW),touseametricprefix. Since<br />
theresistorhasapowerratingof1/4watt(0.25watts,or250mW),itismorethancapableof<br />
sustainingthislevelofpowerdissipation. Becausetheactualpowerlevelisalmosthalfthe<br />
ratedpower,theresistorshouldbecomenoticeablywarmbutitshouldnotoverheat.Touchthe<br />
thermometerendtothemiddleoftheresistorandseehowwarmitgets.<br />
Thepowerratingofanyelectricalcomponentdoesnottellushowmuchpoweritwilldissipate,butsimplyhowmuchpoweritmaydissipatewithoutsustainingdamage.Iftheactual<br />
amountofdissipatedpowerexceedsacomponent’spowerrating,thatcomponentwillincrease<br />
temperaturetothepointofdamage.<br />
Toillustrate,disconnectthe330 Ωresistorandreplaceitwiththe10 Ωresistor. Again,<br />
avoidtouchingtheresistoroncethecircuitiscomplete,asitwillheatuprapidly. Thesafest<br />
waytodothisistodisconnectonejumperwirefromabatteryterminal,thendisconnectthe<br />
330 Ωresistorfromthetwoalligatorclips,thenconnectthe10 Ωresistorbetweenthetwoclips,<br />
andfinallyreconnectthejumperwirebacktothebatteryterminal.<br />
Caution: keepthe10 Ωresistorawayfromanyflammablematerialswhenitis<br />
poweredbythebattery!<br />
Youmaynothaveenoughtimetotakevoltageandcurrentmeasurementsbeforetheresistorbeginstosmoke.Atthefirstsignofdistress,disconnectoneofthejumperwiresfroma<br />
batteryterminaltointerruptcircuitcurrent,andgivetheresistorafewmomentstocooldown.<br />
Withpowerstilldisconnected,measuretheresistor’sresistancewithanohmmeterandnote<br />
anysubstantialdeviationfromitsoriginalvalue. Iftheresistorstillmeasureswithin+/-5%<br />
ofitsadvertisedvalue(between9.5and10.5 Ω),re-connectthejumperwireandletitsmokea<br />
bitmore.<br />
Whattrenddoyounoticewiththeresistor’svalueasitisdamagedmoreandmoreby<br />
overpowering? Itistypicalofresistorstofailwithagreater-than-normalresistancewhen<br />
overheated. Thisisoftenaself-protectivemodeoffailure,asanincreasedresistanceresults<br />
inlesscurrentand(generally)lesspowerdissipation,coolingitdownagain. However,the<br />
resistor’snormalresistancevaluewillnotreturnifsufficientlydamaged.<br />
PerformingsomeJoule’sLawcalculationsforresistorpoweragain,wefindthata10 Ω<br />
resistorconnectedtoa6voltbatterydissipatesabout3.6wattsofpower,about14.4timesits<br />
ratedpowerdissipation.Littlewonderitsmokessoquicklyafterconnectiontothebattery!
2.8. CIRCUITWITHASWITCH 53<br />
2.8 Circuitwithaswitch<br />
PARTSANDMATERIALS<br />
• 6-voltbattery<br />
• Low-voltageincandescentlamp(RadioShackcatalog#272-1130orequivalent)<br />
• Longlengthsofwire,22-gaugeorlarger<br />
• Householdlightswitch(thesearereadilyavailableatanyhardwarestore)<br />
Householdlightswitchesareabargainforstudentsofbasicelectricity. Theyarereadily<br />
available,veryinexpensive,andalmostimpossibletodamagewithbatterypower.Donotget<br />
”dimmer”switches,justthesimpleon-off”toggle”varietyusedforordinaryhouseholdwallmountedlightcontrols.<br />
CROSS-REFERENCES<br />
LessonsInElectricCircuits,Volume1,chapter1:”BasicConceptsofElectricity”<br />
LEARNINGOBJECTIVES<br />
• Switchbehavior<br />
• Usinganohmmetertocheckswitchaction<br />
SCHEMATICDIAGRAM<br />
Switch<br />
ILLUSTRATION
54 CHAPTER2. BASICCONCEPTSANDTESTEQUIPMENT<br />
Switch<br />
+ -<br />
INSTRUCTIONS<br />
Buildaone-battery,one-switch,one-lampcircuitasshownintheschematicdiagramandin<br />
theillustration.Thiscircuitismostimpressivewhenthewiresarelong,asitshowshowthe<br />
switchisabletocontrolcircuitcurrentnomatterhowphysicallylargethecircuitmaybe.<br />
Measurevoltageacrossthebattery,acrosstheswitch(measurefromonescrewterminalto<br />
anotherwiththevoltmeter),andacrossthelampwiththeswitchinbothpositions.Whenthe<br />
switchisturnedoff,itissaidtobeopen,andthelampwillgooutjustthesameasifawire<br />
werepulledloosefromaterminal. Asbefore,anybreakinthecircuitatanylocationcauses<br />
thelamptoimmediatelyde-energize(darken).
2.9. ELECTROMAGNETISM 55<br />
2.9 Electromagnetism<br />
PARTSANDMATERIALS<br />
• 6-voltbattery<br />
• Magneticcompass<br />
• Smallpermanentmagnet<br />
• Spoolof28-gaugemagnetwire<br />
• Largebolt,nail,orsteelrod<br />
• <strong>Electrical</strong>tape<br />
Magnetwireisatermforthin-gaugecopperwirewithenamelinsulationinsteadofrubber<br />
orplasticinsulation.Itssmallsizeandverythininsulationallowformany”turns”tobewound<br />
inacompactcoil. Youwillneedenoughmagnetwiretowraphundredsofturnsaroundthe<br />
bolt,nail,orotherrod-shapedsteelform.<br />
Besuretoselectabolt,nail,orrodthatismagnetic. Stainlesssteel,forexample,isnonmagneticandwillnotfunctionforthepurposeofanelectromagnetcoil!Theidealmaterialfor<br />
thisexperimentissoftiron,butanycommonlyavailablesteelwillsuffice.<br />
CROSS-REFERENCES<br />
LessonsInElectricCircuits,Volume1,chapter14:”MagnetismandElectromagnetism”<br />
LEARNINGOBJECTIVES<br />
• Applicationoftheleft-handrule<br />
• Electromagnetconstruction<br />
SCHEMATICDIAGRAM<br />
ILLUSTRATION
56 CHAPTER2. BASICCONCEPTSANDTESTEQUIPMENT<br />
Compass<br />
N<br />
W E<br />
S<br />
+ -<br />
Electromagnet<br />
(wire coil wrapped<br />
around steel bar)<br />
INSTRUCTIONS<br />
Wrapasinglelayerofelectricaltapearoundthesteelbar(orbolt,ormail)toprotectthe<br />
wirefromabrasion.Proceedtowrapseveralhundredturnsofwirearoundthesteelbar,makingthecoilasevenaspossible.Itisokaytooverlapwire,anditisokaytowrapinthesame<br />
stylethatafishingreelwrapslinearoundthespool.Theonlyruleyoumustfollowisthatall<br />
turnsmustbewrappedaroundthebarinthesamedirection(noreversingfromclockwiseto<br />
counter-clockwise!). Ifindthatadrillpressworksasagreattoolforcoilwinding:clampthe<br />
rodinthedrill’schuckasifitwereadrillbit,thenturnthedrillmotoronataslowspeedand<br />
letitdothewrapping!Thisallowsyoutofeedwireontotherodinaverysteady,evenmanner.<br />
Afteryou’vewrappedseveralhundredturnsofwirearoundtherod,wrapalayerortwoof<br />
electricaltapeoverthewirecoiltosecurethewireinplace.Scrapetheenamelinsulationoff<br />
theendsofthecoilwiresforconnectiontojumperleads,thenconnectthecoiltoabattery.<br />
Whenelectriccurrentgoesthroughthecoil,itwillproduceastrongmagneticfield: one<br />
”pole”ateachendoftherod.Thisphenomenonisknownaselectromagnetism.Themagnetic<br />
compassisusedtoidentifythe”North”and”South”polesoftheelectromagnet.<br />
Withtheelectromagnetenergized(connectedtothebattery),placeapermanentmagnet<br />
nearonepoleandnotewhetherthereisanattractiveorrepulsiveforce.Reversetheorientationofthepermanentmagnetandnotethedifferenceinforce.<br />
Electromagnetismhasmanyapplications,includingrelays,electricmotors,solenoids,doorbells,buzzers,computerprintermechanisms,andmagneticmedia”write”heads(taperecorders,<br />
diskdrives).<br />
Youmightnoticeasignificantsparkwheneverthebatteryisdisconnectedfromtheelectromagnetcoil:muchgreaterthanthesparkproducedifthebatteryissimplyshort-circuited.<br />
Thissparkistheresultofahigh-voltagesurgecreatedwhenevercurrentissuddenlyinterruptedthroughthecoil.Theeffectisknownasinductive”kickback”andiscapableofdeliveringasmallbutharmlesselectricshock!Toavoidreceivingthisshock,donotplaceyourbody<br />
acrossthebreakinthecircuitwhende-energizing!Useonehandatatimewhenun-powering<br />
thecoilandyou’llbeperfectlysafe.Thisphenomenonwillbeexploredingreaterdetailinthe<br />
nextchapter(DCCircuits).
2.10. ELECTROMAGNETICINDUCTION 57<br />
2.10 Electromagneticinduction<br />
PARTSANDMATERIALS<br />
• Electromagnetfrompreviousexperiment<br />
• Permanentmagnet<br />
Seepreviousexperimentforinstructionsonelectromagnetconstruction.<br />
CROSS-REFERENCES<br />
LessonsInElectricCircuits,Volume1,chapter14:”MagnetismandElectromagnetism”<br />
LEARNINGOBJECTIVES<br />
• Relationshipbetweenmagneticfieldstrengthandinducedvoltage<br />
SCHEMATICDIAGRAM<br />
Voltmeter<br />
+<br />
V<br />
-<br />
ILLUSTRATION<br />
V<br />
A<br />
Electromagnet<br />
V<br />
OFF<br />
A<br />
A<br />
COM<br />
Magnet<br />
N<br />
S<br />
INSTRUCTIONS
58 CHAPTER2. BASICCONCEPTSANDTESTEQUIPMENT<br />
Electromagneticinductionisthecomplementaryphenomenontoelectromagnetism. Insteadofproducingamagneticfieldfromelectricity,weproduceelectricityfromamagnetic<br />
field.Thereisoneimportantdifference,though:whereaselectromagnetismproducesasteady<br />
magneticfieldfromasteadyelectriccurrent,electromagneticinductionrequiresmotionbetweenthemagnetandthecoiltoproduceavoltage.<br />
Connectthemultimetertothecoil,andsetittothemostsensitiveDCvoltagerangeavailable.<br />
Movethemagnetslowlytoandfromoneendoftheelectromagnet,notingthepolarity<br />
andmagnitudeoftheinducedvoltage.Experimentwithmovingthemagnet,anddiscoverfor<br />
yourselfwhatfactor(s)determinetheamountofvoltageinduced.Trytheotherendofthecoil<br />
andcompareresults.Trytheotherendofthepermanentmagnetandcompare.<br />
Ifusingananalogmultimeter,besuretouselongjumperwiresandlocatethemeterfar<br />
awayfromthecoil,asthemagneticfieldfromthepermanentmagnetmayaffectthemeter’s<br />
operationandproducefalsereadings.Digitalmetersareunaffectedbymagneticfields.
Chapter3<br />
DCCIRCUITS<br />
Contents<br />
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59<br />
3.2 Seriesbatteries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60<br />
3.3 Parallelbatteries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63<br />
3.4 Voltagedivider . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67<br />
3.5 Currentdivider . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78<br />
3.6 Potentiometerasavoltagedivider. . . . . . . . . . . . . . . . . . . . . . . . 87<br />
3.7 Potentiometerasarheostat . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93<br />
3.8 Precisionpotentiometer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99<br />
3.9 Rheostatrangelimiting. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .102<br />
3.10 Thermoelectricity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .109<br />
3.11 Makeyourownmultimeter . . . . . . . . . . . . . . . . . . . . . . . . . . . .112<br />
3.12 Sensitivevoltagedetector . . . . . . . . . . . . . . . . . . . . . . . . . . . . .117<br />
3.13 Potentiometricvoltmeter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .122<br />
3.14 4-wireresistancemeasurement . . . . . . . . . . . . . . . . . . . . . . . . . .127<br />
3.15 Averysimplecomputer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .131<br />
3.16 Potatobattery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .136<br />
3.17 Capacitorcharginganddischarging. . . . . . . . . . . . . . . . . . . . . . .138<br />
3.18 Rate-of-changeindicator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .142<br />
3.1 Introduction<br />
”DC”standsforDirectCurrent,whichcanrefertoeithervoltageorcurrentinaconstant<br />
polarityordirection,respectively.Theseexperimentsaredesignedtointroduceyoutoseveral<br />
importantconceptsofelectricityrelatedtoDCcircuits.<br />
59
60 CHAPTER3. DCCIRCUITS<br />
3.2 Seriesbatteries<br />
PARTSANDMATERIALS<br />
• Two6-voltbatteries<br />
• One9-voltbattery<br />
Actually,anysizebatterieswillsufficeforthisexperiment,butitisrecommendedtohave<br />
atleasttwodifferentvoltagesavailabletomakeitmoreinteresting.<br />
CROSS-REFERENCES<br />
LessonsInElectricCircuits,Volume1,chapter5:”SeriesandParallelCircuits”<br />
LessonsInElectricCircuits,Volume1,chapter11:”BatteriesandPowerSystems”<br />
LEARNINGOBJECTIVES<br />
• Howtoconnectbatteriestoobtaindifferentvoltagelevels<br />
SCHEMATICDIAGRAM<br />
+<br />
-<br />
+<br />
+<br />
V Voltmeter<br />
-<br />
-<br />
ILLUSTRATION
3.2. SERIESBATTERIES 61<br />
+ -<br />
V<br />
A<br />
V<br />
OFF<br />
A<br />
A<br />
COM<br />
+ -<br />
INSTRUCTIONS<br />
Connectingcomponentsinseriesmeanstoconnectthemin-linewitheachother,sothat<br />
thereisbutasinglepathforelectronstoflowthroughthemall. Ifyouconnectbatteriesso<br />
thatthepositiveofoneconnectstothenegativeoftheother,youwillfindthattheirrespective<br />
voltagesadd.Measurethevoltageacrosseachbatteryindividuallyastheyareconnected,then<br />
measurethetotalvoltageacrossthemboth,likethis:
62 CHAPTER3. DCCIRCUITS<br />
V<br />
A<br />
V<br />
OFF<br />
A<br />
A<br />
COM<br />
+ - V A<br />
Measuring first battery<br />
V A<br />
Measuring<br />
OFF<br />
total voltage<br />
A COM<br />
+ -<br />
+ -<br />
+ -<br />
+ - Measuring<br />
V A<br />
second battery<br />
V<br />
OFF<br />
A<br />
A<br />
COM<br />
+ -<br />
Tryconnectingbatteriesofdifferentsizesinserieswitheachother,forinstancea6-volt<br />
batterywitha9-voltbattery.Whatisthetotalvoltageinthiscase?Tryreversingtheterminal<br />
connectionsofjustoneofthesebatteries,sothattheyareopposingeachotherlikethis:<br />
+<br />
Seriesopposing<br />
-<br />
-<br />
+<br />
V Voltmeter<br />
-<br />
+<br />
Howdoesthetotalvoltagecompareinthissituationtothepreviousonewithbothbatteries<br />
”aiding?”Notethepolarityofthetotalvoltageasindicatedbythevoltmeterindicationand<br />
testprobeorientation.Remember,ifthemeter’sdigitalindicationisapositivenumber,thered<br />
probeispositive(+)andtheblackprobenegative(-);iftheindicationisanegativenumber,<br />
thepolarityis”backward”(red=negative,black=positive).Analogmeterssimplywillnotread<br />
properlyifreverse-connected,becausetheneedletriestomovethewrongdirection(leftinstead<br />
ofright). Canyoupredictwhattheoverallvoltagepolaritywillbe,knowingthepolaritiesof<br />
theindividualbatteriesandtheirrespectivestrengths?
3.3. PARALLELBATTERIES 63<br />
3.3 Parallelbatteries<br />
PARTSANDMATERIALS<br />
• Four6-voltbatteries<br />
• 12-voltlightbulb,25or50watt<br />
• Lampsocket<br />
High-wattage12-voltlampsmaybepurchasedfromrecreationalvehicle(RV)andboating<br />
supplystores.Commonsizesare25wattand50watt.Thislampwillbeusedasa”heavy”load<br />
foryourbatteries(heavyload=onethatdrawssubstantialcurrent).<br />
Aregularhousehold(120volt)lampsocketwillworkjustfinefortheselow-voltage”RV”<br />
lamps.<br />
CROSS-REFERENCES<br />
LessonsInElectricCircuits,Volume1,chapter5:”SeriesandParallelCircuits”<br />
LessonsInElectricCircuits,Volume1,chapter11:”BatteriesandPowerSystems”<br />
LEARNINGOBJECTIVES<br />
• Voltagesourceregulation<br />
• Boostingcurrentcapacitythroughparallelconnections<br />
SCHEMATICDIAGRAM<br />
+ +<br />
+<br />
+<br />
- -<br />
-<br />
-<br />
ILLUSTRATION<br />
+ - + - + - + -
64 CHAPTER3. DCCIRCUITS<br />
INSTRUCTIONS<br />
Beginthisexperimentbyconnectingone6-voltbatterytothelamp.Thelamp,designedto<br />
operateon12volts,shouldglowdimlywhenpoweredbythe6-voltbattery.Useyourvoltmeter<br />
toreadvoltageacrossthelamplikethis:<br />
+ -<br />
V<br />
A<br />
V<br />
OFF<br />
A<br />
A<br />
COM<br />
Thevoltmetershouldregisteravoltagelowerthantheusualvoltageofthebattery.Ifyou<br />
useyourvoltmetertoreadthevoltagedirectlyatthebatteryterminals,youwillmeasurealow<br />
voltagethereaswell.Whyisthis?Thelargecurrentdrawnbythehigh-powerlampcausesthe<br />
voltageatthebatteryterminalsto”sag”or”droop,”duetovoltagedroppedacrossresistance<br />
internaltothebattery.<br />
Wemayovercomethisproblembyconnectingbatteriesinparallelwitheachother,sothat<br />
eachbatteryonlyhastosupplyafractionofthetotalcurrentdemandedbythelamp.Parallel<br />
connectionsinvolvemakingallthepositive(+)batteryterminalselectricallycommontoeach<br />
otherbyconnectionthroughjumperwires,andallnegative(-)terminalscommontoeachother<br />
aswell. Addonebatteryatatimeinparallel,notingthelampvoltagewiththeadditionof<br />
eachnew,parallel-connectedbattery:
3.3. PARALLELBATTERIES 65<br />
. . . additional batteries . . .<br />
+ -<br />
+ -<br />
+ -<br />
+ -<br />
V<br />
A<br />
V<br />
OFF<br />
A<br />
A<br />
COM<br />
Thereshouldalsobeanoticeabledifferenceinlightintensityasthevoltage”sag”isimproved.<br />
Trymeasuringthecurrentofonebatteryandcomparingittothetotalcurrent(lightbulb<br />
current).Shownhereistheeasiestwaytomeasuresingle-batterycurrent:<br />
V<br />
A<br />
V<br />
OFF<br />
A<br />
A<br />
COM<br />
+ - + - + - + -<br />
Bybreakingthecircuitforjustonebattery,andinsertingourammeterwithinthatbreak,<br />
weinterceptthecurrentofthatonebatteryandarethereforeabletomeasureit.Measuring<br />
totalcurrentinvolvesasimilarprocedure: makeabreaksomewhereinthepaththattotal<br />
currentmusttake,theninserttheammeterwithinthanbreak:
66 CHAPTER3. DCCIRCUITS<br />
+ - + - + - + - COM<br />
V<br />
A<br />
V<br />
OFF<br />
A<br />
A<br />
Notethedifferenceincurrentbetweenthesingle-batteryandtotalmeasurements.<br />
Toobtainmaximumbrightnessfromthelightbulb,aseries-parallelconnectionisrequired.<br />
Two6-voltbatteriesconnectedseries-aidingwillprovide12volts. Connectingtwoofthese<br />
series-connectedbatterypairsinparallelimprovestheircurrent-sourcingabilityforminimum<br />
voltagesag:<br />
+ -<br />
+ -<br />
+ -<br />
+ -
3.4. VOLTAGEDIVIDER 67<br />
3.4 Voltagedivider<br />
PARTSANDMATERIALS<br />
• Calculator(orpencilandpaperfordoingarithmetic)<br />
• 6-voltbattery<br />
• Assortmentofresistorsbetween1KΩand100kΩinvalue<br />
I’mpurposelyrestrictingtheresistancevaluesbetween1kΩand100kΩforthesakeof<br />
obtainingaccuratevoltageandcurrentreadingswithyourmeter. Withverylowresistance<br />
values,theinternalresistanceoftheammeterhasasignificantimpactonmeasurementaccuracy.Veryhighresistancevaluesmaycauseproblemsforvoltagemeasurement,theinternal<br />
resistanceofthevoltmetersubstantiallychangingcircuitresistancewhenitisconnectedin<br />
parallelwithahigh-valueresistor.<br />
CROSS-REFERENCES<br />
LessonsInElectricCircuits,Volume1,chapter6:”DividerCircuitsandKirchhoff’sLaws”<br />
LEARNINGOBJECTIVES<br />
• Voltmeteruse<br />
• Ammeteruse<br />
• Ohmmeteruse<br />
• UseofOhm’sLaw<br />
• UseofKirchhoff’sVoltageLaw(”KVL”)<br />
• Voltagedividerdesign<br />
SCHEMATICDIAGRAM<br />
R 1<br />
R 2<br />
+<br />
V Voltmeter<br />
-<br />
R 3
68 CHAPTER3. DCCIRCUITS<br />
ILLUSTRATION<br />
+ - R 1<br />
R 2<br />
R 3<br />
Breadboard<br />
+ - R 1<br />
R 2<br />
R 3<br />
Terminal strip
3.4. VOLTAGEDIVIDER 69<br />
R 1 R 2 R 3<br />
+ -<br />
"Free-form" construction<br />
INSTRUCTIONS<br />
Shownherearethreedifferentmethodsofcircuitconstruction:onabreadboard,onaterminalstrip,and”free-form.”Trybuildingthesamecircuiteachwaytofamiliarizeyourselfwith<br />
thedifferentconstructiontechniquesandtheirrespectivemerits. The”free-form”method–<br />
whereallcomponentsareconnectedtogetherwith”alligator-”stylejumperwires–istheleast<br />
professional,butappropriateforasimpleexperimentsuchasthis. Breadboardconstruction<br />
isversatileandallowsforhighcomponentdensity(manypartsinasmallspace),butisquite<br />
temporary. Terminalstripsofferamuchmorepermanentformofconstructionatthecostof<br />
lowcomponentdensity.<br />
Selectthreeresistorsfromyourresistorassortmentandmeasuretheresistanceofeachone<br />
withanohmmeter. Notetheseresistancevalueswithpenandpaper,forreferenceinyour<br />
circuitcalculations.<br />
Connectthethreeresistorsinseries,andtothe6-voltbattery,asshownintheillustrations.<br />
Measurebatteryvoltagewithavoltmeteraftertheresistorshavebeenconnectedtoit,noting<br />
thisvoltagefigureonpaperaswell.Itisadvisabletomeasurebatteryvoltagewhileitspoweringtheresistorcircuitbecausethisvoltagemaydifferslightlyfromano-loadcondition.We<br />
sawthiseffectexaggeratedinthe”parallelbattery”experimentwhilepoweringahigh-wattage<br />
lamp:batteryvoltagetendsto”sag”or”droop”underload.Althoughthisthree-resistorcircuit<br />
shouldnotpresentaheavyenoughload(notenoughcurrentdrawn)tocausesignificantvoltage”sag,”measuringbatteryvoltageunderloadisagoodscientificpracticebecauseitprovides<br />
morerealisticdata.<br />
UseOhm’sLaw(I=E/R)tocalculatecircuitcurrent,thenverifythiscalculatedvalueby<br />
measuringcurrentwithanammeterlikethis(”terminalstrip”versionofthecircuitshownas<br />
anarbitrarychoiceinconstructionmethod):
70 CHAPTER3. DCCIRCUITS<br />
V<br />
A<br />
V<br />
OFF<br />
A<br />
A COM<br />
+ - R 2<br />
R 1 R 3<br />
Ifyourresistorvaluesareindeedbetween1kΩand100kΩ,andthebatteryvoltageapproximately6volts,thecurrentshouldbeaverysmallvalue,inthemilliamp(mA)ormicroamp<br />
(µA)range. Whenyoumeasurecurrentwithadigitalmeter,themetermayshowtheappropriatemetricprefixsymbol(mor<br />
µ)insomecornerofthedisplay.Thesemetricprefixtelltales<br />
areeasytooverlookwhenreadingthedisplayofadigitalmeter,sopaycloseattention!<br />
ThemeasuredvalueofcurrentshouldagreecloselywithyourOhm’sLawcalculation.Now,<br />
takethatcalculatedvalueforcurrentandmultiplyitbytherespectiveresistancesofeach<br />
resistortopredicttheirvoltagedrops(E=IR).Switchyoumultimetertothe”voltage”modeand<br />
measurethevoltagedroppedacrosseachresistor,verifyingtheaccuracyofyourpredictions.<br />
Again,thereshouldbecloseagreementbetweenthecalculatedandmeasuredvoltagefigures.<br />
Eachresistorvoltagedropwillbesomefractionorpercentageofthetotalvoltage,hencethe<br />
namevoltagedividergiventothiscircuit.Thisfractionalvalueisdeterminedbytheresistance<br />
oftheparticularresistorandthetotalresistance.Ifaresistordrops50%ofthetotalbattery<br />
voltageinavoltagedividercircuit,thatproportionof50%willremainthesameaslongasthe<br />
resistorvaluesarenotaltered.So,ifthetotalvoltageis6volts,thevoltageacrossthatresistor<br />
willbe50%of6,or3volts. Ifthetotalvoltageis20volts,thatresistorwilldrop10volts,or<br />
50%of20volts.<br />
ThenextpartofthisexperimentisavalidationofKirchhoff’sVoltageLaw. Forthis,you<br />
needtoidentifyeachuniquepointinthecircuitwithanumber. Pointsthatareelectrically<br />
common(directlyconnectedtoeachotherwithinsignificantresistancebetween)mustbearthe<br />
samenumber. Anexampleusingthenumbers0through3isshownhereinbothillustrative
3.4. VOLTAGEDIVIDER 71<br />
andschematicform.Intheillustration,Ishowhowpointsinthecircuitmaybelabeledwith<br />
smallpiecesoftape,numberswrittenonthetape:<br />
0<br />
3<br />
3<br />
+ - R 1<br />
R 2<br />
R 3<br />
Terminal strip<br />
2<br />
1<br />
0<br />
3<br />
2<br />
1<br />
0<br />
3 3<br />
R 1<br />
2<br />
R 2<br />
R 3<br />
1<br />
0 0<br />
Usingadigitalvoltmeter(thisisimportant!),measurevoltagedropsaroundtheloopformed<br />
bythepoints0-1-2-3-0. Writeonpapereachofthesevoltages,alongwithitsrespectivesign<br />
asindicatedbythemeter. Inotherwords,ifthevoltmeterregistersanegativevoltagesuch<br />
as-1.325volts,youshouldwritethatfigureasanegativenumber. Donotreversethemeter<br />
probeconnectionswiththecircuittomakethenumberread”correctly.”Mathematicalsignis<br />
verysignificantinthisphaseoftheexperiment! Hereisasequenceofillustrationsshowing<br />
howto”steparound”thecircuitloop,startingandendingatpoint0:
72 CHAPTER3. DCCIRCUITS<br />
Measure voltage from<br />
1 to 0<br />
0<br />
V<br />
A<br />
3<br />
V<br />
OFF<br />
A<br />
3<br />
2<br />
1<br />
0<br />
A<br />
COM<br />
3<br />
+ - R 1<br />
R 2<br />
R 3<br />
2<br />
1<br />
0<br />
Measure voltage from<br />
2 to 1<br />
0<br />
V<br />
A<br />
3<br />
V<br />
OFF<br />
A<br />
3<br />
2<br />
1<br />
0<br />
A<br />
COM<br />
3<br />
+ - R 1<br />
R 2<br />
R 3<br />
2<br />
1<br />
0
3.4. VOLTAGEDIVIDER 73<br />
Measure voltage from<br />
3 to 2<br />
0<br />
V<br />
A<br />
3<br />
V<br />
OFF<br />
A<br />
3<br />
2<br />
1<br />
0<br />
A<br />
COM<br />
+ - R 1<br />
R 2<br />
R 3<br />
3<br />
2<br />
1<br />
0<br />
Measure voltage from<br />
0 to 3<br />
0<br />
V<br />
A<br />
3<br />
V<br />
OFF<br />
A<br />
3<br />
2<br />
1<br />
0<br />
A<br />
COM<br />
+ - R 1<br />
R 2<br />
R 3<br />
3<br />
2<br />
1<br />
0<br />
Usingthevoltmeterto”step”aroundthecircuitinthismanneryieldsthreepositivevoltage<br />
figuresandonenegative:
74 CHAPTER3. DCCIRCUITS<br />
3 3<br />
3-2<br />
(+)<br />
R 1<br />
2<br />
2-1<br />
(+)<br />
0-3<br />
(-)<br />
1-0<br />
(+)<br />
R 2<br />
1<br />
0 0<br />
R 3<br />
Thesefigures,algebraicallyadded(”algebraically”=respectingthesignsofthenumbers),<br />
shouldequalzero. ThisisthefundamentalprincipleofKirchhoff’sVoltageLaw: thatthe<br />
algebraicsumofallvoltagedropsina”loop”addtozero.<br />
Itisimportanttorealizethatthe”loop”steppedarounddoesnothavetobethesamepath<br />
thatcurrenttakesinthecircuit,orevenalegitimatecurrentpathatall.Theloopinwhichwe<br />
tallyvoltagedropscanbeanycollectionofpoints,solongasitbeginsandendswiththesame<br />
point. Forexample,wemaymeasureandaddthevoltagesintheloop1-2-3-1,andtheywill<br />
formasumofzeroaswell:<br />
3 3<br />
3-2<br />
(+)<br />
2-1<br />
(+)<br />
R 1<br />
2<br />
R 2<br />
1<br />
R 3<br />
1-3<br />
(-)<br />
0 0
3.4. VOLTAGEDIVIDER 75<br />
Measure voltage from<br />
2 to 1<br />
0<br />
V<br />
A<br />
3<br />
V<br />
OFF<br />
A<br />
3<br />
2<br />
1<br />
0<br />
A<br />
COM<br />
+ - R 1<br />
R 2<br />
R 3<br />
3<br />
2<br />
1<br />
0<br />
Measure voltage from<br />
3 to 2<br />
0<br />
V<br />
A<br />
3<br />
V<br />
OFF<br />
A<br />
3<br />
2<br />
1<br />
0<br />
A<br />
COM<br />
+ - R 1<br />
R 2<br />
R 3<br />
3<br />
2<br />
1<br />
0
76 CHAPTER3. DCCIRCUITS<br />
Measure voltage from<br />
1 to 3<br />
0<br />
V<br />
A<br />
3<br />
V<br />
OFF<br />
A<br />
3<br />
2<br />
1<br />
0<br />
A<br />
COM<br />
3<br />
+ - R 1<br />
R 2<br />
R 3<br />
2<br />
1<br />
0<br />
Trysteppingbetweenanysetofpoints,inanyorder,aroundyourcircuitandseeforyourself<br />
thatthealgebraicsumalwaysequalszero.ThisLawholdstruenomatterwhattheconfigurationofthecircuit:series,parallel,series-parallel,orevenanirreduciblenetwork.<br />
Kirchhoff’sVoltageLawisapowerfulconcept,allowingustopredictthemagnitudeand<br />
polarityofvoltagesinacircuitbydevelopingmathematicalequationsforanalysisbasedonthe<br />
truthofallvoltagesinaloopaddinguptozero.Thisexperimentisintendedtogiveempirical<br />
evidenceforandadeepunderstandingofKirchhoff’sVoltageLawasageneralprinciple.<br />
COMPUTERSIMULATION<br />
Netlist(makeatextfilecontainingthefollowingtext,verbatim):<br />
Voltage divider<br />
v1 3 0<br />
r1 3 2 5k<br />
r2 2 1 3k<br />
r3 1 0 2k<br />
.dc v1 6 6 1<br />
* Voltages around 0-1-2-3-0 loop algebraically add to zero:<br />
.print dc v(1,0) v(2,1) v(3,2) v(0,3)<br />
* Voltages around 1-2-3-1 loop algebraically add to zero:<br />
.print dc v(2,1) v(3,2) v(1,3)<br />
.end<br />
Thiscomputersimulationisbasedonthepointnumbersshowninthepreviousdiagrams<br />
forillustratingKirchhoff’sVoltageLaw(points0through3). Resistorvalueswerechosento<br />
provide50%,30%,and20%proportionsoftotalvoltageacrossR 1 ,R 2 ,andR 3 ,respectively.<br />
Feelfreetomodifythevoltagesourcevalue(inthe”.dc”line,shownhereas6volts),and/or<br />
theresistorvalues.<br />
Whenrun,SPICEwillprintalineoftextcontainingfourvoltagefigures,thenanother<br />
lineoftextcontainingthreevoltagefigures,alongwithlotsofothertextlinesdescribingthe
3.4. VOLTAGEDIVIDER 77<br />
analysisprocess.Addthevoltagefiguresineachlinetoseethatthesumiszero.
78 CHAPTER3. DCCIRCUITS<br />
3.5 Currentdivider<br />
PARTSANDMATERIALS<br />
• Calculator(orpencilandpaperfordoingarithmetic)<br />
• 6-voltbattery<br />
• Assortmentofresistorsbetween1KΩand100kΩinvalue<br />
CROSS-REFERENCES<br />
LessonsInElectricCircuits,Volume1,chapter6:”DividerCircuitsandKirchhoff’sLaws”<br />
LEARNINGOBJECTIVES<br />
• Voltmeteruse<br />
• Ammeteruse<br />
• Ohmmeteruse<br />
• UseofOhm’sLaw<br />
• UseofKirchhoff’sCurrentLaw(KCL)<br />
• Currentdividerdesign<br />
SCHEMATICDIAGRAM<br />
R 1 R 2 R 3<br />
+<br />
A Ammeter<br />
-<br />
ILLUSTRATION
3.5. CURRENTDIVIDER 79<br />
+ - R 1 R 2 R 3<br />
Breadboard<br />
Terminal<br />
+ - strip<br />
R 1 R 2 R 3<br />
Normally,itisconsideredimpropertosecuremorethantwowiresunderasingleterminal<br />
stripscrew. Inthisillustration,Ishowthreewiresjoiningatthetopscrewoftherightmost<br />
lugusedonthisstrip.Thisisdonefortheeaseofprovingaconcept(ofcurrentsummingata<br />
circuitnode),anddoesnotrepresentprofessionalassemblytechnique.
80 CHAPTER3. DCCIRCUITS<br />
Piece of stiff wire serves<br />
as a connection point<br />
+ - R 1 R 2 R 3<br />
"Free-form" construction<br />
INSTRUCTIONS<br />
Onceagain,Ishowdifferentmethodsofconstructingthesamecircuit:breadboard,terminal<br />
strip,and”free-form.”Experimentwithalltheseconstructionformatsandbecomefamiliar<br />
withtheirrespectiveadvantagesanddisadvantages.<br />
Selectthreeresistorsfromyourresistorassortmentandmeasuretheresistanceofeachone<br />
withanohmmeter. Notetheseresistancevalueswithpenandpaper,forreferenceinyour<br />
circuitcalculations.<br />
Connectthethreeresistorsinparalleltoandeachother,andwiththe6-voltbattery,as<br />
shownintheillustrations.Measurebatteryvoltagewithavoltmeteraftertheresistorshave<br />
beenconnectedtoit,notingthisvoltagefigureonpaperaswell. Itisadvisabletomeasure<br />
batteryvoltagewhileitspoweringtheresistorcircuitbecausethisvoltagemaydifferslightly<br />
fromano-loadcondition.<br />
Measurevoltageacrosseachofthethreeresistors.Whatdoyounotice?Inaseriescircuit,<br />
currentisequalthroughallcomponentsatanygiventime.Inaparallelcircuit,voltageisthe<br />
commonvariablebetweenallcomponents.<br />
Thenon-professionalnatureofthe”free-form”constructionmethodmeritsnofurthercomment.<br />
UseOhm’sLaw(I=E/R)tocalculatecurrentthrougheachresistor,thenverifythiscalculatedvaluebymeasuringcurrentwithadigitalammeter.Placetheredprobeoftheammeter<br />
atthepointwherethepositive(+)endsoftheresistorsconnecttoeachotherandliftoneresistorwireatatime,connectingthemeter’sblackprobetotheliftedwire.<br />
Inthismanner,<br />
measureeachresistorcurrent,notingboththemagnitudeofthecurrentandthepolarity.In<br />
theseillustrations,IshowanammeterusedtomeasurethecurrentthroughR 1 :
3.5. CURRENTDIVIDER 81<br />
V<br />
A<br />
V<br />
OFF<br />
A<br />
A<br />
COM<br />
+ - R 1 R 2 R 3<br />
Breadboard
82 CHAPTER3. DCCIRCUITS<br />
V<br />
A<br />
V<br />
OFF<br />
A<br />
A<br />
COM<br />
Terminal<br />
+ - strip<br />
R 1 R 2 R 3<br />
Measurecurrentforeachofthethreeresistors,comparingwiththecurrentfigurescalculatedpreviously.Withthedigitalammeterconnectedasshown,allthreeindicationsshouldbe<br />
positive,notnegative.<br />
Now,measuretotalcircuitcurrent,keepingtheammeter’sredprobeonthesamepoint<br />
ofthecircuit,butdisconnectingthewireleadingtothepositive(+)sideofthebatteryand<br />
touchingtheblackprobetoit:
3.5. CURRENTDIVIDER 83<br />
V<br />
A<br />
V<br />
OFF<br />
A<br />
A<br />
COM<br />
+ - R 1 R 2 R 3<br />
Breadboard
84 CHAPTER3. DCCIRCUITS<br />
V<br />
A<br />
V<br />
OFF<br />
A<br />
A<br />
COM<br />
Terminal<br />
+ - strip<br />
R 1 R 2 R 3<br />
Noteboththemagnitudeandthesignofthecurrentasindicatedbytheammeter.Addthis<br />
figure(algebraically)tothethreeresistorcurrents.Whatdoyounoticeabouttheresultthat<br />
issimilartotheKirchhoff’sVoltageLawexperiment?Kirchhoff’sCurrentLawistocurrents<br />
”summing”atapoint(node)inacircuit,justasKirchhoff’sVoltageLawistovoltagesadding<br />
inaseriesloop:inbothcases,thealgebraicsumisequaltozero.<br />
ThisLawisalsoveryusefulinthemathematicalanalysisofcircuits.AlongwithKirchhoff’s<br />
VoltageLaw,itallowsustogenerateequationsdescribingseveralvariablesinacircuit,which<br />
maythenbesolvedusingavarietyofmathematicaltechniques.<br />
Nowconsiderthefourcurrentmeasurementsasallpositivenumbers:thefirstthreerepresentingthecurrentthrougheachresistor,andthefourthrepresentingtotalcircuitcurrentas<br />
apositivesumofthethree”branch”currents.Eachresistor(branch)currentisafraction,or<br />
percentage,ofthetotalcurrent.Thisiswhyaparallelresistorcircuitisoftencalledacurrent<br />
divider.<br />
Disconnectthebatteryfromtherestofthecircuit,andmeasureresistanceacrosstheparallelresistors.Youmayreadtotalresistanceacrossanyoftheindividualresistors’terminals<br />
andobtainthesameindication:itwillbeavaluelessthananyoftheindividualresistorvalues.Thisisoftensurprisingtonewstudentsofelectricity,thatyoureadtheexactsame(total)<br />
resistancefigurewhenconnectinganohmmeteracrossanyoneofasetofparallel-connected<br />
resistors. Itmakessense,though,ifyouconsiderthepointsinaparallelcircuitintermsof<br />
electricalcommonality.Allparallelcomponentsareconnectedbetweentwosetsofelectrically
3.5. CURRENTDIVIDER 85<br />
commonpoints.Sincethemetercannotdistinguishbetweenpointscommontoeachotherby<br />
wayofdirectconnection,toreadresistanceacrossoneresistoristoreadtheresistanceofthem<br />
all.Thesameistrueforvoltage,whichiswhybatteryvoltagecouldbereadacrossanyoneof<br />
theresistorsaseasilyasitcouldbereadacrossthebatteryterminalsdirectly.<br />
Ifyoudividethebatteryvoltage(previouslymeasured)bythistotalresistancefigure,you<br />
shouldobtainafigurefortotalcurrent(I=E/R)closelymatchingthemeasuredfigure.<br />
Theratioofresistorcurrenttototalcurrentisthesameastheratiooftotalresistanceto<br />
individualresistance.Forexample,ifa10kΩresistorispartofacurrentdividercircuitwith<br />
atotalresistanceof1kΩ,thatresistorwillconduct1/10ofthetotalcurrent,whatevervalue<br />
thatcurrenttotalhappenstobe.<br />
COMPUTERSIMULATION<br />
SchematicwithSPICEnodenumbers:<br />
2 2 2 2<br />
V itotal V ir1 V ir2 V ir3<br />
V 1<br />
1<br />
3 4 5<br />
R 1 R 2 R 3<br />
0 0 0 0<br />
AmmetersinSPICEsimulationsareactuallyzero-voltagesourcesinsertedinthepathsof<br />
electronflow. YouwillnoticethevoltagesourcesV ir1 ,V ir2 ,andV ir3 aresetto0voltsinthe<br />
netlist.Whenelectronsenterthenegativesideofoneofthese”dummy”batteriesandoutthe<br />
positive,thebattery’scurrentindicationwillbeapositivenumber.Inotherwords,these0-volt<br />
sourcesaretoberegardedasammeterswiththeredprobeonthelong-linesideofthebattery<br />
symbolandtheblackprobeontheshort-lineside.<br />
Netlist(makeatextfilecontainingthefollowingtext,verbatim):<br />
Current divider<br />
v1 1 0<br />
r1 3 0 2k<br />
r2 4 0 3k<br />
r3 5 0 5k<br />
vitotal 2 1 dc 0<br />
vir1 2 3 dc 0<br />
vir2 2 4 dc 0<br />
vir3 2 5 dc 0<br />
.dc v1 6 6 1<br />
.print dc i(vitotal) i(vir1) i(vir2) i(vir3)<br />
.end
86 CHAPTER3. DCCIRCUITS<br />
Whenrun,SPICEwillprintalineoftextcontainingfourcurrentfigures,thefirstcurrent<br />
representingthetotalasanegativequantity,andtheotherthreerepresentingcurrentsfor<br />
resistorsR 1 ,R 2 ,andR 3 . Whenalgebraicallyadded,theonenegativefigureandthethree<br />
positivefigureswillformasumofzero,asdescribedbyKirchhoff’sCurrentLaw.
3.6. POTENTIOMETERASAVOLTAGEDIVIDER 87<br />
3.6 Potentiometerasavoltagedivider<br />
PARTSANDMATERIALS<br />
• Two6-voltbatteries<br />
• Carbonpencil”lead”foramechanical-stylepencil<br />
• Potentiometer,singleturn,5kΩto50kΩ,lineartaper(RadioShackcatalog#271-1714<br />
through271-1716)<br />
• Potentiometer,multiturn,1kΩto20kΩ,(RadioShackcatalog#271-342,271-343,900-<br />
8583,or900-8587through900-8590)<br />
Potentiometersarevariablevoltagedividerswithashaftorslidecontrolforsettingthe<br />
divisionratio. Theyaremanufacturedinpanel-mountaswellasbreadboard(printed-circuit<br />
board)mountversions.Anystyleofpotentiometerwillsufficeforthisexperiment.<br />
Ifyousalvageapotentiometerfromanoldradioorotheraudiodevice,youwilllikelybe<br />
gettingwhatiscalledanaudiotaperpotentiometer.Thesepotentiometersexhibitalogarithmicrelationshipbetweendivisionratioandshaftposition.Bycontrast,alinearpotentiometer<br />
exhibitsadirectcorrelationbetweenshaftpositionandvoltagedivisionratio.Ihighlyrecommendalinearpotentiometerforthisexperiment,andformostexperimentsingeneral.<br />
CROSS-REFERENCES<br />
LessonsInElectricCircuits,Volume1,chapter6:”DividerCircuitsandKirchhoff’sLaws”<br />
LEARNINGOBJECTIVES<br />
• Voltmeteruse<br />
• Ohmmeteruse<br />
• Voltagedividerdesignandfunction<br />
• Howvoltagesaddinseries<br />
SCHEMATICDIAGRAM<br />
Potentiometer<br />
+<br />
V<br />
-<br />
ILLUSTRATION
88 CHAPTER3. DCCIRCUITS<br />
+ - Pencil "lead"<br />
V<br />
V<br />
OFF<br />
A<br />
A<br />
A<br />
COM<br />
V<br />
A<br />
V<br />
OFF<br />
A<br />
+ - A COM<br />
Potentiometer
3.6. POTENTIOMETERASAVOLTAGEDIVIDER 89<br />
V<br />
A<br />
V<br />
OFF<br />
A<br />
+ - A<br />
Potentiometer<br />
COM<br />
INSTRUCTIONS<br />
Beginthisexperimentwiththepencil”lead”circuit.Pencilsusearodmadeofagraphiteclaymixture,notlead(themetal),tomakeblackmarksonpaper.Graphite,beingamediocre<br />
electricalconductor,actsasaresistorconnectedacrossthebatterybythetwoalligator-clip<br />
jumperwires. Connectthevoltmeterasshownandtouchtheredtestprobetothegraphite<br />
rod. Movetheredprobealongthelengthoftherodandnoticethevoltmeter’sindication<br />
change.Whatprobepositiongivesthegreatestvoltageindication?<br />
Essentially,therodactsasapairofresistors,theratiobetweenthetworesistancesestablishedbythepositionoftheredtestprobealongtherod’slength:
90 CHAPTER3. DCCIRCUITS<br />
+ - Pencil "lead"<br />
equivalent to<br />
Now,changethevoltmeterconnectiontothecircuitsoastomeasurevoltageacrossthe<br />
”upperresistor”ofthepencillead,likethis:<br />
+ - Pencil "lead"<br />
V<br />
V<br />
A<br />
OFF<br />
COM<br />
A<br />
A
3.6. POTENTIOMETERASAVOLTAGEDIVIDER 91<br />
Movetheblacktestprobepositionalongthelengthoftherod,notingthevoltmeterindication.Whichpositiongivesthegreatestvoltagedropforthemetertomeasure?Doesthisdiffer<br />
fromthepreviousarrangement?Why?<br />
Manufacturedpotentiometersenclosearesistivestripinsideametalorplastichousing,<br />
andprovidesomekindofmechanismformovinga”wiper”acrossthelengthofthatresistive<br />
strip.Hereisanillustrationofarotarypotentiometer’sconstruction:<br />
Terminals<br />
Rotary potentiometer<br />
construction<br />
Wiper<br />
Resistive strip<br />
Somerotarypotentiometershaveaspiralresistivestrip,andawiperthatmovesaxiallyas<br />
itrotates,soastorequiremultipleturnsoftheshafttodrivethewiperfromoneendofthe<br />
potentiometer’srangetotheother.Multi-turnpotentiometersareusedinapplicationswhere<br />
precisesettingisimportant.<br />
Linearpotentiometersalsocontainaresistivestrip,theonlydifferencebeingthewiper’s<br />
directionoftravel.Somelinearpotentiometersuseaslidemechanismtomovethewiper,while<br />
othersascrew,tofacilitatemultiple-turnoperation:<br />
Linear potentiometer construction<br />
Wiper<br />
Resistive strip<br />
Terminals<br />
Itshouldbenotedthatnotalllinearpotentiometershavethesamepinassignments. On<br />
some,themiddlepinisthewiper.<br />
Setupacircuitusingamanufacturedpotentiometer,notthe”home-made”onemadefrom<br />
apencillead.Youmayuseanyformofconstructionthatisconvenient.<br />
Measurebatteryvoltagewhilepoweringthepotentiometer,andmakenoteofthisvoltage<br />
figureonpaper. Measurevoltagebetweenthewiperandthepotentiometerendconnectedto<br />
thenegative(-)sideofthebattery. Adjustthepotentiometermechanismuntilthevoltmeter
92 CHAPTER3. DCCIRCUITS<br />
registersexactly1/3oftotalvoltage.Fora6-voltbattery,thiswillbeapproximately2volts.<br />
Now,connecttwobatteriesinaseries-aidingconfiguration,toprovideapproximately12<br />
voltsacrossthepotentiometer.Measurethetotalbatteryvoltage,andthenmeasurethevoltagebetweenthesametwopointsonthepotentiometer(wiperandnegativeside).Dividethe<br />
potentiometer’smeasuredoutputvoltagebythemeasuredtotalvoltage.Thequotientshould<br />
be1/3,thesamevoltagedivisionratioaswassetpreviously:<br />
V<br />
A<br />
V<br />
OFF<br />
A<br />
+ - A COM<br />
+ - Voltmeter measuring output<br />
of potentiometer.
3.7. POTENTIOMETERASARHEOSTAT 93<br />
3.7 Potentiometerasarheostat<br />
PARTSANDMATERIALS<br />
• 6voltbattery<br />
• Potentiometer,singleturn,5kΩ,lineartaper(RadioShackcatalog#271-1714)<br />
• Small”hobby”motor,permanent-magnettype(RadioShackcatalog#273-223orequivalent)<br />
Forthisexperiment,youwillneedarelativelylow-valuepotentiometer,certainlynotmore<br />
than5kΩ.<br />
CROSS-REFERENCES<br />
LessonsInElectricCircuits,Volume1,chapter2:”Ohm’sLaw”<br />
LEARNINGOBJECTIVES<br />
• Rheostatuse<br />
• Wiringapotentiometerasarheostat<br />
• Simplemotorspeedcontrol<br />
• Useofvoltmeteroverammetertoverifyacontinuouscircuit<br />
SCHEMATICDIAGRAM<br />
Mtr<br />
ILLUSTRATION
94 CHAPTER3. DCCIRCUITS<br />
+ - optional<br />
Potentiometer<br />
Motor<br />
INSTRUCTIONS<br />
Potentiometersfindtheirmostsophisticatedapplicationasvoltagedividers,whereshaft<br />
positiondeterminesaspecificvoltagedivisionratio.However,thereareapplicationswherewe<br />
don’tnecessarilyneedavariablevoltagedivider,butmerelyavariableresistor:atwo-terminal<br />
device.Technically,avariableresistorisknownasarheostat,butpotentiometerscanbemade<br />
tofunctionasrheostatsquiteeasily.<br />
Initssimplestconfiguration,apotentiometermaybeusedasarheostatbysimplyusing<br />
thewiperterminalandoneoftheotherterminals,thethirdterminalleftunconnectedand<br />
unused:<br />
Mtr
3.7. POTENTIOMETERASARHEOSTAT 95<br />
+ - Potentiometer<br />
Motor<br />
Movingthepotentiometercontrolinthedirectionthatbringsthewiperclosesttotheother<br />
usedterminalresultsinalowerresistance. Thedirectionofmotionrequiredtoincreaseor<br />
decreaseresistancemaybechangedbyusingadifferentsetofterminals:<br />
Less resistance when turned clockwise<br />
More resistance when turned clockwise<br />
Wiper<br />
Resistive strip<br />
Wiper<br />
Resistive strip<br />
Becareful,though,thatyoudon’tusethetwoouterterminals,asthiswillresultinno<br />
changeinresistanceasthepotentiometershaftisturned. Inotherwords,itwillnolonger<br />
functionasavariableresistance:
96 CHAPTER3. DCCIRCUITS<br />
No resistance change when wiper moves!<br />
Buildthecircuitasshownintheschematicandillustration,usingjusttwoterminalson<br />
thepotentiometer,andseehowmotorspeedmaybecontrolledbyadjustingshaftposition.<br />
Experimentwithdifferentterminalconnectionsonthepotentiometer,notingthechangesin<br />
motorspeedcontrol. Ifyourpotentiometerhasahighresistance(asmeasuredbetweenthe<br />
twoouterterminals),themotormightnotmoveatalluntilthewiperisbroughtverycloseto<br />
theconnectedouterterminal.<br />
Asyoucansee,motorspeedmaybemadevariableusingaseries-connectedrheostatto<br />
changetotalcircuitresistanceandlimittotalcurrent. Thissimplemethodofmotorspeed<br />
control,however,isinefficient,asitresultsinsubstantialamountsofpowerbeingdissipated<br />
(wasted)bytherheostat.Amuchmoreefficientmeansofmotorcontrolreliesonfast”pulsing”<br />
ofpowertothemotor,usingahigh-speedswitchingdevicesuchasatransistor. Asimilar<br />
methodofpowercontrolisusedinhouseholdlight”dimmer”switches. Unfortunately,these<br />
techniquesaremuchtoosophisticatedtoexploreatthispointintheexperiments.<br />
Whenapotentiometerisusedasarheostat,the”unused”terminalisoftenconnectedtothe<br />
wiperterminal,likethis:<br />
Mtr<br />
Atfirst,thisseemsratherpointless,asithasnoimpactonresistancecontrol. Youmay<br />
verifythisfactforyourselfbyinsertinganotherwireinyourcircuitandcomparingmotor<br />
behaviorbeforeandafterthechange:
3.7. POTENTIOMETERASARHEOSTAT 97<br />
+ - add wire<br />
Potentiometer<br />
Motor<br />
Ifthepotentiometerisingoodworkingorder,thisadditionalwiremakesnodifference<br />
whatsoever.However,ifthewipereverlosescontactwiththeresistivestripinsidethepotentiometer,thisconnectionensuresthecircuitdoesnotcompletelyopen:thattherewillstillbe<br />
aresistivepathforcurrentthroughthemotor. Insomeapplications,thismaybeanimportant.Oldpotentiometerstendtosufferfromintermittentlossesofcontactbetweenthewiper<br />
andtheresistivestrip,andifacircuitcannottoleratethecompletelossofcontinuity(infinite<br />
resistance)createdbythiscondition,that”extra”wireprovidesameasureofprotectionby<br />
maintainingcircuitcontinuity.<br />
Youmaysimulatesuchawipercontact”failure”bydisconnectingthepotentiometer’smiddleterminalfromtheterminalstrip,measuringvoltageacrossthemotortoensurethereis<br />
stillpowergettingtoit,howeversmall:
98 CHAPTER3. DCCIRCUITS<br />
+ -<br />
break connection<br />
V<br />
A<br />
V<br />
OFF<br />
A<br />
A<br />
COM<br />
Itwouldhavebeenvalidtomeasurecircuitcurrentinsteadofmotorvoltagetoverifya<br />
completedcircuit,butthisisasafermethodbecauseitdoesnotinvolvebreakingthecircuit<br />
toinsertanammeterinseries.Wheneveranammeterisused,thereisriskofcausingashort<br />
circuitbyconnectingitacrossasubstantialvoltagesource,possiblyresultingininstrument<br />
damageorpersonalinjury.Voltmeterslackthisinherentsafetyrisk,andsowheneveravoltage<br />
measurementmaybemadeinsteadofacurrentmeasurementtoverifythesamething,itis<br />
thewiserchoice.
3.8. PRECISIONPOTENTIOMETER 99<br />
3.8 Precisionpotentiometer<br />
PARTSANDMATERIALS<br />
• Twosingle-turn,linear-taperpotentiometers,5kΩeach(RadioShackcatalog#271-1714)<br />
• Onesingle-turn,linear-taperpotentiometer,50kΩ(RadioShackcatalog#271-1716)<br />
• Plasticormetalmountingbox<br />
• Three”banana”jackstylebindingposts,orotherterminalhardware,forconnectionto<br />
potentiometercircuit(RadioShackcatalog#274-662orequivalent)<br />
Thisisaprojectusefultothosewhowantaprecisionpotentiometerwithoutspendingalot<br />
ofmoney.Ordinarily,multi-turnpotentiometersareusedtoobtainprecisevoltagedivisionratios,butacheaperalternativeexistsusingmultiple,single-turn(sometimescalled”3/4-turn”)<br />
potentiometersconnectedtogetherinacompounddividernetwork.<br />
Becausethisisausefulproject,Irecommendbuildingitinpermanentformusingsome<br />
formofprojectenclosure. SupplierssuchasRadioShackofferniceprojectboxes,butboxes<br />
purchasedatageneralhardwarestorearemuchlessexpensive,ifabitugly. Theultimate<br />
inlowcostforanewboxaretheplasticboxessoldaslightswitchandreceptacleboxesfor<br />
householdelectricalwiring.<br />
”Banana”jacksallowforthetemporaryconnectionoftestleadsandjumperwiresequipped<br />
withmatching”banana”plugends. Mostmultimetertestleadshavethisstyleofplugfor<br />
insertionintothemeterjacks.Bananaplugsaresonamedbecauseoftheiroblongappearance<br />
formedbyspringsteelstrips,whichmaintainfirmcontactwiththejackwallswheninserted.<br />
Somebananajacksarecalledbindingpostsbecausetheyalsoallowplainwirestobefirmly<br />
attached.Bindingpostshavescrew-onsleevesthatfitoverametalpost.Thesleeveisusedasa<br />
nuttosecureawirewrappedaroundthepost,orinsertedthroughaperpendicularholedrilled<br />
throughthepost.Abriefinspectionofanybindingpostwillclarifythisverbaldescription.<br />
CROSS-REFERENCES<br />
LessonsInElectricCircuits,Volume1,chapter6:”DividerCircuitsandKirchhoff’sLaws”<br />
LEARNINGOBJECTIVES<br />
• Solderingpractice<br />
• Potentiometerfunctionandoperation<br />
SCHEMATICDIAGRAM
100 CHAPTER3. DCCIRCUITS<br />
R 1<br />
5 kΩ<br />
R 3<br />
50<br />
kΩ<br />
+<br />
R 2 V<br />
5 kΩ<br />
-<br />
ILLUSTRATION<br />
V<br />
A<br />
V<br />
OFF<br />
A<br />
R 1<br />
5 kΩ<br />
R 2<br />
50 kΩ<br />
+ - 5 kΩ<br />
R 3<br />
A COM<br />
INSTRUCTIONS<br />
Itisessentialthattheconnectingwiresbesolderedtothepotentiometerterminals,not<br />
twistedortaped. Sincepotentiometeractionisdependentonresistance,theresistanceof<br />
allwiringconnectionsmustbecarefullycontrolledtoabareminimum. Solderingensuresa<br />
conditionoflowresistancebetweenjoinedconductors,andalsoprovidesverygoodmechanical<br />
strengthfortheconnections.<br />
Whenthecircuitisassembled,connecta6-voltbatterytotheoutertwobindingposts.<br />
Connectavoltmeterbetweenthe”wiper”postandthebattery’snegative(-)terminal. This<br />
voltmeterwillmeasurethe”output”ofthecircuit.<br />
Thecircuitworksontheprincipleofcompressedrange: thevoltageoutputrangeofthis<br />
circuitavailablebyadjustingpotentiometerR 3 isrestrictedbetweenthelimitssetbypotentiometersR<br />
1 andR 2 . Inotherwords,ifR 1 andR 2 weresettooutput5voltsand3volts,
3.8. PRECISIONPOTENTIOMETER 101<br />
respectively,froma6-voltbattery,therangeofoutputvoltagesobtainablebyadjustingR 3<br />
wouldberestrictedfrom3to5voltsforthefullrotationofthatpotentiometer.Ifonlyasingle<br />
potentiometerwereusedinsteadofthisthree-potentiometercircuit,fullrotationwouldproduceanoutputvoltagefrom0voltstofullbatteryvoltage.The”rangecompression”afforded<br />
bythiscircuitallowsformoreprecisevoltageadjustmentthanwouldbenormallyobtainable<br />
usingasinglepotentiometer.<br />
Operatingthispotentiometernetworkismorecomplexthanusingasinglepotentiometer.<br />
Tobegin,turntheR 3 potentiometerfullyclockwise,sothatitswiperisinthefull”up”position<br />
asreferencedtotheschematicdiagram(electrically”closest”toR 1 ’swiperterminal). Adjust<br />
potentiometerR 1 untiltheuppervoltagelimitisreached,asindicatedbythevoltmeter.<br />
TurntheR 3 potentiometerfullycounter-clockwise,sothatitswiperisinthefull”down”<br />
positionasreferencedtotheschematicdiagram(electrically”closest”toR 2 ’swiperterminal).<br />
AdjustpotentiometerR 2 untilthelowervoltagelimitisreached,asindicatedbythevoltmeter.<br />
WheneithertheR 1 ortheR 2 potentiometerisadjusted,itinterfereswiththepriorsetting<br />
oftheother.Inotherwords,ifR 1 isinitiallyadjustedtoprovideanuppervoltagelimitof5.000<br />
voltsfroma6voltbattery,andthenR 2 isadjustedtoprovidesomelowerlimitvoltagedifferent<br />
fromwhatitwasbefore,R 1 willnolongerbesetto5.000volts.<br />
Toobtainpreciseupperandlowervoltagelimits,turnR 3 fullyclockwisetoreadandadjust<br />
thevoltageofR 1 ,thenturnR 3 fullycounter-clockwisetoreadandadjustthevoltageofR 2 ,<br />
repeatingasnecessary.<br />
Technically,thisphenomenonofoneadjustmentaffectingtheotherisknownasinteraction,<br />
anditisusuallyundesirableduetotheextraeffortrequiredtosetandre-settheadjustments.<br />
ThereasonthatR 1 andR 2 werespecifiedas10timeslessresistancethanR 3 istominimizethis<br />
effect. Ifallthreepotentiometerswereofequalresistancevalue,theinteractionbetweenR 1<br />
andR 2 wouldbemoresevere,thoughmanageablewithpatience.Bearinmindthattheupper<br />
andlowervoltagelimitsneednotbesetpreciselyinorderforthiscircuittoachieveitsgoalof<br />
increasedprecision.SolongasR 3 ’sadjustmentrangeiscompressedtosomelesservaluethan<br />
fullbatteryvoltage,wewillenjoygreaterprecisionthanasinglepotentiometercouldprovide.<br />
Oncetheupperandlowervoltagelimitshavebeenset,potentiometerR 3 maybeadjusted<br />
toproduceanoutputvoltageanywherebetweenthoselimits.
102 CHAPTER3. DCCIRCUITS<br />
3.9 Rheostatrangelimiting<br />
PARTSANDMATERIALS<br />
• Several10kΩresistors<br />
• One10kΩpotentiometer,lineartaper(RadioShackcatalog#271-1715)<br />
CROSS-REFERENCES<br />
LessonsInElectricCircuits,Volume1,chapter5:”SeriesandParallelCircuits”<br />
LessonsInElectricCircuits,Volume1,chapter7:”Series-ParallelCombinationCircuits”<br />
LessonsInElectricCircuits,Volume1,chapter8:”DCMeteringCircuits”<br />
LEARNINGOBJECTIVES<br />
• Series-parallelresistances<br />
• Calibrationtheoryandpractice<br />
SCHEMATICDIAGRAM<br />
R total<br />
ILLUSTRATION
3.9. RHEOSTATRANGELIMITING 103<br />
V<br />
A<br />
V<br />
OFF<br />
A<br />
A<br />
COM<br />
INSTRUCTIONS<br />
Thisexperimentexploresthedifferentresistancerangesobtainablefromcombiningfixedvalueresistorswithapotentiometerconnectedasarheostat.Tobegin,connecta10kΩpotentiometerasarheostatwithnootherresistorsconnected.Adjustingthepotentiometerthrough<br />
itsfullrangeoftravelshouldresultinaresistancethatvariessmoothlyfrom0Ωto10,000 Ω:
104 CHAPTER3. DCCIRCUITS<br />
V<br />
A<br />
V<br />
OFF<br />
A<br />
A<br />
COM<br />
Supposewewantedtoelevatethelowerendofthisresistancerangesothatwehadan<br />
adjustablerangefrom10kΩto20kΩwithafullsweepofthepotentiometer’sadjustment.This<br />
couldbeeasilyaccomplishedbyaddinga10kΩresistorinserieswiththepotentiometer.Add<br />
onetothecircuitasshownandre-measuretotalresistancewhileadjustingthepotentiometer:
3.9. RHEOSTATRANGELIMITING 105<br />
V<br />
A<br />
V<br />
OFF<br />
A<br />
A<br />
COM<br />
Ashiftinthelowendofanadjustmentrangeiscalledazerocalibration,inmetrological<br />
terms. Withtheadditionofaseries10kΩresistor,the”zeropoint”wasshiftedupwardby<br />
10,000 Ω.Thedifferencebetweenhighandlowendsofarange–calledthespanofthecircuit<br />
–hasnotchanged,though:arangeof10kΩto20kΩhasthesame10,000 Ωspanasarange<br />
of0Ωto10kΩ. Ifwewishtoshiftthespanofthisrheostatcircuitaswell,wemustchange<br />
therangeofthepotentiometeritself.Wecouldreplacethepotentiometerwithoneofanother<br />
value,orwecouldsimulatealower-valuepotentiometerbyplacingaresistorinparallelwith<br />
it,diminishingitsmaximumobtainableresistance.Thiswilldecreasethespanofthecircuit<br />
from10kΩtosomethingless.<br />
Adda10kΩresistorinparallelwiththepotentiometer,toreducethespantoone-halfofits<br />
formervalue:from10KΩto5kΩ.Nowthecalibratedresistancerangeofthiscircuitwillbe<br />
10kΩto15kΩ:
106 CHAPTER3. DCCIRCUITS<br />
V<br />
A<br />
V<br />
OFF<br />
A<br />
A<br />
COM<br />
Thereisnothingwecandotoincreasethespanofthisrheostatcircuit,shortofreplacing<br />
thepotentiometerwithanotherofgreatertotalresistance. Addingresistorsinparallelcan<br />
onlydecreasethespan.However,thereisnosuchrestrictionwithcalibratingthezeropointof<br />
thiscircuit,asitbeganat0Ωandmaybemadeasgreataswewishbyaddingresistancein<br />
series.<br />
Amultitudeofresistancerangesmaybeobtainedusingonly10KΩfixed-valueresistors,if<br />
wearecreativewithseries-parallelcombinationsofthem.Forinstance,wecancreatearange<br />
of7.5kΩto10kΩbybuildingthefollowingcircuit:
3.9. RHEOSTATRANGELIMITING 107<br />
R total<br />
2.5 kΩ 5 kΩ<br />
0 to 2.5 kΩ<br />
All resistors = 10 kΩ<br />
V<br />
A<br />
V<br />
OFF<br />
A<br />
A<br />
COM<br />
Creatingacustomresistancerangefromfixed-valueresistorsandapotentiometerisa<br />
veryusefultechniqueforproducingpreciseresistancesrequiredforcertaincircuits,especially<br />
metercircuits. Inmanyelectricalinstruments–multimetersespecially–resistanceisthe<br />
determiningfactorfortheinstrument’srangeofmeasurement. Ifaninstrument’sinternal<br />
resistancevaluesarenotprecise,neitherwillitsindicationsbe.Findingafixed-valueresistor
108 CHAPTER3. DCCIRCUITS<br />
ofjusttherightresistanceforplacementinaninstrumentcircuitdesignisunlikely,socustomresistance”networks”mayneedtobebuilttoprovidethedesiredresistance.<br />
Havinga<br />
potentiometeraspartoftheresistornetworkprovidesameansofcorrectionifthenetwork’s<br />
resistanceshould”drift”fromitsoriginalvalue. Designingthenetworkforminimumspan<br />
ensuresthatthepotentiometer’seffectwillbesmall,sothatpreciseadjustmentispossibleand<br />
sothataccidentalmovementofitsmechanismwillnotresultinseverecalibrationerrors.<br />
Experimentwithdifferentresistor”networks”andnotetheeffectsontotalresistancerange.
3.10. THERMOELECTRICITY 109<br />
3.10 Thermoelectricity<br />
PARTSANDMATERIALS<br />
• Lengthofbare(uninsulated)copperwire<br />
• Lengthofbare(uninsulated)ironwire<br />
• Candle<br />
• Icecubes<br />
Ironwiremaybeobtainedfromahardwarestore.Ifsomecannotbefound,aluminumwire<br />
alsoworks.<br />
CROSS-REFERENCES<br />
LessonsInElectricCircuits,Volume1,chapter9:”<strong>Electrical</strong>InstrumentationSignals”<br />
LEARNINGOBJECTIVES<br />
• Thermocouplefunctionandpurpose<br />
SCHEMATICDIAGRAM<br />
Thermocouple<br />
+<br />
V<br />
-<br />
Voltmeter<br />
ILLUSTRATION
110 CHAPTER3. DCCIRCUITS<br />
V<br />
A<br />
V<br />
OFF<br />
A<br />
A<br />
COM<br />
iron wire<br />
copper wire<br />
Candle<br />
INSTRUCTIONS<br />
Twistoneendoftheironwiretogetherwithoneendofthecopperwire.Connectthefree<br />
endsofthesewirestorespectiveterminalsonaterminalstrip.Setyourvoltmetertoitsmost<br />
sensitiverangeandconnectittotheterminalswherethewiresattach. Themetershould<br />
indicatenearlyzerovoltage.<br />
Whatyouhavejustconstructedisathermocouple:adevicewhichgeneratesasmallvoltage<br />
proportionaltothetemperaturedifferencebetweenthetipandthemeterconnectionpoints.<br />
Whenthetipisatatemperatureequaltotheterminalstrip,therewillbenovoltageproduced,<br />
andthusnoindicationseenonthevoltmeter.<br />
Lightacandleandinsertthetwisted-wiretipintotheflame.Youshouldnoticeanindication<br />
onyourvoltmeter.Removethethermocoupletipfromtheflameandletcooluntilthevoltmeter<br />
indicationisnearlyzeroagain. Now,touchthethermocoupletiptoanicecubeandnotethe<br />
voltageindicatedbythemeter.Isitagreaterorlessermagnitudethantheindicationobtained<br />
withtheflame? Howdoesthepolarityofthisvoltagecomparewiththatgeneratedbythe<br />
flame?<br />
Aftertouchingthethermocoupletiptotheicecube,warmitbyholdingitbetweenyour<br />
fingers.Itmaytakeashortwhiletoreachbodytemperature,sobepatientwhileobservingthe<br />
voltmeter’sindication.
3.10. THERMOELECTRICITY 111<br />
AthermocoupleisanapplicationoftheSeebeckeffect: theproductionofasmallvoltage<br />
proportionaltoatemperaturegradientalongthelengthofawire. Thisvoltageisdependent<br />
uponthemagnitudeofthetemperaturedifferenceandthetypeofwire. Directlymeasuring<br />
theSeebeckvoltageproducedalongalengthofcontinuouswirefromatemperaturegradient<br />
isquitedifficult,andsowillnotbeattemptedinthisexperiment.<br />
Thermocouples,beingmadeoftwodissimilarmetalsjoinedatoneend,produceavoltage<br />
proportionaltothetemperatureofthejunction. Thetemperaturegradientalongbothwires<br />
resultingfromaconstanttemperatureatthejunctionproducesdifferentSeebeckvoltages<br />
alongthosewires’lengths,becausethewiresaremadeofdifferentmetals. Theresultant<br />
voltagebetweenthetwofreewireendsisthedifferencebetweenthetwoSeebeckvoltages:<br />
iron wire voltage<br />
HOT<br />
COOL<br />
copper wire voltage<br />
Resultant<br />
voltage<br />
Thermocouplesarewidelyusedastemperature-sensingdevicesbecausethemathematicalrelationshipbetweentemperaturedifferenceandresultantvoltageisbothrepeatableand<br />
fairlylinear. Bymeasuringvoltage,itispossibletoinfertemperature. Differentrangesof<br />
temperaturemeasurementarepossiblebyselectingdifferentmetalpairstobejoinedtogether.
112 CHAPTER3. DCCIRCUITS<br />
3.11 Makeyourownmultimeter<br />
PARTSANDMATERIALS<br />
• Sensitivemetermovement(RadioShackcatalog#22-410)<br />
• Selectorswitch,single-pole,multi-throw,break-before-make(RadioShackcatalog#275-<br />
1386isa2-pole,6-positionunitthatworkswell)<br />
• Multi-turnpotentiometers,PCBmount(RadioShackcatalog#271-342and271-343are<br />
15-turn,1kΩand10kΩ”trimmer”units,respectively)<br />
• Assortedresistors,preferablyhigh-precisionmetalfilmorwire-woundtypes(RadioShack<br />
catalog#271-309isanassortmentofmetal-filmresistors,+/-1%tolerance)<br />
• Plasticormetalmountingbox<br />
• Three”banana”jackstylebindingposts,orotherterminalhardware,forconnectionto<br />
potentiometercircuit(RadioShackcatalog#274-662orequivalent)<br />
Themostimportantandexpensivecomponentinameteristhemovement: theactual<br />
needle-and-scalemechanismwhosetaskitistotranslateanelectricalcurrentintomechanical<br />
displacementwhereitmaybevisuallyinterpreted. Theidealmetermovementisphysically<br />
large(foreaseofviewing)andassensitiveaspossible(requiresminimalcurrenttoproduce<br />
full-scaledeflectionoftheneedle). High-qualitymetermovementsareexpensive,butRadio<br />
Shackcarriessomeofacceptablequalitythatarereasonablypriced.Themodelrecommended<br />
inthepartslistissoldasavoltmeterwitha0-15voltrange,butisactuallyamilliammeter<br />
witharange(”multiplier”)resistorincludedseparately.<br />
Itmaybecheapertopurchaseaninexpensiveanalogmeteranddisassembleitforthemeter<br />
movementalone. Althoughthethoughtofdestroyingaworkingmultimeterinordertohave<br />
partstomakeyourownmaysoundcounter-productive,thegoalhereislearning,notmeter<br />
function.<br />
Icannotspecifyresistorvaluesforthisexperiment,asthesedependontheparticularmeter<br />
movementandmeasurementrangeschosen. Besuretousehigh-precisionfixed-valueresistorsratherthancarbon-compositionresistors.Evenifyouhappentofindcarbon-composition<br />
resistorsofjusttherightvalue(s),thosevalueswillchangeor”drift”overtimeduetoaging<br />
andtemperaturefluctuations.Ofcourse,ifyoudon’tcareaboutthelong-termstabilityofthis<br />
meterbutarebuildingitjustforthelearningexperience,resistorprecisionmatterslittle.<br />
CROSS-REFERENCES<br />
LessonsInElectricCircuits,Volume1,chapter8:”DCMeteringCircuits”<br />
LEARNINGOBJECTIVES<br />
• Voltmeterdesignanduse<br />
• Ammeterdesignanduse<br />
• Rheostatrangelimiting
3.11. MAKEYOUROWNMULTIMETER 113<br />
• Calibrationtheoryandpractice<br />
• Solderingpractice<br />
SCHEMATICDIAGRAM<br />
Movement<br />
-<br />
+<br />
R shunt<br />
R multiplier1<br />
R multiplier2<br />
A<br />
mA<br />
V<br />
Off<br />
R multiplier3<br />
V<br />
V<br />
"Common"<br />
jack<br />
A<br />
V/mA<br />
"R multiplier " resistors are actually rheostat networks<br />
R multiplier<br />
ILLUSTRATION
114 CHAPTER3. DCCIRCUITS<br />
Meter<br />
movement<br />
Common<br />
- +<br />
R shunt<br />
A<br />
V/mA<br />
Selector<br />
switch<br />
INSTRUCTIONS<br />
First,youneedtodeterminethecharacteristicsofyourmetermovement.Mostimportant<br />
istoknowthefullscaledeflectioninmilliampsormicroamps. Todeterminethis,connect<br />
themetermovement,apotentiometer,battery,anddigitalammeterinseries. Adjustthepotentiometeruntilthemetermovementisdeflectedexactlytofull-scale.<br />
Readtheammeter’s<br />
displaytofindthefull-scalecurrentvalue:
3.11. MAKEYOUROWNMULTIMETER 115<br />
Meter<br />
movement<br />
- +<br />
+ - Potentiometer<br />
V<br />
A<br />
V<br />
OFF<br />
A<br />
A<br />
COM<br />
Beverycarefulnottoapplytoomuchcurrenttothemetermovement,asmovementsare<br />
verysensitivedevicesandeasilydamagedbyovercurrent.Mostmetermovementshavefullscaledeflectioncurrentratingsof1mAorless,sochooseapotentiometervaluehighenough<br />
tolimitcurrentappropriately,andbegintestingwiththepotentiometerturnedtomaximum<br />
resistance.Thelowerthefull-scalecurrentratingofamovement,themoresensitiveitis.<br />
Afterdeterminingthefull-scalecurrentratingofyourmetermovement,youmustaccuratelymeasureitsinternalresistance.<br />
Todothis,disconnectallcomponentsfromtheprevioustestingcircuitandconnectyourdigitalohmmeteracrossthemetermovementterminals.<br />
Recordthisresistancefigurealongwiththefull-scalecurrentfigureobtainedinthelastprocedure.<br />
Perhapsthemostchallengingportionofthisprojectisdeterminingtheproperrangeresistancevaluesandimplementingthosevaluesintheformofrheostatnetworks.Thecalculations<br />
areoutlinedinchapter8ofvolume1(”MeteringCircuits”),butanexampleisgivenhere.Supposeyourmetermovementhadafull-scaleratingof1mAandaninternalresistanceof400<br />
Ω.Ifwewantedtodeterminethenecessaryrangeresistance(”R multiplier ”)togivethismovementarangeof0to15volts,wewouldhavetodivide15volts(totalappliedvoltage)by1mA<br />
(full-scalecurrent)toobtainthetotalprobe-to-proberesistanceofthevoltmeter(R=E/I).For<br />
thisexample,thattotalresistanceis15kΩ.Fromthistotalresistancefigure,wesubtractthe<br />
movement’sinternalresistance,leaving14.6kΩfortherangeresistorvalue.Asimplerheostat<br />
networktoproduce14.6kΩ(adjustable)wouldbea10kΩpotentiometerinparallelwitha10<br />
kΩfixedresistor,allinserieswithanother10kΩfixedresistor:
116 CHAPTER3. DCCIRCUITS<br />
≈ 15 kΩ, adjustable<br />
10 kΩ<br />
10 kΩ<br />
10 kΩ<br />
Onepositionoftheselectorswitchdirectlyconnectsthemetermovementbetweentheblack<br />
CommonbindingpostandtheredV/mAbindingpost.Inthisposition,themeterisasensitive<br />
ammeterwitharangeequaltothefull-scalecurrentratingofthemetermovement. Thefar<br />
clockwisepositionoftheswitchdisconnectsthepositive(+)terminalofthemovementfrom<br />
eitherredbindingpostandshortsitdirectlytothenegative(-)terminal. Thisprotectsthe<br />
meterfromelectricaldamagebyisolatingitfromtheredtestprobe,andit”dampens”the<br />
needlemechanismtofurtherguardagainstmechanicalshock.<br />
Theshuntresistor(R shunt )necessaryforahigh-currentammeterfunctionneedstobea<br />
low-resistanceunitwithahighpowerdissipation. Youwilldefinitelynotbeusingany1/4<br />
wattresistorsforthis,unlessyouformaresistancenetworkwithseveralsmallerresistorsin<br />
parallelcombination.Ifyouplanonhavinganammeterrangeinexcessof1amp,Irecommend<br />
usingathickpieceofwireorevenaskinnypieceofsheetmetalasthe”resistor,”suitablyfiled<br />
ornotchedtoprovidejusttherightamountofresistance.<br />
Tocalibrateahome-madeshuntresistor,youwillneedtoconnecttheyourmultimeter<br />
assemblytoacalibratedsourceofhighcurrent,orahigh-currentsourceinserieswithadigital<br />
ammeterforreference.Useasmallmetalfiletoshaveoffshuntwirethicknessortonotchthe<br />
sheetmetalstripinsmall,carefulamounts. Theresistanceofyourshuntwillincreasewith<br />
everystrokeofthefile,causingthemetermovementtodeflectmorestrongly.Rememberthat<br />
youcanalwaysapproachtheexactvalueinslowerandslowersteps(filestrokes),butyou<br />
cannotgo”backward”anddecreasetheshuntresistance!<br />
Buildthemultimetercircuitonabreadboardfirstwhiledeterminingproperrangeresistancevalues,andperformallcalibrationadjustmentsthere.Forfinalconstruction,solderthe<br />
componentsontoaprinted-circuitboard. RadioShacksellsprintedcircuitboardsthathave<br />
thesamelayoutasabreadboard,forconvenience(catalog#276-170). Feelfreetoalterthe<br />
componentlayoutfromwhatisshown.<br />
Istronglyrecommendthatyoumountthecircuitboardandallcomponentsinasturdybox,<br />
sothatthemeterisdurablyfinished.Despitethelimitationsofthismultimeter(noresistance<br />
function,inabilitytomeasurealternatingcurrent,andlowerprecisionthanmostpurchased<br />
analogmultimeters),itisanexcellentprojecttoassistlearningfundamentalinstrumentprinciplesandcircuitfunction.Afarmoreaccurateandversatilemultimetermaybeconstructed<br />
usingmanyofthesamepartsifanamplifiercircuitisaddedtoit,sosavethepartsandpieces<br />
foralaterexperiment!
3.12. SENSITIVEVOLTAGEDETECTOR 117<br />
3.12 Sensitivevoltagedetector<br />
PARTSANDMATERIALS<br />
• High-quality”closed-cup”audioheadphones<br />
• Headphonejack:femalereceptacleforheadphoneplug(RadioShackcatalog#274-312)<br />
• Smallstep-downpowertransformer(RadioShackcatalog#273-1365orequivalent,using<br />
the6-voltsecondarywindingtap)<br />
• Two1N4001rectifyingdiodes(RadioShackcatalog#276-1101)<br />
• 1kΩresistor<br />
• 100kΩpotentiometer(RadioShackcatalog#271-092)<br />
• Two”banana”jackstylebindingposts,orotherterminalhardware,forconnectionto<br />
potentiometercircuit(RadioShackcatalog#274-662orequivalent)<br />
• Plasticormetalmountingbox<br />
Regardingtheheadphones,thehigherthe”sensitivity”ratingindecibels(dB),thebetter,<br />
butlisteningisbelieving:ifyou’reseriousaboutbuildingadetectorwithmaximumsensitivity<br />
forsmallelectricalsignals,youshouldtryafewdifferentheadphonemodelsatahigh-quality<br />
audiostoreand”listen”forwhichonesproduceanaudiblesoundforthelowestvolumesetting<br />
onaradioorCDplayer. Beware,asyoucouldspendhundredsofdollarsonapairofheadphonestogettheabsolutebestsensitivity!Takeheart,though:I’veusedanoldpairofRadio<br />
Shack”Realistic”brandheadphoneswithperfectlyadequateresults,soyoudon’tneedtobuy<br />
thebest.<br />
Atransformerisadevicenormallyusedwithalternatingcurrent(”AC”)circuits,usedto<br />
converthigh-voltageACpowerintolow-voltageACpower,andformanyotherpurposes. It<br />
isnotimportantthatyouunderstanditsintendedfunctioninthisexperiment,otherthanit<br />
makestheheadphonesbecomemoresensitivetolow-currentelectricalsignals.<br />
Normally,thetransformerusedinthistypeofapplication(audiospeakerimpedancematching)iscalledan”audiotransformer,”withitsprimaryandsecondarywindingsrepresentedby<br />
impedancevalues(1000 Ω:8 Ω)insteadofvoltages.Anaudiotransformerwillwork,butI’ve<br />
foundsmallstep-downpowertransformersof120/6voltratiotobeperfectlyadequateforthe<br />
task,cheaper(especiallywhentakenfromanoldthrift-storealarmclockradio),andfarmore<br />
rugged.<br />
Thetolerance(precision)ratingforthe1kΩresistorisirrelevant.The100kΩpotentiometerisarecommendedoptionforincorporationintothisproject,asitgivestheusercontrol<br />
overtheloudnessforanygivensignal. Eventhoughanaudio-taperpotentiometerwouldbe<br />
appropriateforthisapplication,itisnotnecessary.Alinear-taperpotentiometerworksquite<br />
well.<br />
CROSS-REFERENCES<br />
LessonsInElectricCircuits,Volume1,chapter8:”DCMeteringCircuits”
118 CHAPTER3. DCCIRCUITS<br />
LessonsInElectricCircuits,Volume1,chapter10:”DCNetworkAnalysis”(inregardtothe<br />
MaximumPowerTransferTheorem)<br />
LessonsInElectricCircuits,Volume2,chapter9:”Transformers”<br />
LessonsInElectricCircuits,Volume2,chapter12:”ACMeteringCircuits”<br />
LEARNINGOBJECTIVES<br />
• Solderingpractice<br />
• Detectionofextremelysmallelectricalsignals<br />
• Usingapotentiometerasavoltagedivider/signalattenuator<br />
• Usingdiodesto”clip”voltageatsomemaximumlevel<br />
SCHEMATICDIAGRAM<br />
headphones<br />
test lead<br />
transformer<br />
1 kΩ<br />
diodes<br />
jack<br />
plug<br />
test lead<br />
ILLUSTRATION<br />
headphones<br />
resistor<br />
120 V<br />
6 V<br />
Binding<br />
posts<br />
diodes<br />
transformer<br />
jack<br />
plug<br />
INSTRUCTIONS<br />
Theheadphones,mostlikelybeingstereounits(separateleftandrightspeakers)willhave<br />
athree-contactplug. Youwillbeconnectingtoonlytwoofthosethreecontactpoints. Ifyou<br />
onlyhavea”mono”headphonesetwithatwo-contactplug,justconnecttothosetwocontact<br />
points.Youmayeitherconnectthetwostereospeakersinseriesorinparallel.I’vefoundthe<br />
seriesconnectiontoworkbest,thatis,toproducethemostsoundfromasmallsignal:
3.12. SENSITIVEVOLTAGEDETECTOR 119<br />
To transformer<br />
To transformer<br />
common right left common right left<br />
Speakers in series<br />
Speakers in parallel<br />
Solderallwireconnectionswell.Thisdetectorsystemisextremelysensitive,andanyloose<br />
wireconnectionsinthecircuitwilladdunwantednoisetothesoundsproducedbythemeasuredvoltagesignal.<br />
Thetwodiodes(arrow-likecomponentsymbols)connectedinparallel<br />
withthetransformer’sprimarywinding,alongwiththeseries-connected1kΩresistor,work<br />
togethertopreventanymorethanabout0.7voltsfrombeingdroppedacrosstheprimarycoil<br />
ofthetransformer.Thisdoesonethingandonethingonly:limittheamountofsoundtheheadphonescanproduce.Thesystemwillworkwithoutthediodesandresistorinplace,butthere<br />
willbenolimittosoundvolumeinthecircuit,andtheresultingsoundcausedbyaccidently<br />
connectingthetestleadsacrossasubstantialvoltagesource(likeabattery)canbedeafening!<br />
Bindingpostsprovidepointsofconnectionforapairoftestprobeswithbanana-styleplugs,<br />
oncethedetectorcomponentsaremountedinsideabox. Youmayuseordinarymultimeter<br />
probes,ormakeyourownprobeswithalligatorclipsattheendsforsecureconnectiontoa<br />
circuit.<br />
Detectorsareintendedtobeusedforbalancingbridgemeasurementcircuits,potentiometric(null-balance)voltmetercircuits,anddetectextremelylow-amplitudeAC(”alternatingcurrent”)signalsintheaudiofrequencyrange.Itisavaluablepieceoftestequipment,especially<br />
forthelow-budgetexperimenterwithoutanoscilloscope. Itisalsovaluableinthatitallows<br />
youtouseadifferentbodilysenseininterpretingthebehaviorofacircuit.<br />
Forconnectionacrossanynon-trivialsourceofvoltage(1voltandgreater),thedetector’s<br />
extremelyhighsensitivityshouldbeattenuated. Thismaybeaccomplishedbyconnectinga<br />
voltagedividertothe”front”ofthecircuit:<br />
SCHEMATICDIAGRAM<br />
test lead<br />
100<br />
kΩ<br />
1 kΩ<br />
test lead<br />
ILLUSTRATION
120 CHAPTER3. DCCIRCUITS<br />
potentiometer<br />
Adjustthe100kΩvoltagedividerpotentiometertoaboutmid-rangewheninitiallysensing<br />
avoltagesignalofunknownmagnitude.Ifthesoundistooloud,turnthepotentiometerdown<br />
andtryagain. Iftoosoft,turnitupandtryagain. Thedetectorproducesa”click”sound<br />
wheneverthetestleadsmakeorbreakcontactwiththevoltagesourceundertest. Withmy<br />
cheapheadphones,I’vebeenabletodetectcurrentsoflessthan1/10ofamicroamp(¡0.1 µA).<br />
Agooddemonstrationofthedetector’ssensitivityistotouchbothtestleadstotheend<br />
ofyourtongue,withthesensitivityadjustmentsettomaximum. Thevoltageproducedby<br />
metal-to-electrolytecontact(calledgalvanicvoltage)isverysmall,butenoughtoproducesoft<br />
”clicking”soundseverytimetheleadsmakeandbreakcontactonthewetskinofyourtongue.<br />
Tryunpluggedtheheadphoneplugfromthejack(receptacle)andsimilarlytouchingitto<br />
theendofyourtongue.Youshouldstillhearsoftclickingsounds,buttheywillbemuchsmaller<br />
inamplitude.Headphonespeakersare”lowimpedance”devices:theyrequirelowvoltageand<br />
”high”currenttodeliversubstantialsoundpower.Impedanceisameasureofoppositiontoany<br />
andallformsofelectriccurrent,includingalternatingcurrent(AC).Resistance,bycomparison,isastrictlymeasureofoppositiontodirectcurrent(DC).Likeresistance,impedanceis<br />
measuredintheunitoftheOhm(Ω),butitissymbolizedinequationsbythecapitalletter”Z”<br />
ratherthanthecapitalletter”R”.Weusetheterm”impedance”todescribetheheadphone’soppositiontocurrentbecauseitisprimarilyACsignalsthatheadphonesarenormallysubjected<br />
to,notDC.<br />
Mostsmallsignalsourceshavehighinternalimpedances,somemuchhigherthanthenominal8Ωoftheheadphonespeakers.Thisisatechnicalwayofsayingthattheyareincapableof<br />
supplyingsubstantialamountsofcurrent.AstheMaximumPowerTransferTheorempredicts,<br />
maximumsoundpowerwillbedeliveredbytheheadphonespeakerswhentheirimpedanceis<br />
”matched”totheimpedanceofthevoltagesource.Thetransformerdoesthis.Thetransformer<br />
alsohelpsaidthedetectionofsmallDCsignalsbyproducinginductive”kickback”everytime<br />
thetestleadcircuitisbroken,thus”amplifying”thesignalbymagneticallystoringupelectrical<br />
energyandsuddenlyreleasingittotheheadphonespeakers.<br />
Irecommendbuildingthisdetectorinapermanentfashion(mountingallcomponentsinside<br />
ofabox,andprovidingnicetestleadwires)soitmaybeeasilyusedinthefuture.Constructed<br />
assuch,itmightlooksomethinglikethis:
3.12. SENSITIVEVOLTAGEDETECTOR 121<br />
headphones<br />
Test leads<br />
Sensitivity<br />
plug
122 CHAPTER3. DCCIRCUITS<br />
3.13 Potentiometricvoltmeter<br />
PARTSANDMATERIALS<br />
• Two6voltbatteries<br />
• Onepotentiometer,singleturn,10kΩ,lineartaper(RadioShackcatalog#271-1715)<br />
• Twohigh-valueresistors(atleast1MΩeach)<br />
• Sensitivevoltagedetector(frompreviousexperiment)<br />
• Analogvoltmeter(frompreviousexperiment)<br />
Thepotentiometervalueisnotcritical:anythingfrom1kΩto100kΩisacceptable.Ifyou<br />
havebuiltthe”precisionpotentiometer”describedearlierinthischapter,itisrecommended<br />
thatyouuseitinthisexperiment.<br />
Likewise,theactualvaluesoftheresistorsarenotcritical.Inthisparticularexperiment,<br />
thegreaterthevalue,thebettertheresults.Theyneednotbepreciselyequalvalue,either.<br />
Ifyouhavenotyetbuiltthesensitivevoltagedetector,itisrecommendedthatyoubuildone<br />
beforeproceedingwiththisexperiment!Itisaveryuseful,yetsimple,pieceoftestequipment<br />
thatyoushouldnotbewithout. Youcanuseadigitalmultimetersettothe”DCmillivolt”<br />
(DCmV)rangeinlieuofavoltagedetector,buttheheadphone-basedvoltagedetectorismore<br />
appropriatebecauseitdemonstrateshowyoucanmakeprecisevoltagemeasurementswithout<br />
usingexpensiveoradvancedmeterequipment.Irecommendusingyourhome-mademultimeterforthesamereason,althoughanyvoltmeterwillsufficeforthisexperiment.<br />
CROSS-REFERENCES<br />
LessonsInElectricCircuits,Volume1,chapter8:”DCMeteringCircuits”<br />
LEARNINGOBJECTIVES<br />
• Voltmeterloading:itscausesanditssolution<br />
• Usingapotentiometerasasourceofvariablevoltage<br />
• Potentiometricmethodofvoltagemeasurement<br />
SCHEMATICDIAGRAM<br />
1 MΩ<br />
6 V<br />
1 MΩ<br />
measure voltage<br />
between these<br />
two test points<br />
Test<br />
probes<br />
null<br />
+<br />
V<br />
-<br />
6 V<br />
Potentiometric voltmeter
3.13. POTENTIOMETRICVOLTMETER 123<br />
ILLUSTRATION<br />
Test circuit<br />
+ - + -<br />
Test probes<br />
Potentiometric voltmeter circuit<br />
headphones<br />
- +<br />
Sensitivity<br />
plug<br />
INSTRUCTIONS<br />
Buildthetwo-resistorvoltagedividercircuitshownontheleftoftheschematicdiagram<br />
andoftheillustration.Ifthetwohigh-valueresistorsareofequalvalue,thebattery’svoltage<br />
shouldbesplitinhalf,withapproximately3voltsdroppedacrosseachresistor.<br />
Measurethebatteryvoltagedirectlywithavoltmeter,thenmeasureeachresistor’svoltage<br />
drop.Doyounoticeanythingunusualaboutthevoltmeter’sreadings?Normally,seriesvoltage<br />
dropsaddtoequalthetotalappliedvoltage,butinthiscaseyouwillnoticeaseriousdiscrepancy.IsKirchhoff’sVoltageLawuntrue?Isthisanexceptiontooneofthemostfundamental<br />
lawsofelectriccircuits?No!Whatishappeningisthis:whenyouconnectavoltmeteracross<br />
eitherresistor,thevoltmeteritselfaltersthecircuitsothatthevoltageisnotthesameaswith<br />
nometerconnected.<br />
Iliketousetheanalogyofanairpressuregaugeusedtocheckthepressureofapneumatic<br />
tire. Whenagaugeisconnectedtothetire’sfillvalve,itreleasessomeairoutofthetire.<br />
Thisaffectsthepressureinthetire,andsothegaugereadsaslightlylowerpressurethan<br />
whatwasinthetirebeforethegaugewasconnected. Inotherwords,theactofmeasuring<br />
tirepressurealtersthetire’spressure. Hopefully,though,thereissolittleairreleasedfrom<br />
thetireduringtheactofmeasurementthatthereductioninpressureisnegligible.Voltmeters<br />
similarlyimpactthevoltagetheymeasure,bybypassingsomecurrentaroundthecomponent<br />
whosevoltagedropisbeingmeasured.Thisaffectsthevoltagedrop,buttheeffectissoslight<br />
thatyouusuallydon’tnoticeit.<br />
Inthiscircuit,though,theeffectisverypronounced. Whyisthis? Tryreplacingthetwo<br />
high-valueresistorswithtwoof100kΩvalueeachandrepeattheexperiment.Replacethose<br />
resistorswithtwo10KΩunitsandrepeat.Whatdoyounoticeaboutthevoltagereadingswith
124 CHAPTER3. DCCIRCUITS<br />
lower-valueresistors?Whatdoesthistellyouaboutvoltmeter”impact”onacircuitinrelation<br />
tothatcircuit’sresistance?Replaceanylow-valueresistorswiththeoriginal,high-value(>=<br />
1MΩ)resistorsbeforeproceeding.<br />
Trymeasuringvoltageacrossthetwohigh-valueresistors–oneatatime–withadigital<br />
voltmeterinsteadofananalogvoltmeter.Whatdoyounoticeaboutthedigitalmeter’sreadings<br />
versustheanalogmeter’s?Digitalvoltmeterstypicallyhavegreaterinternal(probe-to-probe)<br />
resistance,meaningtheydrawlesscurrentthanacomparableanalogvoltmeterwhenmeasuringthesamevoltagesource.Anidealvoltmeterwoulddrawzerocurrentfromthecircuit<br />
undertest,andthussuffernovoltage”impact”problems.<br />
Ifyouhappentohavetwovoltmeters,trythis:connectonevoltmeteracrossoneresistor,<br />
andtheothervoltmeteracrosstheotherresistor. Thevoltagereadingsyougetwilladdup<br />
tothetotalvoltagethistime,nomatterwhattheresistorvaluesare,eventhoughthey’re<br />
differentfromthereadingsobtainedfromasinglemeterusedtwice.Unfortunately,though,it<br />
isunlikelythatthevoltagereadingsobtainedthiswayareequaltothetruevoltagedropswith<br />
nometersconnected,andsoitisnotapracticalsolutiontotheproblem.<br />
Isthereanywaytomakea”perfect”voltmeter:onethathasinfiniteresistanceanddraws<br />
nocurrentfromthecircuitundertest? Modernlaboratoryvoltmetersapproachthisgoalby<br />
usingsemiconductor”amplifier”circuits,butthismethodistootechnologicallyadvancedfor<br />
thestudentorhobbyisttoduplicate. Amuchsimplerandmucholdertechniqueiscalledthe<br />
potentiometricornull-balancemethod. Thisinvolvesusinganadjustablevoltagesourceto<br />
”balance”themeasuredvoltage. Whenthetwovoltagesareequal,asindicatedbyavery<br />
sensitivenulldetector,theadjustablevoltagesourceismeasuredwithanordinaryvoltmeter.<br />
Becausethetwovoltagesourcesareequaltoeachother,measuringtheadjustablesourceis<br />
thesameasmeasuringacrossthetestcircuit,exceptthatthereisno”impact”errorbecause<br />
theadjustablesourceprovidesanycurrentneededbythevoltmeter.Consequently,thecircuit<br />
undertestremainsunaffected,allowingmeasurementofitstruevoltagedrop.<br />
Examinethefollowingschematictoseehowthepotentiometricvoltmetermethodisimplemented:<br />
1 MΩ<br />
6 V<br />
1 MΩ<br />
-<br />
Test circuit<br />
+<br />
null<br />
+<br />
V<br />
-<br />
Potentiometric voltmeter<br />
Thecirclesymbolwiththeword”null”writteninsiderepresentsthenulldetector.Thiscan<br />
beanyarbitrarilysensitivemetermovementorvoltageindicator.Itssolepurposeinthiscircuit<br />
istoindicatewhenthereiszerovoltage:whentheadjustablevoltagesource(potentiometer)<br />
ispreciselyequaltothevoltagedropinthecircuitundertest. Themoresensitivethisnull<br />
detectoris,themorepreciselytheadjustablesourcemaybeadjustedtoequalthevoltage<br />
6 V
3.13. POTENTIOMETRICVOLTMETER 125<br />
undertest,andthemorepreciselythattestvoltagemaybemeasured.<br />
Buildthiscircuitasshownintheillustrationandtestitsoperationmeasuringthevoltage<br />
dropacrossoneofthehigh-valueresistorsinthetestcircuit.Itmaybeeasiertousearegular<br />
multimeterasanulldetectoratfirst,untilyoubecomefamiliarwiththeprocessofadjustingthepotentiometerfora”null”indication,thenreadingthevoltmeterconnectedacrossthe<br />
potentiometer.<br />
Ifyouareusingtheheadphone-basedvoltagedetectorasyournullmeter,youwillneed<br />
tointermittentlymakeandbreakcontactwiththecircuitundertestandlistenfor”clicking”<br />
sounds. Dothisbyfirmlysecuringoneofthetestprobestothetestcircuitandmomentarily<br />
touchingtheothertestprobetotheotherpointinthetestcircuitagainandagain,listening<br />
forsoundsintheheadphonesindicatingadifferenceofvoltagebetweenthetestcircuitand<br />
thepotentiometer. Adjustthepotentiometeruntilnoclickingsoundscanbeheardfromthe<br />
headphones.Thisindicatesa”null”or”balanced”condition,andyoumayreadthevoltmeter<br />
indicationtoseehowmuchvoltageisdroppedacrossthetestcircuitresistor. Unfortunately,<br />
theheadphone-basednulldetectorprovidesnoindicationofwhetherthepotentiometervoltage<br />
isgreaterthan,orlessthanthetestcircuitvoltage,soyouwillhavetolistenfordecreasing<br />
”click”intensitywhileturningthepotentiometertodetermineifyouneedtoadjustthevoltage<br />
higherorlower.<br />
Youmayfindthatasingle-turn(”3/4turn”)potentiometeristoocoarseofanadjustment<br />
devicetoaccurately”null”themeasurementcircuit.Amulti-turnpotentiometermaybeused<br />
insteadofthesingle-turnunitforgreateradjustmentprecision,orthe”precisionpotentiometer”circuitdescribedinanearlierexperimentmaybeused.<br />
Priortotheadventofamplifiedvoltmetertechnology,thepotentiometricmethodwasthe<br />
onlymethodformakinghighlyaccuratevoltagemeasurements.Evennow,electricalstandards<br />
laboratoriesmakeuseofthistechniquealongwiththelatestmetertechnologytominimizemeter”impact”errorsandmaximizemeasurementaccuracy.Althoughthepotentiometricmethod<br />
requiresmoreskilltousethansimplyconnectingamoderndigitalvoltmeteracrossacomponent,andisconsideredobsoleteforallbutthemostprecisemeasurementapplications,itis<br />
stillavaluablelearningprocessforthenewstudentofelectronics,andausefultechniquefor<br />
thehobbyistwhomaylackexpensiveinstrumentationintheirhomelaboratory.<br />
COMPUTERSIMULATION<br />
SchematicwithSPICEnodenumbers:
126 CHAPTER3. DCCIRCUITS<br />
V 1<br />
1<br />
1 MΩ<br />
1 MΩ<br />
-<br />
0 0<br />
1<br />
R 1<br />
2 2<br />
null<br />
3 3<br />
+<br />
R 2<br />
+<br />
V<br />
-<br />
0 0<br />
V 2<br />
Netlist(makeatextfilecontainingthefollowingtext,verbatim):<br />
Potentiometric voltmeter<br />
v1 1 0 dc 6<br />
v2 3 0<br />
r1 1 2 1meg<br />
r2 2 0 1meg<br />
rnull 2 3 10k<br />
rmeter 3 0 50k<br />
.dc v2 0 6 0.5<br />
.print dc v(2,0) v(2,3) v(3,0)<br />
.end<br />
ThisSPICEsimulationshowstheactualvoltageacrossR 2 ofthetestcircuit,thenulldetector’svoltage,andthevoltageacrosstheadjustablevoltagesource,asthatsourceisadjusted<br />
from0voltsto6voltsin0.5voltsteps. Intheoutputofthissimulation,youwillnoticethat<br />
thevoltageacrossR 2 isimpactedsignificantlywhenthemeasurementcircuitisunbalanced,<br />
returningtoitstruevoltageonlywhenthereispracticallyzerovoltageacrossthenulldetector.Atthatpoint,ofcourse,theadjustablevoltagesourceisatavalueof3.000volts:precisely<br />
equaltothe(unaffected)testcircuitvoltagedrop.<br />
Whatisthelessontobelearnedfromthissimulation? Thatapotentiometricvoltmeter<br />
avoidsimpactingthetestcircuitonlywhenitisinaconditionofperfectbalance(”null”)with<br />
thetestcircuit!
3.14. 4-WIRERESISTANCEMEASUREMENT 127<br />
3.14 4-wireresistancemeasurement<br />
PARTSANDMATERIALS<br />
• 6-voltbattery<br />
• Electromagnetmadefromexperimentinpreviouschapter,oralargespoolofwire<br />
Itwouldbeidealinthisexperimenttohavetwometers:onevoltmeterandoneammeter.<br />
Forexperimentersonabudget,thismaynotbepossible.Whateverammeterisusedshouldbe<br />
capablemeasuringatleastafewampsofcurrent.A6-volt”lantern”batteryessentiallyshortcircuitedbyalongpieceofwiremayproducecurrentsofthismagnitude,andyourammeter<br />
needstobecapableofmeasuringitwithoutblowingafuseorsustainingotherdamage.Make<br />
surethehighestcurrentrangeonthemeterisatleast5amps!<br />
CROSS-REFERENCES<br />
LessonsInElectricCircuits,Volume1,chapter8:”DCMeteringCircuits”<br />
LEARNINGOBJECTIVES<br />
• OperatingprincipleofKelvin(4-wire)resistancemeasurement<br />
• Howtomeasurelowresistanceswithcommontestequipment<br />
SCHEMATICDIAGRAM<br />
+<br />
A<br />
-<br />
+<br />
V<br />
-<br />
R unknown<br />
ILLUSTRATION
128 CHAPTER3. DCCIRCUITS<br />
V<br />
A<br />
V<br />
A<br />
V<br />
OFF<br />
A<br />
V<br />
OFF<br />
A<br />
A<br />
COM<br />
+ - COM<br />
A<br />
R unknown<br />
INSTRUCTIONS<br />
Althoughthisexperimentisbestperformedwithtwometers,andindeedisshownassuch<br />
intheschematicdiagramandillustration,onemultimeterissufficient.<br />
Mostohmmetersoperateontheprincipleofapplyingasmallvoltageacrossanunknown<br />
resistance(R unknown )andinferringresistancefromtheamountofcurrentdrawnbyit.Except<br />
inspecialcasessuchasthemegger,boththevoltageandcurrentquantitiesemployedbythe<br />
meterarequitesmall.<br />
Thispresentsaproblemformeasurementoflowresistances,asalowresistancespecimen<br />
maybeofmuchsmallerresistancevaluethanthemetercircuitryitself. Imaginetryingto<br />
measurethediameterofacottonthreadwithayardstick,ormeasuringtheweightofacoin<br />
withascalebuiltforweighingfreighttrucks,andyouwillappreciatetheproblemathand.<br />
Oneofthemanysourcesoferrorinmeasuringsmallresistanceswithanordinaryohmmeteristheresistanceoftheohmmeter’sowntestleads.Beingpartofthemeasurementcircuit,<br />
thetestleadsmaycontainmoreresistancethantheresistanceofthetestspecimen,incurring<br />
significantmeasurementerrorbytheirpresence:
3.14. 4-WIRERESISTANCEMEASUREMENT 129<br />
Ω<br />
V<br />
A<br />
V<br />
A<br />
OFF<br />
COM<br />
A<br />
Lead resistance:<br />
0.25 Ω<br />
Lead resistance:<br />
0.25 Ω<br />
1.5 Ω<br />
OnesolutioniscalledtheKelvin,or4-wire,resistancemeasurementmethod.Itinvolvesthe<br />
useofanammeterandvoltmeter,determiningspecimenresistancebyOhm’sLawcalculation.<br />
Acurrentispassedthroughtheunknownresistanceandmeasured. Thevoltagedropped<br />
acrosstheresistanceismeasuredbythevoltmeter,andresistancecalculatedusingOhm’s<br />
Law(R=E/I).Verysmallresistancesmaybemeasuredeasilybyusinglargecurrent,providing<br />
amoreeasilymeasuredvoltagedropfromwhichtoinferresistancethanifasmallcurrent<br />
wereused.<br />
Becauseonlythevoltagedroppedbytheunknownresistanceisfactoredintothecalculation–notthevoltagedroppedacrosstheammeter’stestleadsoranyotherconnectingwires<br />
carryingthemaincurrent–errorsotherwisecausedbythesestrayresistancesarecompletely<br />
eliminated.<br />
First,selectasuitablylowresistancespecimentouseinthisexperiment. Isuggestthe<br />
electromagnetcoilspecifiedinthelastchapter,oraspoolofwirewherebothendsmaybe<br />
accessed. Connecta6-voltbatterytothisspecimen,withanammeterconnectedinseries.<br />
WARNING:theammeterusedshouldbecapableofmeasuringatleast5ampsofcurrent,<br />
sothatitwillnotbedamagedbythe(possibly)highcurrentgeneratedinthisnear-short<br />
circuitcondition.Ifyouhaveasecondmeter,useittomeasurevoltageacrossthespecimen’s<br />
connectionpoints,asshownintheillustration,andrecordbothmeters’indications.<br />
Ifyouhaveonlyonemeter,useittomeasurecurrentfirst,recordingitsindicationasquickly<br />
aspossible,thenimmediatelyopening(breaking)thecircuit. Switchthemetertoitsvoltage<br />
mode,connectitacrossthespecimen’sconnectionpoints,andre-connectthebattery,quickly<br />
notingthevoltageindication. Youdon’twanttoleavethebatteryconnectedtothespecimen
130 CHAPTER3. DCCIRCUITS<br />
foranylongerthannecessaryforobtainingmetermeasurements,asitwillbegintorapidly<br />
dischargeduetothehighcircuitcurrent,thuscompromisingmeasurementaccuracywhenthe<br />
meterisre-configuredandthecircuitclosedoncemoreforthenextmeasurement.Whentwo<br />
metersareused,thisisnotassignificantanissue,becausethecurrentandvoltageindications<br />
mayberecordedsimultaneously.<br />
Takethevoltagemeasurementanddivideitbythecurrentmeasurement. Thequotient<br />
willbeequaltothespecimen’sresistanceinohms.
3.15. AVERYSIMPLECOMPUTER 131<br />
3.15 Averysimplecomputer<br />
PARTSANDMATERIALS<br />
• Threebatteries,eachonewithadifferentvoltage<br />
• Threeequal-valueresistors,between10kΩand47kΩeach<br />
Whenselectingresistors,measureeachonewithanohmmeterandchoosethreethatare<br />
theclosestinvaluetoeachother.Precisionisveryimportantforthisexperiment!<br />
CROSS-REFERENCES<br />
LessonsInElectricCircuits,Volume1,chapter10:”DCNetworkAnalysis”<br />
LEARNINGOBJECTIVES<br />
• Howaresistornetworkcanfunctionasavoltagesignalaverager<br />
• ApplicationofMillman’sTheorem<br />
SCHEMATICDIAGRAM<br />
R 1 R 2 R 3<br />
+<br />
V<br />
-<br />
ILLUSTRATION
132 CHAPTER3. DCCIRCUITS<br />
V<br />
A<br />
V<br />
OFF<br />
A<br />
A<br />
COM<br />
+ -<br />
+ -
3.15. AVERYSIMPLECOMPUTER 133<br />
V<br />
A<br />
V<br />
OFF<br />
A<br />
A<br />
COM<br />
+ -<br />
+ -<br />
INSTRUCTIONS<br />
Thisdeceptivelycrudecircuitperformsthefunctionofmathematicallyaveragingthreevoltagesignalstogether,andsofulfillsaspecializedcomputationalrole.<br />
Inotherwords,itisa<br />
computerthatcanonlydoonemathematicaloperation:averagingthreequantitiestogether.<br />
Buildthiscircuitasshownandmeasureallbatteryvoltageswithavoltmeter.Writethese<br />
voltagefiguresonpaperandaveragethemtogether(E 1 +E 2 +E 3 ,dividedbythree). When<br />
youmeasureeachbatteryvoltage,keeptheblacktestprobeconnectedtothe”ground”point<br />
(thesideofthebatterydirectlyjoinedtotheotherbatteriesbyjumperwires),andtouchthe<br />
redprobetotheotherbatteryterminal. Polarityisimportanthere! Youwillnoticeonebatteryintheschematicdiagramconnected”backward”totheothertwo,negativeside”up.”This<br />
battery’svoltageshouldreadasanegativequantitywhenmeasuredbyaproperlyconnected<br />
digitalmeter,theotherbatteriesmeasuringpositive.<br />
Whenthevoltmeterisconnectedtothecircuitatthepointshownintheschematicand<br />
illustrations,itshouldregisterthealgebraicaverageofthethreebatteries’voltages. Ifthe
134 CHAPTER3. DCCIRCUITS<br />
resistorvaluesarechosentomatcheachotherveryclosely,the”output”voltageofthiscircuit<br />
shouldmatchthecalculatedaverageverycloselyaswell.<br />
Ifonebatteryisdisconnected,theoutputvoltagewillequaltheaveragevoltageoftheremainingbatteries.Ifthejumperwiresformerlyconnectingtheremovedbatterytotheaverager<br />
circuitareconnectedtoeachother,thecircuitwillaveragethetworemainingvoltagestogether<br />
with0volts,producingasmalleroutputsignal:<br />
V<br />
A<br />
V<br />
OFF<br />
A<br />
A<br />
COM<br />
+ -<br />
+ -<br />
Thesheersimplicityofthiscircuitdetersmostpeoplefromcallingita”computer,”butit<br />
undeniablyperformsthemathematicalfunctionofaveraging. Notonlydoesitperformthis<br />
function,butitperformsitmuchfasterthananymoderndigitalcomputercan! Digitalcomputers,suchaspersonalcomputers(PCs)andpushbuttoncalculators,performmathematical<br />
operationsinaseriesofdiscretesteps. Analogcomputersperformcalculationsincontinuousfashion,exploitingOhm’sandKirchhoff’sLawsforanarithmeticpurpose,the”answer”<br />
computedasfastasvoltagepropagatesthroughthecircuit(ideally,atthespeedoflight!).<br />
Withtheadditionofcircuitscalledamplifiers,voltagesignalsinanalogcomputernetworks<br />
maybeboostedandre-usedinothernetworkstoperformawidevarietyofmathematicalfunctions.<br />
Suchanalogcomputersexcelatperformingthecalculusoperationsofnumericaldifferentiationandintegration,andassuchmaybeusedtosimulatethebehaviorofcomplex<br />
mechanical,electrical,andevenchemicalsystems. Atonetime,analogcomputerswerethe
3.15. AVERYSIMPLECOMPUTER 135<br />
ultimatetoolforengineeringresearch,butsincethenhavebeenlargelysupplantedbydigital<br />
computertechnology.Digitalcomputersenjoytheadvantageofperformingmathematicaloperationswithmuchbetterprecisionthananalogcomputers,albeitatmuchslowertheoretical<br />
speeds.<br />
COMPUTERSIMULATION<br />
SchematicwithSPICEnodenumbers:<br />
4<br />
4 4 4<br />
R 1 R 2 R 3<br />
+<br />
1 2 3<br />
V<br />
-<br />
V 1 V 2 V 3<br />
0<br />
0 0<br />
0<br />
Netlist(makeatextfilecontainingthefollowingtext,verbatim):<br />
Voltage averager<br />
v1 1 0<br />
v2 0 2 dc 9<br />
v3 3 0 dc 1.5<br />
r1 1 4 10k<br />
r2 2 4 10k<br />
r3 3 4 10k<br />
.dc v1 6 6 1<br />
.print dc v(4,0)<br />
.end<br />
WiththisSPICEnetlist,wecanforceadigitalcomputertosimulateandanalogcomputer,<br />
whichaveragesthreenumberstogether.Obviously,wearen’tdoingthisforthepracticaltask<br />
ofaveragingnumbers,butrathertolearnmoreaboutcircuitsandmoreaboutcomputersimulationofcircuits!
136 CHAPTER3. DCCIRCUITS<br />
3.16 Potatobattery<br />
PARTSANDMATERIALS<br />
• Onelargepotato<br />
• Onelemon(optional)<br />
• Stripofzinc,orgalvanizedmetal<br />
• Pieceofthickcopperwire<br />
Thebasicexperimentisbasedontheuseofapotato,butmanyfruitsandvegetableswork<br />
aspotentialbatteries!<br />
Forthezincelectrode,alargegalvanizednailworkswell. Nailswithathick,roughzinc<br />
texturearepreferabletogalvanizednailsthataresmooth.<br />
CROSS-REFERENCES<br />
LessonsInElectricCircuits,Volume1,chapter11:”BatteriesandPowerSystems”<br />
LEARNINGOBJECTIVES<br />
• Theimportanceofchemicalactivityinbatteryoperation<br />
• Howelectrodesurfaceareaaffectsbatteryoperation<br />
ILLUSTRATION<br />
V<br />
V<br />
OFF<br />
A<br />
A<br />
Galvanized<br />
nail<br />
Copper<br />
wire<br />
A<br />
COM<br />
Potato<br />
INSTRUCTIONS
3.16. POTATOBATTERY 137<br />
Pushboththenailandthewiredeepintothepotato.Measurevoltageoutputbythepotato<br />
batterywithavoltmeter.Now,wasn’tthateasy?<br />
Seriously,though,experimentwithdifferentmetals,electrodedepths,andelectrodespacingstoobtainthegreatestvoltagepossiblefromthepotato.Tryothervegetablesorfruitsand<br />
comparevoltageoutputwiththesameelectrodemetals.<br />
Itcanbedifficulttopoweraloadwithasingle”potato”battery,sodon’texpecttolightup<br />
anincandescentlamporpowerahobbymotorordoanythinglikethat. Evenifthevoltage<br />
outputisadequate,apotatobatteryhasafairlyhighinternalresistancewhichcausesits<br />
voltageto”sag”badlyunderevenalightload. Withmultiplepotatobatteriesconnectedin<br />
series,parallel,orseries-parallelarrangement,though,itispossibletoobtainenoughvoltage<br />
andcurrentcapacitytopowerasmallload.
138 CHAPTER3. DCCIRCUITS<br />
3.17 Capacitorcharginganddischarging<br />
PARTSANDMATERIALS<br />
• 6voltbattery<br />
• Twolargeelectrolyticcapacitors,1000 µFminimum(RadioShackcatalog#272-1019,<br />
272-1032,orequivalent)<br />
• Two1kΩresistors<br />
• Onetoggleswitch,SPST(”Single-Pole,Single-Throw”)<br />
Large-valuecapacitorsarerequiredforthisexperimenttoproducetimeconstantsslow<br />
enoughtotrackwithavoltmeterandstopwatch.Bewarnedthatmostlargecapacitorsareof<br />
the”electrolytic”type,andtheyarepolaritysensitive! Oneterminalofeachcapacitorshould<br />
bemarkedwithadefinitepolaritysign.Usuallycapacitorsofthesizespecifiedhaveanegative<br />
(-)markingorseriesofnegativemarkingspointingtowardthenegativeterminal.Verylarge<br />
capacitorsareoftenpolarity-labeledbyapositive(+)markingnexttooneterminal.Failureto<br />
heedproperpolaritywillalmostsurelyresultincapacitorfailure,evenwithasourcevoltage<br />
aslowas6volts. Whenelectrolyticcapacitorsfail,theytypicallyexplode,spewingcaustic<br />
chemicalsandemittingfoulodors.Please,trytoavoidthis!<br />
Irecommendahouseholdlightswitchforthe”SPSTtoggleswitch”specifiedintheparts<br />
list.<br />
CROSS-REFERENCES<br />
LessonsInElectricCircuits,Volume1,chapter13:”Capacitors”<br />
LessonsInElectricCircuits,Volume1,chapter16:”RCandL/RTimeConstants”<br />
LEARNINGOBJECTIVES<br />
• Capacitorchargingaction<br />
• Capacitordischargingaction<br />
• Timeconstantcalculation<br />
• Seriesandparallelcapacitance<br />
SCHEMATICDIAGRAM
3.17. CAPACITORCHARGINGANDDISCHARGING 139<br />
+<br />
V<br />
-<br />
Charging circuit<br />
+<br />
V<br />
-<br />
Discharging circuit<br />
ILLUSTRATION<br />
-<br />
-<br />
+ - Charging circuit
140 CHAPTER3. DCCIRCUITS<br />
-<br />
-<br />
+ - Discharging circuit<br />
INSTRUCTIONS<br />
Buildthe”charging”circuitandmeasurevoltageacrossthecapacitorwhentheswitchis<br />
closed. Noticehowitincreasesslowlyovertime,ratherthansuddenlyaswouldbethecase<br />
witharesistor. Youcan”reset”thecapacitorbacktoavoltageofzerobyshortingacrossits<br />
terminalswithapieceofwire.<br />
The”timeconstant”(τ)ofaresistorcapacitorcircuitiscalculatedbytakingthecircuit<br />
resistanceandmultiplyingitbythecircuitcapacitance. Fora1kΩresistoranda1000 µF<br />
capacitor,thetimeconstantshouldbe1second. Thisistheamountoftimeittakesforthe<br />
capacitorvoltagetoincreaseapproximately63.2%fromitspresentvaluetoitsfinalvalue:the<br />
voltageofthebattery.<br />
Itiseducationaltoplotthevoltageofachargingcapacitorovertimeonasheetofgraph<br />
paper,toseehowtheinverseexponentialcurvedevelops. Inordertoplottheactionofthis<br />
circuit,though,wemustfindawayofslowingitdown. Aone-secondtimeconstantdoesn’t<br />
providemuchtimetotakevoltmeterreadings!<br />
Wecanincreasethiscircuit’stimeconstanttwodifferentways:changingthetotalcircuit<br />
resistance,and/orchangingthetotalcircuitcapacitance.Givenapairofidenticalresistorsand<br />
apairofidenticalcapacitors,experimentwithvariousseriesandparallelcombinationstoobtaintheslowestchargingaction.Youshouldalreadyknowbynowhowmultipleresistorsneed<br />
tobeconnectedtoformagreatertotalresistance,butwhataboutcapacitors?Thiscircuitwill<br />
demonstratetoyouhowcapacitancechangeswithseriesandparallelcapacitorconnections.<br />
Justbesurethatyouinsertthecapacitor(s)intheproperdirection: withtheendslabeled<br />
negative(-)electrically”closest”tothebattery’snegativeterminal!<br />
Thedischargingcircuitprovidesthesamekindofchangingcapacitorvoltage,exceptthis<br />
timethevoltagejumpstofullbatteryvoltagewhentheswitchclosesandslowlyfallswhen<br />
theswitchisopened. Experimentonceagainwithdifferentcombinationsofresistorsand<br />
capacitors,makingsureasalwaysthatthecapacitor’spolarityiscorrect.<br />
COMPUTERSIMULATION<br />
SchematicwithSPICEnodenumbers:
3.17. CAPACITORCHARGINGANDDISCHARGING 141<br />
1<br />
2<br />
V 1<br />
R 1<br />
C 1<br />
0 0<br />
Netlist(makeatextfilecontainingthefollowingtext,verbatim):<br />
Capacitor charging circuit<br />
v1 1 0 dc 6<br />
r1 1 2 1k<br />
c1 2 0 1000u ic=0<br />
.tran 0.1 5 uic<br />
.plot tran v(2,0)<br />
.end
142 CHAPTER3. DCCIRCUITS<br />
3.18 Rate-of-changeindicator<br />
PARTSANDMATERIALS<br />
• Two6voltbatteries<br />
• Capacitor,0.1 µF(RadioShackcatalog#272-135)<br />
• 1MΩresistor<br />
• Potentiometer,singleturn,5kΩ,lineartaper(RadioShackcatalog#271-1714)<br />
Thepotentiometervalueisnotespeciallycritical,althoughlower-resistanceunitswill,in<br />
theory,workbetterforthisexperimentthanhigh-resistanceunits. I’veuseda10kΩpotentiometerforthiscircuitwithexcellentresults.<br />
CROSS-REFERENCES<br />
LessonsInElectricCircuits,Volume1,chapter13:”Capacitors”<br />
LEARNINGOBJECTIVES<br />
• Howtobuildadifferentiatorcircuit<br />
• Obtainanempiricalunderstandingofthederivativecalculusfunction<br />
SCHEMATICDIAGRAM<br />
6 V<br />
6 V<br />
5 kΩ<br />
0.1 µF<br />
1 MΩ<br />
+<br />
V<br />
-<br />
ILLUSTRATION
3.18. RATE-OF-CHANGEINDICATOR 143<br />
V<br />
A<br />
V<br />
OFF<br />
A<br />
A COM<br />
+ -<br />
+ -<br />
INSTRUCTIONS<br />
Measurevoltagebetweenthepotentiometer’swiperterminalandthe”ground”pointshown<br />
intheschematicdiagram(thenegativeterminalofthelower6-voltbattery).Thisistheinput<br />
voltageforthecircuit,andyoucanseehowitsmoothlyvariesbetweenzeroand12voltsasthe<br />
potentiometercontrolisturnedfull-range. Sincethepotentiometerisusedhereasavoltage<br />
divider,thisbehaviorshouldbeunsurprisingtoyou.<br />
Now,measurevoltageacrossthe1MΩresistorwhilemovingthepotentiometercontrol.A<br />
digitalvoltmeterishighlyrecommended,andIadvisesettingittoaverysensitive(millivolt)<br />
rangetoobtainthestrongestindications. Whatdoesthevoltmeterindicatewhilethepotentiometerisnotbeingmoved?Turnthepotentiometerslowlyclockwiseandnotethevoltmeter’s<br />
indication. Turnthepotentiometerslowlycounter-clockwiseandnotethevoltmeter’sindication.Whatdifferencedoyouseebetweenthetwodifferentdirectionsofpotentiometercontrol<br />
motion?<br />
Trymovingthepotentiometerinsuchawaythatthevoltmetergivesasteady,smallindication.<br />
Whatkindofpotentiometermotionprovidesthesteadiestvoltageacrossthe1MΩ<br />
resistor?<br />
Incalculus,afunctionrepresentingtherateofchangeofonevariableascomparedtoanotheriscalledthederivative.<br />
Thissimplecircuitillustratestheconceptofthederivativeby<br />
producinganoutputvoltageproportionaltotheinputvoltage’srateofchangeovertime. Be-
144 CHAPTER3. DCCIRCUITS<br />
causethiscircuitperformsthecalculusfunctionofdifferentiationwithrespecttotime(outputtingthetime-derivativeofanincomingsignal),itiscalledadifferentiatorcircuit.<br />
Liketheaveragercircuitshownearlierinthischapter,thedifferentiatorcircuitisakindof<br />
analogcomputer.Differentiationisafarmorecomplexmathematicalfunctionthanaveraging,<br />
especiallywhenimplementedinadigitalcomputer,sothiscircuitisanexcellentdemonstration<br />
oftheeleganceofanalogcircuitryinperformingmathematicalcomputations.<br />
Moreaccuratedifferentiatorcircuitsmaybebuiltbycombiningresistor-capacitornetworks<br />
withelectronicamplifiercircuits.Formoredetailoncomputationalcircuitry,gotothe”Analog<br />
IntegratedCircuits”chapterinthis<strong>Experiments</strong>volume.
Chapter4<br />
ACCIRCUITS<br />
Contents<br />
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .145<br />
4.2 Transformer–powersupply............................147<br />
4.3 Buildatransformer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .151<br />
4.4 Variableinductor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .153<br />
4.5 Sensitiveaudiodetector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .155<br />
4.6 SensingACmagneticfields. . . . . . . . . . . . . . . . . . . . . . . . . . . . .160<br />
4.7 SensingACelectricfields. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .162<br />
4.8 Automotivealternator. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .164<br />
4.9 Inductionmotor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .170<br />
4.10 Inductionmotor,large . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .174<br />
4.11 Phaseshift . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .177<br />
4.12 Soundcancellation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .180<br />
4.13 Musicalkeyboardasasignalgenerator. . . . . . . . . . . . . . . . . . . . .183<br />
4.14 PCOscilloscope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .186<br />
4.15 Waveformanalysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .189<br />
4.16 Inductor-capacitor”tank”circuit. . . . . . . . . . . . . . . . . . . . . . . . .191<br />
4.17 Signalcoupling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .194<br />
4.1 Introduction<br />
”AC”standsforAlternatingCurrent,whichcanrefertoeithervoltageorcurrentthatalternatesinpolarityordirection,respectively.Theseexperimentsaredesignedtointroduceyouto<br />
severalimportantconceptsspecifictoAC.<br />
AconvenientsourceofACvoltageishouseholdwall-socketpower,whichpresentssignificantshockhazard.Inordertominimizethishazardwhiletakingadvantageoftheconvenience<br />
145
146 CHAPTER4. ACCIRCUITS<br />
ofthissourceofAC,asmallpowersupplywillbethefirstproject,consistingofatransformer<br />
thatstepsthehazardousvoltage(110to120voltsAC,RMS)downto12voltsorless.Thetitle<br />
of”powersupply”issomewhatmisleading.Thisdevicedoesnotreallyactasasourceorsupply<br />
ofpower,butratherasapowerconverter,toreducethehazardousvoltageofwall-socketpower<br />
toamuchsaferlevel.
4.2. TRANSFORMER–POWERSUPPLY 147<br />
4.2 Transformer–powersupply<br />
PARTSANDMATERIALS<br />
• Powertransformer,120VACstep-downto12VAC,withcenter-tappedsecondarywinding<br />
(RadioShackcatalog#273-1365,273-1352,or273-1511).<br />
• Terminalstripwithatleastthreeterminals.<br />
• Householdwall-socketpowerplugandcord.<br />
• Linecordswitch.<br />
• Box(optional).<br />
• Fuseandfuseholder(optional).<br />
Powertransformersmaybeobtainedfromoldradios,whichcanusuallybeobtainedfrom<br />
athriftstoreforafewdollars(orless!). Theradiowouldalsoprovidethepowercordand<br />
plugnecessaryforthisproject.Linecordswitchesmaybeobtainedfromahardwarestore.If<br />
youwanttobeabsolutelysurewhatkindoftransformeryou’regetting,though,youshould<br />
purchaseonefromanelectronicssupplystore.<br />
Ifyoudecidetoequipyourpowersupplywithafuse,besuretogetaslow-acting,orslowblowfuse.<br />
Transformersmaydrawhigh”surge”currentswheninitiallyconnectedtoanAC<br />
source,andthesetransientcurrentswillblowafast-actingfuse. Determinethepropercurrentratingofthefusebydividingthetransformer’s”VA”ratingby120volts:inotherwords,<br />
calculatethefullallowableprimarywindingcurrentandsizethefuseaccordingly.<br />
CROSS-REFERENCES<br />
LessonsInElectricCircuits,Volume2,chapter1:”BasicACTheory”<br />
LessonsInElectricCircuits,Volume2,chapter9:”Transformers”<br />
LEARNINGOBJECTIVES<br />
• Transformervoltagestep-downbehavior.<br />
• Purposeoftappedwindings.<br />
• Safewiringtechniquesforpowercords.<br />
SCHEMATICDIAGRAM
148 CHAPTER4. ACCIRCUITS<br />
Switch<br />
Fuse<br />
Box (optional)<br />
Plug<br />
(optional)<br />
Transformer<br />
ILLUSTRATION<br />
plug<br />
Terminal<br />
strip<br />
12 / 6 volts CT<br />
120 volts<br />
Transformer<br />
wires soldered and taped<br />
with electrical tape<br />
2-conductor<br />
"zip" cord<br />
line switch<br />
"zip" cord split into<br />
separate wires<br />
wires soldered and taped<br />
with electrical tape<br />
INSTRUCTIONS<br />
Warning!Thisprojectinvolvestheuseofdangerousvoltages.Youmustmakesureallhighvoltage(120volthouseholdpower)conductorsaresafelyinsulatedfromaccidentalcontact.No<br />
barewiresshouldbeseenanywhereonthe”primary”sideofthetransformercircuit.Besure<br />
tosolderallwireconnectionssothatthey’resecure,anduserealelectricaltape(notducttape,<br />
scotchtape,packingtape,oranyotherkind!)toinsulateyoursolderedconnections.<br />
Ifyouwishtoenclosethetransformerinsideofabox,youmayuseanelectrical”junction”<br />
box,obtainedfromahardwarestoreorelectricalsupplyhouse.Iftheenclosureusedismetal<br />
ratherthanplastic,athree-prongplugshouldbeused,withthe”ground”prong(thelongest<br />
oneontheplug)connecteddirectlytothemetalcaseformaximumsafety.<br />
Beforepluggingtheplugintoawallsocket,doasafetycheckwithanohmmeter.Withthe<br />
lineswitchinthe”on”position,measureresistancebetweeneitherplugprongandthetransformercase.Thereshouldbeinfinite(maximum)resistance.Ifthemeterregisterscontinuity<br />
(someresistancevaluelessthaninfinity),thenyouhavea”short”betweenoneofthepower<br />
conductorsandthecase,whichisdangerous!
4.2. TRANSFORMER–POWERSUPPLY 149<br />
Next,checkthetransformerwindingsthemselvesforcontinuity.Withthelineswitchinthe<br />
”on”position,thereshouldbeasmallamountofresistancebetweenthetwoplugprongs.When<br />
theswitchisturned”off,”theresistanceindicationshouldincreasetoinfinity(opencircuit–no<br />
continuity).Measureresistancebetweenpairsofwiresonthesecondaryside.Thesesecondary<br />
windingsshouldregistermuchlowerresistancesthantheprimary.Whyisthis?<br />
Plugthecordintoawallsocketandturntheswitchon.YoushouldbeabletomeasureAC<br />
voltageatthesecondarysideofthetransformer,betweenpairsofterminals.Betweentwoof<br />
theseterminals,youshouldmeasureabout12volts. Betweeneitherofthesetwoterminals<br />
andthethirdterminal,youshouldmeasurehalfthat.Thisthirdwireisthe”center-tap”wire<br />
ofthesecondarywinding.<br />
Itwouldbeadvisabletokeepthisprojectassembledforuseinpoweringotherexperiments<br />
showninthisbook.Fromhereon,Iwilldesignatethis”low-voltageACpowersupply”using<br />
thisillustration:<br />
Low-voltage<br />
AC power supply<br />
12<br />
6 6<br />
COMPUTERSIMULATION<br />
SchematicwithSPICEnodenumbers:<br />
1<br />
120 V<br />
R bogus1<br />
1 mΩ<br />
2<br />
L 1<br />
L 2<br />
L 3<br />
0 0<br />
1 TΩ<br />
5<br />
4<br />
3<br />
R load1<br />
R load2<br />
R bogus2<br />
Netlist(makeatextfilecontainingthefollowingtext,verbatim):<br />
transformer with center-tap secondary<br />
v1 1 0 ac 120 sin<br />
rbogus1 1 2 1e-3<br />
l1 2 0 10<br />
l2 5 4 0.025<br />
l3 4 3 0.025<br />
k1 l1 l2 0.999<br />
k2 l2 l3 0.999
150 CHAPTER4. ACCIRCUITS<br />
k3 l1 l3 0.999<br />
rbogus2 3 0 1e12<br />
rload1 5 4 1k<br />
rload2 4 3 1k<br />
* Sets up AC analysis at 60 Hz:<br />
.ac lin 1 60 60<br />
* Prints primary voltage between nodes 2 and 0:<br />
.print ac v(2,0)<br />
* Prints (top) secondary voltage between nodes 5 and 4:<br />
.print ac v(5,4)<br />
* Prints (bottom) secondary voltage between nodes 4 and 3:<br />
.print ac v(4,3)<br />
* Prints (total) secondary voltage between nodes 5 and 3:<br />
.print ac v(5,3)<br />
.end
4.3. BUILDATRANSFORMER 151<br />
4.3 Buildatransformer<br />
PARTSANDMATERIALS<br />
• Steelflatbar,4pieces<br />
• Miscellaneousbolts,nuts,washers<br />
• 28gauge”magnet”wire<br />
• Low-voltageACpowersupply<br />
”Magnetwire”issmall-gaugewireinsulatedwithathinenamelcoating.Itisintendedto<br />
beusedtomakeelectromagnets,becausemany”turns”ofwiremaybewrappedinarelatively<br />
small-diametercoil.Anygaugeofwirewillwork,but28gaugeisrecommendedsoastomake<br />
acoilwithasmanyturnsaspossibleinasmalldiameter.<br />
CROSS-REFERENCES<br />
LessonsInElectricCircuits,Volume2,chapter9:”Transformers”<br />
LEARNINGOBJECTIVES<br />
• Effectsofelectromagnetism.<br />
• Effectsofelectromagneticinduction.<br />
• Effectsofmagneticcouplingonvoltageregulation.<br />
• Effectsofwindingturnson”step”ratio.<br />
SCHEMATICDIAGRAM<br />
Transformer<br />
ILLUSTRATION
152 CHAPTER4. ACCIRCUITS<br />
bolt<br />
wire coil<br />
wire coil<br />
steel "flatbar"<br />
INSTRUCTIONS<br />
Wraptwo,equal-lengthbarsofsteelwithathinlayerofelectrically-insulatingtape.Wrap<br />
severalhundredturnsofmagnetwirearoundthesetwobars.Youmaymakethesewindings<br />
withanequalorunequalnumberofturns,dependingonwhetherornotyouwantthetransformertobeableto”step”voltageupordown.<br />
Irecommendequalturnstobeginwith,then<br />
experimentlaterwithcoilsofunequalturncount.<br />
Jointhosebarstogetherinarectanglewithtwoother,shorter,barsofsteel. Useboltsto<br />
securethebarstogether(itisrecommendedthatyoudrillboltholesthroughthebarsbefore<br />
youwrapwirearoundthem).<br />
Checkforshortedwindings(ohmmeterreadingbetweenwireendsandsteelbar)after<br />
you’refinishedwrappingthewindings. Thereshouldbenocontinuity(infiniteresistance)<br />
betweenthewindingandthesteelbar.Checkforcontinuitybetweenwindingendstoensure<br />
thatthewireisn’tbrokenopensomewherewithinthecoil.Ifeitherresistancemeasurements<br />
indicateaproblem,thewindingmustbere-made.<br />
Poweryourtransformerwiththelow-voltageoutputofthe”powersupply”describedatthe<br />
beginningofthischapter. Donotpoweryourtransformerdirectlyfromwall-socketvoltage<br />
(120volts),asyourhome-madewindingsreallyaren’tratedforanysignificantvoltage!<br />
Measuretheoutputvoltage(secondarywinding)ofyourtransformerwithanACvoltmeter.<br />
Connectaloadofsomekind(lightbulbsaregood!)tothesecondarywindingandre-measure<br />
voltage.Notethedegreeofvoltage”sag”atthesecondarywindingasloadcurrentisincreased.<br />
Loosenorremovetheconnectingboltsfromoneoftheshortbarpieces,thusincreasing<br />
thereluctance(analogoustoresistance)ofthemagnetic”circuit”couplingthetwowindings<br />
together.Notetheeffectonoutputvoltageandvoltage”sag”underload.<br />
Ifyou’vemadeyourtransformerwithunequal-turnwindings.tryitinstep-upversusstepdownmode,poweringdifferentACloads.
4.4. VARIABLEINDUCTOR 153<br />
4.4 Variableinductor<br />
PARTSANDMATERIALS<br />
• Papertube,fromatoilet-paperroll<br />
• Barofironorsteel,largeenoughtoalmostfilldiameterofpapertube<br />
• 28gauge”magnet”wire<br />
• Low-voltageACpowersupply<br />
• Incandescentlamp,ratedforpowersupplyvoltage<br />
CROSS-REFERENCES<br />
LessonsInElectricCircuits,Volume1,chapter14:”MagnetismandElectromagnetism”<br />
LessonsInElectricCircuits,Volume1,chapter15:”Inductors”<br />
LessonsInElectricCircuits,Volume2,chapter3:”ReactanceandImpedance–Inductive”<br />
LEARNINGOBJECTIVES<br />
• Effectsofmagneticpermeabilityoninductance.<br />
• HowinductivereactancecancontrolcurrentinanACcircuit.<br />
SCHEMATICDIAGRAM<br />
Variable inductor<br />
Lamp<br />
ILLUSTRATION
154 CHAPTER4. ACCIRCUITS<br />
wire coil<br />
Steel<br />
bar<br />
Paper<br />
tube<br />
Low-voltage<br />
AC power supply<br />
12<br />
6 6<br />
INSTRUCTIONS<br />
Wraphundredsofturnsofmagnetwirearoundthepapertube. Connectthishome-made<br />
inductorinserieswithanACpowersupplyandlamptoformacircuit.Whenthetubeisempty,<br />
thelampshouldglowbrightly.Whenthesteelbarisinsertedinthetube,thelampdimsfrom<br />
increasedinductance(L)andconsequentlyincreasedinductivereactance(X L ).<br />
Tryusingbarsofdifferentmaterials,suchascopperandstainlesssteel,ifavailable. Not<br />
allmetalshavethesameeffect,duetodifferencesinmagneticpermeability.
4.5. SENSITIVEAUDIODETECTOR 155<br />
4.5 Sensitiveaudiodetector<br />
PARTSANDMATERIALS<br />
• High-quality”closed-cup”audioheadphones<br />
• Headphonejack:femalereceptacleforheadphoneplug(RadioShackcatalog#274-312)<br />
• Smallstep-downpowertransformer(RadioShackcatalog#273-1365orequivalent,using<br />
the6-voltsecondarywindingtap)<br />
• Two1N4001rectifyingdiodes(RadioShackcatalog#276-1101)<br />
• 1kΩresistor<br />
• 100kΩpotentiometer(RadioShackcatalog#271-092)<br />
• Two”banana”jackstylebindingposts,orotherterminalhardware,forconnectionto<br />
potentiometercircuit(RadioShackcatalog#274-662orequivalent)<br />
• Plasticormetalmountingbox<br />
Regardingtheheadphones,thehigherthe”sensitivity”ratingindecibels(dB),thebetter,<br />
butlisteningisbelieving:ifyou’reseriousaboutbuildingadetectorwithmaximumsensitivity<br />
forsmallelectricalsignals,youshouldtryafewdifferentheadphonemodelsatahigh-quality<br />
audiostoreand”listen”forwhichonesproduceanaudiblesoundforthelowestvolumesetting<br />
onaradioorCDplayer. Beware,asyoucouldspendhundredsofdollarsonapairofheadphonestogettheabsolutebestsensitivity!Takeheart,though:I’veusedanoldpairofRadio<br />
Shack”Realistic”brandheadphoneswithperfectlyadequateresults,soyoudon’tneedtobuy<br />
thebest.<br />
Normally,thetransformerusedinthistypeofapplication(audiospeakerimpedancematching)iscalledan”audiotransformer,”withitsprimaryandsecondarywindingsrepresentedby<br />
impedancevalues(1000 Ω:8 Ω)insteadofvoltages.Anaudiotransformerwillwork,butI’ve<br />
foundsmallstep-downpowertransformersof120/6voltratiotobeperfectlyadequateforthe<br />
task,cheaper(especiallywhentakenfromanoldthrift-storealarmclockradio),andfarmore<br />
rugged.<br />
Thetolerance(precision)ratingforthe1kΩresistorisirrelevant.The100kΩpotentiometerisarecommendedoptionforincorporationintothisproject,asitgivestheusercontrol<br />
overtheloudnessforanygivensignal. Eventhoughanaudio-taperpotentiometerwouldbe<br />
appropriateforthisapplication,itisnotnecessary.Alinear-taperpotentiometerworksquite<br />
well.<br />
CROSS-REFERENCES<br />
LessonsInElectricCircuits,Volume1,chapter8:”DCMeteringCircuits”<br />
LessonsInElectricCircuits,Volume2,chapter9:”Transformers”<br />
LessonsInElectricCircuits,Volume2,chapter12:”ACMeteringCircuits”<br />
LEARNINGOBJECTIVES
156 CHAPTER4. ACCIRCUITS<br />
• Solderingpractice<br />
• Useofatransformerforimpedancematching<br />
• Detectionofextremelysmallelectricalsignals<br />
• Usingdiodesto”clip”voltageatsomemaximumlevel<br />
SCHEMATICDIAGRAM<br />
headphones<br />
test lead<br />
transformer<br />
1 kΩ<br />
diodes<br />
jack<br />
plug<br />
test lead<br />
ILLUSTRATION<br />
headphones<br />
resistor<br />
120 V<br />
6 V<br />
Binding<br />
posts<br />
diodes<br />
transformer<br />
jack<br />
plug<br />
INSTRUCTIONS<br />
Thisexperimentisidenticalinconstructiontothe”SensitiveVoltageDetector”described<br />
intheDCexperimentschapter.Ifyou’vealreadybuiltthisdetector,youmayskipthisexperiment.<br />
Theheadphones,mostlikelybeingstereounits(separateleftandrightspeakers)willhave<br />
athree-contactplug. Youwillbeconnectingtoonlytwoofthosethreecontactpoints. Ifyou<br />
onlyhavea”mono”headphonesetwithatwo-contactplug,justconnecttothosetwocontact<br />
points.Youmayeitherconnectthetwostereospeakersinseriesorinparallel.I’vefoundthe<br />
seriesconnectiontoworkbest,thatis,toproducethemostsoundfromasmallsignal:
4.5. SENSITIVEAUDIODETECTOR 157<br />
To transformer<br />
To transformer<br />
common right left common right left<br />
Speakers in series<br />
Speakers in parallel<br />
Solderallwireconnectionswell.Thisdetectorsystemisextremelysensitive,andanyloose<br />
wireconnectionsinthecircuitwilladdunwantednoisetothesoundsproducedbythemeasuredvoltagesignal.<br />
Thetwodiodesconnectedinparallelwiththetransformer’sprimary<br />
winding,alongwiththeseries-connected1kΩresistor,worktogetherto”clip”theinputvoltagetoamaximumofabout0.7volts.Thisdoesonethingandonethingonly:limittheamount<br />
ofsoundtheheadphonescanproduce.Thesystemwillworkwithoutthediodesandresistorin<br />
place,buttherewillbenolimittosoundvolumeinthecircuit,andtheresultingsoundcaused<br />
byaccidentallyconnectingthetestleadsacrossasubstantialvoltagesource(likeabattery)<br />
canbedeafening!<br />
Bindingpostsprovidepointsofconnectionforapairoftestprobeswithbanana-styleplugs,<br />
oncethedetectorcomponentsaremountedinsideabox. Youmayuseordinarymultimeter<br />
probes,ormakeyourownprobeswithalligatorclipsattheendsforsecureconnectiontoa<br />
circuit.<br />
Detectorsareintendedtobeusedforbalancingbridgemeasurementcircuits,potentiometric(null-balance)voltmetercircuits,anddetectextremelylow-amplitudeAC(”alternatingcurrent”)signalsintheaudiofrequencyrange.Itisavaluablepieceoftestequipment,especially<br />
forthelow-budgetexperimenterwithoutanoscilloscope. Itisalsovaluableinthatitallows<br />
youtouseadifferentbodilysenseininterpretingthebehaviorofacircuit.<br />
Forconnectionacrossanynon-trivialsourceofvoltage(1voltandgreater),thedetector’s<br />
extremelyhighsensitivityshouldbeattenuated. Thismaybeaccomplishedbyconnectinga<br />
voltagedividertothe”front”ofthecircuit:<br />
SCHEMATICDIAGRAM<br />
test lead<br />
100<br />
kΩ<br />
1 kΩ<br />
test lead<br />
ILLUSTRATION
158 CHAPTER4. ACCIRCUITS<br />
potentiometer<br />
Adjustthe100kΩvoltagedividerpotentiometertoaboutmid-rangewheninitiallysensing<br />
avoltagesignalofunknownmagnitude.Ifthesoundistooloud,turnthepotentiometerdown<br />
andtryagain. Iftoosoft,turnitupandtryagain. ThisdetectorevensensesDCandradiofrequencysignals(frequenciesbelowandabovetheaudiorange,respectively),a”click”being<br />
heardwheneverthetestleadsmakeorbreakcontactwiththesourceundertest. Withmy<br />
cheapheadphones,I’vebeenabletodetectcurrentsoflessthan1/10ofamicroamp(¡0.1 µA)<br />
DC,andsimilarlylow-magnitudeRFsignalsupto2MHz.<br />
Agooddemonstrationofthedetector’ssensitivityistotouchbothtestleadstotheend<br />
ofyourtongue,withthesensitivityadjustmentsettomaximum. Thevoltageproducedby<br />
metal-to-electrolytecontact(calledgalvanicvoltage)isverysmall,butenoughtoproducesoft<br />
”clicking”soundseverytimetheleadsmakeandbreakcontactonthewetskinofyourtongue.<br />
Tryunpluggingtheheadphoneplugfromthejack(receptacle)andsimilarlytouchingitto<br />
theendofyourtongue.Youshouldstillhearsoftclickingsounds,buttheywillbemuchsmaller<br />
inamplitude.Headphonespeakersare”lowimpedance”devices:theyrequirelowvoltageand<br />
”high”currenttodeliversubstantialsoundpower.Impedanceisameasureofoppositiontoany<br />
andallformsofelectriccurrent,includingalternatingcurrent(AC).Resistance,bycomparison,isastrictlymeasureofoppositiontodirectcurrent(DC).Likeresistance,impedanceis<br />
measuredintheunitoftheOhm(Ω),butitissymbolizedinequationsbythecapitalletter”Z”<br />
ratherthanthecapitalletter”R”.Weusetheterm”impedance”todescribetheheadphone’soppositiontocurrentbecauseitisprimarilyACsignalsthatheadphonesarenormallysubjected<br />
to,notDC.<br />
Mostsmallsignalsourceshavehighinternalimpedances,somemuchhigherthanthenominal8Ωoftheheadphonespeakers.Thisisatechnicalwayofsayingthattheyareincapableof<br />
supplyingsubstantialamountsofcurrent.AstheMaximumPowerTransferTheorempredicts,<br />
maximumsoundpowerwillbedeliveredbytheheadphonespeakerswhentheirimpedanceis<br />
”matched”totheimpedanceofthevoltagesource.Thetransformerdoesthis.Thetransformer<br />
alsohelpsaidthedetectionofsmallDCsignalsbyproducinginductive”kickback”everytime<br />
thetestleadcircuitisbroken,thus”amplifying”thesignalbymagneticallystoringupelectrical<br />
energyandsuddenlyreleasingittotheheadphonespeakers.<br />
Aswiththelow-voltageACpowersupplyexperiment,Irecommendbuildingthisdetector<br />
inapermanentfashion(mountingallcomponentsinsideofabox,andprovidingnicetestlead<br />
wires)soitcanbeeasilyusedinthefuture.Constructedassuch,itmightlooksomethinglike<br />
this:
4.5. SENSITIVEAUDIODETECTOR 159<br />
headphones<br />
Test leads<br />
Sensitivity<br />
plug
160 CHAPTER4. ACCIRCUITS<br />
4.6 SensingACmagneticfields<br />
PARTSANDMATERIALS<br />
• Audiodetectorwithheadphones<br />
• Electromagnetcoilfromrelayorsolenoid<br />
Whatisneededforanelectromagnetcoilisacoilwithmanyturnsofwire,soastoproduce<br />
themostvoltagepossiblefrominductionwithstraymagneticfields.Thecoiltakenfromanold<br />
relayorsolenoidworkswellforthispurpose.<br />
CROSS-REFERENCES<br />
LessonsInElectricCircuits,Volume2,chapter7:”Mixed-FrequencyACSignals”<br />
LEARNINGOBJECTIVES<br />
• Effectsofelectromagneticinduction.<br />
• Electromagneticshieldingtechniques.<br />
SCHEMATICDIAGRAM<br />
Audio detector circuit<br />
sensing<br />
coil<br />
100<br />
kΩ<br />
1 kΩ<br />
ILLUSTRATION<br />
headphones<br />
sensing<br />
coil<br />
Audio<br />
detector<br />
circuit<br />
Sensitivity<br />
plug
4.6. SENSINGACMAGNETICFIELDS 161<br />
INSTRUCTIONS<br />
UsingtheaudiodetectorcircuitexplainedearliertodetectACvoltageintheaudiofrequencies,acoilofwiremayserveassensorofACmagneticfields.Thevoltagesproducedbythecoil<br />
willbequitesmall,soitisadvisabletoadjustthedetector’ssensitivitycontrolto”maximum.”<br />
TherearemanysourcesofACmagneticfieldstobefoundintheaveragehome.Try,forinstance,holdingthecoilclosetoatelevisionscreenorcircuit-breakerbox.Thecoil’sorientation<br />
iseverybitasimportantasitsproximitytothesource,asyouwillsoondiscoveronyourown!<br />
Ifyouwanttolistentomoreinterestingtones,tryholdingthecoilclosetothemotherboard<br />
ofanoperatingcomputer(becarefulnotto”short”anyconnectionstogetheronthecomputer’s<br />
circuitboardwithanyexposedmetalpartsonthesensingcoil!),ortoitsharddrivewhilea<br />
read/writeoperationistakingplace.<br />
OneverystrongsourceofACmagneticfieldsisthehome-madetransformerprojectdescribedearlier.<br />
Tryexperimentingwithvariousdegreesof”coupling”betweenthecoils(the<br />
steelbarstightlyfastenedtogether, versuslooselyfastened, versusdismantled). Another<br />
sourceisthevariableinductorandlampcircuitdescribedinanothersectionofthischapter.<br />
Notethatphysicalcontactwithamagneticfieldsourceisunnecessary: magneticfields<br />
extendthroughspacequiteeasily.Youmayalsowanttotry”shielding”thecoilfromastrong<br />
sourceusingvariousmaterials. Tryaluminumfoil,paper,sheetsteel,plastic,orwhatever<br />
othermaterialsyoucanthinkof.Whatmaterialsworkbest?Why?Whatangles(orientations)<br />
ofcoilpositionminimizemagneticcoupling(resultinaminimumofdetectedsignal)? What<br />
doesthistellusregardinginductorpositioningifinter-circuitinterferencefromotherinductors<br />
isabadthing?<br />
Whetherornotstraymagneticfieldsliketheseposeanyhealthhazardtothehumanbody<br />
isahotlydebatedsubject. Onethingisclear: intoday’smodernsociety,low-levelmagnetic<br />
fieldsofallfrequenciesareeasytofind!
162 CHAPTER4. ACCIRCUITS<br />
4.7 SensingACelectricfields<br />
PARTSANDMATERIALS<br />
• Audiodetectorwithheadphones<br />
CROSS-REFERENCES<br />
LessonsInElectricCircuits,Volume2,chapter7:”Mixed-FrequencyACSignals”<br />
LEARNINGOBJECTIVES<br />
• Effectsofelectrostatic(capacitive)coupling.<br />
• Electrostaticshieldingtechniques.<br />
SCHEMATICDIAGRAM<br />
sensing<br />
wire<br />
Audio detector circuit<br />
100<br />
kΩ<br />
1 kΩ<br />
ILLUSTRATION<br />
headphones<br />
sensing<br />
wire<br />
Audio<br />
detector<br />
circuit<br />
Sensitivity<br />
plug<br />
connection to<br />
water pipe
4.7. SENSINGACELECTRICFIELDS 163<br />
INSTRUCTIONS<br />
”Ground”oneleadofthedetectortoametalobjectincontactwiththeearth(dirt). Most<br />
anywaterpipeorfaucetinahousewillsuffice. Taketheotherleadandholditclosetoan<br />
electricalapplianceorlampfixture. Donottrytomakecontactwiththeapplianceor<br />
withanyconductorswithin!AnyACelectricfieldsproducedbytheappliancewillbeheard<br />
intheheadphonesasabuzzingtone.<br />
Tryholdingthewireindifferentpositionsnexttoagood,strongsourceofelectricfields.Try<br />
usingapieceofaluminumfoilclippedtothewire’sendtomaximizecapacitance(andtherefore<br />
itsabilitytointerceptanelectricfield). Tryusingdifferenttypesofmaterialto”shield”the<br />
wirefromanelectricfieldsource. Whatmaterial(s)workbest? Howdoesthiscomparewith<br />
theACmagneticfieldexperiment?<br />
Aswithmagneticfields,thereiscontroversywhetherornotstrayelectricfieldslikethese<br />
poseanyhealthhazardtothehumanbody.
164 CHAPTER4. ACCIRCUITS<br />
4.8 Automotivealternator<br />
PARTSANDMATERIALS<br />
• Automotivealternator(onerequired,buttworecommended)<br />
Oldalternatorsmaybeobtainedforlowpricesatautomobilewreckingyards.Manyyards<br />
havealternatorsalreadyremovedfromtheautomobile,foryourconvenience.Idonotrecommendpayingfullpriceforanewalternator,asusedunitscostfarlessmoneyandfunctionjust<br />
aswellforthepurposesofthisexperiment.<br />
IhighlyrecommendusingaDelco-Remybrandofalternator. Thisisthetypeusedon<br />
GeneralMotors(GMC,Chevrolet,Cadillac,Buick,Oldsmobile)vehicles.Oneparticularmodel<br />
hasbeenproducedbyDelco-Remysincetheearly1960’swithlittledesignchange.Itisavery<br />
commonunittolocateinawreckingyard,andveryeasytoworkwith.<br />
Ifyouobtaintwoalternators,youmayuseoneasageneratorandtheotherasamotor.The<br />
stepsneededtoprepareanalternatorasathree-phasegeneratorandasathree-phasemotor<br />
arethesame.<br />
CROSS-REFERENCES<br />
LessonsInElectricCircuits,Volume1,chapter14:”MagnetismandElectromagnetism”<br />
LessonsInElectricCircuits,Volume2,chapter10:”PolyphaseACCircuits”<br />
LEARNINGOBJECTIVES<br />
• Effectsofelectromagnetism<br />
• Effectsofelectromagneticinduction<br />
• Constructionofrealelectromagneticmachines<br />
• Constructionandapplicationofthree-phasewindings<br />
SCHEMATICDIAGRAM<br />
Typical alternator<br />
"field"<br />
terminals<br />
"battery"<br />
terminal<br />
shaft<br />
Anautomotivealternatorisathree-phasegeneratorwithabuilt-inrectifiercircuitconsistingofsixdiodes.<br />
Asthesheave(mostpeoplecallita”pulley”)isrotatedbyabeltconnected
4.8. AUTOMOTIVEALTERNATOR 165<br />
totheautomobileengine’scrankshaft,amagnetisspunpastastationarysetofthree-phase<br />
windings(calledthestator),usuallyconnectedinaYconfiguration. Thespinningmagnetis<br />
actuallyanelectromagnet,notapermanentmagnet.Alternatorsaredesignedthiswaysothat<br />
themagneticfieldstrengthcanbecontrolled,inorderthatoutputvoltagemaybecontrolled<br />
independentlyofrotorspeed. Thisrotormagnetcoil(calledthefieldcoil,orsimplyfield)is<br />
energizedbybatterypower,sothatittakesasmallamountofelectricalpowerinputtothe<br />
alternatortogetittogeneratealotofoutputpower.<br />
<strong>Electrical</strong>powerisconductedtotherotatingfieldcoilthroughapairofcopper”sliprings”<br />
mountedconcentricallyontheshaft,contactedbystationarycarbon”brushes.”Thebrushes<br />
areheldinfirmcontactwiththeslipringsbyspringpressure.<br />
Manymodernalternatorsareequippedwithbuilt-in”regulator”circuitsthatautomatically<br />
switchbatterypoweronandofftotherotorcoiltoregulateoutputvoltage. Thiscircuit,if<br />
presentinthealternatoryouchoosefortheexperiment,isunnecessaryandwillonlyimpede<br />
yourstudyifleftinplace.Feelfreeto”surgicallyremove”it,justmakesureyouleaveaccess<br />
tothebrushterminalssothatyoucanpowerthefieldcoilwiththealternatorfullyassembled.<br />
ILLUSTRATION<br />
INSTRUCTIONS<br />
First,consultanautomotiverepairmanualonthespecificdetailsofyouralternator. The<br />
documentationprovidedinthebookyou’rereadingnowisasgeneralaspossibletoaccommodatedifferentbrandsofalternators.<br />
Youmayneedmorespecificinformation,andaservice<br />
manualisthebestplacetoobtainit.<br />
Forthisexperiment,you’llbeconnectingwirestothecoilsinsidethealternatorandextendingthemoutsidethealternatorcase,foreasyconnectiontotestequipmentandcircuits.<br />
Unfortunately,theconnectionterminalsprovidedbythemanufacturerwon’tsuitourneeds<br />
here,soyouneedtomakeyourownconnections.<br />
Disassembletheunitandlocateterminalsforconnectingtothetwocarbonbrushes.Solder<br />
apairofwirestotheseterminals(atleast20gaugeinsize)andextendthesewiresthrough<br />
ventholesinthealternatorcase,makingsuretheywon’tgetsnaggedonthespinningrotor<br />
whenthealternatorisre-assembledandused.<br />
Locatethethree-phaselineconnectionscomingfromthestatorwindingsandconnectwires<br />
tothemaswell,extendingthesewiresoutsidethealternatorcasethroughsomeventholes.<br />
Usethelargestgaugewirethatisconvenienttoworkwithforthesewires,astheymaybe<br />
carryingsubstantialcurrent.Aswiththefieldwires,routetheminsuchawaythattherotor<br />
willturnfreelywiththealternatorreassembled. Thestatorwindinglineterminalsareeasy
166 CHAPTER4. ACCIRCUITS<br />
tolocate: thethreeofthemconnecttothreeterminalsonthediodeassembly,usuallywith<br />
”ring-lug”terminalssolderedtotheendsofthewires.<br />
Interior view of alternator,<br />
rotor removed<br />
add these<br />
wires<br />
diodes<br />
brush<br />
stator<br />
Irecommendthatyousolderring-lugterminalstoyourwires,andattachthemunderneath<br />
theterminalnutsalongwiththestatorwireends,sothateachdiodeblockterminalissecuring<br />
tworinglugs.<br />
Re-assemblethealternator,takingcaretosecurethecarbonbrushesinaretractedposition<br />
sothattherotordoesn’tdamagethemuponre-insertion.OnDelco-Remyalternators,asmall<br />
holeisprovidedonthebackcasehalf,andalsoatthefrontofthebrushholderassembly,<br />
throughwhichapapercliporthin-gaugewiremaybeinsertedtoholdthebrushesbackagainst<br />
theirspringpressure.Consulttheservicemanualformoredetailsonalternatorassembly.<br />
Whenthealternatorhasbeenassembled,tryspinningtheshaftandlistenforanysounds<br />
indicativeofcollidingpartsorsnaggedwires.Ifthereisanysuchtrouble,takeitapartagain<br />
andcorrectwhateveriswrong.<br />
Ifandwhenitspinsfreelyasitshould,connectthetwo”field”wirestoa6-voltbattery.<br />
Connectanvoltmetertoanytwoofthethree-phaselineconnections:<br />
V<br />
A<br />
V<br />
OFF<br />
A<br />
A<br />
COM<br />
+ -
4.8. AUTOMOTIVEALTERNATOR 167<br />
Withthemultimetersettothe”DCvolts”function,slowlyrotatethealternatorshaft.The<br />
voltmeterreadingshouldalternatebetweenpositiveandnegativeastheshaftitturned: a<br />
demonstrationofveryslowalternatingvoltage(ACvoltage)beinggenerated. Ifthistestis<br />
successful,switchthemultimetertothe”ACvolts”settingandtryagain. Tryspinningthe<br />
shaftslowandfast,comparingvoltmeterreadingsbetweenthetwoconditions.<br />
Short-circuitanytwoofthethree-phaselinewiresandtryspinningthealternator. What<br />
youshouldnoticeisthatthealternatorshaftbecomesmoredifficulttospin.Theheavyelectricalloadyou’vecreatedviatheshortcircuitcausesaheavymechanicalloadonthealternator,<br />
asmechanicalenergyisconvertedintoelectricalenergy.<br />
Now,tryconnecting12voltsDCtothefieldwires.RepeattheDCvoltmeter,ACvoltmeter,<br />
andshort-circuittestsdescribedabove.Whatdifference(s)doyounotice?<br />
Findsomesortofpolarity-insensitive6or12voltsloads,suchassmallincandescentlamps,<br />
andconnectthemtothethree-phaselinewires.Wrapathinropeorheavystringaroundthe<br />
grooveofthesheave(”pulley”)andspinthealternatorrapidly,andtheloadsshouldfunction.<br />
Ifyouhaveasecondalternator,modifyitasyoumodifiedthefirstone,connectingfiveof<br />
yourownwirestothefieldbrushesandstatorlineterminals,respectively.Youcanthenuseit<br />
asathree-phasemotor,poweredbythefirstalternator.<br />
Connecteachofthethree-phaselinewiresofthefirstalternatortotherespectivewires<br />
ofthesecondalternator. Connectthefieldwiresofonealternatortoa6voltbattery. This<br />
alternatorwillbethegenerator.Wrapropearoundthesheaveinpreparationtospinit.Take<br />
thetwofieldwiresofthesecondalternatorandshortthemtogether. Thisalternatorwillbe<br />
themotor:<br />
Motor<br />
Generator<br />
+ -<br />
Spinthegeneratorshaftwhilewatchingthemotorshaft’srotation.Tryreversinganytwo<br />
ofthethree-phaselineconnectionsbetweenthetwounitsandspinthegeneratoragain.What<br />
isdifferentthistime?<br />
Connectthefieldwiresofthemotorunittothea6voltbattery(youmayparallel-connect<br />
thisfieldwiththefieldofthegeneratorunit,acrossthesamebatteryterminals,ifthebattery
168 CHAPTER4. ACCIRCUITS<br />
isstrongenoughtodelivertheseveralampsofcurrentbothcoilswilldrawtogether).Thiswill<br />
magnetizetherotorofthemotor.Tryspinningthegeneratoragainandnoteanydifferencesin<br />
operation.<br />
Inthefirstmotorsetup,wherethefieldwiresweresimpleshortedtogether,themotor<br />
wasfunctioningasaninductionmotor. Inthesecondsetup,wherethemotor’srotorwas<br />
magnetized,itfunctionedasasynchronousmotor.<br />
Ifyouarefeelingparticularlyambitiousandareskilledinmetalfabricationtechniques,<br />
youmaymakeyourownhigh-powergeneratorplatformbyconnectingthemodifiedalternator<br />
toabicycle.I’vebuiltanarrangementthatlookslikethis:<br />
alternator<br />
Therearwheeldrivesthegeneratorsheavewithalongv-belt. Thisbeltalsosupports<br />
therearofthebicycle,maintainingaconstanttensionwhenariderispedalingthebicycle.<br />
Thegeneratorhangsfromasteelsupportstructure(Iusedwelded2-inchsquaretubing,but<br />
aframecouldbemadeoutoflumber). Notonlyisthismachinepractical,butitisreliable<br />
enoughtobeusedasanexercisemachine,anditisinexpensivetomake:<br />
Youcanseeabankofthree12-volt”RV”lightbulbsbehindthebicycleunit(inthelowerleftcornerofthephotograph),whichIuseforaloadwhenridingthebicycleasanexercise<br />
machine.Asetofthreeswitchesismountedatthefrontofthebicycle,whereIcanturnloads
4.8. AUTOMOTIVEALTERNATOR 169<br />
onandoffwhileriding.<br />
Byrectifyingthethree-phaseACpowerproduced,itispossibletohavethealternatorpower<br />
itsownfieldcoilwithDCvoltage,eliminatingtheneedforabattery.However,someindependentsourceofDCvoltagewillstillbenecessaryforstart-up,asthefieldcoilmustbeenergized<br />
beforeanyACpowercanbeproduced.
170 CHAPTER4. ACCIRCUITS<br />
4.9 Inductionmotor<br />
PARTSANDMATERIALS<br />
• ACpowersource:120VAC<br />
• Capacitor,3.3 µF(or2.2 µF)120VACor350VDC,non-polarized<br />
• 15to25wattincandescentlampor820Ω25wattresistors<br />
• #32AWGmagnetwire<br />
• woodenboardapprox.5in.square.<br />
• AClinecordwithplug<br />
• 1.75inchdia.cardboardtubing(toiletpaperroll)<br />
• lampsocket<br />
• ACpowersource:220VAC<br />
• Capacitor,1.5 µF240VACor680VDC,non-polarized<br />
• 25to40wattincandescentlampor820Ω25wattresistors<br />
• #32AWGmagnetwire<br />
• woodenboardapprox.15cm.square.<br />
• AClinecordwithplug<br />
• 4.5to5cm.dia.cardboardtubing.<br />
• lampsocket<br />
CROSS-REFERENCES<br />
LessonsInElectricCircuits,Volume2,chapter13: ”ACmotors”,”SinglePhaseinduction<br />
motors”,”Permanentsplit-capacitormotor”.<br />
LEARNINGOBJECTIVES<br />
• TobuildanACpermanentcapacitorsplit-phaseinductionmotor.<br />
• ToillustratethesimplicityoftheACinductionmotor.<br />
SCHEMATICDIAGRAM
4.9. INDUCTIONMOTOR 171<br />
1"<br />
120 Vac<br />
440 turns<br />
25 watt lamp<br />
440 turns<br />
1.75"<br />
3.3 µF<br />
(a)<br />
(b)<br />
ILLUSTRATION<br />
INSTRUCTIONS<br />
Therearetwopartsliststochoosefromdependingupontheavailabilityof120VACor<br />
220VAC.Choosetheoneforyourlocation.Thissetofinstructionsisforthe120VACversion.<br />
Thisisasimplifiedversionofa”permanentcapacitorsplit-phaseinductionmotor”.Bysimplified,wemeanthecoilsonlyrequiresafewhundredturnsofwireinsteadofafewthousand.<br />
Thisiseasiertowind. Though,thelargerfewthousandturnsmodelisimpressive. There<br />
aretwostatorcoilsasshownintheillustrationabove.Approximately440turnsof#32AWG<br />
(Americanwiregauge)enameledmagnetwirearewoundoveraoneinchlengthofaslightly<br />
longersectionof1.75inchdiametertoiletpapertube.Toavoidcountingtheturns,close-wind<br />
fourlayersofmagnetwireoveraoneinchwidthofthetube.See(b)above.Leaveafewinches<br />
ofmagnetwirefortheleads. Tapethebeginningleadneartheendofthetubesothatthe<br />
windingswillcoverandanchorthetape.Donotcutthefinalwidthofthecardboardtubeuntil
172 CHAPTER4. ACCIRCUITS<br />
thewindingisfinished.Closewindasinglelayer.Tapeorcementthefirstlayertopreventunwindingbeforeproceedingtothesecondlayer.Thoughitispossibletowindadditionallayers<br />
directlyoverexistinglayers,considerapplyingtapeorpaperbetweenthelayersasshownin<br />
schematic(b).Afterfourlayersarewound,gluethewindingsinplace.<br />
Ifclosewindingfourlayersofmagnetwireittoodifficult,scramblewind440turnsofthe<br />
magnetwireovertheendofthecardboardtube.However,theclose-woundstylecoilmounts<br />
moreeasilytothebaseboard.Keepthewindingswithinaoneinchlength.<br />
Cutthefinishedwindingfromtheendofthecardboardtubewitharazorknifeallowing<br />
theformtoextendalittlebeyondthewinding.Striptheenamelfromaninchofftheendsof<br />
thepairofleadwireswithsandpaper.Splicethebareendstoheaviergaugeinsulatedhook-up<br />
wire.Solderthesplice.Insulatewithtapeorheat-shrinktubing.Securethesplicetothecoil<br />
body.Thenproceedwithasecondidenticalcoil.<br />
Refertoboththeschematicdiagramandtheillustrationforassembly.Notethatthecoils<br />
aremountedatrightangles.Theymaybecementedtoaninsulatingbaseboardlikewood.The<br />
25wattlampiswiredinserieswithonecoil.Thislimitsthecurrentflowingthroughthecoil.<br />
Thelampisasubstituteforan820 Ωpowerresistor.Thecapacitoriswiredinserieswiththe<br />
othercoil.Italsolimitsthecurrentthroughthecoil.Inaddition,itprovidesaleadingphase<br />
shiftofthecurrentwithrespecttovoltage. Theschematicandillustrationshownopower<br />
switchorfuse.Addtheseifdesired.<br />
Therotormustbemadeofaferromagneticmateriallikeasteelcanlidorbottlecap.The<br />
illustrationbelowshowshowtomaketherotor.Selectacircularrotoreithersmallerthanthe<br />
coilformsoralittlelarger.Usegeometrytolocateandmarkthecenter.Thecenterneedstobe<br />
dimpled.Selectaneighthinchdiameter(afewmm)nail(a)andfileorgrindthepointround<br />
asshownat(b). Placetherotoratopapieceofsoftwood(c)andhammertheroundedpoint<br />
intothecenter(d).Practiceonapieceofsimilarscrapmetal.Takecarenottopiercetherotor.<br />
Adishedrotor(f)oralid(g)balancebetterthantheflatrotor(e).Thepivotpoint(e)maybe<br />
astraightpindriventhroughamovablewoodenpedestal,orthroughthemainboard.Thetip<br />
ofaball-pointpenalsoworks.Iftherotordoesnotbalanceatopthepivot,removemetalfrom<br />
theheavyside.<br />
(g)<br />
(f)<br />
(a) (b) (c) (d) (e)<br />
Doublecheckthewiring. Checkthatanybarewirehasbeeninsulated. Thecircuitmay<br />
bepowered-upwithouttherotor. Thelampshouldlight. Bothcoilswillwarmwithinafew<br />
minutes.Excessiveheatingmeansthatalowerwattage(higherresistance)lampandalower<br />
valuecapacitorshouldbesubstitutedinserieswiththerespectivecoils.
4.9. INDUCTIONMOTOR 173<br />
Placetherotoratopthepivotandmoveitbetweenbothcoils.Itshouldspin.Thecloserit<br />
is,thefasteritshouldspin. Bothcoilsshouldbewarm,indicatingpower. Trydifferentsize<br />
andstylerotors.Tryasmallrotorontheoppositesideofthecoilscomparedtotheillustration.<br />
Forlackof#32AWGmagnetwiretry440turnsofslightlyalargerdiameter(lesserAWG<br />
number)wire.Thiswillrequiremorethan4layersfortherequiredturns.Anight-lightfixture<br />
mightbelessexpensivethanthefull-sizelampsocketillustrated.Thoughnight-lightbulbsare<br />
toolowawattageat3or7watts,15wattbulbsfitthesocket.
174 CHAPTER4. ACCIRCUITS<br />
4.10 Inductionmotor,large<br />
PARTSANDMATERIALS<br />
• ACpowersource:120VAC<br />
• Capacitor,3.3 µF120VACor350VDC,non-polarized<br />
• #33AWGmagnetwire,2pounds<br />
• woodenboardapprox.6to12in.square.<br />
• AClinecordwithplug<br />
• 5.1inchdia.plastic3litersodabottle<br />
• discardedballpointpen<br />
• misc.smallwoodblocks<br />
CROSS-REFERENCES<br />
LessonsInElectricCircuits,Volume2,chapter13: ”ACmotors”,”SinglePhaseinduction<br />
motors”,”Permanentsplit-capacitormotor”.<br />
LEARNINGOBJECTIVES<br />
• TobuildalargeexhibitsizeACpermanentsplit-capacitorinductionmotor.<br />
• ToillustratethesimplicityoftheACinductionmotor.<br />
SCHEMATICDIAGRAM<br />
1"<br />
120<br />
Vac<br />
L2<br />
3200 turns<br />
L1<br />
3800 turns<br />
5.1 in.<br />
C1<br />
3.3 µF<br />
(a)<br />
(b)
4.10. INDUCTIONMOTOR,LARGE 175<br />
ILLUSTRATION<br />
L2<br />
L1<br />
C1<br />
INSTRUCTIONS<br />
Thisisalargerversionofa”permanentcapacitorsplit-phaseinductionmotor”.Thereare<br />
twodifferentstatorcoils.The1.0inchwide3200turnL2windingisshownintheillustration<br />
above(b),woundoverasectionof5.1inchdiameterplastic3-litersodabottle. L1isapproximately3800turnsof#33AWG(Americanwiregauge)enameledmagnetwirewoundovera<br />
1.25widthofasectionofsodabottle,widerthanshownat(b).Marka1.25inchwidecylinder<br />
with0.25inchmarginsoneachend.Thewirewillbewoundonthe1.25inchzone.Theform<br />
iscutfromthebottleontheoutsideedgesofthemargin. Cutsof0.25inchfromthemargin<br />
towindingzonearespacedat1inchintervalsaroundthecircumferenceofbothendssothat<br />
themarginmaybebentupat90 o toholdthewireontheform. Toavoidcountingthe3800<br />
turns,scramblewinda1/8inchthicknessofmagnetwireovertheoneinchwidthoftheform.<br />
Else,counttheturns.Scrapetheenamelfrom1-inchonthefreeend,andscrapeonlyasmall<br />
sectionfromtheleadtothespool.DoNOTcuttheleadtothespool.Measuretheresistance,<br />
andestimatehowmuchmorewiretowindtoachieve894 Ω.Applyenamel,nailpolish,tape,<br />
orotherinsulationtothebarespotonthespoollead.Continuewinding,andrechecktheresistance.Oncetheapproximate894<br />
Ωisachieved,leaveafewinchesofmagnetwireforthelead.<br />
Cuttheleadfromthespool.Securethewindingstotheformwithlacingtwineorothermeans.<br />
TheL1windingof3200turnsisapproximately744 Ωandiswoundona1.0inchwideform<br />
asshownat(b)inamannersimilartothepreviousL2winding.<br />
Striptheenameloff1-inchoftheendsofmagnetwireleadsifnotalreadydone.Splicethe<br />
bareendstoheaviergaugeinsulatedhook-upwire. Solderthesplice. Insulatewithtapeor<br />
heat-shrinktubing.Securethesplicetothecoilbody.Thenproceedwiththesecondcoil.The<br />
coilsmaybemountedinonecornerofthewoodenbase. Alternatively,formoreflexabilityin<br />
use,theymaybemountedtomovablepallets.<br />
Refertoboththeschematicdiagramandtheillustrationforassembly.Notethatthecoils<br />
aremountedatrightangles.L2,thesmallercoiliswiredtobothsidesofthe120Vacline.The<br />
capacitoriswiredinserieswiththewidercoilL1.Thecapacitorprovidesaleadingphaseshift<br />
ofthecurrentwithrespecttovoltage.Theschematicandillustrationshownopowerswitchor<br />
fuse.Addtheseadditionsarerecommended.
176 CHAPTER4. ACCIRCUITS<br />
Ifthisdeviceisintendedforusebynon-techniciansasanunsupervisedexhibit,allexposed<br />
bareterminationslikethecapacitormustbemadefingersafebycoveringwithshields. The<br />
switchandfusementionedabovearenecessary.Finally,theenamelonthecoilsonlyprovidesa<br />
singlelayerofinsulation.Forsafety,asecondlayersuchasaninsulatingwrapping,Plexiglas<br />
box,orothermeansiscalledfor. ReplaceallwoodencomponentswithPlexiglasforsuperior<br />
firesafetyinanunsupervisedexhibit.<br />
Therotormustbemadeofaferromagneticmateriallikeasteelvegetablecan,fruitcake<br />
can,etc. Atoolongvegetablecanmaybecutinhalf. Theillustrationfortheprevioussmall<br />
inductionmotorshowsrotordimpledbearingandpivotdetails.Therotormaybesmallerthan<br />
thecoilformsasinthecaseofacutdownvegetablecan. Itcanevenbeassmallasthecan<br />
lidrotorusedwiththeprevioussmallmotor. Itisalsopossibletodrivearotorlargerthan<br />
thecoils,whichisthecasewiththefruitcakecan. Locateandmarkthecenteroftherotor.<br />
Thecenterneedstobedimpled. Selectaneighthinchdiameter(afewmm)nail(a)andfile<br />
orgrindthepointround. Usethisandablockofwoodtodimpletherotorasshowninthe<br />
previoussmallmotorAfairlylongcanbalancesbetterthanaflatrotorduetothelowercenter<br />
ofgravity.Thetipofaballpointpenworkswellasapivotforlargerrotors.Mountthepivotto<br />
amovablewoodenpedestal.<br />
Doublecheckthewiring.Checkthatanybarewirehasbeeninsulated.Thecircuitmaybe<br />
powered-upwithouttherotor.ExcessiveheatinginL2indicatesthatmoreturnsarerequired.<br />
ExcessiveheatinL1callsforareductioninthecapacitanceofC1. Noheatatallindicates<br />
indicatesanopencircuittotheaffectedcoil.<br />
Placetherotoratopthepivotandmoveitbetweenbothenergizedcoils. Itshouldspin.<br />
Thecloseritis,thefasteritshouldspin. Bothcoilsshouldbewarm,indicatingpower. Try<br />
differentsizeandstylerotors.Tryasmallrotorontheoppositesideofthecoilscomparedto<br />
theillustration.<br />
Threemodelsofthismotorhavebeenbuiltusing#33AWGmagnetwirebecausealarge<br />
spoolwasonhand.AWG#32magnetwireisprobablyeasiertoget.Itshouldwork.Although<br />
thecurrentwillbehigherduetothelowerresistanceofthelargerdiameter#32wire. Ifa<br />
3.3µFcapacitorisnotavailable,usesomentingcloseaslongasithasanadequatevoltage<br />
rating.AdiscardedACmotorruncapacitor(bathtubshaped)wasusedbytheauthor.Dono<br />
useamotorstartcapacitor(blackcylinder).Theseareonlyusableforafewsecondsofmotor<br />
starting,andmayexplodeifusedlongerthanthat.<br />
Trythis: Itispossibletosimultaneouslyspinmorethanonerotor. Forexample,in<br />
additiontothemainrotorinsidetherightangleformedbythecoils,placeasecondsmaller<br />
rotor(canorbottlelid)nearthepairofcoilsoutsidetherightangleatthevertex.<br />
Itispossibletoreversethedirectionofrotationbyreversingoneofthecoils.Ifthecoilsare<br />
mountedtomovablepallets,rotateonecoil180 o .Anothermethod,especiallyusefullwithfixed<br />
coils,istowireoneofthecoilstoaDPDTpolarityreversingswitch.Forexample,disconnect<br />
L2andwireittothewipers(centercontacts)oftheDPDTswitch.Thetopcontactsgotothe<br />
120Vac.ThetopcontactsalsogotothethebottomcontactsinanX-crossoverpattern.
4.11. PHASESHIFT 177<br />
4.11 Phaseshift<br />
PARTSANDMATERIALS<br />
• Low-voltageACpowersupply<br />
• Twocapacitors,0.1 µFeach,non-polarized(RadioShackcatalog#272-135)<br />
• Two27kΩresistors<br />
Irecommendceramicdiskcapacitors,becausetheyareinsensitivetopolarity(non-polarized),<br />
inexpensive,anddurable.Avoidcapacitorswithanykindofpolaritymarking,asthesewillbe<br />
destroyedwhenpoweredbyAC!<br />
CROSS-REFERENCES<br />
LessonsInElectricCircuits,Volume2,chapter1:”BasicACTheory”<br />
LessonsInElectricCircuits,Volume2,chapter4:”ReactanceandImpedance–Capacitive”<br />
LEARNINGOBJECTIVES<br />
• Howout-of-phaseACvoltagesdonotaddalgebraically,butaccordingtovector(phasor)<br />
arithmetic<br />
SCHEMATICDIAGRAM<br />
R 1<br />
27 kΩ<br />
12 V<br />
RMS<br />
R 2<br />
C 1<br />
27 kΩ<br />
0.1 µF<br />
C 2<br />
0.1 µF<br />
ILLUSTRATION
178 CHAPTER4. ACCIRCUITS<br />
Low-voltage<br />
AC power supply<br />
12<br />
6 6<br />
C 2<br />
C 1<br />
R 2<br />
R 1<br />
INSTRUCTIONS<br />
BuildthecircuitandmeasurevoltagedropsacrosseachcomponentwithanACvoltmeter.<br />
Measuretotal(supply)voltagewiththesamevoltmeter. Youwilldiscoverthatthevoltage<br />
dropsdonotadduptoequalthetotalvoltage.Thisisduetophaseshiftsinthecircuit:voltage<br />
droppedacrossthecapacitorsisout-of-phasewithvoltagedroppedacrosstheresistors,and<br />
thusthevoltagedropfiguresdonotaddupasonemightexpect. Takingphaseangleinto<br />
consideration,theydoadduptoequalthetotal,butavoltmeterdoesn’tprovidephaseangle<br />
measurements,onlyamplitude.<br />
Trymeasuringvoltagedroppedacrossbothresistorsatonce.Thisvoltagedropwillequal<br />
thesumofthevoltagedropsmeasuredacrosseachresistorseparately.Thistellsyouthatboth<br />
theresistors’voltagedropwaveformsarein-phasewitheachother,sincetheyaddsimplyand<br />
directly.<br />
Measurevoltagedroppedacrossbothcapacitorsatonce. Thisvoltagedrop,likethedrop<br />
measuredacrossthetworesistors,willequalthesumofthevoltagedropsmeasuredacross<br />
eachcapacitorseparately.Likewise,thistellsyouthatboththecapacitors’voltagedropwaveformsarein-phasewitheachother.<br />
Giventhatthepowersupplyfrequencyis60Hz(householdpowerfrequencyintheUnited<br />
States),calculateimpedancesforallcomponentsanddetermineallvoltagedropsusingOhm’s<br />
Law(E=IZ;I=E/Z;Z=E/I).Thepolarmagnitudesoftheresultsshouldcloselyagreewithyour<br />
voltmeterreadings.<br />
COMPUTERSIMULATION<br />
SchematicwithSPICEnodenumbers:
4.11. PHASESHIFT 179<br />
V 1<br />
1<br />
3<br />
R bogus1<br />
4<br />
R bogus2<br />
R 1<br />
R 2<br />
C 1<br />
C 2<br />
0<br />
0 0<br />
1<br />
27 kΩ<br />
2<br />
27 kΩ<br />
3<br />
4<br />
0.1 µF<br />
0.1 µF<br />
Thetwolarge-valueresistorsR bogus1 andR bogus1 areconnectedacrossthecapacitorsto<br />
provideaDCpathtogroundinorderthatSPICEwillwork.Thisisa”fix”foroneofSPICE’s<br />
quirks,toavoiditfromseeingthecapacitorsasopencircuitsinitsanalysis.Thesetworesistors<br />
areentirelyunnecessaryintherealcircuit.<br />
Netlist(makeatextfilecontainingthefollowingtext,verbatim):<br />
phase shift<br />
v1 1 0 ac 12 sin<br />
r1 1 2 27k<br />
r2 2 3 27k<br />
c1 3 4 0.1u<br />
c2 4 0 0.1u<br />
rbogus1 3 4 1e9<br />
rbogus2 4 0 1e9<br />
.ac lin 1 60 60<br />
* Voltage across each component:<br />
.print ac v(1,2) v(2,3) v(3,4) v(4,0)<br />
* Voltage across pairs of similar components<br />
.print ac v(1,3) v(3,0)<br />
.end
180 CHAPTER4. ACCIRCUITS<br />
4.12 Soundcancellation<br />
PARTSANDMATERIALS<br />
• Low-voltageACpowersupply<br />
• Twoaudiospeakers<br />
• Two220 Ωresistors<br />
Large,low-frequency(”woofer”)speakersaremostappropriateforthisexperiment. For<br />
optimumresults,thespeakersshouldbeidenticalandmountedinenclosures.<br />
CROSS-REFERENCES<br />
LessonsInElectricCircuits,Volume2,chapter1:”BasicACTheory”<br />
LEARNINGOBJECTIVES<br />
• Howphaseshiftcancausewavestoeitherreinforceorinterferewitheachother<br />
• Theimportanceofspeaker”phasing”instereosystems<br />
SCHEMATICDIAGRAM<br />
220 Ω<br />
220 Ω<br />
12 V<br />
ILLUSTRATION
4.12. SOUNDCANCELLATION 181<br />
Low-voltage<br />
AC power supply<br />
12<br />
6 6<br />
Speaker<br />
Speaker<br />
INSTRUCTIONS<br />
Connecteachspeakertothelow-voltageACpowersupplythrougha220 Ωresistor. The<br />
resistorlimitstheamountofpowerdeliveredtoeachspeakerbythepowersupply. Alowpitched,60-Hertztoneshouldbeheardfromthespeakers.<br />
Ifthetonesoundstooloud,use<br />
higher-valueresistors.<br />
Withbothspeakersconnectedandproducingsound,positionthemsothattheyareonlya<br />
footortwoaway,facingtowardeachother. Listentothevolumeofthe60-Hertztone. Now,<br />
reversetheconnections(the”polarity”)ofjustoneofthespeakersandnotethevolumeagain.<br />
Tryswitchingthepolarityofonespeakerbackandforthfromoriginaltoreversed,comparing<br />
volumelevelseachway.Whatdoyounotice?<br />
Byreversingwireconnectionstoonespeaker,youarereversingthephaseofthatspeaker’s<br />
soundwaveinreferencetotheotherspeaker.Inonemode,thesoundwaveswillreinforceone<br />
anotherforastrongvolume.Intheothermode,thesoundwaveswilldestructivelyinterfere,<br />
resultingindiminishedvolume.Thisphenomenoniscommontoallwaveevents:soundwaves,<br />
electricalsignals(voltage”waves”),wavesinwater,andevenlightwaves!<br />
Multiplespeakersinastereosoundsystemmustbeproperly”phased”sothattheirrespectivesoundwavesdon’tcanceleachother,leavinglesstotalsoundlevelforthelistener(s)to<br />
hear.So,eveninanACsystemwheretherereallyisnosuchthingasconstant”polarity,”the<br />
sequenceofwireconnectionsmaymakeasignificantdifferenceinsystemperformance.<br />
Thisprincipleofvolumereductionbydestructiveinterferencemaybeexploitedfornoise<br />
cancellation.Suchsystemssamplethewaveformoftheambientnoise,thenproduceaniden-
182 CHAPTER4. ACCIRCUITS<br />
ticalsoundsignal180 o outofphasewiththenoise. Whenthetwosoundsignalsmeet,they<br />
canceleachotherout,ideallyeliminatingallthenoise.Asonemightguess,thisismucheasier<br />
accomplishedwithnoisesourcesofsteadyfrequencyandamplitude.Cancellationofrandom,<br />
broad-spectrumnoiseisverydifficult,assomesortofsignal-processingcircuitmustsample<br />
thenoiseandgeneratepreciselytherightamountofcancellationsoundatjusttherighttime<br />
inordertobeeffective.
4.13. MUSICALKEYBOARDASASIGNALGENERATOR 183<br />
4.13 Musicalkeyboardasasignalgenerator<br />
PARTSANDMATERIALS<br />
• Electronic”keyboard”(musical)<br />
• ”Mono”(notstereo)headphone-typeplug<br />
• Impedancematchingtransformer(1k Ωto8Ωratio;RadioShackcatalog#273-1380)<br />
• 10kΩresistor<br />
Inthisexperiment,you’lllearnhowtouseanelectronicmusicalkeyboardasasourceof<br />
variable-frequencyACvoltagesignals.Youneednotpurchaseanexpensivekeyboardforthis<br />
–butonewithatleastafewdozen”voice”selections(piano,flute,harp,etc.) wouldbegood.<br />
The”mono”plugwillbepluggedintotheheadphonejackofthemusicalkeyboard,sogetaplug<br />
that’sthecorrectsizeforthekeyboard.<br />
The”impedancematchingtransformer”isasmall-sizetransformereasilyobtainedfroman<br />
electronicssupplystore.Onemaybescavengedfromasmall,junkradio:itconnectsbetween<br />
thespeakerandthecircuitboard(amplifier),soiseasilyidentifiablebylocation.Theprimary<br />
windingisratedinohmsofimpedance(1000 Ω),andisusuallycenter-tapped.Thesecondary<br />
windingis8Ωandnotcenter-tapped. TheseimpedancefiguresarenotthesameasDCresistance,sodon’texpecttoread1000<br />
Ωand8Ωwithyourohmmeter–however,the1000 Ω<br />
windingwillreadmoreresistancethanthe8Ωwinding,becauseithasmoreturns.<br />
Ifsuchatransformercannotbeobtainedfortheexperiment,aregular120V/6Vstep-down<br />
powertransformerworksfairlywell,too.<br />
CROSS-REFERENCES<br />
LessonsInElectricCircuits,Volume2,chapter1:”BasicACTheory”<br />
LessonsInElectricCircuits,Volume2,chapter7:”Mixed-FrequencyACSignals”<br />
LEARNINGOBJECTIVES<br />
• Differencebetweenamplitudeandfrequency<br />
• MeasuringACvoltage,currentwithameter<br />
• Transformeroperation,step-up<br />
SCHEMATICDIAGRAM<br />
Keyboard<br />
plug<br />
8 Ω 1 kΩ<br />
10 kΩ
184 CHAPTER4. ACCIRCUITS<br />
ILLUSTRATION<br />
V<br />
A<br />
V<br />
OFF<br />
A<br />
1000 Ω<br />
A<br />
COM<br />
8 Ω<br />
plug<br />
"Voice" selection<br />
Volume<br />
INSTRUCTIONS<br />
Normally,astudentofelectronicsinaschoolwouldhaveaccesstoadevicecalledasignal<br />
generator,orfunctiongenerator,usedtomakevariable-frequencyvoltagewaveformstopower<br />
ACcircuits. Aninexpensiveelectronickeyboardisacheaperalternativetoaregularsignal<br />
generator,andprovidesfeaturesthatmostsignalgeneratorscannotmatch,suchasproducing<br />
mixed-frequencywaves.<br />
To”tapin”totheACvoltageproducedbythekeyboard,you’llneedtoinsertaplugintothe<br />
headphonejack(sometimesjustlabeled”phone”onthekeyboard)completewithtwowiresfor<br />
connectiontocircuitsofyourowndesign.Whenyouinserttheplugintothejack,thenormal<br />
speakerbuiltintothekeyboardwillbedisconnected(assumingthekeyboardisequippedwith<br />
one),andthesignalthatusedtopowerthatspeakerwillbeavailableattheplugwires. In
4.13. MUSICALKEYBOARDASASIGNALGENERATOR 185<br />
thisparticularexperiment,Irecommendusingthekeyboardtopowerthe8Ωsideofanaudio<br />
”output”transformertostepupvoltagetoahigherlevel.Ifusingapowertransformerinstead<br />
ofanaudiooutputtransformer,connectthekeyboardtothelow-voltagewindingsothatit<br />
operatesasastep-updevice.Keyboardsproduceverylowvoltagesignals,sothereisnoshock<br />
hazardinthisexperiment.<br />
UsinganinexpensiveYamahakeyboard,Ihavefoundthatthe”panflute”voicesettingproducesthetruestsine-wavewaveform.<br />
Thiswaveform,orsomethingclosetoit(flute,forexample),isrecommendedtostartexperimentingwithsinceitisrelativelyfreeofharmonics<br />
(manywaveformsmixedtogether,ofinteger-multiplefrequency).Beingcomposedofjustone<br />
frequency,itisalesscomplexwaveformforyourmultimetertomeasure.Makesurethekeyboardissettoamodewherethenotewillbesustainedasanykeyishelddown–otherwise,<br />
theamplitude(voltage)ofthewaveformwillbeconstantlychanging(highwhenthekeyisfirst<br />
pressed,thendecayingrapidlytozero).<br />
UsinganACvoltmeter,readthevoltagedirectfromtheheadphoneplug. Then,readthe<br />
voltageassteppedupbythetransformer,notingthestepratio.Ifyourmultimeterhasa”frequency”function,useittomeasurethefrequencyofthewaveformproducedbythekeyboard.<br />
Trydifferentnotesonthekeyboardandrecordtheirfrequencies. Doyounoticeapatternin<br />
frequencyasyouactivatedifferentnotes,especiallykeysthataresimilartoeachother(notice<br />
the12-keyblack-and-whitepatternrepeatedonthekeyboardfromlefttoright)?Ifyoudon’t<br />
mindmakingmarksonyourkeyboard,writethefrequenciesinHertzinblackinkonthewhite<br />
keys,nearthetopswherefingersarelesslikelytorubthenumbersoff.<br />
Ideally,thereshouldbenochangeinsignalamplitude(voltage)asdifferentfrequencies<br />
(notesonthekeyboard)aretried.Ifyouadjustthevolumeupanddown,youshoulddiscover<br />
thatchangesinamplitudeshouldhavelittleornoimpactonfrequencymeasurement.AmplitudeandfrequencyaretwocompletelyindependentaspectsofanACsignal.<br />
Tryconnectingthekeyboardoutputtoa10kΩloadresistance(throughtheheadphone<br />
plug),andmeasureACcurrentwithyourmultimeter. Ifyourmultimeterhasafrequency<br />
function,youcanmeasurethefrequencyofthiscurrentaswell.Itshouldbethesameasfor<br />
thevoltageforanygivennote(keyboardkey).
186 CHAPTER4. ACCIRCUITS<br />
4.14 PCOscilloscope<br />
PARTSANDMATERIALS<br />
• IBM-compatiblepersonalcomputerwithsoundcard,runningWindows3.1orbetter<br />
• Winscopesoftware,downloadedfreefrominternet<br />
• Electronic”keyboard”(musical)<br />
• ”Mono”(notstereo)headphone-typeplugforkeyboard<br />
• ”Mono”(notstereo)headphone-typeplugforcomputersoundcardmicrophoneinput<br />
• 10kΩpotentiometer<br />
TheWinscopeprogramI’veusedwaswrittenbyDr.ConstantinZeldovich,forfreepersonal<br />
andacademicuse.ItplotswaveformsonthecomputerscreeninresponsetoACvoltagesignals<br />
interpretedbythesoundcardmicrophoneinput. Asimilarprogram,calledOscope,ismade<br />
fortheLinuxoperatingsystem. Ifyoudon’thaveaccesstoeithersoftware,youmayusethe<br />
”soundrecorder”utilitythatcomesstockwithmostversionsofMicrosoftWindowstodisplay<br />
crudewaveshapes.<br />
CROSS-REFERENCES<br />
LessonsInElectricCircuits,Volume2,chapter7:”Mixed-FrequencyACSignals”<br />
LessonsInElectricCircuits,Volume2,chapter12:”ACMeteringCircuits”<br />
LEARNINGOBJECTIVES<br />
• Computeruse<br />
• Basicoscilloscopefunction<br />
SCHEMATICDIAGRAM<br />
Keyboard<br />
Computer<br />
plug<br />
10 kΩ<br />
plug<br />
ILLUSTRATION
4.14. PCOSCILLOSCOPE 187<br />
Computer<br />
plug<br />
mic. input<br />
plug<br />
"Voice" selection<br />
Volume<br />
Monitor<br />
INSTRUCTIONS<br />
Theoscilloscopeisanindispensabletestinstrumentfortheelectronicsstudentandprofessional.Noseriouselectronicslabshouldbewithoutone(ortwo!).Unfortunately,commercial<br />
oscilloscopestendtobeexpensive,anditisalmostimpossibletodesignandbuildyourown<br />
withoutanotheroscilloscopetotroubleshootit! However,thesoundcardofapersonalcomputeriscapableof”digitizing”low-voltageACsignalsfromarangeofafewhundredHertzto<br />
severalthousandHertzwithrespectableresolution,andfreesoftwareisavailablefordisplayingthesesignalsinoscilloscopeformonthecomputerscreen.<br />
Sincemostpeopleeitherhave<br />
apersonalcomputerorcanobtainoneforlesscostthananoscilloscope,thisbecomesaviable<br />
alternativefortheexperimenteronabudget.<br />
Onewordofcaution:youcancausesignificanthardwaredamagetoyourcomputer<br />
ifsignalsofexcessivevoltageareconnectedtothesoundcard’smicrophoneinput!<br />
TheACvoltagesproducedbyamusicalkeyboardaretoolowtocausedamagetoyourcomputer<br />
throughthesoundcard,butothervoltagesourcesmightbehazardoustoyourcomputer’s<br />
health.Usethis”oscilloscope”atyourownrisk!<br />
Usingthekeyboardandplugarrangementdescribedinthepreviousexperiment,connect<br />
thekeyboardoutputtotheouterterminalsofa10kΩpotentiometer.Soldertwowirestothe<br />
connectionpointsonthesoundcardmicrophoneinputplug,sothatyouhaveasetof”test<br />
leads”forthe”oscilloscope.”Connectthesetestleadstothepotentiometer:betweenthemiddle<br />
terminal(thewiper)andeitheroftheouterterminals.<br />
StarttheWinscopeprogramandclickonthe”arrow”iconintheupper-leftcorner(itlooks<br />
likethe”play”arrowseenontapeplayerandCDplayercontrolbuttons).Ifyoupressakeyon<br />
themusicalkeyboard,youshouldseesomekindofwaveformdisplayedonthescreen.Choose<br />
the”panflute”orsomeotherflute-likevoiceonthemusicalkeyboardforthebestsine-wave<br />
shape.Ifthecomputerdisplaysawaveformthatlookskindoflikeasquarewave,youneedto<br />
adjustthepotentiometerforalower-amplitudesignal.Almostanywaveshapewillbe”clipped”<br />
tolooklikeasquarewaveifitexceedstheamplitudelimitofthesoundcard.
188 CHAPTER4. ACCIRCUITS<br />
Testdifferentinstrument”voices”onthemusicalkeyboardandnotethedifferentwaveshapes.<br />
Notehowcomplexsomeofthewaveshapesare,comparedtothepanflutevoice. ExperimentwiththedifferentcontrolsintheWinscopewindow,notinghowtheychangethe<br />
appearanceofthewaveform.<br />
Asatestinstrument,this”oscilloscope”isquitepoor.Ithasalmostnocapabilitytomake<br />
precisionmeasurementsofvoltage,althoughitsfrequencyprecisionissurprisinglygood.Itis<br />
verylimitedintherangesofvoltageandfrequencyitcandisplay,relegatingittotheanalysis<br />
oflow-andmid-rangeaudiotones.Ihavehadverylittlesuccessgettingthe”oscilloscope”to<br />
displaygoodsquarewaves,presumablybecauseofitslimitedfrequencyresponse. Also,the<br />
couplingcapacitorfoundinsoundcardmicrophoneinputcircuitspreventsitfrommeasuring<br />
DCvoltage:itisasthoughthe”ACcoupling”featureofanormaloscilloscopewerestuck”on.”<br />
Despitetheseshortcomings,itisusefulasademonstrationtool,andforinitialexplorations<br />
intowaveformanalysisforthebeginningstudentofelectronics.Forthosewhoareinterested,<br />
thereareseveralprofessional-qualityoscilloscopeadapterdevicesmanufacturedforpersonal<br />
computerswhoseperformanceisfarbeyondthatofasoundcard,andtheyaretypicallysoldat<br />
lesscostthanacompletestand-aloneoscilloscope(around$400,year2002).RadioShacksells<br />
onemadebyVelleman,catalog#910-3914. Havingacomputerserveasthedisplaymedium<br />
bringsmanyadvantages,nottheleastofwhichistheabilitytoeasilystorewaveformpictures<br />
asdigitalfiles.
4.15. WAVEFORMANALYSIS 189<br />
4.15 Waveformanalysis<br />
PARTSANDMATERIALS<br />
• IBM-compatiblepersonalcomputerwithsoundcard,runningWindows3.1orbetter<br />
• Winscopesoftware,downloadedfreefrominternet<br />
• Electronic”keyboard”(musical)<br />
• ”Mono”(notstereo)headphone-typeplugforkeyboard<br />
• ”Mono”(notstereo)headphone-typeplugforcomputersoundcardmicrophoneinput,with<br />
wiresforconnectingtovoltagesources<br />
• 10kΩpotentiometer<br />
Partsandequipmentforthisexperimentareidenticaltothoserequiredforthe”PCoscilloscope”experiment.<br />
CROSS-REFERENCES<br />
LessonsInElectricCircuits,Volume2,chapter7:”Mixed-FrequencyACSignals”<br />
LEARNINGOBJECTIVES<br />
• Understandthedifferencebetweentime-domainandfrequency-domainplots<br />
• DevelopaqualitativesenseofFourieranalysis<br />
SCHEMATICDIAGRAM<br />
Keyboard<br />
Computer<br />
plug<br />
10 kΩ<br />
plug<br />
ILLUSTRATION
190 CHAPTER4. ACCIRCUITS<br />
Computer<br />
plug<br />
mic. input<br />
plug<br />
"Voice" selection<br />
Volume<br />
Monitor<br />
INSTRUCTIONS<br />
TheWinscopeprogramcomeswithanotherfeatureotherthanthetypical”time-domain”oscilloscopedisplay:”frequency-domain”display,whichplotsamplitude(vertical)overfrequency<br />
(horizontal).Anoscilloscope’s”time-domain”displayplotsamplitude(vertical)overtime(horizontal),whichisfinefordisplayingwaveshape.<br />
However,whenitisdesirabletoseethe<br />
harmonicconstituencyofacomplexwave,afrequency-domainplotisthebesttool.<br />
IfusingWinscope,clickonthe”rainbow”icontoswitchtofrequency-domainmode. Generateasine-wavesignalusingthemusicalkeyboard(panfluteorflutevoice),andyoushould<br />
seeasingle”spike”onthedisplay,correspondingtotheamplitudeofthesingle-frequencysignal.Movingthemousecursorbeneaththepeakshouldresultinthefrequencybeingdisplayed<br />
numericallyatthebottomofthescreen.<br />
Iftwonotesareactivatedonthemusicalkeyboard,theplotshouldshowtwodistinctpeaks,<br />
eachonecorrespondingtoaparticularnote(frequency). Basicchords(threenotes)produce<br />
threespikesonthefrequency-domainplot,andsoon.Contrastthiswithnormaloscilloscope<br />
(time-domain)plotbyclickingonceagainonthe”rainbow”icon.Amusicalchorddisplayedin<br />
time-domainformatisaverycomplexwaveform,butisquitesimpletoresolveintoconstituent<br />
notes(frequencies)onafrequency-domaindisplay.<br />
Experimentwithdifferentinstrument”voices”onthemusicalkeyboard,correlatingthe<br />
time-domainplotwiththefrequency-domainplot.Waveformsthataresymmetricalaboveand<br />
belowtheircenterlinescontainonlyodd-numberedharmonics(odd-integermultiplesofthe<br />
base,orfundamentalfrequency),whilenonsymmetricalwaveformscontaineven-numbered<br />
harmonicsaswell.Usethecursortolocatethespecificfrequencyofeachpeakontheplot,and<br />
acalculatortodeterminewhethereachpeakiseven-orodd-numbered.
4.16. INDUCTOR-CAPACITOR”TANK”CIRCUIT 191<br />
4.16 Inductor-capacitor”tank”circuit<br />
PARTSANDMATERIALS<br />
• Oscilloscope<br />
• Assortmentofnon-polarizedcapacitors(0.1 µFto10 µF)<br />
• Step-downpowertransformer(120V/6V)<br />
• 10kΩresistors<br />
• Six-voltbattery<br />
Thepowertransformerisusedsimplyasaninductor,withonlyonewindingconnected.The<br />
unusedwindingshouldbeleftopen. Asimpleironcore,single-windinginductor(sometimes<br />
knownasachoke)mayalsobeused,butsuchinductorsaremoredifficulttoobtainthanpower<br />
transformers.<br />
CROSS-REFERENCES<br />
LessonsInElectricCircuits,Volume2,chapter6:”Resonance”<br />
LEARNINGOBJECTIVES<br />
• Howtobuildaresonantcircuit<br />
• Effectsofcapacitorsizeonresonantfrequency<br />
• Howtoproduceantiresonance<br />
SCHEMATICDIAGRAM<br />
L<br />
C<br />
ILLUSTRATION
192 CHAPTER4. ACCIRCUITS<br />
+ - touch<br />
clips<br />
together<br />
(transformer used<br />
as an inductor)<br />
INSTRUCTIONS<br />
Ifaninductorandacapacitorareconnectedinparallelwitheachother,andthenbriefly<br />
energizedbyconnectiontoaDCvoltagesource,oscillationswillensueasenergyisexchanged<br />
fromthecapacitortoinductorandviceversa. Theseoscillationsmaybeviewedwithanoscilloscopeconnectedinparallelwiththeinductor/capacitorcircuit.Parallelinductor/capacitor<br />
circuitsarecommonlyknownastankcircuits.<br />
Importantnote:IrecommendagainstusingaPC/soundcardasanoscilloscopeforthis<br />
experiment,becauseveryhighvoltagescanbegeneratedbytheinductorwhenthebatteryis<br />
disconnected(inductive”kickback”).Thesehighvoltageswillsurelydamagethesoundcard’s<br />
input,andperhapsotherportionsofthecomputeraswell.<br />
Atankcircuit’snaturalfrequency,calledtheresonantfrequency,isdeterminedbythesize<br />
oftheinductorandthesizeofthecapacitor,accordingtothefollowingequation:<br />
1<br />
f resonant =<br />
2π LC<br />
Manysmallpowertransformershaveprimary(120volt)windinginductancesofapproximately1H.Usethisfigureasaroughestimateofinductanceforyourcircuittocalculate<br />
expectedoscillationfrequency.<br />
Ideally,theoscillationsproducedbyatankcircuitcontinueindefinitely. Realistically,oscillationswilldecayinamplitudeoverthecourseofseveralcyclesduetotheresistiveand<br />
magneticlossesoftheinductor.Inductorswithahigh”Q”ratingwill,ofcourse,producelongerlastingoscillationsthanlow-Qinductors.<br />
Trychangingcapacitorvaluesandnotingtheeffectonoscillationfrequency. Youmight<br />
noticechangesinthedurationofoscillationsaswell,duetocapacitorsize. Sinceyouknow<br />
howtocalculateresonantfrequencyfrominductanceandcapacitance,canyoufigureouta<br />
waytocalculateinductorinductancefromknownvaluesofcircuitcapacitance(asmeasured<br />
byacapacitancemeter)andresonantfrequency(asmeasuredbyanoscilloscope)?<br />
Resistancemaybeintentionallyaddedtothecircuit–eitherinseriesorparallel–forthe<br />
expresspurposeofdampeningoscillations. Thiseffectofresistancedampeningtankcircuit
4.16. INDUCTOR-CAPACITOR”TANK”CIRCUIT 193<br />
oscillationisknownasantiresonance. Itisanalogoustotheactionofashockabsorberin<br />
dampeningthebouncingofacarafterstrikingabumpintheroad.<br />
COMPUTERSIMULATION<br />
SchematicwithSPICEnodenumbers:<br />
1<br />
R stray<br />
2<br />
L 1 C 1<br />
0 0<br />
R stray isplacedinthecircuittodampenoscillationsandproduceamorerealisticsimulation.<br />
AlowerR stray valuecauseslonger-livedoscillationsbecauselessenergyisdissipated.<br />
Eliminatingthisresistorfromthecircuitresultsinendlessoscillation.<br />
Netlist(makeatextfilecontainingthefollowingtext,verbatim):<br />
tank circuit with loss<br />
l1 1 0 1 ic=0<br />
rstray 1 2 1000<br />
c1 2 0 0.1u ic=6<br />
.tran 0.1m 20m uic<br />
.plot tran v(1,0)<br />
.end
194 CHAPTER4. ACCIRCUITS<br />
4.17 Signalcoupling<br />
PARTSANDMATERIALS<br />
• 6voltbattery<br />
• Onecapacitor,0.22 µF(RadioShackcatalog#272-1070orequivalent)<br />
• Onecapacitor,0.047 µF(RadioShackcatalog#272-134orequivalent)<br />
• Small”hobby”motor,permanent-magnettype(RadioShackcatalog#273-223orequivalent)<br />
• Audiodetectorwithheadphones<br />
• Lengthoftelephonecable,severalfeetlong(RadioShackcatalog#278-872)<br />
Telephonecableisalsoavailablefromhardwarestores. Anyunshieldedmulticonductor<br />
cablewillsufficeforthisexperiment.Cableswiththinconductors(telephonecableistypically<br />
24-gauge)produceamorepronouncedeffect.<br />
CROSS-REFERENCES<br />
LessonsInElectricCircuits,Volume2,chapter7:”Mixed-FrequencyACSignals”<br />
LessonsInElectricCircuits,Volume2,chapter8:”Filters”<br />
LEARNINGOBJECTIVES<br />
• Howto”couple”ACsignalsandblockDCsignalstoameasuringinstrument<br />
• Howstraycouplinghappensincables<br />
• Techniquestominimizeinter-cablecoupling<br />
SCHEMATICDIAGRAM<br />
Telephone cable<br />
Mtr<br />
ILLUSTRATION
4.17. SIGNALCOUPLING 195<br />
Telephone<br />
cable<br />
Motor<br />
+ - plug<br />
headphones<br />
Sensitivity<br />
INSTRUCTIONS<br />
Connectthemotortothebatteryusingtwoofthetelephonecable’sfourconductors. The<br />
motorshouldrun,asexpected.Now,connecttheaudiosignaldetectoracrossthemotorterminals,withthe0.047<br />
µFcapacitorinseries,likethis:
196 CHAPTER4. ACCIRCUITS<br />
+ - plug<br />
headphones<br />
Sensitivity<br />
Youshouldbeabletoheara”buzz”or”whine”intheheadphones,representingtheAC<br />
”noise”voltageproducedbythemotorasthebrushesmakeandbreakcontactwiththerotating<br />
commutatorbars.Thepurposeoftheseriescapacitoristoactasahigh-passfilter,sothatthe<br />
detectoronlyreceivestheACvoltageacrossthemotor’sterminals,notanyDCvoltage.Thisis<br />
preciselyhowoscilloscopesprovidean”ACcoupling”featureformeasuringtheACcontentof<br />
asignalwithoutanyDCbiasvoltage:acapacitorisconnectedinserieswithonetestprobe.<br />
Ideally,onewouldexpectnothingbutpureDCvoltageatthemotor’sterminals,because<br />
themotorisconnecteddirectlyinparallelwiththebattery. Sincethemotor’sterminalsare<br />
electricallycommonwiththerespectiveterminalsofthebattery,andthebattery’snatureisto<br />
maintainaconstantDCvoltage,nothingbutDCvoltageshouldappearatthemotorterminals,<br />
right? Well,becauseofresistanceinternaltothebatteryandalongtheconductorlengths,<br />
currentpulsesdrawnbythemotorproduceoscillatingvoltage”dips”atthemotorterminals,<br />
causingtheAC”noise”heardbythedetector:
4.17. SIGNALCOUPLING 197<br />
Battery<br />
R wire<br />
Motor<br />
R wire<br />
Usetheaudiodetectortomeasure”noise”voltagedirectlyacrossthebattery.SincetheAC<br />
noiseisproducedinthiscircuitbypulsatingvoltagedropsalongstrayresistances,theless<br />
resistancewemeasureacross,thelessnoisevoltageweshoulddetect:<br />
+ - plug<br />
headphones<br />
Sensitivity<br />
Youmayalsomeasurenoisevoltagedroppedalongeitherofthetelephonecableconductors<br />
supplyingpowertothemotor,byconnectingtheaudiodetectorbetweenbothendsofasingle<br />
cableconductor.Thenoisedetectedhereoriginatesfromcurrentpulsesthroughtheresistance<br />
ofthewire:
198 CHAPTER4. ACCIRCUITS<br />
+ - plug<br />
headphones<br />
Sensitivity<br />
NowthatwehaveestablishedhowACnoiseiscreatedanddistributedinthiscircuit,let’s<br />
explorehowitiscoupledtoadjacentwiresinthecable. Usetheaudiodetectortomeasure<br />
voltagebetweenoneofthemotorterminalsandoneoftheunusedwiresinthetelephonecable.<br />
The0.047 µFcapacitorisnotneededinthisexercise,becausethereisnoDCvoltagebetween<br />
thesepointsforthedetectortodetectanyway:<br />
+ - plug<br />
headphones<br />
Sensitivity
4.17. SIGNALCOUPLING 199<br />
ThenoisevoltagedetectedhereisduetostraycapacitancebetweenadjacentcableconductorscreatinganACcurrent”path”betweenthewires.Rememberthatnocurrentactually<br />
goesthroughacapacitance,butthealternatecharginganddischargingactionofacapacitance,<br />
whetheritbeintentionalorunintentional,providesalternatingcurrentapathwayofsorts.<br />
Ifweweretotryandconductavoltagesignalbetweenoneoftheunusedwiresandapoint<br />
commonwiththemotor,thatsignalwouldbecometaintedwithnoisevoltagefromthemotor.<br />
Thiscouldbequitedetrimental,dependingonhowmuchnoisewascoupledbetweenthetwo<br />
circuitsandhowsensitiveonecircuitwastotheother’snoise. Sincetheprimarycoupling<br />
phenomenoninthiscircuitiscapacitiveinnature,higher-frequencynoisevoltagesaremore<br />
stronglycoupledthanlower-frequencynoisevoltages.<br />
IftheadditionalsignalwasaDCsignal,withnoACexpectedinit,wecouldmitigate<br />
theproblemofcouplednoiseby”decoupling”theACnoisewitharelativelylargecapacitor<br />
connectedacrosstheDCsignal’sconductors. Usethe0.22 µFcapacitorforthispurpose,as<br />
shown:<br />
+ - plug<br />
headphones<br />
"decoupling"<br />
capacitor<br />
Sensitivity<br />
Thedecouplingcapacitoractsasapracticalshort-circuittoanyACnoisevoltage,while<br />
notaffectingDCvoltagesignalsbetweenthosetwopointsatall. Solongasthedecoupling<br />
capacitorvalueissignificantlylargerthanthestray”coupling”capacitancebetweenthecable’s<br />
conductors,theACnoisevoltagewillbeheldtoaminimum.<br />
Anotherwayofminimizingcouplednoiseinacableistoavoidhavingtwocircuitsshare<br />
acommonconductor.Toillustrate,connecttheaudiodetectorbetweenthetwounusedwires<br />
andlistenforanoisesignal:
200 CHAPTER4. ACCIRCUITS<br />
+ - plug<br />
headphones<br />
Sensitivity<br />
Thereshouldbefarlessnoisedetectedbetweenanytwooftheunusedconductorsthan<br />
betweenoneunusedconductorandoneusedinthemotorcircuit.Thereasonforthisdrastic<br />
reductioninnoiseisthatstraycapacitancebetweencableconductorstendstocouplethesame<br />
noisevoltagetobothoftheunusedconductorsinapproximatelyequalproportions. Thus,<br />
whenmeasuringvoltagebetweenthosetwoconductors,thedetectoronly”sees”thedifference<br />
betweentwoapproximatelyidenticalnoisesignals.
Chapter5<br />
DISCRETESEMICONDUCTOR<br />
CIRCUITS<br />
Contents<br />
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .202<br />
5.2 Commutatingdiode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .203<br />
5.3 Half-waverectifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .205<br />
5.4 Full-wavecenter-taprectifier . . . . . . . . . . . . . . . . . . . . . . . . . . .213<br />
5.5 Full-wavebridgerectifier. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .218<br />
5.6 Rectifier/filtercircuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .221<br />
5.7 Voltageregulator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .227<br />
5.8 Transistorasaswitch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .230<br />
5.9 Staticelectricitysensor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .235<br />
5.10 Pulsed-lightsensor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .238<br />
5.11 Voltagefollower. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .241<br />
5.12 Common-emitteramplifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . .246<br />
5.13 Multi-stageamplifier. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .251<br />
5.14 Currentmirror . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .255<br />
5.15 JFETcurrentregulator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .261<br />
5.16 Differentialamplifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .266<br />
5.17 Simpleop-amp. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .269<br />
5.18 Audiooscillator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .274<br />
5.19 Vacuumtubeaudioamplifier . . . . . . . . . . . . . . . . . . . . . . . . . . .277<br />
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .288<br />
201
202 CHAPTER5. DISCRETESEMICONDUCTORCIRCUITS<br />
5.1 Introduction<br />
Asemiconductordeviceisonemadeofsiliconoranynumberofotherspeciallypreparedmaterialsdesignedtoexploittheuniquepropertiesofelectronsinacrystallattice,whereelectrons<br />
arenotasfreetomoveasinaconductor,butarefarmoremobilethaninaninsulator. A<br />
discretedeviceisonecontainedinitsownpackage,notbuiltonacommonsemiconductorsubstratewithothercomponents,asisthecasewithICs,orintegratedcircuits.<br />
Thus,”discrete<br />
semiconductorcircuits”arecircuitsbuiltoutofindividualsemiconductorcomponents,connectedtogetheronsomekindofcircuitboardorterminalstrip.Thesecircuitsemployallthe<br />
componentsandconceptsexploredinthepreviouschapters,soafirmcomprehensionofDC<br />
andACelectricityisessentialbeforeembarkingontheseexperiments.<br />
Justforfun,onecircuitisincludedinthissectionusingavacuumtubeforamplification<br />
insteadofasemiconductortransistor. Beforetheadventoftransistors,”vacuumtubes”were<br />
theworkhorsesoftheelectronicsindustry:usedtomakerectifiers,amplifiers,oscillators,and<br />
manyothercircuits. Thoughnowconsideredobsoleteformostpurposes,therearestillsome<br />
applicationsforvacuumtubes,anditcanbefunbuildingandoperatingcircuitsusingthese<br />
devices.
5.2. COMMUTATINGDIODE 203<br />
5.2 Commutatingdiode<br />
PARTSANDMATERIALS<br />
• 6voltbattery<br />
• Powertransformer,120VACstep-downto12VAC(RadioShackcatalog#273-1365,273-<br />
1352,or273-1511).<br />
• One1N4001rectifyingdiode(RadioShackcatalog#276-1101)<br />
• Oneneonlamp(RadioShackcatalog#272-1102)<br />
• Twotoggleswitches,SPST(”Single-Pole,Single-Throw”)<br />
Apowertransformerisspecified,butanyiron-coreinductorwillsuffice,eventhehomemadeinductorortransformerfromtheACexperimentschapter!<br />
Thediodeneednotbeanexactmodel1N4001. Anyofthe”1N400X”seriesofrectifying<br />
diodesaresuitableforthetask,andtheyarequiteeasytoobtain.<br />
Irecommendhouseholdlightswitchesfortheirlowcostanddurability.<br />
CROSS-REFERENCES<br />
LessonsInElectricCircuits,Volume1,chapter16:”RCandL/RTimeConstants”<br />
LessonsInElectricCircuits,Volume3,chapter3:”DiodesandRectifiers”<br />
LEARNINGOBJECTIVES<br />
• Reviewinductive”kickback”<br />
• Learnhowtosuppress”kickback”usingadiode<br />
SCHEMATICDIAGRAM<br />
Switch<br />
#1<br />
Switch<br />
#2<br />
Battery<br />
Inductor<br />
Diode<br />
Neon<br />
lamp<br />
ILLUSTRATION
204 CHAPTER5. DISCRETESEMICONDUCTORCIRCUITS<br />
+ - Switch #1<br />
120 V<br />
Switch #2<br />
12 V<br />
INSTRUCTIONS<br />
Whenassemblingthecircuit,beverycarefulofthediode’sorientation.Thecathodeendof<br />
thediode(theendmarkedwithasingleband)mustfacethepositive(+)sideofthebattery.<br />
Thediodeshouldbereverse-biasedandnonconductingwithswitch#1inthe”on”position.Use<br />
thehigh-voltage(120V)windingofthetransformerfortheinductorcoil.Theprimarywinding<br />
ofastep-downtransformerhasmoreinductancethanthesecondarywinding,andwillgivea<br />
greaterlamp-flashingeffect.<br />
Setswitch#2tothe”off”position.Thisdisconnectsthediodefromthecircuitsothatithas<br />
noeffect. Quicklycloseandopen(turn”on”andthen”off”)switch#1. Whenthatswitchis<br />
opened,theneonbulbwillflashfromtheeffectofinductive”kickback.”Rapidcurrentdecrease<br />
causedbytheswitch’sopeningcausestheinductortocreatealargevoltagedropasitattempts<br />
tokeepcurrentatthesamemagnitudeandgoinginthesamedirection.<br />
Inductivekickbackisdetrimentaltoswitchcontacts,asitcausesexcessivearcingwhenever<br />
theyareopened. Inthiscircuit,theneonlampactuallydiminishestheeffectbyproviding<br />
analternatecurrentpathfortheinductor’scurrentwhentheswitchopens,dissipatingthe<br />
inductor’sstoredenergyharmlesslyintheformoflightandheat. However,thereisstilla<br />
fairlyhighvoltagedroppedacrosstheopeningcontactsofswitch#1,causingunduearcingand<br />
shortenedswitchlife.<br />
Ifswitch#2isclosed(turned”on”),thediodewillnowbeapartofthecircuit. Quickly<br />
closeandopenswitch#1again,notingthedifferenceincircuitbehavior.Thistime,theneon<br />
lampdoesnotflash.Connectavoltmeteracrosstheinductortoverifythattheinductorisstill<br />
receivingfullbatteryvoltagewithswitch#1closed. Ifthevoltmeterregistersonlyasmall<br />
voltagewithswitch#1”on,”thediodeisprobablyconnectedbackward,creatingashort-circuit.
5.3. HALF-WAVERECTIFIER 205<br />
5.3 Half-waverectifier<br />
PARTSANDMATERIALS<br />
• Low-voltageACpowersupply(6voltoutput)<br />
• 6voltbattery<br />
• One1N4001rectifyingdiode(RadioShackcatalog#276-1101)<br />
• Small”hobby”motor,permanent-magnettype(RadioShackcatalog#273-223orequivalent)<br />
• Audiodetectorwithheadphones<br />
• 0.1 µFcapacitor(RadioShackcatalog#272-135orequivalent)<br />
Thediodeneednotbeanexactmodel1N4001. Anyofthe”1N400X”seriesofrectifying<br />
diodesaresuitableforthetask,andtheyarequiteeasytoobtain.<br />
SeetheACexperimentschapterfordetailedinstructionsonbuildingthe”audiodetector”<br />
listedhere. Ifyouhaven’tbuiltonealready,you’remissingasimpleandvaluabletoolfor<br />
experimentation.<br />
A0.1 µFcapacitorisspecifiedfor”coupling”theaudiodetectortothecircuit,sothatonlyAC<br />
reachesthedetectorcircuit.Thiscapacitor’svalueisnotcritical.I’veusedcapacitorsranging<br />
from0.27 µFto0.015 µFwithsuccess.Lowercapacitorvaluesattenuatelow-frequencysignals<br />
toagreaterdegree,resultinginlesssoundintensityfromtheheadphones,souseagreatervaluecapacitorvalueifyouexperiencedifficultyhearingthetone(s).<br />
CROSS-REFERENCES<br />
LessonsInElectricCircuits,Volume3,chapter3:”DiodesandRectifiers”<br />
LEARNINGOBJECTIVES<br />
• Functionofadiodeasarectifier<br />
• Permanent-magnetmotoroperationonACversusDCpower<br />
• Measuring”ripple”voltagewithavoltmeter<br />
SCHEMATICDIAGRAM<br />
Diode<br />
AC<br />
power<br />
supply<br />
Mtr<br />
(motor)<br />
ILLUSTRATION
206 CHAPTER5. DISCRETESEMICONDUCTORCIRCUITS<br />
Low-voltage<br />
AC power supply<br />
12<br />
6 6<br />
Diode<br />
Motor<br />
INSTRUCTIONS<br />
Connectthemotortothelow-voltageACpowersupplythroughtherectifyingdiodeas<br />
shown.Thediodeonlyallowscurrenttopassthroughduringonehalf-cycleofafullpositiveand-negativecycleofpowersupplyvoltage,eliminatingonehalf-cyclefromeverreachingthe<br />
motor. Asaresult,themotoronly”sees”currentinonedirection,albeitapulsatingcurrent,<br />
allowingittospininonedirection.<br />
Takeajumperwireandshortpastthediodemomentarily,notingtheeffectonthemotor’s<br />
operation:
5.3. HALF-WAVERECTIFIER 207<br />
Low-voltage<br />
AC power supply<br />
12 Temporary<br />
6 6<br />
jumper<br />
Asyoucansee,permanent-magnet”DC”motorsdonotfunctionwellonalternatingcurrent.<br />
Removethetemporaryjumperwireandreversethediode’sorientationinthecircuit.Notethe<br />
effectonthemotor.<br />
MeasureDCvoltageacrossthemotorlikethis:
208 CHAPTER5. DISCRETESEMICONDUCTORCIRCUITS<br />
V<br />
A<br />
Low-voltage<br />
AC power supply<br />
V<br />
OFF<br />
A<br />
12<br />
6 6<br />
A<br />
COM<br />
Then,measureACvoltageacrossthemotoraswell:<br />
V<br />
A<br />
Low-voltage<br />
AC power supply<br />
V<br />
OFF<br />
A<br />
12<br />
6 6<br />
A<br />
COM
5.3. HALF-WAVERECTIFIER 209<br />
MostdigitalmultimetersdoagoodjobofdiscriminatingACfromDCvoltage,andthese<br />
twomeasurementsshowtheDCaverageandAC”ripple”voltages,respectivelyofthepower<br />
”seen”bythemotor.Ripplevoltageisthevaryingportionofthevoltage,interpretedasanAC<br />
quantitybymeasurementequipmentalthoughthevoltagewaveformneveractuallyreverses<br />
polarity. RipplemaybeenvisionedasanACsignalsuperimposedonasteadyDC”bias”or<br />
”offset”signal.ComparethesemeasurementsofDCandACwithvoltagemeasurementstaken<br />
acrossthemotorwhilepoweredbyabattery:<br />
V<br />
A<br />
V<br />
OFF<br />
A<br />
A<br />
COM<br />
+ -<br />
Batteriesgivevery”pure”DCpower,andasaresultthereshouldbeverylittleACvoltage<br />
measuredacrossthemotorinthiscircuit.WhateverACvoltageismeasuredacrossthemotor<br />
isduetothemotor’spulsatingcurrentdrawasthebrushesmakeandbreakcontactwiththe<br />
rotatingcommutatorbars. Thispulsatingcurrentcausespulsatingvoltagestobedropped<br />
acrossanystrayresistancesinthecircuit,resultinginpulsatingvoltage”dips”atthemotor<br />
terminals.<br />
Aqualitativeassessmentofripplevoltagemaybeobtainedbyusingthesensitiveaudio<br />
detectordescribedintheACexperimentschapter(thesamedevicedescribedasa”sensitive<br />
voltagedetector”intheDCexperimentschapter).Turnthedetector’ssensitivitydownforlow<br />
volume,andconnectitacrossthemotorterminalsthroughasmall(0.1 µF)capacitor,likethis:
210 CHAPTER5. DISCRETESEMICONDUCTORCIRCUITS<br />
headphones<br />
Capacitor<br />
Sensitivity<br />
0.1 µF<br />
plug<br />
+ -<br />
Thecapacitoractsasahigh-passfilter,blockingDCvoltagefromreachingthedetector<br />
andallowingeasier”listening”oftheremainingACvoltage.Thisistheexactsametechnique<br />
usedinoscilloscopecircuitryfor”ACcoupling,”whereDCsignalsareblockedfromviewing<br />
byaseries-connectedcapacitor. Withabatterypoweringthemotor,therippleshouldsound<br />
likeahigh-pitched”buzz”or”whine.”TryreplacingthebatterywiththeACpowersupply<br />
andrectifyingdiode,”listening”withthedetectortothelow-pitched”buzz”ofthehalf-wave<br />
rectifiedpower:
5.3. HALF-WAVERECTIFIER 211<br />
headphones<br />
Low-voltage<br />
AC power supply<br />
12 Sensitivity<br />
plug<br />
6 6<br />
COMPUTERSIMULATION<br />
SchematicwithSPICEnodenumbers:<br />
V 1<br />
D 1<br />
1 2<br />
R load<br />
0 0<br />
Netlist(makeatextfilecontainingthefollowingtext,verbatim):<br />
Halfwave rectifier<br />
v1 1 0 sin(0 8.485 60 0 0)<br />
rload 2 0 10k<br />
d1 1 2 mod1<br />
.model mod1 d<br />
.tran .5m 25m<br />
.plot tran v(1,0) v(2,0)<br />
.end<br />
Thissimulationplotstheinputvoltageasasinewaveandtheoutputvoltageasaseriesof<br />
”humps”correspondingtothepositivehalf-cyclesoftheACsourcevoltage.Thedynamicsofa<br />
DCmotorarefartoocomplextobesimulatedusingSPICE,unfortunately.
212 CHAPTER5. DISCRETESEMICONDUCTORCIRCUITS<br />
ACsourcevoltageisspecifiedas8.485insteadof6voltsbecauseSPICEunderstandsAC<br />
voltageintermsofpeakvalueonly. A6voltRMSsine-wavevoltageisactually8.485volts<br />
peak.InsimulationswherethedistinctionbetweenRMSandpeakvalueisn’trelevant,Iwill<br />
notbotherwithanRMS-to-peakconversionlikethis. Tobetruthful,thedistinctionisnot<br />
terriblyimportantinthissimulation,butIdiscussithereforyouredification.
5.4. FULL-WAVECENTER-TAPRECTIFIER 213<br />
5.4 Full-wavecenter-taprectifier<br />
PARTSANDMATERIALS<br />
• Low-voltageACpowersupply(6voltoutput)<br />
• Two1N4001rectifyingdiodes(RadioShackcatalog#276-1101)<br />
• Small”hobby”motor,permanent-magnettype(RadioShackcatalog#273-223orequivalent)<br />
• Audiodetectorwithheadphones<br />
• 0.1 µFcapacitor<br />
• Onetoggleswitch,SPST(”Single-Pole,Single-Throw”)<br />
Itisessentialforthisexperimentthatthelow-voltageACpowersupplybeequippedwitha<br />
centertap.Atransformerwithanon-tappedsecondarywindingsimplywillnotworkforthis<br />
circuit.<br />
Thediodesneednotbeexactmodel1N4001units.Anyofthe”1N400X”seriesofrectifying<br />
diodesaresuitableforthetask,andtheyarequiteeasytoobtain.<br />
CROSS-REFERENCES<br />
LessonsInElectricCircuits,Volume3,chapter3:”DiodesandRectifiers”<br />
LEARNINGOBJECTIVES<br />
• Designofacenter-taprectifiercircuit<br />
• Measuring”ripple”voltagewithavoltmeter<br />
SCHEMATICDIAGRAM<br />
Diode<br />
AC<br />
power<br />
supply<br />
Mtr<br />
(motor)<br />
Diode<br />
ILLUSTRATION
214 CHAPTER5. DISCRETESEMICONDUCTORCIRCUITS<br />
Low-voltage<br />
AC power supply<br />
12<br />
6 6<br />
Terminal<br />
strip<br />
Motor<br />
INSTRUCTIONS<br />
Thisrectifiercircuitiscalledfull-wavebecauseitmakesuseoftheentirewaveform,both<br />
positiveandnegativehalf-cycles,oftheACsourcevoltageinpoweringtheDCload. Asa<br />
result,thereisless”ripple”voltageseenattheload. TheRMS(Root-Mean-Square)valueof<br />
therectifier’soutputisalsogreaterforthiscircuitthanforthehalf-waverectifier.<br />
UseavoltmetertomeasureboththeDCandACvoltagedeliveredtothemotor.Youshould<br />
noticetheadvantagesofthefull-waverectifierimmediatelybythegreaterDCandlowerAC<br />
indicationsascomparedtothelastexperiment.<br />
Anexperimentaladvantageofthiscircuitistheeaseofwhichitmaybe”de-converted”<br />
toahalf-waverectifier: simplydisconnecttheshortjumperwireconnectingthetwodiodes’<br />
cathodeendstogetherontheterminalstrip.Betteryet,forquickcomparisonbetweenhalfand<br />
full-waverectification,youmayaddaswitchinthecircuittoopenandclosethisconnectionat<br />
will:<br />
Mtr<br />
Switch<br />
(close for full-wave operation)
5.4. FULL-WAVECENTER-TAPRECTIFIER 215<br />
Low-voltage<br />
AC power supply<br />
Switch<br />
12<br />
6 6<br />
Withtheabilitytoquicklyswitchbetweenhalf-andfull-waverectification,youmayeasily<br />
performqualitativecomparisonsbetweenthetwodifferentoperatingmodes. Usetheaudio<br />
signaldetectorto”listen”totheripplevoltagepresentbetweenthemotorterminalsforhalfwaveandfull-waverectificationmodes,notingboththeintensityandthequalityofthetone.<br />
Remembertouseacouplingcapacitorinserieswiththedetectorsothatitonlyreceivesthe<br />
AC”ripple”voltageandnotDCvoltage:
216 CHAPTER5. DISCRETESEMICONDUCTORCIRCUITS<br />
headphones<br />
Capacitor<br />
0.1 µF<br />
Sensitivity<br />
plug<br />
Test<br />
"probes"<br />
COMPUTERSIMULATION<br />
SchematicwithSPICEnodenumbers:<br />
D 1<br />
1 2 2<br />
V 1<br />
R load<br />
0 0<br />
V 2<br />
3<br />
D 2<br />
2<br />
Netlist(makeatextfilecontainingthefollowingtext,verbatim):<br />
Fullwave center-tap rectifier<br />
v1 1 0 sin(0 8.485 60 0 0)<br />
v2 0 3 sin(0 8.485 60 0 0)<br />
rload 2 0 10k<br />
d1 1 2 mod1
5.4. FULL-WAVECENTER-TAPRECTIFIER 217<br />
d2 3 2 mod1<br />
.model mod1 d<br />
.tran .5m 25m<br />
.plot tran v(1,0) v(2,0)<br />
.end
218 CHAPTER5. DISCRETESEMICONDUCTORCIRCUITS<br />
5.5 Full-wavebridgerectifier<br />
PARTSANDMATERIALS<br />
• Low-voltageACpowersupply(6voltoutput)<br />
• Four1N4001rectifyingdiodes(RadioShackcatalog#276-1101)<br />
• Small”hobby”motor,permanent-magnettype(RadioShackcatalog#273-223orequivalent)<br />
CROSS-REFERENCES<br />
LessonsInElectricCircuits,Volume3,chapter3:”DiodesandRectifiers”<br />
LEARNINGOBJECTIVES<br />
• Designofabridgerectifiercircuit<br />
• Advantagesanddisadvantagesofthebridgerectifiercircuit,comparedtothecenter-tap<br />
circuit<br />
SCHEMATICDIAGRAM<br />
AC<br />
power<br />
supply<br />
Mtr<br />
(motor)<br />
ILLUSTRATION
5.5. FULL-WAVEBRIDGERECTIFIER 219<br />
Low-voltage<br />
AC power supply<br />
12<br />
6 6<br />
Terminal<br />
strip<br />
Motor<br />
INSTRUCTIONS<br />
Thiscircuitprovidesfull-waverectificationwithoutthenecessityofacenter-tappedtransformer.Inapplicationswhereacenter-tapped,orsplit-phase,sourceisunavailable,thisisthe<br />
onlypracticalmethodoffull-waverectification.<br />
Inadditiontorequiringmorediodesthanthecenter-tapcircuit,thefull-wavebridgesuffersaslightperformancedisadvantageaswell:theadditionalvoltagedropcausedbycurrent<br />
havingtogothroughtwodiodesineachhalf-cycleratherthanthroughonlyone.Withalowvoltagesourcesuchastheoneyou’reusing(6voltsRMS),thisdisadvantageiseasilymeasured.<br />
ComparetheDCvoltagereadingacrossthemotorterminalswiththereadingobtainedfrom<br />
thelastexperiment,giventhesameACpowersupplyandthesamemotor.<br />
COMPUTERSIMULATION<br />
SchematicwithSPICEnodenumbers:<br />
1<br />
D 1 1 D 2<br />
3<br />
V 1<br />
0<br />
2<br />
D<br />
0<br />
3 D<br />
R load<br />
4<br />
Netlist(makeatextfilecontainingthefollowingtext,verbatim):<br />
Fullwave bridge rectifier<br />
v1 1 0 sin(0 8.485 60 0 0)<br />
2<br />
3
220 CHAPTER5. DISCRETESEMICONDUCTORCIRCUITS<br />
rload 2 3 10k<br />
d1 3 1 mod1<br />
d2 1 2 mod1<br />
d3 3 0 mod1<br />
d4 0 2 mod1<br />
.model mod1 d<br />
.tran .5m 25m<br />
.plot tran v(1,0) v(2,3)<br />
.end
5.6. RECTIFIER/FILTERCIRCUIT 221<br />
5.6 Rectifier/filtercircuit<br />
PARTSANDMATERIALS<br />
• Low-voltageACpowersupply<br />
• Bridgerectifierpack(RadioShackcatalog#276-1185orequivalent)<br />
• Electrolyticcapacitor,1000 µF,atleast25WVDC(RadioShackcatalog#272-1047or<br />
equivalent)<br />
• Four”banana”jackstylebindingposts,orotherterminalhardware,forconnectionto<br />
potentiometercircuit(RadioShackcatalog#274-662orequivalent)<br />
• Metalbox<br />
• 12-voltlightbulb,25watt<br />
• Lampsocket<br />
Abridgerectifier”pack”ishighlyrecommendedoverconstructingabridgerectifiercircuit<br />
fromindividualdiodes,becausesuch”packs”aremadetoboltontoametalheatsink.Ametal<br />
boxisrecommendedoveraplasticboxforitsabilitytofunctionasaheatsinkfortherectifier.<br />
Alargercapacitorvalueisfinetouseinthisexperiment,solongasitsworkingvoltageis<br />
highenough. Tobesafe,chooseacapacitorwithaworkingvoltageratingatleasttwicethe<br />
RMSACvoltageoutputofthelow-voltageACpowersupply.<br />
High-wattage12-voltlampsmaybepurchasedfromrecreationalvehicle(RV)andboating<br />
supplystores.Commonsizesare25wattand50watt.Thislampwillbeusedasa”heavy”load<br />
forthepowersupply.<br />
CROSS-REFERENCES<br />
LessonsInElectricCircuits,Volume2,chapter8:”Filters”<br />
LEARNINGOBJECTIVES<br />
• CapacitivefilterfunctioninanAC/DCpowersupply<br />
• Importanceofheatsinksforpowersemiconductors<br />
SCHEMATICDIAGRAM<br />
Rectifier<br />
AC<br />
in<br />
- +<br />
DC<br />
out
222 CHAPTER5. DISCRETESEMICONDUCTORCIRCUITS<br />
ILLUSTRATION<br />
Rectifier<br />
AC in<br />
AC<br />
-<br />
+<br />
AC<br />
-<br />
-<br />
Capacitor<br />
DC<br />
out<br />
INSTRUCTIONS<br />
Thisexperimentinvolvesconstructingarectifierandfiltercircuitforattachmenttothe<br />
low-voltageACpowersupplyconstructedearlier. Withthisdevice,youwillhaveasourceof<br />
low-voltage,DCpowersuitableasareplacementforabatteryinbattery-poweredexperiments.<br />
Ifyouwouldliketomakethisdeviceitsown,self-contained120VAC/DCpowersupply,you<br />
mayaddallthecomponentryofthelow-voltageACsupplytothe”ACin”sideofthiscircuit:<br />
atransformer,powercord,andplug.Evenifyoudon’tchoosetodothis,Irecommendusinga<br />
metalboxlargerthannecessarytoprovideroomforadditionalvoltageregulationcircuitryyou<br />
mightchoosetoaddtothisprojectlater.<br />
Thebridgerectifierunitshouldberatedforacurrentatleastashighasthetransformer’s<br />
secondarywindingisratedfor,andforavoltageatleasttwiceashighastheRMSvoltageof<br />
thetransformer’soutput(thisallowsforpeakvoltage,plusanadditionalsafetymargin).The<br />
RadioShackrectifierspecifiedinthepartslistisratedfor25ampsand50volts,morethan<br />
enoughfortheoutputofthelow-voltageACpowersupplyspecifiedintheACexperiments<br />
chapter.<br />
Rectifierunitsofthissizeareoftenequippedwith”quick-disconnect”terminals. Complementary”quick-disconnect”lugsaresoldthatcrimpontothebareendsofwire.<br />
Thisisthe<br />
preferredmethodofterminalconnection.Youmaysolderwiresdirectlytothelugsoftherectifier,butIrecommendagainstdirectsolderingtoanysemiconductorcomponentfortworeasons:<br />
possibleheatdamageduringsoldering,anddifficultyofreplacingthecomponentintheevent<br />
offailure.<br />
Semiconductordevicesaremorepronetofailurethanmostofthecomponentscoveredin<br />
theseexperimentsthusfar,andsoifyouhaveanyintentofmakingacircuitpermanent,you<br />
shouldbuildittobemaintained. ”Maintainableconstruction”involves,amongotherthings,<br />
makingalldelicatecomponentsreplaceable. Italsomeansmaking”testpoints”accessibleto<br />
meterprobesthroughoutthecircuit,sothattroubleshootingmaybeexecutedwithamini-
5.6. RECTIFIER/FILTERCIRCUIT 223<br />
mumofinconvenience.Terminalstripsinherentlyprovidetestpointsfortakingvoltagemeasurements,andtheyalsoallowforeasydisconnectionofwireswithoutsacrificingconnection<br />
durability.<br />
Bolttherectifierunittotheinsideofthemetalbox. Thebox’ssurfaceareawillactasa<br />
radiator,keepingtherectifierunitcoolasitpasseshighcurrents.Anymetalradiatorsurface<br />
designedtolowertheoperatingtemperatureofanelectroniccomponentiscalledaheatsink.<br />
Semiconductordevicesingeneralarepronetodamagefromoverheating,soprovidingapath<br />
forheattransferfromthedevice(s)totheambientairisveryimportantwhenthecircuitin<br />
questionmayhandlelargeamountsofpower.<br />
Acapacitorisincludedinthecircuittoactasafiltertoreduceripplevoltage.Makesurethat<br />
youconnectthecapacitorproperlyacrosstheDCoutputterminalsoftherectifier,sothatthe<br />
polaritiesmatch.Beinganelectrolyticcapacitor,itissensitivetodamagebypolarityreversal.<br />
Inthiscircuitespecially,wheretheinternalresistanceofthetransformerandrectifierarelow<br />
andtheshort-circuitcurrentconsequentlyishigh,thepotentialfordamageisgreat.Warning:<br />
afailedcapacitorinthiscircuitwilllikelyexplodewithalarmingforce!<br />
Aftertherectifier/filtercircuitisbuilt,connectittothelow-voltageACpowersupplylike<br />
this:<br />
Low-voltage<br />
AC power supply<br />
12<br />
6 6<br />
Rectifier<br />
AC in<br />
AC<br />
-<br />
+<br />
AC<br />
-<br />
-<br />
Capacitor<br />
DC<br />
out<br />
MeasuretheACvoltageoutputbythelow-voltagepowersupply.Yourmetershouldindicate<br />
approximately6voltsifthecircuitisconnectedasshown. Thisvoltagemeasurementisthe<br />
RMSvoltageoftheACpowersupply.<br />
Now,switchyourmultimetertotheDCvoltagefunctionandmeasuretheDCvoltageoutput<br />
bytherectifier/filtercircuit.ItshouldreadsubstantiallyhigherthantheRMSvoltageofthe<br />
ACinputmeasuredbefore.ThefilteringactionofthecapacitorprovidesaDCoutputvoltage<br />
equaltothepeakACvoltage,hencethegreatervoltageindication:
224 CHAPTER5. DISCRETESEMICONDUCTORCIRCUITS<br />
Full-wave, rectified DC voltage<br />
Time<br />
Full-wave, rectified DC voltage, with filtering<br />
Time<br />
MeasuretheACripplevoltagemagnitudewithadigitalvoltmetersettoACvolts(orAC<br />
millivolts). Youshouldnoticeamuchsmallerripplevoltageinthiscircuitthanwhatwas<br />
measuredinanyoftheunfilteredrectifiercircuitspreviouslybuilt.Feelfreetouseyouraudio<br />
detectorto”listen”totheACripplevoltageoutputbytherectifier/filterunit.Asusual,connect<br />
asmall”coupling”capacitorinserieswiththedetectorsothatitdoesnotrespondtotheDC<br />
voltage,butonlytheACripple.Verylittlesoundshouldbeheard.<br />
AftertakingunloadedACripplevoltagemeasurements,connectthe25wattlightbulbto<br />
theoutputoftherectifier/filtercircuitlikethis:<br />
Low-voltage<br />
AC power supply<br />
12<br />
6 6<br />
Rectifier<br />
AC in<br />
AC<br />
-<br />
+<br />
AC<br />
-<br />
-<br />
Capacitor<br />
DC<br />
out<br />
Re-measuretheripplevoltagepresentbetweentherectifier/filterunit’s”DCout”terminals.<br />
Withaheavyload,thefiltercapacitorbecomesdischargedbetweenrectifiedvoltagepeaks,<br />
resultingingreaterripplethanbefore:
5.6. RECTIFIER/FILTERCIRCUIT 225<br />
Full-wave, filtered DC voltage under heavy load<br />
Time<br />
Iflessrippleisdesiredunderheavy-loadconditions,alargercapacitormaybeused,ora<br />
morecomplexfiltercircuitmaybebuiltusingtwocapacitorsandaninductor:<br />
DC<br />
out<br />
Ifyouchoosetobuildsuchafiltercircuit,besuretouseaniron-coreinductorformaximum<br />
inductance,andonewiththickenoughwiretosafelyhandlethefullratedcurrentofpower<br />
supply.Inductorsusedforthepurposeoffilteringaresometimesreferredtoaschokes,because<br />
they”choke”ACripplevoltagefromgettingtotheload.Ifasuitablechokecannotbeobtained,<br />
thesecondarywindingofastep-downpowertransformerlikethetypeusedtostep120volts<br />
ACdownto12or6voltsACinthelow-voltagepowersupplymaybeused.Leavetheprimary<br />
(120volt)windingopen:<br />
Leave these wires<br />
disconnected!<br />
DC<br />
out<br />
COMPUTERSIMULATION<br />
SchematicwithSPICEnodenumbers:
226 CHAPTER5. DISCRETESEMICONDUCTORCIRCUITS<br />
1<br />
D 1 1 D 2<br />
3<br />
V 1<br />
0<br />
2<br />
D<br />
0<br />
3 D<br />
R load<br />
4<br />
C 1<br />
Netlist(makeatextfilecontainingthefollowingtext,verbatim):<br />
Fullwave bridge rectifier<br />
v1 1 0 sin(0 8.485 60 0 0)<br />
rload 2 3 10k<br />
c1 2 3 1000u ic=0<br />
d1 3 1 mod1<br />
d2 1 2 mod1<br />
d3 3 0 mod1<br />
d4 0 2 mod1<br />
.model mod1 d<br />
.tran .5m 25m<br />
.plot tran v(1,0) v(2,3)<br />
.end<br />
YoumaydecreasethevalueofR load inthesimulationfrom10kΩtosomelowervalueto<br />
exploretheeffectsofloadingonripplevoltage.Asitiswitha10kΩloadresistor,therippleis<br />
undetectableonthewaveformplottedbySPICE.<br />
2<br />
3
5.7. VOLTAGEREGULATOR 227<br />
5.7 Voltageregulator<br />
PARTSANDMATERIALS<br />
• Four6voltbatteries<br />
• Zenerdiode,12volt–type1N4742(RadioShackcatalog#276-563orequivalent)<br />
• One10kΩresistor<br />
Anylow-voltagezenerdiodeisappropriateforthisexperiment. The1N4742modellisted<br />
here(zenervoltage=12volts)isbutonesuggestion. Whateverdiodemodelyouchoose,I<br />
highlyrecommendonewithazenervoltageratinggreaterthanthevoltageofasinglebattery,<br />
formaximumlearningexperience. Itisimportantthatyouseehowazenerdiodefunctions<br />
whenexposedtoavoltagelessthanitsbreakdownrating.<br />
CROSS-REFERENCES<br />
LessonsInElectricCircuits,Volume3,chapter3:”DiodesandRectifiers”<br />
LEARNINGOBJECTIVES<br />
• Zenerdiodefunction<br />
SCHEMATICDIAGRAM<br />
10 kΩ<br />
Zener<br />
diode<br />
ILLUSTRATION<br />
+ -
228 CHAPTER5. DISCRETESEMICONDUCTORCIRCUITS<br />
INSTRUCTIONS<br />
Buildthissimplecircuit,beingsuretoconnectthediodein”reverse-bias”fashion(cathode<br />
positiveandanodenegative),andmeasurethevoltageacrossthediodewithonebatteryas<br />
apowersource. Recordthisvoltagedropforfuturereference. Also,measureandrecordthe<br />
voltagedropacrossthe10kΩresistor.<br />
Modifythecircuitbyconnectingtwo6-voltbatteriesinseries,for12voltstotalpowersource<br />
voltage. Re-measurethediode’svoltagedrop,aswellastheresistor’svoltagedrop,witha<br />
voltmeter:<br />
V<br />
A<br />
V<br />
OFF<br />
A<br />
A COM<br />
+ -<br />
+ -<br />
Connectthree,thenfour6-voltbatteriestogetherinseries,formingan18voltand24volt<br />
powersource,respectively. Measureandrecordthediode’sandresistor’svoltagedropsfor<br />
eachnewpowersupplyvoltage. Whatdoyounoticeaboutthediode’svoltagedropforthese<br />
fourdifferentsourcevoltages? Doyouseehowthediodevoltageneverexceedsalevelof12<br />
volts? Whatdoyounoticeabouttheresistor’svoltagedropforthesefourdifferentsource<br />
voltagelevels?<br />
Zenerdiodesarefrequentlyusedasvoltageregulatingdevices,becausetheyacttoclamp<br />
thevoltagedropacrossthemselvesatapredeterminedlevel.Whateverexcessvoltageissuppliedbythepowersourcebecomesdroppedacrosstheseriesresistor.However,itisimportant<br />
tonotethatazenerdiodecannotmakeupforadeficiencyinsourcevoltage.Forinstance,this<br />
12-voltzenerdiodedoesnotdrop12voltswhenthepowersourceisonly6voltsstrong. Itis<br />
helpfultothinkofazenerdiodeasavoltagelimiter:establishingamaximumvoltagedrop,
5.7. VOLTAGEREGULATOR 229<br />
butnotaminimumvoltagedrop.<br />
COMPUTERSIMULATION<br />
SchematicwithSPICEnodenumbers:<br />
1<br />
10 kΩ<br />
2<br />
Zener<br />
diode<br />
0 0<br />
Netlist(makeatextfilecontainingthefollowingtext,verbatim):<br />
Zener diode<br />
v1 1 0<br />
r1 1 2 10k<br />
d1 0 2 mod1<br />
.model mod1 d bv=12<br />
.dc v1 18 18 1<br />
.print dc v(2,0)<br />
.end<br />
AzenerdiodemaybesimulatedinSPICEwithanormaldiode,thereversebreakdown<br />
parameter(bv=12)settothedesiredzenerbreakdownvoltage.
230 CHAPTER5. DISCRETESEMICONDUCTORCIRCUITS<br />
5.8 Transistorasaswitch<br />
PARTSANDMATERIALS<br />
• Two6-voltbatteries<br />
• OneNPNtransistor–models2N2222or2N3403recommended(RadioShackcatalog#<br />
276-1617isapackageoffifteenNPNtransistorsidealforthisandotherexperiments)<br />
• One100kΩresistor<br />
• One560 Ωresistor<br />
• Onelight-emittingdiode(RadioShackcatalog#276-026orequivalent)<br />
Resistorvaluesarenotcriticalforthisexperiment.Neitheristheparticularlightemitting<br />
diode(LED)selected.<br />
CROSS-REFERENCES<br />
LessonsInElectricCircuits,Volume3,chapter4:”BipolarJunctionTransistors”<br />
LEARNINGOBJECTIVES<br />
• Currentamplificationofabipolarjunctiontransistor<br />
SCHEMATICDIAGRAM<br />
6 V<br />
560 Ω<br />
6 V 100 kΩ<br />
Q 1<br />
ILLUSTRATION
5.8. TRANSISTORASASWITCH 231<br />
CBE<br />
+ - + -<br />
INSTRUCTIONS<br />
Theredwireshowninthediagram(theoneterminatinginanarrowhead,connectedtoone<br />
endofthe100kΩresistor)isintendedtoremainloose,sothatyoumaytouchitmomentarily<br />
tootherpointsinthecircuit.<br />
Ifyoutouchtheendoftheloosewiretoanypointinthecircuitmorepositivethanit,such<br />
asthepositivesideoftheDCpowersource,theLEDshouldlightup.Ittakes20mAtofully<br />
illuminateastandardLED,sothisbehaviorshouldstrikeyouasinteresting,becausethe100<br />
kΩresistortowhichtheloosewireisattachedrestrictscurrentthroughittoafarlesservalue<br />
than20mA.Atmost,atotalvoltageof12voltsacrossa100kΩresistanceyieldsacurrentof<br />
only0.12mA,or120 µA!Theconnectionmadebyyourtouchingthewiretoapositivepoint<br />
inthecircuitconductsfarlesscurrentthan1mA,yetthroughtheamplifyingactionofthe<br />
transistor,isabletocontrolamuchgreatercurrentthroughtheLED.<br />
Tryusinganammetertoconnecttheloosewiretothepositivesideofthepowersource,like<br />
this:
232 CHAPTER5. DISCRETESEMICONDUCTORCIRCUITS<br />
CBE<br />
+ - + -<br />
V<br />
A<br />
V<br />
OFF<br />
A<br />
A<br />
COM<br />
Youmayhavetoselectthemostsensitivecurrentrangeonthemetertomeasurethissmall<br />
flow.Aftermeasuringthiscontrollingcurrent,trymeasuringtheLED’scurrent(thecontrolled<br />
current)andcomparemagnitudes.Don’tbesurprisedifyoufindaratioinexcessof200(the<br />
controlledcurrent200timesasgreatasthecontrollingcurrent)!<br />
Asyoucansee,thetransistorisactingasakindofelectrically-controlledswitch,switching<br />
currentonandofftotheLEDatthecommandofamuchsmallercurrentsignalconducted<br />
throughitsbaseterminal.<br />
Tofurtherillustratejusthowminisculethecontrollingcurrentis,removetheloosewire<br />
fromthecircuitandtry”bridging”theunconnectedendofthe100kΩresistortothepower<br />
source’spositivepolewithtwofingersofonehand. Youmayneedtowettheendsofthose<br />
fingerstomaximizeconductivity:
5.8. TRANSISTORASASWITCH 233<br />
CBE<br />
+ - + - Bridge the two points identified by arrows<br />
with two fingers of one hand, to conduct a<br />
small current to the transistor’s base.<br />
Tryvaryingthecontactpressureofyourfingerswiththesetwopointsinthecircuittovary<br />
theamountofresistanceinthecontrollingcurrent’spath.Canyouvarythebrightnessofthe<br />
LEDbydoingso? Whatdoesthisindicateaboutthetransistor’sabilitytoactasmorethan<br />
justaswitch;i.e.asavariable<br />
COMPUTERSIMULATION<br />
SchematicwithSPICEnodenumbers:<br />
V 1<br />
1<br />
0<br />
1<br />
1<br />
560 Ω<br />
3<br />
R 2<br />
D 1<br />
4<br />
Q 1<br />
R 1<br />
100 kΩ<br />
1 2<br />
0<br />
Netlist(makeatextfilecontainingthefollowingtext,verbatim):<br />
Transistor as a switch<br />
v1 1 0<br />
r1 1 2 100k<br />
r2 1 3 560<br />
d1 3 4 mod2
234 CHAPTER5. DISCRETESEMICONDUCTORCIRCUITS<br />
q1 4 2 0 mod1<br />
.model mod1 npn bf=200<br />
.model mod2 d is=1e-28<br />
.dc v1 12 12 1<br />
.print dc v(2,0) v(4,0) v(1,2) v(1,3) v(3,4)<br />
.end<br />
Inthissimulation,thevoltagedropacrossthe560 Ωresistorv(1,3)turnsouttobe10.26<br />
volts,indicatingaLEDcurrentof18.32mAbyOhm’sLaw(I=E/R).R 1 ’svoltagedrop(voltage<br />
betweennodes1and2)endsupbeing11.15volts,whichacross100kΩgivesacurrentofonly<br />
111.5 µA.Obviously,averysmallcurrentisexertingcontroloveramuchlargercurrentinthis<br />
circuit.<br />
Incaseyouwerewondering,the is=1e-28parameterinthediode’s .modellineisthere<br />
tomakethediodeactmorelikeanLEDwithahigherforwardvoltagedrop.
5.9. STATICELECTRICITYSENSOR 235<br />
5.9 Staticelectricitysensor<br />
PARTSANDMATERIALS<br />
• OneN-channeljunctionfield-effecttransistor,models2N3819orJ309recommended(RadioShackcatalog#276-2035isthemodel2N3819)<br />
• One6voltbattery<br />
• One100kΩresistor<br />
• Onelight-emittingdiode(RadioShackcatalog#276-026orequivalent)<br />
• Plasticcomb<br />
Theparticularjunctionfield-effecttransistor,orJFET,modelusedinthisexperimentisnot<br />
critical.P-channelJFETsarealsookaytouse,butarenotaspopularasN-channeltransistors.<br />
Bewarethatnotalltransistorssharethesameterminaldesignations,orpinouts,evenif<br />
theysharethesamephysicalappearance. Thiswilldictatehowyouconnectthetransistors<br />
togetherandtoothercomponents,sobesuretocheckthemanufacturer’sspecifications(componentdatasheet),easilyobtainedfromthemanufacturer’swebsite.Bewarethatitispossible<br />
forthetransistor’spackageandeventhemanufacturer’sdatasheettoshowincorrectterminal<br />
identificationdiagrams! Double-checkingpinidentitieswithyourmultimeter’s”diodecheck”<br />
functionishighlyrecommended.Fordetailsonhowtoidentifyjunctionfield-effecttransistor<br />
terminalsusingamultimeter,consultchapter5oftheSemiconductorvolume(volumeIII)of<br />
thisbookseries.<br />
CROSS-REFERENCES<br />
LessonsInElectricCircuits,Volume3,chapter5:”JunctionField-EffectTransistors”<br />
LEARNINGOBJECTIVES<br />
• HowtheJFETisusedasanon/offswitch<br />
• HowJFETcurrentgaindiffersfromabipolartransistor<br />
SCHEMATICDIAGRAM<br />
6 V 100 kΩ<br />
Q 1
236 CHAPTER5. DISCRETESEMICONDUCTORCIRCUITS<br />
ILLUSTRATION<br />
+ - SGD<br />
INSTRUCTIONS<br />
Thisexperimentisverysimilartothepreviousexperimentusingabipolarjunctiontransistor(BJT)asaswitchingdevicetocontrolcurrentthroughanLED.Inthisexperiment,a<br />
junctionfield-effecttransistorisusedinstead,givingdramaticallyimprovedsensitivity.<br />
Buildthiscircuitandtouchtheloosewireend(thewireshowninredontheschematic<br />
diagramandintheillustration,connectedtothe100kΩresistor)withyourhand. Simply<br />
touchingthiswirewilllikelyhaveaneffectontheLED’sstatus. Thiscircuitmakesafine<br />
sensorofstaticelectricity!Tryscuffingyourfeetonacarpetandthentouchingthewireendif<br />
noeffectonthelightisseenyet.<br />
Foramorecontrolledtest,touchthewirewithonehandandalternatelytouchthepositive<br />
(+)andnegative(-)terminalsofthebatterywithonefingerofyourotherhand.Yourbodyacts<br />
asaconductor(albeitapoorone),connectingthegateterminaloftheJFETtoeitherterminal<br />
ofthebatteryasyoutouchthem. MakenotewhichterminalmakestheLEDturnonand<br />
whichmakestheLEDturnoff.Trytorelatethisbehaviorwithwhatyou’vereadaboutJFETs<br />
inchapter5oftheSemiconductorvolume.<br />
ThefactthataJFETisturnedonandoffsoeasily(requiringsolittlecontrolcurrent),as<br />
evidencedbyfullon-and-offcontrolsimplybyconductionofacontrolcurrentthroughyour<br />
body,demonstrateshowgreatofacurrentgainithas. WiththeBJT”switch”experiment,a<br />
muchmore”solid”connectionbetweenthetransistor’sgateterminalandasourceofvoltage<br />
wasneededtoturniton.NotsowiththeJFET.Infact,themerepresenceofstaticelectricity<br />
canturnitonandoffatadistance.<br />
Tofurtherexperimentwiththeeffectsofstaticelectricityonthiscircuit,brushyourhair<br />
withtheplasticcombandthenwavethecombnearthetransistor,watchingtheeffectonthe<br />
LED.Theactionofcombingyourhairwithaplasticobjectcreatesahighstaticvoltagebetween<br />
thecombandyourbody. Thestrongelectricfieldproducedbetweenthesetwoobjectsshould<br />
bedetectablebythiscircuitfromasignificantdistance!<br />
Incaseyou’rewonderingwhythereisno560 Ω”dropping”resistortolimitcurrentthrough<br />
theLED,manysmall-signalJFETstendtoself-limittheircontrolledcurrenttoalevelacceptablebyLEDs.Themodel2N3819,forexample,hasatypicalsaturateddraincurrent(I<br />
DSS )of
5.9. STATICELECTRICITYSENSOR 237<br />
10mAandamaximumof20mA.SincemostLEDsareratedataforwardcurrentof20mA,<br />
thereisnoneedforadroppingresistortolimitcircuitcurrent:theJFETdoesitintrinsically.
238 CHAPTER5. DISCRETESEMICONDUCTORCIRCUITS<br />
5.10 Pulsed-lightsensor<br />
PARTSANDMATERIALS<br />
• Two6-voltbatteries<br />
• OneNPNtransistor–models2N2222or2N3403recommended(RadioShackcatalog#<br />
276-1617isapackageoffifteenNPNtransistorsidealforthisandotherexperiments)<br />
• Onelight-emittingdiode(RadioShackcatalog#276-026orequivalent)<br />
• Audiodetectorwithheadphones<br />
Ifyoudon’thaveanaudiodetectoralreadyconstructed,youcanuseanicesetofaudioheadphones(closed-cupstyle,thatcompletelycoversyourears)anda120V/6Vstep-downtransformertobuildasensitiveaudiodetectorwithoutvolumecontrolorovervoltageprotection,<br />
justforthisexperiment.<br />
Connecttheseportionsoftheheadphonestereoplugtothetransformer’ssecondary(6volt)<br />
winding:<br />
To transformer<br />
To transformer<br />
common right left common right left<br />
Speakers in series<br />
Speakers in parallel<br />
Tryboththeseriesandtheparallelconnectionschemesfortheloudestsound.<br />
Ifyouhaven’tmadeanaudiodetectorasoutlinedinboththeDCandACexperiments<br />
chapters,youreallyshould–itisavaluablepieceoftestequipmentforyourcollection.<br />
CROSS-REFERENCES<br />
LessonsInElectricCircuits,Volume3,chapter4:”BipolarJunctionTransistors”<br />
LEARNINGOBJECTIVES<br />
• Howtouseatransistorasacrudecommon-emitteramplifier<br />
• HowtouseanLEDasalightsensor<br />
SCHEMATICDIAGRAM
5.10. PULSED-LIGHTSENSOR 239<br />
6 V<br />
ILLUSTRATION<br />
+ - CBE<br />
headphones<br />
Sensitivity<br />
plug<br />
INSTRUCTIONS<br />
ThiscircuitdetectspulsesoflightstrikingtheLEDandconvertsthemintorelativelystrong<br />
audiosignalstobeheardthroughtheheadphones.ForrestMimsteachesthatLEDshavethe
240 CHAPTER5. DISCRETESEMICONDUCTORCIRCUITS<br />
abilitytoproducecurrentwhenexposedtolight,inamannernotunlikeasemiconductorsolar<br />
cell.[1]Byitself,theLEDdoesnotproduceenoughelectricalpowertodrivetheaudiodetector<br />
circuit,soatransistorisusedtoamplifytheLED’ssignals.IftheLEDisexposedtoapulsing<br />
sourceoflight,atonewillbeheardintheheadphones.<br />
Sourcesoflightsuitableforthisexperimentincludefluorescentandneonlamps,which<br />
blinkrapidlywiththe60HzACpowerenergizingthem.Youmayalsotryusingbrightsunlight<br />
forasteadylightsource,thenwavingyourfingersinfrontoftheLED.Therapidlypassing<br />
shadowswillcausetheLEDtogeneratepulsesofvoltage,creatingabrief”buzzing”soundin<br />
theheadphones.<br />
LEDsservingasphoto-detectorsarenarrow-banddevices,respondingtoanarrowband<br />
ofwavelengthsclose,butnotidentical,tothatnormallyemitted. Infraredremotecontrols<br />
areagoodilluminationsourcefornear-infraredLEDsemployedasphoto-sensors,producinga<br />
receiversound.[3]<br />
Withalittleimagination,itisnotdifficulttograsptheconceptoftransmittingaudioinformation–suchasmusicorspeech–overabeamofpulsinglight.Givenasuitable”transmitter”<br />
circuittopulseanLEDonandoffwiththepositiveandnegativecrestsofanaudiowaveform<br />
fromamicrophone,the”receiver”circuitshownherewouldconvertthoselightpulsesbackinto<br />
audiosignals.[2]
5.11. VOLTAGEFOLLOWER 241<br />
5.11 Voltagefollower<br />
PARTSANDMATERIALS<br />
• OneNPNtransistor–models2N2222or2N3403recommended(RadioShackcatalog#<br />
276-1617isapackageoffifteenNPNtransistorsidealforthisandotherexperiments)<br />
• Two6-voltbatteries<br />
• Two1kΩresistors<br />
• One10kΩpotentiometer,single-turn,lineartaper(RadioShackcatalog#271-1715)<br />
Bewarethatnotalltransistorssharethesameterminaldesignations,orpinouts,evenif<br />
theysharethesamephysicalappearance. Thiswilldictatehowyouconnectthetransistors<br />
togetherandtoothercomponents,sobesuretocheckthemanufacturer’sspecifications(componentdatasheet),easilyobtainedfromthemanufacturer’swebsite.Bewarethatitispossible<br />
forthetransistor’spackageandeventhemanufacturer’sdatasheettoshowincorrectterminal<br />
identificationdiagrams! Double-checkingpinidentitieswithyourmultimeter’s”diodecheck”<br />
functionishighlyrecommended. Fordetailsonhowtoidentifybipolartransistorterminals<br />
usingamultimeter,consultchapter4oftheSemiconductorvolume(volumeIII)ofthisbook<br />
series.<br />
CROSS-REFERENCES<br />
LessonsInElectricCircuits,Volume3,chapter4:”BipolarJunctionTransistors”<br />
LEARNINGOBJECTIVES<br />
• Purposeofcircuit”ground”whenthereisnoactualconnectiontoearthground<br />
• Usingashuntresistortomeasurecurrentwithavoltmeter<br />
• Measureamplifiervoltagegain<br />
• Measureamplifiercurrentgain<br />
• Amplifierimpedancetransformation<br />
SCHEMATICDIAGRAM<br />
6 V<br />
R base<br />
6 V<br />
10 kΩ<br />
1 kΩ<br />
R load<br />
Q 1<br />
1 kΩ
242 CHAPTER5. DISCRETESEMICONDUCTORCIRCUITS<br />
ILLUSTRATION<br />
CBE<br />
+ - + -<br />
INSTRUCTIONS<br />
Again,bewarethatthetransistoryouselectforthisexperimentmaynothavethesame<br />
terminaldesignationsshownhere,andsothebreadboardlayoutshownintheillustrationmay<br />
notbecorrectforyou.Inmyillustrations,IshowallTO-92packagetransistorswithterminals<br />
labeled”CBE”:Collector,Base,andEmitter,fromlefttoright. Thisiscorrectforthemodel<br />
2N2222transistorandsomeothers,butnotforall;notevenforallNPN-typetransistors!As<br />
usual,checkwiththemanufacturerfordetailsontheparticularcomponent(s)youchoosefor<br />
aproject. Withbipolarjunctiontransistors,itiseasyenoughtoverifyterminalassignments<br />
withamultimeter.<br />
Thevoltagefolloweristhesafestandeasiesttransistoramplifiercircuittobuild. Itspurposeistoprovideapproximatelythesamevoltagetoaloadaswhatisinputtotheamplifier,<br />
butatamuchgreatercurrent.Inotherwords,ithasnovoltagegain,butitdoeshavecurrent<br />
gain.<br />
Notethatthenegative(-)sideofthepowersupplyisshownintheschematicdiagramtobe<br />
connectedtoground,asindicatedbythesymbolinthelower-leftcornerofthediagram.This<br />
doesnotnecessarilyrepresentaconnectiontotheactualearth. Whatitmeansisthatthis<br />
pointinthecircuit–andallpointselectricallycommontoit–constitutethedefaultreference<br />
pointforallvoltagemeasurementsinthecircuit. Sincevoltageisbynecessityaquantity<br />
relativebetweentwopoints,a”common”pointofreferencedesignatedinacircuitgivesusthe<br />
abilitytospeakmeaningfullyofvoltageatparticular,singlepointsinthatcircuit.
5.11. VOLTAGEFOLLOWER 243<br />
6 V<br />
R base<br />
6 V<br />
10 kΩ<br />
1 kΩ<br />
R load<br />
Q 1<br />
1 kΩ<br />
These points are all considered "ground"<br />
Forexample,ifIweretospeakofvoltageatthebaseofthetransistor(V B ),Iwouldmean<br />
thevoltagemeasuredbetweenthetransistor’sbaseterminalandthenegativesideofthepower<br />
supply(ground),withtheredprobetouchingthebaseterminalandtheblackprobetouching<br />
ground. Normally,itisnonsensetospeakofvoltageatasinglepoint,buthavinganimplicit<br />
referencepointforvoltagemeasurementsmakessuchstatementsmeaningful:<br />
6 V<br />
R base<br />
6 V<br />
10 kΩ<br />
1 kΩ<br />
R load<br />
Q 1<br />
1 kΩ<br />
Voltmeter measuring<br />
base voltage (V B )<br />
+<br />
V<br />
-<br />
Buildthiscircuit,andmeasureoutputvoltageversusinputvoltageforseveraldifferent<br />
potentiometersettings. Inputvoltageisthevoltageatthepotentiometer’swiper(voltagebetweenthewiperandcircuitground),whileoutputvoltageistheloadresistorvoltage(voltage<br />
acrosstheloadresistor,oremittervoltage:betweenemitterandcircuitground). Youshould<br />
seeaclosecorrelationbetweenthesetwovoltages:oneisjustalittlebitgreaterthantheother<br />
(about0.6voltsorso?),butachangeintheinputvoltagegivesalmostequalchangeinthe<br />
outputvoltage. Becausetherelationshipbetweeninputchangeandoutputchangeisalmost<br />
1:1,wesaythattheACvoltagegainofthisamplifierisnearly1.<br />
Notveryimpressive,isit?Nowmeasurecurrentthroughthebaseofthetransistor(input<br />
current)versuscurrentthroughtheloadresistor(outputcurrent). Beforeyoubreakthecircuitandinsertyourammetertotakethesemeasurements,consideranalternativemethod:<br />
measurevoltageacrossthebaseandloadresistors,whoseresistancevaluesareknown.Using<br />
Ohm’sLaw,currentthrougheachresistormaybeeasilycalculated:dividethemeasuredvolt-
244 CHAPTER5. DISCRETESEMICONDUCTORCIRCUITS<br />
agebytheknownresistance(I=E/R).Thiscalculationisparticularlyeasywithresistorsof1kΩ<br />
value:therewillbe1milliampofcurrentforeveryvoltofdropacrossthem.Forbestprecision,<br />
youmaymeasuretheresistanceofeachresistorratherthanassumeanexactvalueof1kΩ,<br />
butitreallydoesn’tmattermuchforthepurposesofthisexperiment.Whenresistorsareused<br />
totakecurrentmeasurementsby”translating”acurrentintoacorrespondingvoltage,theyare<br />
oftenreferredtoasshuntresistors.<br />
Youshouldexpecttofindhugedifferencesbetweeninputandoutputcurrentsforthisamplifiercircuit.<br />
Infact,itisnotuncommontoexperiencecurrentgainswellinexcessof200<br />
forasmall-signaltransistoroperatingatlowcurrentlevels.Thisistheprimarypurposeofa<br />
voltagefollowercircuit: toboostthecurrentcapacityofa”weak”signalwithoutalteringits<br />
voltage.<br />
Anotherwayofthinkingofthiscircuit’sfunctionisintermsofimpedance.Theinputsideof<br />
thisamplifieracceptsavoltagesignalwithoutdrawingmuchcurrent.Theoutputsideofthis<br />
amplifierdeliversthesamevoltage,butatacurrentlimitedonlybyloadresistanceandthe<br />
current-handlingabilityofthetransistor.Castintermsofimpedance,wecouldsaythatthis<br />
amplifierhasahighinputimpedance(voltagedroppedwithverylittlecurrentdrawn)anda<br />
lowoutputimpedance(voltagedroppedwithalmostunlimitedcurrent-sourcingcapacity).<br />
COMPUTERSIMULATION<br />
SchematicwithSPICEnodenumbers:<br />
1<br />
1 1<br />
R pot1<br />
5 kΩ<br />
V 1<br />
2<br />
R pot2<br />
5 kΩ<br />
R base<br />
1 kΩ<br />
3<br />
R load<br />
Q 1<br />
4<br />
1 kΩ<br />
0<br />
0 0<br />
Netlist(makeatextfilecontainingthefollowingtext,verbatim):<br />
Voltage follower<br />
v1 1 0<br />
rpot1 1 2 5k<br />
rpot2 2 0 5k<br />
rbase 2 3 1k<br />
rload 4 0 1k<br />
q1 1 3 4 mod1<br />
.model mod1 npn bf=200<br />
.dc v1 12 12 1<br />
.print dc v(2,0) v(4,0) v(2,3)<br />
.end
5.11. VOLTAGEFOLLOWER 245<br />
WhenthissimulationisrunthroughtheSPICEprogram,itshowsaninputvoltageof5.937<br />
voltsandanoutputvoltageof5.095volts,withaninputcurrentof25.35 µA(2.535E-02volts<br />
droppedacrossthe1kΩR base resistor).Outputcurrentis,ofcourse,5.095mA,inferredfrom<br />
theoutputvoltageof5.095voltsdroppedacrossaloadresistanceofexactly1kΩ. Youmay<br />
changethe”potentiometer”settinginthiscircuitbyadjustingthevaluesofR pot1 andR pot2 ,<br />
alwayskeepingtheirsumat10kΩ.
246 CHAPTER5. DISCRETESEMICONDUCTORCIRCUITS<br />
5.12 Common-emitteramplifier<br />
PARTSANDMATERIALS<br />
• OneNPNtransistor–model2N2222or2N3403recommended(RadioShackcatalog#<br />
276-1617isapackageoffifteenNPNtransistorsidealforthisandotherexperiments)<br />
• Two6-voltbatteries<br />
• One10kΩpotentiometer,single-turn,lineartaper(RadioShackcatalog#271-1715)<br />
• One1MΩresistor<br />
• One100kΩresistor<br />
• One10kΩresistor<br />
• One1.5kΩresistor<br />
CROSS-REFERENCES<br />
LessonsInElectricCircuits,Volume3,chapter4:”BipolarJunctionTransistors”<br />
LEARNINGOBJECTIVES<br />
• Designofasimplecommon-emitteramplifiercircuit<br />
• Howtomeasureamplifiervoltagegain<br />
• Thedifferencebetweenaninvertingandanoninvertingamplifier<br />
• Waystointroducenegativefeedbackinanamplifiercircuit<br />
SCHEMATICDIAGRAM<br />
6 V<br />
6 V<br />
10 kΩ<br />
V in<br />
100 kΩ<br />
Q 1<br />
10 kΩ<br />
V out<br />
ILLUSTRATION
5.12. COMMON-EMITTERAMPLIFIER 247<br />
CBE<br />
+ - + -<br />
INSTRUCTIONS<br />
Buildthiscircuitandmeasureoutputvoltage(voltagemeasuredbetweenthetransistor’s<br />
collectorterminalandground)andinputvoltage(voltagemeasuredbetweenthepotentiometer’swiperterminalandground)forseveralpositionsettingsofthepotentiometer.<br />
Irecommenddeterminingtheoutputvoltagerangeasthepotentiometerisadjustedthroughitsentire<br />
rangeofmotion,thenchoosingseveralvoltagesspanningthatoutputrangetotakemeasurementsat.Forexample,iffullrotationonthepotentiometerdrivestheamplifiercircuit’soutput<br />
voltagefrom0.1volts(low)to11.7volts(high),chooseseveralvoltagelevelsbetweenthoselimits(1volt,3volts,5volts,7volts,9volts,and11volts).Measuringtheoutputvoltagewitha<br />
meter,adjustthepotentiometertoobtaineachofthesepredeterminedvoltagesattheoutput,<br />
notingtheexactfigureforlaterreference. Then,measuretheexactinputvoltageproducing<br />
thatoutputvoltage,andrecordthatvoltagefigureaswell.<br />
Intheend,youshouldhaveatableofnumbersrepresentingseveraldifferentoutputvoltagesalongwiththeircorrespondinginputvoltages.Takeanytwopairsofvoltagefiguresand<br />
calculatevoltagegainbydividingthedifferenceinoutputvoltagesbythedifferenceininput<br />
voltages. Forexample,ifaninputvoltageof1.5voltsgivesmeanoutputvoltageof7.0volts<br />
andaninputvoltageof1.66voltsgivesmeanoutputvoltageof1.0volt,theamplifier’svoltage<br />
gainis(7.0-1.0)/(1.66-1.5),or6dividedby0.16:againratioof37.50.<br />
Youshouldimmediatelynoticetwocharacteristicswhiletakingthesevoltagemeasurements:first,thattheinput-to-outputeffectis”reversed;”thatis,anincreasinginputvoltage<br />
resultsinadecreasingoutputvoltage.Thiseffectisknownassignalinversion,andthiskind<br />
ofamplifierasaninvertingamplifier. Secondly,thisamplifierexhibitsaverystrongvoltage<br />
gain:asmallchangeininputvoltageresultsinalargechangeinoutputvoltage.Thisshould<br />
standinstarkcontrasttothe”voltagefollower”amplifiercircuitdiscussedearlier,whichhad<br />
avoltagegainofabout1.<br />
Common-emitteramplifiersarewidelyusedduetotheirhighvoltagegain,buttheyare<br />
rarelyusedinascrudeaformasthis.Althoughthisamplifiercircuitworkstodemonstratethe<br />
basicconcept,itisverysusceptibletochangesintemperature.Tryleavingthepotentiometer<br />
inonepositionandheatingthetransistorbygraspingitfirmlywithyourhandorheatingit<br />
withsomeothersourceofheatsuchasanelectrichairdryer(WARNING:becarefulnotto<br />
getitsohotthatyourplasticbreadboardmelts!).Youmayalsoexploretemperatureeffectsby<br />
coolingthetransistor:touchanicecubetoitssurfaceandnotethechangeinoutputvoltage.
248 CHAPTER5. DISCRETESEMICONDUCTORCIRCUITS<br />
Whenthetransistor’stemperaturechanges,itsbase-emitterdiodecharacteristicschange,<br />
resultingindifferentamountsofbasecurrentforthesameinputvoltage. Thisinturnaltersthecontrolledcurrentthroughthecollectorterminal,thusaffectingoutputvoltage.Such<br />
changesmaybeminimizedthroughtheuseofsignalfeedback,wherebyaportionoftheoutput<br />
voltageis”fedback”totheamplifier’sinputsoastohaveanegative,orcanceling,effecton<br />
voltagegain.Stabilityisimprovedattheexpenseofvoltagegain,acompromisesolution,but<br />
practicalnonetheless.<br />
Perhapsthesimplestwaytoaddnegativefeedbacktoacommon-emitteramplifieristoadd<br />
someresistancebetweentheemitterterminalandground,sothattheinputvoltagebecomes<br />
dividedbetweenthebase-emitterPNjunctionandthevoltagedropacrossthenewresistance:<br />
6 V<br />
6 V<br />
10 kΩ<br />
V in<br />
100 kΩ<br />
Q 1<br />
10 kΩ<br />
V out<br />
1.5 kΩ<br />
CBE<br />
+ - + -<br />
Repeatthesamevoltagemeasurementandrecordingexercisewiththe1.5kΩresistorinstalled,calculatingthenew(reduced)voltagegain.Tryalteringthetransistor’stemperature<br />
againandnotingtheoutputvoltageforasteadyinputvoltage. Doesitchangemoreorless<br />
thanwithoutthe1.5kΩresistor?<br />
Anothermethodofintroducingnegativefeedbacktothisamplifiercircuitisto”couple”the<br />
outputtotheinputthroughahigh-valueresistor. Connectinga1MΩresistorbetweenthe<br />
transistor’scollectorandbaseterminalsworkswell:
5.12. COMMON-EMITTERAMPLIFIER 249<br />
6 V<br />
6 V<br />
10 kΩ<br />
V in<br />
100 kΩ<br />
1 MΩ<br />
Q 1<br />
10 kΩ<br />
V out<br />
CBE<br />
+ - + -<br />
Althoughthisdifferentmethodoffeedbackaccomplishesthesamegoalofincreasedstabilitybydiminishinggain,thetwofeedbackcircuitswillnotbehaveidentically.Notetherangeof<br />
possibleoutputvoltageswitheachfeedbackscheme(thelowandhighvoltagevaluesobtained<br />
withafullsweepoftheinputvoltagepotentiometer),andhowthisdiffersbetweenthetwo<br />
circuits.<br />
COMPUTERSIMULATION<br />
SchematicwithSPICEnodenumbers:
250 CHAPTER5. DISCRETESEMICONDUCTORCIRCUITS<br />
V supply<br />
1<br />
3<br />
2<br />
100 kΩ<br />
R b<br />
4<br />
R c<br />
1<br />
Q 1<br />
10 kΩ<br />
V out<br />
V in<br />
0 0 0<br />
Netlist(makeatextfilecontainingthefollowingtext,verbatim):<br />
Common-emitter amplifier<br />
vsupply 1 0 dc 12<br />
vin 3 0<br />
rc 1 2 10k<br />
rb 3 4 100k<br />
q1 2 4 0 mod1<br />
.model mod1 npn bf=200<br />
.dc vin 0 2 0.05<br />
.plot dc v(2,0) v(3,0)<br />
.end<br />
ThisSPICEsimulationsetsupacircuitwithavariableDCvoltagesource(vin)asthe<br />
inputsignal,andmeasuresthecorrespondingoutputvoltagebetweennodes2and0. The<br />
inputvoltageisvaried,or”swept,”from0to2voltsin0.05voltincrements.Resultsareshown<br />
onaplot,withtheinputvoltageappearingasastraightlineandtheoutputvoltageasa”step”<br />
figurewherethevoltagebeginsandendslevel,withasteepchangeinthemiddlewherethe<br />
transistorisinitsactivemodeofoperation.
5.13. MULTI-STAGEAMPLIFIER 251<br />
5.13 Multi-stageamplifier<br />
PARTSANDMATERIALS<br />
• ThreeNPNtransistors–model2N2222or2N3403recommended(RadioShackcatalog#<br />
276-1617isapackageoffifteenNPNtransistorsidealforthisandotherexperiments)<br />
• Two6-voltbatteries<br />
• One10kΩpotentiometer,single-turn,lineartaper(RadioShackcatalog#271-1715)<br />
• One1MΩresistor<br />
• Three100kΩresistors<br />
• Three10kΩresistors<br />
CROSS-REFERENCES<br />
LessonsInElectricCircuits,Volume3,chapter4:”BipolarJunctionTransistors”<br />
LEARNINGOBJECTIVES<br />
• Designofamulti-stage,direct-coupledcommon-emitteramplifiercircuit<br />
• Effectofnegativefeedbackinanamplifiercircuit<br />
SCHEMATICDIAGRAM<br />
1 MΩ<br />
10 kΩ<br />
V in<br />
10 kΩ<br />
10 kΩ<br />
10 kΩ<br />
V out<br />
6 V<br />
100 kΩ<br />
100 kΩ<br />
100 kΩ<br />
6 V<br />
ILLUSTRATION
252 CHAPTER5. DISCRETESEMICONDUCTORCIRCUITS<br />
+ - + - CBE CBE CBE<br />
INSTRUCTIONS<br />
Byconnectingthreecommon-emitteramplifiercircuittogether–thecollectorterminalof<br />
theprevioustransistortothebase(resistor)ofthenexttransistor–thevoltagegainsofeach<br />
stagecompoundtogiveaveryhighoverallvoltagegain. Irecommendbuildingthiscircuit<br />
withoutthe1MΩfeedbackresistortobeginwith,toseeforyourselfjusthowhightheunrestrictedvoltagegainis.<br />
Youmayfinditimpossibletoadjustthepotentiometerforastable<br />
outputvoltage(thatisn’tsaturatedatfullsupplyvoltageorzero),thegainbeingsohigh.<br />
Evenifyoucan’tadjusttheinputvoltagefineenoughtostabilizetheoutputvoltagein<br />
theactiverangeofthelasttransistor,youshouldbeabletotellthattheoutput-to-inputrelationshipisinverting;thatis,theoutputtendstodrivetoahighvoltagewhentheinput<br />
goeslow,andviceversa. Sinceanyoneofthecommon-emitter”stages”isinvertinginitself,<br />
anevennumberofstagedcommon-emitteramplifiersgivesnoninvertingresponse,whilean<br />
oddnumberofstagesgivesinverting. Youmayexperiencetheserelationshipsbymeasuring<br />
thecollector-to-groundvoltageateachtransistorwhileadjustingtheinputvoltagepotentiometer,notingwhetherornottheoutputvoltageincreasesordecreaseswithanincreaseininput<br />
voltage.<br />
Connectthe1MΩfeedbackresistorintothecircuit,couplingthecollectorofthelasttransistortothebaseofthefirst.Sincetheoverallresponseofthisthree-stageamplifierisinverting,<br />
thefeedbacksignalprovidedthroughthe1MΩresistorfromtheoutputofthelasttransistortotheinputofthefirstshouldbenegativeinnature.<br />
Assuch,itwillacttostabilizethe<br />
amplifier’sresponseandminimizethevoltagegain. Youshouldnoticethereductioningain<br />
immediatelybythedecreasedsensitivityoftheoutputsignaloninputsignalchanges(changes<br />
inpotentiometerposition).Simplyput,theamplifierisn’tnearlyas”touchy”asitwaswithout<br />
thefeedbackresistorinplace.<br />
Aswiththesimplecommon-emitteramplifierdiscussedinanearlierexperiment,itisa<br />
goodideaheretomakeatableofinputversusoutputvoltagefigureswithwhichyoumay<br />
calculatevoltagegain.<br />
Experimentwithdifferentvaluesoffeedbackresistance. Whateffectdoyouthinkadecreaseinfeedbackresistancehaveonvoltagegain?Whataboutanincreaseinfeedbackresistance?Tryitandfindout!
5.13. MULTI-STAGEAMPLIFIER 253<br />
Anadvantageofusingnegativefeedbackto”tame”ahigh-gainamplifiercircuitisthatthe<br />
resultingvoltagegainbecomesmoredependentupontheresistorvaluesandlessdependent<br />
uponthecharacteristicsoftheconstituenttransistors.Thisisgood,becauseitisfareasierto<br />
manufactureconsistentresistorsthanconsistenttransistors. Thus,itiseasiertodesignan<br />
amplifierwithpredictablegainbybuildingastagednetworkoftransistorswithanarbitrarily<br />
highvoltagegain,thenmitigatethatgainpreciselythroughnegativefeedback.Itisthissame<br />
principlethatisusedtomakeoperationalamplifiercircuitsbehavesopredictably.<br />
Thisamplifiercircuitisabitsimplifiedfromwhatyouwillnormallyencounterinpractical<br />
multi-stagecircuits. Rarelyisapurecommon-emitterconfiguration(i.e. withnoemitter-togroundresistor)used,andiftheamplifier’sserviceisforACsignals,theinter-stagecoupling<br />
isoftencapacitivewithvoltagedividernetworksconnectedtoeachtransistorbaseforproper<br />
biasingofeachstage. Radio-frequencyamplifiercircuitsareoftentransformer-coupled,with<br />
capacitorsconnectedinparallelwiththetransformerwindingsforresonanttuning.<br />
COMPUTERSIMULATION<br />
SchematicwithSPICEnodenumbers:<br />
3<br />
1 MΩ<br />
6<br />
1<br />
1<br />
1<br />
V in<br />
2<br />
10 kΩ<br />
R 2 R<br />
R 6<br />
10 kΩ 4<br />
10 kΩ<br />
4 5 6<br />
R 1 3<br />
R 3 7<br />
R 5 8<br />
Q 1 Q 2 Q 3<br />
100 kΩ 100 kΩ 100 kΩ<br />
V out<br />
V supply<br />
0<br />
0<br />
R f 1<br />
0<br />
0<br />
0<br />
Netlist(makeatextfilecontainingthefollowingtext,verbatim):<br />
Multi-stage amplifier<br />
vsupply 1 0 dc 12<br />
vin 2 0<br />
r1 2 3 100k<br />
r2 1 4 10k<br />
q1 4 3 0 mod1<br />
r3 4 7 100k<br />
r4 1 5 10k<br />
q2 5 7 0 mod1<br />
r5 5 8 100k<br />
r6 1 6 10k<br />
q3 6 8 0 mod1<br />
rf 3 6 1meg<br />
.model mod1 npn bf=200<br />
.dc vin 0 2.5 0.1
254 CHAPTER5. DISCRETESEMICONDUCTORCIRCUITS<br />
.plot dc v(6,0) v(2,0)<br />
.end<br />
Thissimulationplotsoutputvoltageagainstinputvoltage,andallowscomparisonbetween<br />
thosevariablesinnumericalform:alistofvoltagefiguresprintedtotheleftoftheplot.You<br />
maycalculatevoltagegainbytakinganytwoanalysispointsanddividingthedifferencein<br />
outputvoltagesbythedifferenceininputvoltages,justlikeyoudofortherealcircuit.<br />
Experimentwithdifferentfeedbackresistancevalues(rf)andseetheimpactonoverall<br />
voltagegain. Doyounoticeapattern? Here’sahint:theoverallvoltagegainmaybeclosely<br />
approximatedbyusingtheresistancefiguresof r1and rf,withoutreferencetoanyother<br />
circuitcomponent!
5.14. CURRENTMIRROR 255<br />
5.14 Currentmirror<br />
PARTSANDMATERIALS<br />
• TwoNPNtransistors–models2N2222or2N3403recommended(RadioShackcatalog#<br />
276-1617isapackageoffifteenNPNtransistorsidealforthisandotherexperiments)<br />
• Two6-voltbatteries<br />
• One10kΩpotentiometer,single-turn,lineartaper(RadioShackcatalog#271-1715)<br />
• Two10kΩresistors<br />
• Four1.5kΩresistors<br />
Smallsignaltransistorsarerecommendedsoastobeabletoexperience”thermalrunaway”<br />
inthelatterportionoftheexperiment.Larger”power”transistorsmaynotexhibitthesame<br />
behaviorattheselowcurrentlevels. However,anypairofidenticalNPNtransistorsmaybe<br />
usedtobuildacurrentmirror.<br />
Bewarethatnotalltransistorssharethesameterminaldesignations,orpinouts,evenif<br />
theysharethesamephysicalappearance. Thiswilldictatehowyouconnectthetransistors<br />
togetherandtoothercomponents,sobesuretocheckthemanufacturer’sspecifications(componentdatasheet),easilyobtainedfromthemanufacturer’swebsite.Bewarethatitispossible<br />
forthetransistor’spackageandeventhemanufacturer’sdatasheettoshowincorrectterminal<br />
identificationdiagrams! Double-checkingpinidentitieswithyourmultimeter’s”diodecheck”<br />
functionishighlyrecommended. Fordetailsonhowtoidentifybipolartransistorterminals<br />
usingamultimeter,consultchapter4oftheSemiconductorvolume(volumeIII)ofthisbook<br />
series.<br />
CROSS-REFERENCES<br />
LessonsInElectricCircuits,Volume3,chapter4:”BipolarJunctionTransistors”<br />
LEARNINGOBJECTIVES<br />
• Howtobuildacurrentmirrorcircuit<br />
• Currentlimitationsofacurrentmirrorcircuit<br />
• TemperaturedependenceofBJTs<br />
• Experienceacontrolled”thermalrunaway”situation<br />
SCHEMATICDIAGRAM
256 CHAPTER5. DISCRETESEMICONDUCTORCIRCUITS<br />
+ -<br />
A<br />
TP5<br />
R load4<br />
TP4<br />
6 V<br />
R load3<br />
R adjust<br />
TP3<br />
R load2<br />
6 V<br />
TP2<br />
R limit<br />
R load1<br />
Q 1 Q 2<br />
TP1<br />
R load1 through R load3<br />
are 1.5 kΩ each<br />
R load4 , R limit , and R adjust<br />
are 10 kΩ each<br />
ILLUSTRATION<br />
V<br />
A<br />
V<br />
OFF<br />
A<br />
+ - + - COM<br />
A<br />
TP5 TP4 TP3 TP2 TP1<br />
CBE<br />
CBE
5.14. CURRENTMIRROR 257<br />
INSTRUCTIONS<br />
Acurrentmirrormaybethoughtofasanadjustablecurrentregulator,thecurrentlimit<br />
beingeasilysetbyasingleresistance. Itisarathercrudecurrentregulatorcircuit,butone<br />
thatfindswideuseduetoitssimplicity. Inthisexperiment,youwillgettheopportunityto<br />
buildoneofthesecircuits,exploreitscurrent-regulatingproperties,andalsoexperiencesome<br />
ofitspracticallimitationsfirsthand.<br />
Buildthecircuitasshownintheschematicandillustration. Youwillhaveoneextra1.5<br />
kΩfixed-valueresistorfromthepartsspecifiedinthepartslist.Youwillbeusingitinthelast<br />
partofthisexperiment.<br />
ThepotentiometersetstheamountofcurrentthroughtransistorQ 1 . Thistransistoris<br />
connectedtoactasasimplediode:justaPNjunction.Whyuseatransistorinsteadofaregular<br />
diode? Becauseitisimportanttomatchthejunctioncharacteristicsofthesetwotransistors<br />
whenusingtheminacurrentmirrorcircuit.Voltagedroppedacrossthebase-emitterjunction<br />
ofQ 1 isimpressedacrossthebase-emitterjunctionoftheothertransistor,Q 2 ,causingitto<br />
turn”on”andlikewiseconductcurrent.<br />
Sincevoltageacrossthetwotransistors’base-emitterjunctionsisthesame–thetwojunctionpairsbeingconnectedinparallelwitheachother–soshouldthecurrentbethroughtheir<br />
baseterminals,assumingidenticaljunctioncharacteristicsandidenticaljunctiontemperatures.<br />
Matchedtransistorsshouldhavethesame βratios,aswell,soequalbasecurrents<br />
meansequalcollectorcurrents. ThepracticalresultofallthisisQ 2 ’scollectorcurrentmimickingwhatevercurrentmagnitudehasbeenestablishedthroughthecollectorofQ<br />
1 bythe<br />
potentiometer.Inotherwords,currentthroughQ 2 mirrorsthecurrentthroughQ 1 .<br />
Changesinloadresistance(resistanceconnectingthecollectorofQ 2 tothepositivesideof<br />
thebattery)havenoeffectonQ 1 ’scurrent,andconsequentlyhavenoeffectuponthebaseemittervoltageorbasecurrentofQ<br />
2 . Withaconstantbasecurrentandanearlyconstant β<br />
ratio,Q 2 willdropasmuchoraslittlecollector-emittervoltageasnecessarytoholditscollector<br />
(load)currentconstant.Thus,thecurrentmirrorcircuitactstoregulatecurrentatavalueset<br />
bythepotentiometer,withoutregardtoloadresistance.<br />
Well,thatishowitissupposedtowork,anyway. Realityisn’tquitesosimple,asyouare<br />
abouttosee.Inthecircuitdiagramshown,theloadcircuitofQ 2 iscompletedtothepositive<br />
sideofthebatterythroughanammeter,foreasycurrentmeasurement. Ratherthansolidly<br />
connecttheammeter’sblackprobetoadefinitepointinthecircuit,I’vemarkedfivetestpoints,<br />
TP1throughTP5,foryoutotouchtheblacktestprobetowhilemeasuringcurrent.Thisallows<br />
youtoquicklyandeffortlesslychangeloadresistance: touchingtheprobetoTP1resultsin<br />
practicallynoloadresistance,whiletouchingittoTP5resultsinapproximately14.5kΩof<br />
loadresistance.<br />
Tobegintheexperiment,touchthetestprobetoTP4andadjustthepotentiometerthrough<br />
itsrangeoftravel.Youshouldseeasmall,changingcurrentindicatedbyyourammeterasyou<br />
movethepotentiometermechanism:nomorethanafewmilliamps.Leavethepotentiometer<br />
settoapositiongivingaroundnumberofmilliampsandmovethemeter’sblacktestprobeto<br />
TP3.Thecurrentindicationshouldbeverynearlythesameasbefore.MovetheprobetoTP2,<br />
thenTP1. Again,youshouldseeanearlyunchangedamountofcurrent. Tryadjustingthe<br />
potentiometertoanotherposition,givingadifferentcurrentindication,andtouchthemeter’s<br />
blackprobetotestpointsTP1throughTP4,notingthestabilityofthecurrentindicationsas<br />
youchangeloadresistance.Thisdemonstratesthecurrentregulatingbehaviorofthiscircuit.
258 CHAPTER5. DISCRETESEMICONDUCTORCIRCUITS<br />
Youshouldnotethatthecurrentregulationisn’tperfect. Despiteregulatingthecurrent<br />
atnearlythevalueforloadresistancesbetween0and4.5kΩ,thereissomevariationover<br />
thisrange. Theregulationmaybemuchworseifloadresistanceisallowedtorisetoohigh.<br />
Tryadjustingthepotentiometersothatmaximumcurrentisobtained,asindicatedwiththe<br />
ammetertestprobeconnectedtoTP1. Leavingthepotentiometeratthatposition,movethe<br />
meterprobetoTP2,thenTP3,thenTP4,andfinallyTP5,notingthemeter’sindicationateach<br />
connectionpoint.Thecurrentshouldberegulatedatanearlyconstantvalueuntilthemeter<br />
probeismovedtothelasttestpoint,TP5.There,thecurrentindicationwillbesubstantially<br />
lowerthanattheothertestpoints. Whyisthis? Becausetoomuchloadresistancehasbeen<br />
insertedintoQ 2 ’scircuit. Simplyput,Q 2 cannot”turnon”anymorethanitalreadyhas,to<br />
maintainthesameamountofcurrentwiththisgreataloadresistanceaswithlesserload<br />
resistances.<br />
Thisphenomenoniscommontoallcurrent-regulatorcircuits: thereisalimitedamount<br />
ofresistanceacurrentregulatorcanhandlebeforeitsaturates. Thisstandstoreason,as<br />
anycurrentregulatorcircuitcapableofsupplyingaconstantamountofcurrentthroughany<br />
loadresistanceimaginablewouldrequireanunlimitedsourceofvoltagetodoit!Ohm’sLaw<br />
(E=IR)dictatestheamountofvoltageneededtopushagivenamountofcurrentthrougha<br />
givenamountofresistance,andwithonly12voltsofpowersupplyvoltageatourdisposal,a<br />
finitelimitofloadcurrentandloadresistancedefinitelyexistsforthiscircuit.Forthisreason,<br />
itmaybehelpfultothinkofcurrentregulatorcircuitsasbeingcurrentlimitercircuits,forall<br />
theycanreallydoislimitcurrenttosomemaximumvalue.<br />
Animportantcaveatforcurrentmirrorcircuitsingeneralisthatofequaltemperature<br />
betweenthetwotransistors.Thecurrent”mirroring”takingplacebetweenthetwotransistors’<br />
collectorcircuitsdependsonthebase-emitterjunctionsofthosetwotransistorshavingthe<br />
exactsameproperties.Asthe”diodeequation”describes,thevoltage/currentrelationshipfor<br />
aPNjunctionstronglydependsonjunctiontemperature. ThehotteraPNjunctionis,the<br />
morecurrentitwillpassforagivenamountofvoltagedrop.Ifonetransistorshouldbecome<br />
hotterthantheother,itwillpassmorecollectorcurrentthantheother,andthecircuitwill<br />
nolonger”mirror”currentasexpected. Whenbuildingarealcurrentmirrorcircuitusing<br />
discretetransistors,thetwotransistorsshouldbeepoxy-gluedtogether(back-to-back)sothat<br />
theyremainatapproximatelythesametemperature.<br />
Toillustratethisdependenceonequaltemperature,trygraspingonetransistorbetween<br />
yourfingerstoheatitup. Whathappenstothecurrentthroughtheloadresistorsasthe<br />
transistor’stemperatureincreases?Now,letgoofthetransistorandblowonittocoolitdown<br />
toambienttemperature.Grasptheothertransistorbetweenyourfingerstoheatitup.What<br />
doestheloadcurrentdonow?<br />
Inthisnextphaseoftheexperiment,wewillintentionallyallowoneofthetransistors<br />
tooverheatandnotetheeffects. Toavoiddamagingatransistor,thisprocedureshouldbe<br />
conductednolongerthanisnecessarytoobserveloadcurrentbeginto”runaway.”Tobegin,<br />
adjustthepotentiometerforminimumcurrent.Next,replacethe10kΩR limit resistorwitha<br />
1.5kΩresistor.ThiswillallowahighercurrenttopassthroughQ 1 ,andconsequentlythrough<br />
Q 2 aswell.<br />
Placetheammeter’sblackprobeonTP1andobservethecurrentindication. Movethe<br />
potentiometerinthedirectionofincreasingcurrentuntilyoureadabout10mAthroughthe<br />
ammeter.Atthatpoint,stopmovingthepotentiometerandjustobservethecurrent.Youwill<br />
noticecurrentbegintoincreaseallonitsown,withoutfurtherpotentiometermotion! Break
5.14. CURRENTMIRROR 259<br />
thecircuitbyremovingthemeterprobefromTP1whenthecurrentexceeds30mA,toavoid<br />
damagingtransistorQ 2 .<br />
Ifyoucarefullytouchbothtransistorswithafinger,youshouldnoticeQ 2 iswarm,while<br />
Q 1 iscool. Warning:ifQ 2 ’scurrenthasbeenallowedto”runaway”toofarorfortoolonga<br />
time,itmaybecomeveryhot! Youcanreceiveabadburnonyourfingertipbytouchingan<br />
overheatedsemiconductorcomponent,sobecarefulhere!<br />
WhatjusthappenedtomakeQ 2 overheatandlosecurrentcontrol?ByconnectingtheammetertoTP1,allloadresistancewasremoved,soQ<br />
2 hadtodropfullbatteryvoltagebetween<br />
collectorandemitterasitregulatedcurrent.TransistorQ 1 atleasthadthe1.5kΩresistance<br />
ofR limit inplacetodropmostofthebatteryvoltage,soitspowerdissipationwasfarlessthan<br />
thatofQ 2 .ThisgrossimbalanceofpowerdissipationcausedQ 2 toheatmorethanQ 1 .Asthe<br />
temperatureincreased,Q 2 begantopassmorecurrentforthesameamountofbase-emitter<br />
voltagedrop. Thiscausedittoheatupevenfaster,asitwaspassingmorecollectorcurrent<br />
whilestilldroppingthefull12voltsbetweencollectorandemitter.Theeffectisknownasthermalrunaway,anditispossibleinmanybipolarjunctiontransistorcircuits,notjustcurrent<br />
mirrors.<br />
COMPUTERSIMULATION<br />
SchematicwithSPICEnodenumbers:<br />
1<br />
1<br />
V ammeter<br />
3<br />
0 V<br />
V 1<br />
12 V<br />
R limit<br />
Q 1 Q 2<br />
R load<br />
2<br />
4<br />
2<br />
0 0 0<br />
Netlist(makeatextfilecontainingthefollowingtext,verbatim):<br />
Current mirror<br />
v1 1 0<br />
vammeter 1 3 dc 0<br />
rlimit 1 2 10k<br />
rload 3 4 3k<br />
q1 2 2 0 mod1<br />
q2 4 2 0 mod1<br />
.model mod1 npn bf=100<br />
.dc v1 12 12 1
260 CHAPTER5. DISCRETESEMICONDUCTORCIRCUITS<br />
.print dc i(vammeter)<br />
.end<br />
V ammeter isnothingmorethanazero-voltDCbatterystrategicallyplacedtointerceptload<br />
current. ThisisnothingmorethanatricktomeasurecurrentinaSPICEsimulation,asno<br />
dedicated”ammeter”componentexistsintheSPICElanguage.<br />
ItisimportanttorememberthatSPICEonlyrecognizesthefirsteightcharactersofa<br />
component’sname. Thename”vammeter”isokay,butifweweretoincorporatemorethan<br />
onecurrent-measuringvoltagesourceinthecircuitandnamethem”vammeter1”and”vammeter2”,respectively,SPICEwouldseethemasbeingtwoinstancesofthesamecomponent<br />
”vammeter”(seeingonlythefirsteightcharacters)andhaltwithanerror.Somethingtobear<br />
inmindwhenalteringthenetlistorprogrammingyourownSPICEsimulation!<br />
YouwillhavetoexperimentwithdifferentresistancevaluesofR load inthissimulation<br />
toappreciatethecurrent-regulatingnatureofthecircuit. WithR limit setto10kΩanda<br />
powersupplyvoltageof12volts,theregulatedcurrentthroughR load willbe1.1mA.SPICE<br />
showstheregulationtobeperfect(isn’tthevirtualworldofcomputersimulationsonice?),the<br />
loadcurrentremainingat1.1mAforawiderangeofloadresistances. However,iftheload<br />
resistanceisincreasedbeyond10kΩ,eventhissimulationshowstheloadcurrentsufferinga<br />
decreaseasinreallife.
5.15. JFETCURRENTREGULATOR 261<br />
5.15 JFETcurrentregulator<br />
PARTSANDMATERIALS<br />
• OneN-channeljunctionfield-effecttransistor,models2N3819orJ309recommended(RadioShackcatalog#276-2035isthemodel2N3819)<br />
• Two6-voltbatteries<br />
• One10kΩpotentiometer,single-turn,lineartaper(RadioShackcatalog#271-1715)<br />
• One1kΩresistor<br />
• One10kΩresistor<br />
• Three1.5kΩresistors<br />
ForthisexperimentyouwillneedanN-channelJFET,notaP-channel!<br />
Bewarethatnotalltransistorssharethesameterminaldesignations,orpinouts,evenif<br />
theysharethesamephysicalappearance. Thiswilldictatehowyouconnectthetransistors<br />
togetherandtoothercomponents,sobesuretocheckthemanufacturer’sspecifications(componentdatasheet),easilyobtainedfromthemanufacturer’swebsite.Bewarethatitispossible<br />
forthetransistor’spackageandeventhemanufacturer’sdatasheettoshowincorrectterminal<br />
identificationdiagrams! Double-checkingpinidentitieswithyourmultimeter’s”diodecheck”<br />
functionishighlyrecommended.Fordetailsonhowtoidentifyjunctionfield-effecttransistor<br />
terminalsusingamultimeter,consultchapter5oftheSemiconductorvolume(volumeIII)of<br />
thisbookseries.<br />
CROSS-REFERENCES<br />
LessonsInElectricCircuits,Volume3,chapter5:”JunctionField-EffectTransistors”<br />
LessonsInElectricCircuits,Volume3,chapter3:”DiodesandRectifiers”<br />
LEARNINGOBJECTIVES<br />
• HowtouseaJFETasacurrentregulator<br />
• HowtheJFETisrelativelyimmunetochangesintemperature<br />
SCHEMATICDIAGRAM
262 CHAPTER5. DISCRETESEMICONDUCTORCIRCUITS<br />
-<br />
A<br />
+<br />
R load4 R load3<br />
TP5 TP4<br />
TP3<br />
R load2<br />
6 V<br />
6 V<br />
R adjust<br />
TP2<br />
R load1<br />
TP1<br />
Q 1<br />
R load1 through R load3<br />
are 1.5 kΩ each<br />
R load4 and R adjust<br />
are 10 kΩ each<br />
R limit is 1 kΩ<br />
R limit<br />
ILLUSTRATION<br />
V<br />
A<br />
V<br />
OFF<br />
A<br />
+ - + - COM<br />
A<br />
TP5 TP4 TP3 TP2<br />
SGD<br />
TP1
5.15. JFETCURRENTREGULATOR 263<br />
INSTRUCTIONS<br />
Previouslyinthischapter,yousawhowapairofbipolarjunctiontransistors(BJTs)could<br />
beusedtoformacurrentmirror,wherebyonetransistorwouldtrytomaintainthesame<br />
currentthroughitasthroughtheother,theother’scurrentlevelbeingestablishedbyavariable<br />
resistance.Thiscircuitperformsthesametaskofregulatingcurrent,butusesasinglejunction<br />
field-effecttransistor(JFET)insteadoftwoBJTs.<br />
ThetwoseriesresistorsR adjust andR limit setthecurrentregulationpoint,whiletheload<br />
resistorsandthetestpointsbetweenthemserveonlytodemonstrateconstantcurrentdespite<br />
changesinloadresistance.<br />
Tobegintheexperiment,touchthetestprobetoTP4andadjustthepotentiometerthrough<br />
itsrangeoftravel.Youshouldseeasmall,changingcurrentindicatedbyyourammeterasyou<br />
movethepotentiometermechanism:nomorethanafewmilliamps.Leavethepotentiometer<br />
settoapositiongivingaroundnumberofmilliampsandmovethemeter’sblacktestprobeto<br />
TP3.Thecurrentindicationshouldbeverynearlythesameasbefore.MovetheprobetoTP2,<br />
thenTP1. Again,youshouldseeanearlyunchangedamountofcurrent. Tryadjustingthe<br />
potentiometertoanotherposition,givingadifferentcurrentindication,andtouchthemeter’s<br />
blackprobetotestpointsTP1throughTP4,notingthestabilityofthecurrentindicationsas<br />
youchangeloadresistance.Thisdemonstratesthecurrentregulatingbehaviorofthiscircuit.<br />
TP5,attheendofa10kΩresistor,isprovidedforintroducingalargechangeinload<br />
resistance.Connectingtheblacktestprobeofyourammetertothattestpointgivesacombined<br />
loadresistanceof14.5kΩ,whichwillbetoomuchresistanceforthetransistortomaintain<br />
maximumregulatedcurrentthrough.ToexperiencewhatI’mdescribinghere,touchtheblack<br />
testprobetoTP1andadjustthepotentiometerformaximumcurrent.Now,movetheblacktest<br />
probetoTP2,thenTP3,thenTP4.Forallthesetestpointpositions,thecurrentwillremain<br />
approximatelyconstant.However,whenyoutouchtheblackprobetoTP5,thecurrentwillfall<br />
dramatically.Why?Becauseatthislevelofloadresistance,thereisinsufficientvoltagedrop<br />
acrossthetransistortomaintainregulation.Inotherwords,thetransistorwillbesaturated<br />
asitattemptstoprovidemorecurrentthanthecircuitresistancewillallow.<br />
MovetheblacktestprobebacktoTP1andadjustthepotentiometerforminimumcurrent.<br />
Now,touchtheblacktestprobetoTP2,thenTP3,thenTP4,andfinallyTP5. Whatdoyou<br />
noticeaboutthecurrentindicationatallthesepoints? Whenthecurrentregulationpointis<br />
adjustedtoalesservalue,thetransistorisabletomaintainregulationoveramuchlarger<br />
rangeofloadresistance.<br />
AnimportantcaveatwiththeBJTcurrentmirrorcircuitisthatbothtransistorsmustbe<br />
atequaltemperatureforthetwocurrentstobeequal. Withthiscircuit,however,transistor<br />
temperatureisalmostirrelevant. Trygraspingthetransistorbetweenyourfingerstoheat<br />
itup,notingtheloadcurrentwithyourammeter. Trycoolingitdownafterwardbyblowing<br />
onit. Notonlyistherequirementoftransistormatchingeliminated(duetotheuseofjust<br />
onetransistor),butthethermaleffectsareallbuteliminatedaswellduetotherelativethermalimmunityofthefield-effecttransistor.<br />
Thisbehavioralsomakesfield-effecttransistors<br />
immunetothermalrunaway;adecidedadvantageoverbipolarjunctiontransistors.<br />
Aninterestingapplicationofthiscurrent-regulatorcircuitistheso-calledconstant-current<br />
diode.Describedinthe”DiodesandRectifiers”chapterofvolumeIII,thisdiodeisn’treallya<br />
PNjunctiondeviceatall.Instead,itisaJFETwithafixedresistanceconnectedbetweenthe<br />
gateandsourceterminals:
264 CHAPTER5. DISCRETESEMICONDUCTORCIRCUITS<br />
Constant-current diode<br />
Anode<br />
Symbol<br />
Anode<br />
Actual<br />
device<br />
Cathode<br />
AnormalPN-junctiondiodeisincludedinserieswiththeJFETtoprotectthetransistor<br />
againstdamagefromreverse-biasvoltage,butotherwisethecurrent-regulatingfacilityofthis<br />
deviceisentirelyprovidedbythefield-effecttransistor.<br />
COMPUTERSIMULATION<br />
SchematicwithSPICEnodenumbers:<br />
1 1<br />
Cathode<br />
R load<br />
4.5 kΩ<br />
2<br />
V source 0 J 1<br />
3<br />
R limit 1 kΩ<br />
0 0 0<br />
Netlist(makeatextfilecontainingthefollowingtext,verbatim):<br />
JFET current regulator<br />
vsource 1 0<br />
rload 1 2 4.5k<br />
j1 2 0 3 mod1<br />
rlimit 3 0 1k<br />
.model mod1 njf<br />
.dc vsource 6 12 0.1<br />
.plot dc i(vsource)
5.15. JFETCURRENTREGULATOR 265<br />
.end<br />
SPICEdoesnotallowfor”sweeping”resistancevalues,sotodemonstratethecurrentregulationofthiscircuitoverawiderangeofconditions,I’veelectedtosweepthesourcevoltage<br />
from6to12voltsin0.1voltsteps.Ifyouwish,youcanset rloadtodifferentresistancevaluesandverifythatthecircuitcurrentremainsconstant.<br />
Withan rlimitvalueof1kΩ,the<br />
regulatedcurrentwillbe291.8 µA.Thiscurrentfigurewillmostlikelynotbethesameasyour<br />
actualcircuitcurrent,duetodifferencesinJFETparameters.<br />
ManymanufacturersgiveSPICEmodelparametersfortheirtransistors,whichmaybe<br />
typedinthe.modellineofthenetlistforamoreaccuratecircuitsimulation.
266 CHAPTER5. DISCRETESEMICONDUCTORCIRCUITS<br />
5.16 Differentialamplifier<br />
PARTSANDMATERIALS<br />
• Two6-voltbatteries<br />
• TwoNPNtransistors–models2N2222or2N3403recommended(RadioShackcatalog#<br />
276-1617isapackageoffifteenNPNtransistorsidealforthisandotherexperiments)<br />
• Two10kΩpotentiometers,single-turn,lineartaper(RadioShackcatalog#271-1715)<br />
• Two22kΩresistors<br />
• Two10kΩresistors<br />
• One100kΩresistor<br />
• One1.5kΩresistor<br />
Resistorvaluesarenotespeciallycriticalinthisexperiment,buthavebeenchosentoprovidehighvoltagegainfora”comparator-like”differentialamplifierbehavior.<br />
CROSS-REFERENCES<br />
LessonsInElectricCircuits,Volume3,chapter4:”BipolarJunctionTransistors”<br />
LessonsInElectricCircuits,Volume3,chapter8:”OperationalAmplifiers”<br />
LEARNINGOBJECTIVES<br />
• Basicdesignofadifferentialamplifiercircuit.<br />
• Workingdefinitionsofdifferentialandcommon-modevoltages<br />
SCHEMATICDIAGRAM<br />
6 V<br />
6 V<br />
22 kΩ 100 22 kΩ<br />
kΩ<br />
V out<br />
10 kΩ 10 kΩ<br />
Q<br />
10 kΩ 1 Q 2<br />
10 kΩ<br />
(noninv)<br />
(inv)<br />
1.5 kΩ
5.16. DIFFERENTIALAMPLIFIER 267<br />
ILLUSTRATION<br />
+ - CBE CBE<br />
Noninverting<br />
+ -<br />
Inverting<br />
INSTRUCTIONS<br />
Thiscircuitformstheheartofmostoperationalamplifiercircuits:thedifferentialpair.In<br />
theformshownhere,itisarathercrudedifferentialamplifier,quitenonlinearandunsymmetricalwithregardtooutputvoltageversusinputvoltage(s).<br />
Withahighvoltagegaincreated<br />
byalargecollector/emitterresistorratio(100kΩ/1.5kΩ),though,itactsprimarilyasacomparator:theoutputvoltagerapidlychangingvalueasthetwoinputvoltagesignalsapproach<br />
equality.<br />
Measuretheoutputvoltage(voltageatthecollectorofQ 2 withrespecttoground)asthe<br />
inputvoltagesarevaried.Notehowthetwopotentiometershavedifferenteffectsontheoutput<br />
voltage:oneinputtendstodrivetheoutputvoltageinthesamedirection(noninverting),while<br />
theothertendstodrivetheoutputvoltageintheoppositedirection(inverting). Thisisthe<br />
essentialnatureofadifferentialamplifier: twocomplementaryinputs,withcontraryeffects<br />
ontheoutputsignal. Ideally,theoutputvoltageofsuchanamplifierisstrictlyafunctionof<br />
thedifferencebetweenthetwoinputsignals.Thiscircuitfallsconsiderablyshortoftheideal,<br />
asevenacursorytestwillreveal.<br />
Anidealdifferentialamplifierignoresallcommon-modevoltage,whichiswhateverlevelof<br />
voltagecommontobothinputs.Forexample,iftheinvertinginputisat3voltsandthenoninvertinginputat2.5volts,thedifferentialvoltagewillbe0.5volts(3-2.5)butthecommon-mode<br />
voltagewillbe2.5volts,sincethatisthelowestinputsignallevel.Ideally,thisconditionshould<br />
producethesameoutputsignalvoltageasiftheinputsweresetat3.5and3volts,respectively<br />
(0.5voltsdifferential,witha3voltcommon-modevoltage).However,thiscircuitdoesnotgive<br />
thesameresultforthetwodifferentinputsignalscenarios.Inotherwords,itsoutputvoltage<br />
dependsonboththedifferentialvoltageandthecommon-modevoltage.<br />
Asimperfectasthisdifferentialamplifieris,itsbehaviorcouldbeworse. Notehowthe<br />
inputsignalpotentiometershavebeenlimitedby22kΩresistorstoanadjustablerangeof<br />
approximately0to4volts,givenapowersupplyvoltageof12volts. Ifyou’dliketoseehow<br />
thiscircuitbehaveswithoutanyinputsignallimiting,justbypassthe22kΩresistorswith<br />
jumperwires,allowingfull0to12voltadjustmentrangefromeachpotentiometer.<br />
Donotworryaboutbuildingupexcessiveheatwhileadjustingpotentiometersinthiscircuit!Unlikethecurrentmirrorcircuit,thiscircuitisprotectedfromthermalrunawaybythe
268 CHAPTER5. DISCRETESEMICONDUCTORCIRCUITS<br />
emitterresistor(1.5kΩ),whichdoesn’tallowenoughtransistorcurrenttocauseanyproblem.
5.17. SIMPLEOP-AMP 269<br />
5.17 Simpleop-amp<br />
PARTSANDMATERIALS<br />
• Two6-voltbatteries<br />
• FourNPNtransistors–models2N2222or2N3403recommended(RadioShackcatalog#<br />
276-1617isapackageoffifteenNPNtransistorsidealforthisandotherexperiments)<br />
• TwoPNPtransistors–models2N2907or2N3906recommended(RadioShackcatalog#<br />
276-1604isapackageoffifteenPNPtransistorsidealforthisandotherexperiments)<br />
• Two10kΩpotentiometers,single-turn,lineartaper(RadioShackcatalog#271-1715)<br />
• One270kΩresistor<br />
• Three100kΩresistors<br />
• One10kΩresistor<br />
CROSS-REFERENCES<br />
LessonsInElectricCircuits,Volume3,chapter4:”BipolarJunctionTransistors”<br />
LessonsInElectricCircuits,Volume3,chapter8:”OperationalAmplifiers”<br />
LEARNINGOBJECTIVES<br />
• Designofadifferentialamplifiercircuitusingcurrentmirrors.<br />
• Effectsofnegativefeedbackonahigh-gaindifferentialamplifier.<br />
SCHEMATICDIAGRAM<br />
100<br />
kΩ<br />
Q 1 Q 2<br />
R prg<br />
Q 3 Q 4<br />
6 V<br />
6 V<br />
10 kΩ<br />
(noninv)<br />
V out<br />
10 kΩ<br />
(inv)<br />
Q 5 Q 6
270 CHAPTER5. DISCRETESEMICONDUCTORCIRCUITS<br />
ILLUSTRATION<br />
CBE<br />
CBE CBE CBE<br />
+ - Noninverting<br />
CBE<br />
CBE<br />
+ -<br />
Inverting<br />
INSTRUCTIONS<br />
Thiscircuitdesignimprovesonthedifferentialamplifiershownpreviously. Ratherthan<br />
useresistorstodropvoltageinthedifferentialpaircircuit,asetofcurrentmirrorsisused<br />
instead,theresultbeinghighervoltagegainandmorepredictableperformance.Withahigher<br />
voltagegain,thiscircuitisabletofunctionasaworkingoperationalamplifier,orop-amp.Opampsformthebasisofagreatmanymodernanalogsemiconductorcircuits,sounderstanding<br />
theinternalworkingsofanoperationalamplifierisimportant.<br />
PNPtransistorsQ 1 andQ 2 formacurrentmirrorwhichtriestokeepcurrentsplitequally<br />
throughthetwodifferentialpairtransistorsQ 3 andQ 4 . NPNtransistorsQ 5 andQ 6 form<br />
anothercurrentmirror,settingthetotaldifferentialpaircurrentatalevelpredeterminedby<br />
resistorR prg .<br />
Measuretheoutputvoltage(voltageatthecollectorofQ 4 withrespecttoground)asthe<br />
inputvoltagesarevaried.Notehowthetwopotentiometershavedifferenteffectsontheoutput<br />
voltage:oneinputtendstodrivetheoutputvoltageinthesamedirection(noninverting),while<br />
theothertendstodrivetheoutputvoltageintheoppositedirection(inverting).Youwillnotice<br />
thattheoutputvoltageismostresponsivetochangesintheinputwhenthetwoinputsignals<br />
arenearlyequaltoeachother.<br />
Oncethecircuit’sdifferentialresponsehasbeenproven(theoutputvoltagesharplytransitioningfromoneextremeleveltoanotherwhenoneinputisadjustedaboveandbelowtheother<br />
input’svoltagelevel),youarereadytousethiscircuitasarealop-amp.Asimpleop-ampcircuit<br />
calledavoltagefollowerisagoodconfigurationtotryfirst.Tomakeavoltagefollowercircuit,<br />
directlyconnecttheoutputoftheamplifiertoitsinvertinginput.Thismeansconnectingthe<br />
collectorandbaseterminalsofQ 4 together,anddiscardingthe”inverting”potentiometer:
5.17. SIMPLEOP-AMP 271<br />
100<br />
kΩ<br />
Q 1 Q 2<br />
R prg<br />
Q 3 Q 4<br />
6 V<br />
6 V<br />
10 kΩ<br />
V in<br />
V out<br />
Q 5 Q 6<br />
Op-amp diagram<br />
−<br />
V in<br />
+<br />
V out<br />
CBE<br />
CBE CBE CBE<br />
+ - Noninverting<br />
CBE<br />
CBE<br />
+ -<br />
Notethetriangularsymboloftheop-ampshowninthelowerschematicdiagram. The<br />
invertingandnoninvertinginputsaredesignatedwith(-)and(+)symbols,respectively,with<br />
theoutputterminalattherightapex.Thefeedbackwireconnectingoutputtoinvertinginput<br />
isshowninredintheabovediagrams.<br />
Asavoltagefollower,theoutputvoltageshould”follow”theinputvoltageveryclosely,deviatingnomorethanafewhundredthsofavolt.Thisisamuchmoreprecisefollowercircuit<br />
thanthatofasinglecommon-collectortransistor,describedinanearlierexperiment!
272 CHAPTER5. DISCRETESEMICONDUCTORCIRCUITS<br />
Amorecomplexop-ampcircuitiscalledthenoninvertingamplifier,anditusesapairofresistorsinthefeedbackloopto”feedback”afractionoftheoutputvoltagetotheinvertinginput,<br />
causingtheamplifiertooutputavoltageequaltosomemultipleofthevoltageatthenoninvertinginput.Ifweusetwoequal-valueresistors,thefeedbackvoltagewillbe1/2theoutput<br />
voltage,causingtheoutputvoltagetobecometwicethevoltageimpressedatthenoninverting<br />
input.Thus,wehaveavoltageamplifierwithaprecisegainof2:<br />
100<br />
kΩ<br />
Q 1 Q 2<br />
R prg<br />
Q 3 Q 4<br />
6 V<br />
6 V<br />
10 kΩ<br />
V in<br />
V out<br />
100 kΩ<br />
100 kΩ<br />
Q 5 Q 6<br />
Op-amp diagram<br />
−<br />
V in<br />
+<br />
V out<br />
CBE<br />
CBE CBE CBE<br />
+ - Noninverting<br />
CBE<br />
CBE<br />
+ -
5.17. SIMPLEOP-AMP 273<br />
Asyoutestthisnoninvertingamplifiercircuit,youmaynoticeslightdiscrepanciesbetween<br />
theoutputandinputvoltages. Accordingtothefeedbackresistorvalues,thevoltagegain<br />
shouldbeexactly2. However,youmaynoticedeviationsintheorderofseveralhundredths<br />
ofavoltbetweenwhattheoutputvoltageisandwhatitshouldbe.Thesedeviationsaredue<br />
toimperfectionsofthedifferentialamplifiercircuit,andmaybegreatlydiminishedifweadd<br />
moreamplificationstagestoincreasethedifferentialvoltagegain.However,onewaywecan<br />
maximizetheprecisionoftheexistingcircuitistochangetheresistanceofR prg .Thisresistor<br />
setsthelowercurrentmirror’scontrolpoint,andinsodoinginfluencesmanyperformance<br />
parametersoftheop-amp.Trysubstitutingdifferenceresistancevalues,rangingfrom10kΩ<br />
to1MΩ.Donotusearesistancelessthan10kΩ,orelsethecurrentmirrortransistorsmay<br />
begintooverheatandthermally”runaway.”<br />
Someoperationalamplifiersavailableinprepackagedunitsprovideawayfortheuserto<br />
similarly”program”thedifferentialpair’scurrentmirror,andarecalledprogrammableopamps.<br />
Mostop-ampsarenotprogrammable,andhavetheirinternalcurrentmirrorcontrol<br />
pointsfixedbyaninternalresistance,trimmedtoprecisevalueatthefactory.
274 CHAPTER5. DISCRETESEMICONDUCTORCIRCUITS<br />
5.18 Audiooscillator<br />
PARTSANDMATERIALS<br />
• Two6-voltbatteries<br />
• ThreeNPNtransistors–models2N2222or2N3403recommended(RadioShackcatalog<br />
#276-1617isapackageoffifteenNPNtransistorsidealforthisandotherexperiments)<br />
• Two0.1 µFcapacitors(RadioShackcatalog#272-135orequivalent)<br />
• One1MΩresistor<br />
• Two100kΩresistors<br />
• One1kΩresistor<br />
• Assortmentofresistorpairs,lessthan100kΩ(ex:two10kΩ,two5kΩ,two1kΩ)<br />
• Onelight-emittingdiode(RadioShackcatalog#276-026orequivalent)<br />
• Audiodetectorwithheadphones<br />
CROSS-REFERENCES<br />
LessonsInElectricCircuits,Volume3,chapter4:”BipolarJunctionTransistors”<br />
LessonsInElectricCircuits,Volume4,chapter10:”Multivibrators”<br />
LEARNINGOBJECTIVES<br />
• Howtobuildanastablemultivibratorcircuitusingdiscretetransistors<br />
SCHEMATICDIAGRAM<br />
100 kΩ 100 kΩ<br />
0.1 µF 0.1 µF<br />
6 V<br />
Probe<br />
1 kΩ<br />
6 V<br />
ILLUSTRATION
5.18. AUDIOOSCILLATOR 275<br />
CBE<br />
CBE CBE<br />
+ - + -<br />
INSTRUCTIONS<br />
Thepropernameforthiscircuitis”astablemultivibrator”. Itisasimple,free-running<br />
oscillatorcircuittimedbythesizesoftheresistors,capacitors,andpowersupplyvoltage.Unfortunately,itsoutputwaveformisverydistorted,neithersinewavenorsquare.Forthesimple<br />
purposeofmakinganaudiotone,however,distortiondoesn’tmattermuch.<br />
Witha12voltsupply,100kΩresistors,and0.1 µFcapacitors,theoscillationfrequencywill<br />
beinthelowaudiorange. Youmaylistentothissignalwiththeaudiodetectorconnected<br />
withonetestprobetogroundandtheothertooneofthetransistor’scollectorterminals. I<br />
recommendplacinga1MΩresistorinserieswiththeaudiodetectortominimizebothcircuit<br />
loadingeffectsandheadphoneloudness:<br />
CBE<br />
CBE CBE<br />
+ - + -<br />
headphones<br />
plug<br />
Sensitivity<br />
1 MΩ<br />
Use resistor lead<br />
as test probe for<br />
audio detector
276 CHAPTER5. DISCRETESEMICONDUCTORCIRCUITS<br />
Themultivibratoritselfisjusttwotransistors,tworesistors,andtwocross-connectingcapacitors.Thethirdtransistorshownintheschematicandillustrationistherefordrivingthe<br />
LED,tobeusedasavisualindicatorofoscillatoraction.Usetheprobewireconnectedtothe<br />
baseofthiscommon-emitteramplifiertodetectvoltageatdifferentpartsofthecircuitwith<br />
respecttoground.Giventhelowoscillatingfrequencyofthismultivibratorcircuit,youshould<br />
beabletoseetheLEDblinkrapidlywiththeprobewireconnectedtothecollectorterminalof<br />
eithermultivibratortransistor.<br />
YoumaynoticethattheLEDfailstoblinkwithitsprobewiretouchingthebaseofeither<br />
multivibratortransistor,yettheaudiodetectortellsyouthereisanoscillatingvoltagethere.<br />
Whyisthis? TheLED’scommon-collectortransistoramplifierisavoltagefollower,meaning<br />
thatitdoesn’tamplifyvoltage. Thus,ifthevoltageundertestislessthantheminimumrequiredbytheLEDtolightup,itwillnotglow.Sincetheforward-biasedbase-emitterjunction<br />
ofanactivetransistordropsonlyabout0.7volts,thereisinsufficientvoltageateithertransistorbasetoenergizetheLED.Theaudiodetector,beingextraordinarilysensitive,though,<br />
detectsthislowvoltagesignaleasily.<br />
Feelfreetosubstitutelower-valueresistorsinplaceofthetwo100kΩunitsshown.What<br />
happenstotheoscillationfrequencywhenyoudoso? Irecommendusingresistorsatleast1<br />
kΩinsizetopreventexcessivetransistorcurrent.<br />
Oneshortcomingofmanyoscillatorcircuitsisitsdependenceonaminimumamountof<br />
powersupplyvoltage. Toolittlevoltageandthecircuitceasestooscillate. Thiscircuitisno<br />
exception.Youmightwanttoexperimentwithlowersupplyvoltagesanddeterminetheminimumvoltagenecessaryforoscillation,aswellasexperiencetheeffectsupplyvoltagechange<br />
hasonoscillationfrequency.<br />
Oneshortcomingspecifictothiscircuitisthedependenceonmismatchedcomponentsfor<br />
successfulstarting. Inorderforthecircuittobeginoscillating,onetransistormustturnon<br />
beforetheotherone. Usually,thereisenoughmismatchinthevariouscomponentvaluesto<br />
enablethistohappen,butitispossibleforthecircuitto”freeze”andfailtooscillateatpowerup.Ifthishappens,trydifferentcomponents(samevalues,butdifferentunits)inthecircuit.
5.19. VACUUMTUBEAUDIOAMPLIFIER 277<br />
5.19 Vacuumtubeaudioamplifier<br />
PARTSANDMATERIALS<br />
• One12AX7dualtriodevacuumtube<br />
• Twopowertransformers,120VACstep-downto12VAC(RadioShackcatalog#273-1365,<br />
273-1352,or273-1511).<br />
• Bridgerectifiermodule(RadioShackcatalog#276-1173)<br />
• Electrolyticcapacitor,atleast47 µF,withaworkingvoltageofatleast200voltsDC.<br />
• Automotiveignitioncoil<br />
• Audiospeaker,8Ωimpedance<br />
• Two100kΩresistors<br />
• One0.1 µFcapacitor,250WVDC(RadioShackcatalog#272-1053)<br />
• ”Low-voltageACpowersupply”asshowninAC<strong>Experiments</strong>chapter<br />
• Onetoggleswitch,SPST(”Single-Pole,Single-Throw”)<br />
• Radio,tapeplayer,musicalkeyboard,orothersourceofaudiovoltagesignal<br />
Wherecanyouobtaina12AX7tube,youask?Thesetubesareverypopularforuseinthe<br />
”preamplifier”stagesofmanyprofessionalelectricguitaramplifiers. Gotoanygoodmusic<br />
storeandyouwillfindthemavailableforamodestprice($12USorless).ARussianmanufacturernamedSovtekmakesthesetubesnew,soyouneednotrelyon”New-Old-Stock”(NOS)<br />
componentsleftoverfromdefunctAmericanmanufacturers. Thismodeloftubewasvery<br />
popularinitsday,andmaybefoundinold”tubed”electronictestequipment(oscilloscopes,oscillators),ifyouhappentohaveaccesstosuchequipment.However,Istronglysuggestbuying<br />
atubenewratherthantakingchanceswithtubessalvagedfromantiqueequipment.<br />
Itisimportanttoselectanelectrolyticcapacitorwithsufficientworkingvoltage(WVDC)<br />
towithstandtheoutputofthisamplifier’spowersupplycircuit(about170volts). Istrongly<br />
recommendchoosingacapacitorwithavoltageratingwellinexcessoftheexpectedoperatingvoltage,soastohandleunexpectedvoltagesurgesoranyothereventthatmaytaxthe<br />
capacitor. IpurchasedtheRadioShackelectrolyticcapacitorassortment(catalog#272-802),<br />
andithappenedtocontaintwo47 µF,250WVDCcapacitors.Ifyouarenotasfortunate,you<br />
maybuildthiscircuitusingfivecapacitors,eachratedat50WVDC,tosubstituteforone250<br />
WVDCunit:
278 CHAPTER5. DISCRETESEMICONDUCTORCIRCUITS<br />
22 kΩ<br />
(Each capacitor rated<br />
for 50 volts DC)<br />
22 kΩ<br />
22 kΩ<br />
equivalent to<br />
22 kΩ<br />
22 kΩ<br />
250<br />
WVDC<br />
110 kΩ<br />
Bearinmindthatthetotalcapacitanceforthisfive-capacitornetworkwillbe1/5,or20%,<br />
ofeachcapacitor’svalue. Also,toensureevenchargingofcapacitorsinthenetwork,besure<br />
allcapacitorvalues(in µF)andallresistorvaluesareidentical.<br />
Anautomotiveignitioncoilisaspecial-purposehigh-voltagetransformerusedincarenginestoproducetensofthousandsofvoltsto”fire”thesparkplugs.<br />
Inthisexperiment,itis<br />
used(veryunconventionally,Imightadd!) asanimpedance-matchingtransformerbetween<br />
thevacuumtubeandan8Ωaudiospeaker.Thespecificchoiceof”coil”isnotcritical,solong<br />
asitisingoodoperatingcondition.HereisaphotographofthecoilIusedforthisexperiment:
5.19. VACUUMTUBEAUDIOAMPLIFIER 279<br />
Theaudiospeakerneednotbeextravagant.I’veusedsmall”bookshelf”speakers,automotive(6”x9”)speakers,aswellasalarge(100watt)3-waystereospeakerforthisexperiment,<br />
andtheyallworkfine. Donotuseasetofheadphonesunderanycircumstances,asthe<br />
ignitioncoildoesnotprovideelectricalisolationbetweenthe170voltsDCofthe”plate”power<br />
supplyandthespeaker,thuselevatingthespeakerconnectionstothatvoltagewithrespectto<br />
ground.Sinceobviouslyplacingwiresonyourheadwithhighvoltagetogroundwouldbevery<br />
hazardous,pleasedonotuseheadphones!<br />
Youwillneedsomesourceofaudio-frequencyACasaninputsignaltothisamplifiercircuit.<br />
Irecommendasmallbattery-poweredradioormusicalkeyboard,withanappropriatecable<br />
pluggedintothe”headphone”or”audioout”jacktoconveythesignaltoyouramplifier.<br />
CROSS-REFERENCES<br />
LessonsInElectricCircuits,Volume3,chapter13:”ElectronTubes”<br />
LessonsInElectricCircuits,Volume3,chapter3:”DiodesandRectifiers”<br />
LessonsInElectricCircuits,Volume2,chapter9:”Transformers”<br />
LEARNINGOBJECTIVES<br />
• Usingavacuumtube(triode)asanaudioamplifier<br />
• Usingtransformersinbothstep-downandstep-upoperation<br />
• Howtobuildahigh-voltageDCpowersupply<br />
• Usingatransformertomatchimpedances
280 CHAPTER5. DISCRETESEMICONDUCTORCIRCUITS<br />
SCHEMATICDIAGRAM<br />
B+<br />
(100 to 300 volts DC)<br />
Class-A single-ended<br />
tube audio amplifier<br />
-<br />
+<br />
8 Ω speaker<br />
Automotive<br />
ignition "coil"<br />
0.1 µF<br />
Audio<br />
input<br />
100 kΩ<br />
12AX7 "hi-mu"<br />
dual triode tube<br />
to filament power<br />
(12 volts AC)
5.19. VACUUMTUBEAUDIOAMPLIFIER 281<br />
High-voltage "plate" DC power supply<br />
Plug<br />
Switch<br />
Fuse<br />
(optional)<br />
Low-voltage AC<br />
power supply<br />
120/12<br />
ratio<br />
Transformer<br />
12 volt AC<br />
to filaments<br />
Plate supply<br />
switch<br />
100 kΩ<br />
DANGER! High voltage!!<br />
≈ 170 volts<br />
B+<br />
12/120<br />
ratio<br />
Transformer<br />
47 µF<br />
250 WVDC<br />
ILLUSTRATION
282 CHAPTER5. DISCRETESEMICONDUCTORCIRCUITS<br />
Low-voltage<br />
AC power supply<br />
12<br />
6 6<br />
"Plate supply"<br />
switch<br />
12 volt<br />
side<br />
120 volt<br />
side<br />
-<br />
-<br />
-<br />
+<br />
Ground<br />
B+<br />
Filament<br />
power<br />
Power supply<br />
Amplifier<br />
+ -<br />
Audio<br />
input<br />
5<br />
4<br />
6<br />
3<br />
7<br />
2<br />
8<br />
1<br />
9<br />
12AX7 tube<br />
Speaker<br />
INSTRUCTIONS<br />
Welcometotheworldofvacuumtubeelectronics!Whilenotexactlyanapplicationofsemiconductortechnology(powersupplyrectifierexcepted),thiscircuitisusefulasanintroduction<br />
tovacuumtubetechnology,andaninterestingapplicationforimpedance-matchingtransformers.<br />
Itshouldbenotedthatbuildingandoperatingthiscircuitinvolvesworkwith<br />
lethalvoltages! Youmustexhibittheutmostcarewhileworkingwiththiscircuit,as170<br />
voltsDCiscapableofelectrocutingyou!!Itisrecommendedthatbeginnersseekqualifiedassistance(experiencedelectricians,electronicstechnicians,orengineers)ifattemptingtobuild<br />
thisamplifier.<br />
WARNING:donottouchanywiresorterminalswhiletheamplifiercircuitisenergized!<br />
Ifyoumustmakecontactwiththecircuitatanypoint,turnoffthe”plate”power<br />
supplyswitchandwaitforthefiltercapacitortodischargebelow30voltsbeforetouchingany<br />
partofthecircuit.Iftestingcircuitvoltageswiththepoweron,useonlyonehandifpossible<br />
toavoidthepossibilityofanarm-to-armelectricshock.
5.19. VACUUMTUBEAUDIOAMPLIFIER 283<br />
Buildingthehigh-voltagepowersupply<br />
VacuumtubesrequirefairlyhighDCvoltageappliedbetweenplateandcathodeterminals<br />
inordertofunctionefficiently.Althoughitispossibletooperatetheamplifiercircuitdescribed<br />
inthisexperimentonaslowas24voltsDC,thepoweroutputwillbeminisculeandthesound<br />
qualitypoor.The12AX7triodeisratedatamaximum”platevoltage”(voltageappliedbetween<br />
plateandcathodeterminals)of330volts,soourpowersupplyof170voltsDCspecifiedhere<br />
iswellwithinthatmaximumlimit. I’veoperatedthisamplifieronashighas235voltsDC,<br />
anddiscoveredthatbothsoundqualityandintensityimprovedslightly,butnotenoughinmy<br />
estimationtowarranttheadditionalhazardtoexperimenters.<br />
Thepowersupplyactuallyhastwodifferentpoweroutputs:the”B+”DCoutputforplate<br />
power,andthe”filament”power,whichisonly12voltsAC.Tubesrequirepowerappliedto<br />
asmallfilament(sometimescalledaheater)inordertofunction,asthecathodemustbehot<br />
enoughtothermallyemitelectrons,andthatdoesn’thappenatroomtemperature!Usingone<br />
powertransformertostephousehold120voltACpowerdownto12voltsACprovideslowvoltageforthefilaments,andanothertransformerconnectedinstep-upfashionbringsthe<br />
voltagebackupto120volts. Youmightbewondering,”whystepthevoltagebackupto120<br />
voltswithanothertransformer? Whynotjusttapoffthewallsocketplugtoobtain120volt<br />
ACpowerdirectly,andthenrectifythatinto170voltsDC?”Theanswertothisistwofold:<br />
first,runningpowerthroughtwotransformersinherentlylimitstheamountofcurrentthat<br />
maybesentintoanaccidentalshort-circuitontheplate-sideoftheamplifiercircuit.Second,it<br />
electricallyisolatestheplatecircuitfromthewiringsystemofyourhouse.Ifweweretorectify<br />
wall-socketpowerwithadiodebridge,itwouldmakebothDCterminals(+and-)elevatedin<br />
voltagefromthesafetygroundconnectionofyourhouse’selectricalsystem,therebyincreasing<br />
theshockhazard.<br />
Notethetoggleswitchconnectedbetweenthe12-voltwindingsofthetwotransformers,<br />
labeled”Platesupplyswitch.”Thisswitchcontrolspowertothestep-uptransformer,thereby<br />
controllingplatevoltagetotheamplifiercircuit. Whynotjustusethemainpowerswitch<br />
connectedtothe120voltplug? WhyhaveasecondswitchtoshutofftheDChighvoltage,<br />
whenshuttingoffonemainswitchwouldaccomplishthesamething? Theanswerliesin<br />
propervacuumtubeoperation:likeincandescentlightbulbs,vacuumtubes”wear”whentheir<br />
filamentsarepoweredupanddownrepeatedly,sohavingthisadditionalswitchinthecircuit<br />
allowsyoutoshutofftheDChighvoltage(forsafetywhenmodifyingoradjustingthecircuit)<br />
withouthavingtoshutoffthefilament.Also,itisagoodhabittowaitforthetubetoreachfull<br />
operatingtemperaturebeforeapplyingplatevoltage,andthissecondswitchallowsyoutodelay<br />
theapplicationofplatevoltageuntilthetubehashadtimetoreachoperatingtemperature.<br />
Duringoperation,youshouldhaveavoltmeterconnectedtothe”B+”outputofthepower<br />
supply(betweentheB+terminalandground),continuouslyprovidingindicationofthepower<br />
supplyvoltage. Thismeterwillshowyouwhenthefiltercapacitorhasdischargedbelowthe<br />
shock-hazardlimit(30volts)whenyouturnoffthe”Platesupplyswitch”toservicetheamplifiercircuit.<br />
The”ground”terminalshownontheDCoutputofthepowersupplycircuitneednotconnecttoearthground.<br />
Rather,itismerelyasymbolshowingacommonconnectionwitha<br />
correspondinggroundterminalsymbolintheamplifiercircuit.Inthecircuityoubuild,there<br />
willbeapieceofwireconnectingthesetwo”ground”pointstogether.Asalways,thedesignationofcertaincommonpointsinacircuitbymeansofasharedsymbolisstandardpracticein<br />
electronicschematics.
284 CHAPTER5. DISCRETESEMICONDUCTORCIRCUITS<br />
Youwillnotethattheschematicdiagramshowsa100kΩresistorinparallelwiththefilter<br />
capacitor.Thisresistorisquitenecessary,asitprovidesthecapacitorapathfordischargewhen<br />
theACpoweristurnedoff.Withoutthis”bleeder”resistorinthecircuit,thecapacitorwould<br />
likelyretainadangerouschargeforalongtimeafter”power-down,”posinganadditionalshock<br />
hazardtoyou.InthecircuitIbuilt–witha47 µFcapacitoranda100kΩbleederresistor–<br />
thetimeconstantofthisRCcircuitwasabrief4.7seconds.Ifyouhappentofindalargerfilter<br />
capacitorvalue(goodforminimizingunwantedpowersupply”hum”inthespeaker),youwill<br />
needtouseacorrespondinglysmallervalueofbleederresistor,orwaitlongerforthevoltage<br />
tobleedoffeachtimeyouturnthe”Platesupply”switchoff.<br />
Besureyouhavethepowersupplysafelyconstructedandworkingreliablybeforeattemptingtopowertheamplifiercircuitwithit.<br />
Thisisgoodcircuit-buildingpracticeingeneral:<br />
buildandtroubleshootthepowersupplyfirst,thenbuildthecircuityouintendtopowerwith<br />
it.Ifthepowersupplydoesnotfunctionasitshould,thenneitherwillthepoweredcircuit,no<br />
matterhowwellitmaybedesignedandbuilt.<br />
Buildingtheamplifier<br />
Oneoftheproblemswithbuildingvacuumtubecircuitsinthe21stcenturyisthatsockets<br />
forthesecomponentscanbedifficulttofind.Giventhelimitedlifetimeofmost”receiver”tubes<br />
(afewyears),most”tubed”electronicdevicesusedsocketsformountingthetubes,sothatthey<br />
couldbeeasilyremovedandreplaced.Thoughtubesmaystillbeobtained(frommusicsupply<br />
stores)withrelativeease,thesocketstheyplugintoareconsiderablyscarcer–yourlocalRadio<br />
Shackwillnothavetheminstock!How,then,dowebuildcircuitswithtubes,ifwemightnot<br />
beabletoobtainsocketsforthemtopluginto?<br />
Forsmalltubes,thisproblemmaybecircumventedbydirectlysolderingshortlengthsof<br />
22-gaugesolidcopperwiretothepinsofthetube,thusenablingyouto”plug”thetubeinto<br />
asolderlessbreadboard. Hereisaphotographofmytubeamplifier,showingthe12AX7in<br />
aninvertedposition(pin-side-up).Pleasedisregardthe10-segmentLEDbargraphtotheleft<br />
andthe8-positionDIPswitchassemblytotherightinthephotograph,astheseareleftover<br />
componentsfromadigitalcircuitexperimentassembledpreviouslyonmybreadboard.
5.19. VACUUMTUBEAUDIOAMPLIFIER 285<br />
Onebenefitofmountingthetubeinthispositioniseaseofpinidentification,sincemost<br />
”pinconnectiondiagrams”fortubesareshownfromabottomview:<br />
12AX7 dual triode tube<br />
Filament 1<br />
5<br />
Filament 2<br />
Plate 1<br />
4<br />
6<br />
Cathode 2<br />
3<br />
7<br />
Grid 1<br />
Grid 2<br />
2<br />
8<br />
Cathode 1<br />
1<br />
9<br />
Filament<br />
Plate 2<br />
tap<br />
(view from bottom)<br />
Youwillnoticeontheamplifierschematicthatbothtriodeelementsinsidethe12AX7’s<br />
glassenvelopearebeingused,inparallel:plateconnectedtoplate,gridconnectedtogrid,and<br />
cathodeconnectedtocathode. Thisisdonetomaximizepoweroutputfromthetube,butit<br />
isnotnecessaryfordemonstratingbasicoperation. Youmayusejustoneofthetriodes,for<br />
simplicity,ifyouwish.<br />
The0.1 µFcapacitorshownontheschematic”couples”theaudiosignalsource(radio,musicalkeyboard,etc.)<br />
tothetube’sgrid(s),allowingACtopassbutblockingDC.The100kΩ<br />
resistorensuresthattheaverageDCvoltagebetweengridandcathodeiszero,andcannot<br />
”float”tosomehighlevel. Typically,biascircuitsareusedtokeepthegridslightlynegative<br />
withrespecttoground,butforthispurposeabiascircuitwouldintroducemorecomplexity<br />
thanitsworth.<br />
WhenItestedmyamplifiercircuit,Iusedtheoutputofaradioreceiver,andlatertheoutput<br />
ofacompactdisk(CD)player,astheaudiosignalsource.Usinga”mono”-to-”phono”connector<br />
extensioncordpluggedintotheheadphonejackofthereceiver/CDplayer,andalligatorclip<br />
jumperwiresconnectingthe”mono”tipofthecordtotheinputterminalsofthetubeamplifier,I<br />
wasabletoeasilysendtheamplifieraudiosignalsofvaryingamplitudetotestitsperformance<br />
overawiderangeofconditions:
286 CHAPTER5. DISCRETESEMICONDUCTORCIRCUITS<br />
Amplifier circuit<br />
Radio<br />
Audio<br />
input<br />
. . .<br />
. . .<br />
phones<br />
"Phono" plug<br />
"Mono" headphone<br />
plug<br />
Atransformerisessentialattheoutputoftheamplifiercircuitfor”matching”theimpedances<br />
ofvacuumtubeandspeaker.Sincethevacuumtubeisahigh-voltage,low-currentdevice,and<br />
mostspeakersarelow-voltage,high-currentdevices,themismatchbetweenthemwouldresultinveryaudiolowpoweroutputiftheyweredirectlyconnected.Tosuccessfullymatchthe<br />
high-voltage,low-currentsourcetothelow-voltage,highcurrentload,wemustuseastep-down<br />
transformer.<br />
Sincethevacuumtubecircuit’sTheveninresistancerangesinthetensofthousandsof<br />
ohms,andthespeakeronlyhasabout8ohmsimpedance,wewillneedatransformerwithan<br />
impedanceratioofabout10,000:1. Sincetheimpedanceratioofatransformeristhesquare<br />
ofitsturnsratio(orvoltageratio),we’relookingforatransformerwithaturnsratioofabout<br />
100:1. Atypicalautomotiveignitioncoilhasapproximatelythisturnsratio,anditisalso<br />
ratedforextremelyhighvoltageonthehigh-voltagewinding,makingitwellsuitedforthis<br />
application.<br />
Theonlybadaspectofusinganignitioncoilisthatitprovidesnoelectricalisolationbetweenprimaryandsecondarywindings,sincethedeviceisactuallyanautotransformer,with<br />
eachwindingsharingacommonterminalatoneend.Thismeansthatthespeakerwireswillbe<br />
atahighDCvoltagewithrespecttocircuitground.Solongasweknowthis,andavoidtouchingthosewiresduringoperation,therewillbenoproblem.<br />
Ideally,though,thetransformer<br />
wouldprovidecompleteisolationaswellasimpedancematching,andthespeakerwireswould<br />
beperfectlysafetotouchduringuse.<br />
Remember,makeallconnectionsinthecircuitwiththepowerturnedoff! Aftercheckingconnectionsvisuallyandwithanohmmetertoensurethatthecircuitisbuiltasperthe<br />
schematicdiagram,applypowertothefilamentsofthetubeandwaitabout30secondsforitto<br />
reachoperatingtemperature.Thebothfilamentsshouldemitasoft,orangeglow,visiblefrom<br />
boththetopandbottomviewsofthetube.
5.19. VACUUMTUBEAUDIOAMPLIFIER 287<br />
Turnthevolumecontrolofyourradio/CDplayer/musicalkeyboardsignalsourcetominimum,thenturnontheplatesupplyswitch.<br />
Thevoltmeteryouhaveconnectedbetweenthe<br />
powersupply’sB+outputterminaland”ground”shouldregisterfullvoltage(about170volts).<br />
Now,increasethevolumecontrolonthesignalsourceandlistentothespeaker.Ifalliswell,<br />
youshouldhearthecorrectsoundsclearlythroughthespeaker.<br />
Troubleshootingthiscircuitisbestdonewiththesensitiveaudiodetectordescribedinthe<br />
DCandACchaptersofthis<strong>Experiments</strong>volume. Connecta0.1 µFcapacitorinserieswith<br />
eachtestleadtoblockDCfromthedetector,thenconnectoneofthetestleadstoground,<br />
whileusingtheothertestleadtocheckforaudiosignalatvariouspointsinthecircuit. Use<br />
capacitorswithahighvoltagerating,liketheoneusedontheinputoftheamplifiercircuit:<br />
B+<br />
Using the sensitive audio<br />
detector as a troubleshooting<br />
instrument for the amplifier<br />
headphones<br />
0.1 µF<br />
. . . . . .<br />
Amplifier circuit<br />
Test<br />
leads<br />
Sensitivity<br />
plug<br />
0.1 µF<br />
"ground"<br />
Usingtwocouplingcapacitorsinsteadofjustoneaddsanadditionaldegreeofsafety,in<br />
helpingtoisolatetheunitfromany(high)DCvoltage. Evenwithouttheextracapacitor,<br />
though,thedetector’sinternaltransformershouldprovidesufficientelectricalisolationfor<br />
yoursafetyinusingittotestforsignalsinahigh-voltagecircuitlikethis,especiallyifyoubuilt<br />
yourdetectorusinga120voltpowertransformer(ratherthanan”audiooutput”transformer)<br />
assuggested.Useittotestforagoodsignalattheinput,thenatthegridpin(s)ofthetube,<br />
thenattheplateofthetube,etc.untiltheproblemisfound.Beingcapacitivelycoupled,the<br />
detectorisalsoabletotestforexcessivepowersupply”hum:”touchthefreetestleadtothe<br />
supply’sB+terminalandlistenforaloud60Hzhummingnoise. Thenoiseshouldbevery<br />
soft,notloud.Ifitisloud,thepowersupplyisnotfilteredadequatelyenough,andmayneed<br />
additionalfiltercapacitance.<br />
AftertestingapointintheamplifiercircuitwithlargeDCvoltagetoground,thecoupling<br />
capacitorsonthedetectormaybuildupsubstantialvoltage.Todischargethisvoltage,briefly<br />
touchthefreetestleadtothegroundedtestlead.A”pop”soundshouldbeheardintheheadphonesasthecouplingcapacitorsdischarge.<br />
Ifyouwouldratheruseavoltmetertotestforthepresenceofaudiosignal,youmaydoso,<br />
settingittoasensitiveACvoltagerange. Theindicationyougetfromavoltmeter,though,
288 CHAPTER5. DISCRETESEMICONDUCTORCIRCUITS<br />
doesn’ttellyouanythingaboutthequalityofthesignal,justitsmerepresence.Bearinmind<br />
thatmostACvoltmeterswillregisteratransientvoltagewheninitiallyconnectedacrossa<br />
sourceofDCvoltage,sodon’tbesurprisedtoseea”spike”(astrong,momentaryvoltageindication)attheverymomentcontactismadewiththemeter’sprobestothecircuit,rapidly<br />
decreasingtothetrueACsignalvalue.<br />
Youmaybepleasantlysurprisedatthequalityanddepthoftonefromthislittleamplifier<br />
circuit,especiallygivenitslowpoweroutput:lessthan1wattofaudiopower.Ofcourse,the<br />
circuitisquitecrudeandsacrificesqualityforsimplicityandpartsavailability,butitserves<br />
todemonstratethebasicprincipleofvacuumtubeamplification. Advancedhobbyistsand<br />
studentsmaywishtoexperimentwithbiasingnetworks,negativefeedback,differentoutput<br />
transformers,differentpowersupplyvoltages,andevendifferenttubes,toobtainmorepower<br />
and/orbettersoundquality.<br />
Hereisaphotoofaverysimilaramplifiercircuit,builtbythehusband-and-wifeteam<br />
ofTerryandCherylGoetz,illustratingwhatcanbedonewhencareandcraftsmanshipare<br />
appliedtoaprojectlikethis.<br />
Bibliography<br />
[1] ForrestM.MimsIII,“SunPhotometerwithLight-EmittingDiodesasSpectrallySelective<br />
Detectors”,AppliedOptics,31,33,6965-6967,1992.<br />
[2] ForrestM.MimsIII,“LightEmittingDiodes”HowardW.Sams&Co.,1973,pp.118-119.<br />
[3] ForrestM.MimsIII,Privatecommunications,February29,2008.
Chapter6<br />
ANALOGINTEGRATED<br />
CIRCUITS<br />
Contents<br />
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .289<br />
6.2 Voltagecomparator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .291<br />
6.3 Precisionvoltagefollower . . . . . . . . . . . . . . . . . . . . . . . . . . . . .294<br />
6.4 Noninvertingamplifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .298<br />
6.5 High-impedancevoltmeter . . . . . . . . . . . . . . . . . . . . . . . . . . . . .301<br />
6.6 Integrator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .305<br />
6.7 555audiooscillator. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .311<br />
6.8 555rampgenerator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .314<br />
6.9 PWMpowercontroller . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .317<br />
6.10 ClassBaudioamplifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .321<br />
6.1 Introduction<br />
Analogcircuitsarecircuitsdealingwithsignalsfreetovaryfromzerotofullpowersupply<br />
voltage. Thisstandsincontrasttodigitalcircuits,whichalmostexclusivelyemploy”allor<br />
nothing”signals: voltagesrestrictedtovaluesofzeroandfullsupplyvoltage,withnovalid<br />
stateinbetweenthoseextremelimits. Analogcircuitsareoftenreferredtoaslinearcircuits<br />
toemphasizethevalidcontinuityofsignalrangeforbiddenindigitalcircuits,butthislabelis<br />
unfortunatelymisleading.Justbecauseavoltageorcurrentsignalisallowedtovarysmoothly<br />
betweentheextremesofzeroandfullpowersupplylimitsdoesnotnecessarilymeanthatall<br />
mathematicalrelationshipsbetweenthesesignalsarelinearinthe”straight-line”or”proportional”senseoftheword.Asyouwillseeinthischapter,manyso-called”linear”circuitsare<br />
quitenonlinearintheirbehavior,eitherbynecessityofphysicsorbydesign.<br />
289
290 CHAPTER6. ANALOGINTEGRATEDCIRCUITS<br />
ThecircuitsinthischaptermakeuseofIC,orintegratedcircuit,components. Suchcomponentsareactuallynetworksofinterconnectedcomponentsmanufacturedonasinglewafer<br />
ofsemiconductingmaterial.Integratedcircuitsprovidingamultitudeofpre-engineeredfunctionsareavailableatverylowcost,benefittingstudents,hobbyistsandprofessionalcircuit<br />
designersalike.Mostintegratedcircuitsprovidethesamefunctionalityas”discrete”semiconductorcircuitsathigherlevelsofreliabilityandatafractionofthecost.<br />
Usually,discretecomponentcircuitconstructionisfavoredonlywhenpowerdissipationlevelsaretoohighfor<br />
integratedcircuitstohandle.<br />
Perhapsthemostversatileandimportantanalogintegratedcircuitforthestudenttomasteristheoperationalamplifier,orop-amp.<br />
Essentiallynothingmorethanadifferentialamplifierwithveryhighvoltagegain,op-ampsaretheworkhorseoftheanalogdesignworld.By<br />
cleverlyapplyingfeedbackfromtheoutputofanop-amptooneormoreofitsinputs,awide<br />
varietyofbehaviorsmaybeobtainedfromthissingledevice.Manydifferentmodelsofop-amp<br />
areavailableatlowcost,butcircuitsdescribedinthischapterwillincorporateonlycommonly<br />
availableop-ampmodels.
6.2. VOLTAGECOMPARATOR 291<br />
6.2 Voltagecomparator<br />
PARTSANDMATERIALS<br />
• Operationalamplifier,model1458or353recommended(RadioShackcatalog#276-038<br />
and900-6298,respectively)<br />
• Three6voltbatteries<br />
• Two10kΩpotentiometers,lineartaper(RadioShackcatalog#271-1715)<br />
• Onelight-emittingdiode(RadioShackcatalog#276-026orequivalent)<br />
• One330 Ωresistor<br />
• One470 Ωresistor<br />
Thisexperimentonlyrequiresasingleoperationalamplifier.Themodel1458and353are<br />
both”dual”op-ampunits,withtwocompleteamplifiercircuitshousedinthesame8-pinDIP<br />
package.Irecommendthatyoupurchaseanduse”dual”op-ampsover”single”op-ampsevenif<br />
aprojectonlyrequiresone,becausetheyaremoreversatile(thesameop-ampunitcanfunction<br />
inprojectsrequiringonlyoneamplifieraswellasinprojectsrequiringtwo).Intheinterestof<br />
purchasingandstockingtheleastnumberofcomponentsforyourhomelaboratory,thismakes<br />
sense.<br />
CROSS-REFERENCES<br />
LessonsInElectricCircuits,Volume3,chapter8:”OperationalAmplifiers”<br />
LEARNINGOBJECTIVES<br />
• Howtouseanop-ampasacomparator<br />
SCHEMATICDIAGRAM<br />
6 V<br />
6 V<br />
6 V<br />
−<br />
1 / 2 1458<br />
+<br />
330 Ω 470 Ω
292 CHAPTER6. ANALOGINTEGRATEDCIRCUITS<br />
ILLUSTRATION<br />
+ -<br />
+ -<br />
+ - 1458<br />
INSTRUCTIONS<br />
Acomparatorcircuitcomparestwovoltagesignalsanddetermineswhichoneisgreater.<br />
Theresultofthiscomparisonisindicatedbytheoutputvoltage: iftheop-amp’soutputis<br />
saturatedinthepositivedirection,thenoninvertinginput(+)isagreater,ormorepositive,<br />
voltagethantheinvertinginput(-),allvoltagesmeasuredwithrespecttoground. Iftheopamp’svoltageisnearthenegativesupplyvoltage(inthiscase,0volts,orgroundpotential),it<br />
meanstheinvertinginput(-)hasagreatervoltageappliedtoitthanthenoninvertinginput<br />
(+).<br />
Thisbehaviorismucheasierunderstoodbyexperimentingwithacomparatorcircuitthan<br />
itisbyreadingsomeone’sverbaldescriptionofit. Inthisexperiment,twopotentiometers<br />
supplyvariablevoltagestobecomparedbytheop-amp. Theoutputstatusoftheop-ampis<br />
indicatedvisuallybytheLED.ByadjustingthetwopotentiometersandobservingtheLED,<br />
onecaneasilycomprehendthefunctionofacomparatorcircuit.<br />
Forgreaterinsightintothiscircuit’soperation,youmightwanttoconnectapairofvoltmeterstotheop-ampinputterminals(bothvoltmetersreferencedtoground)sothatbothinput<br />
voltagesmaybenumericallycomparedwitheachother,thesemeterindicationscomparedto<br />
theLEDstatus:
6.2. VOLTAGECOMPARATOR 293<br />
+ -<br />
+ -<br />
+ - 1458<br />
A<br />
V Ω<br />
COM<br />
A<br />
V Ω<br />
COM<br />
Comparatorcircuitsarewidelyusedtocomparephysicalmeasurements,providedthose<br />
physicalvariablescanbetranslatedintovoltagesignals. Forinstance,ifasmallgenerator<br />
wereattachedtoananemometerwheeltoproduceavoltageproportionaltowindspeed,that<br />
windspeedsignalcouldbecomparedwitha”set-point”voltageandcomparedbyanop-ampto<br />
driveahighwindspeedalarm:<br />
6 V<br />
6 V<br />
+<br />
6 V Gen<br />
-<br />
−<br />
1 / 2 1458<br />
+<br />
330 Ω 470 Ω<br />
LED lights up when wind speed exceeds<br />
"set-point" limit established by the<br />
potentiometer position.
294 CHAPTER6. ANALOGINTEGRATEDCIRCUITS<br />
6.3 Precisionvoltagefollower<br />
PARTSANDMATERIALS<br />
• Operationalamplifier,model1458or353recommended(RadioShackcatalog#276-038<br />
and900-6298,respectively)<br />
• Three6voltbatteries<br />
• One10kΩpotentiometer,lineartaper(RadioShackcatalog#271-1715)<br />
CROSS-REFERENCES<br />
LessonsInElectricCircuits,Volume3,chapter8:”OperationalAmplifiers”<br />
LEARNINGOBJECTIVES<br />
• Howtouseanop-ampasavoltagefollower<br />
• Purposeofnegativefeedback<br />
• Troubleshootingstrategy<br />
SCHEMATICDIAGRAM<br />
6 V<br />
6 V<br />
−<br />
1 / 2 1458<br />
+<br />
6 V V input<br />
V output<br />
ILLUSTRATION
6.3. PRECISIONVOLTAGEFOLLOWER 295<br />
+ -<br />
+ -<br />
+ - 1458<br />
INSTRUCTIONS<br />
Inthepreviousop-ampexperiment,theamplifierwasusedin”open-loop”mode;thatis,<br />
withoutanyfeedbackfromoutputtoinput. Assuch,thefullvoltagegainoftheoperational<br />
amplifierwasavailable,resultingintheoutputvoltagesaturatingforvirtuallyanyamount<br />
ofdifferentialvoltageappliedbetweenthetwoinputterminals.Thisisgoodifwedesirecomparatoroperation,butifwewanttheop-amptobehaveasatrueamplifier,weneedittoexhibit<br />
amanageablevoltagegain.<br />
Sincewedonothavetheluxuryofdisassemblingtheintegratedcircuitryoftheop-amp<br />
andchangingresistorvaluestogivealesservoltagegain,wearelimitedtoexternalconnectionsandcomponentry.<br />
Actually,thisisnotadisadvantageasonemightthink,becausethe<br />
combinationofextremelyhighopen-loopvoltagegaincoupledwithfeedbackallowsustouse<br />
theop-ampforamuchwidervarietyofpurposes,mucheasierthanifweweretoexercisethe<br />
optionofmodifyingitsinternalcircuitry.<br />
Ifweconnecttheoutputofanop-amptoitsinverting(-)input,theoutputvoltagewillseek<br />
whateverlevelisnecessarytobalancetheinvertinginput’svoltagewiththatappliedtothe<br />
noninverting(+)input. Ifthisfeedbackconnectionisdirect,asinastraightpieceofwire,<br />
theoutputvoltagewillprecisely”follow”thenoninvertinginput’svoltage.Unlikethevoltage<br />
followercircuitmadefromasingletransistor(seechapter5:DiscreteSemiconductorCircuits),<br />
whichapproximatedtheinputvoltagetowithinseveraltenthsofavolt,thisvoltagefollower<br />
circuitwilloutputavoltageaccuratetowithinmeremicrovoltsoftheinputvoltage!<br />
Measuretheinputvoltageofthiscircuitwithavoltmeterconnectedbetweentheop-amp’s<br />
noninverting(+)inputterminalandcircuitground(thenegativesideofthepowersupply),<br />
andtheoutputvoltagebetweentheop-amp’soutputterminalandcircuitground. Watchthe<br />
op-amp’soutputvoltagefollowtheinputvoltageasyouadjustthepotentiometerthroughits<br />
range.
296 CHAPTER6. ANALOGINTEGRATEDCIRCUITS<br />
Youmaydirectlymeasurethedifference,orerror,betweenoutputandinputvoltagesby<br />
connectingthevoltmeterbetweentheop-amp’stwoinputterminals.Throughoutmostofthe<br />
potentiometer’srange,thiserrorvoltageshouldbealmostzero.<br />
Trymovingthepotentiometertooneofitsextremepositions,farclockwiseorfarcounterclockwise.<br />
Measureerrorvoltage,orcompareoutputvoltageagainstinputvoltage. Doyou<br />
noticeanythingunusual? Ifyouareusingthemodel1458ormodel353op-ampforthisexperiment,youshouldmeasureasubstantialerrorvoltage,ordifferencebetweenoutputand<br />
input. Manyop-amps,thespecifiedmodelsincluded,cannot”swing”theiroutputvoltageexactlytofullpowersupply(”rail”)voltagelevels.Inthiscase,the”rail”voltagesare+18volts<br />
and0volts,respectively.Duetolimitationsinthe1458’sinternalcircuitry,itsoutputvoltage<br />
isunabletoexactlyreachthesehighandlowlimits. Youmayfindthatitcanonlygowithin<br />
avoltortwoofthepowersupply”rails.”Thisisaveryimportantlimitationtounderstand<br />
whendesigningcircuitsusingoperationalamplifiers.Iffull”rail-to-rail”outputvoltageswing<br />
isrequiredinacircuitdesign,otherop-ampmodelsmaybeselectedwhichofferthiscapability.<br />
Themodel3130isonesuchop-amp.<br />
Precisionvoltagefollowercircuitsareusefulifthevoltagesignaltobeamplifiedcannottolerate”loading;”thatis,ifithasahighsourceimpedance.Sinceavoltagefollowerbydefinition<br />
hasavoltagegainof1,itspurposehasnothingtodowithamplifyingvoltage,butratherwith<br />
amplifyingasignal’scapacitytodelivercurrenttoaload.<br />
Voltagefollowercircuitshaveanotherimportantuseforcircuitbuilders: theyallowfor<br />
simplelineartestingofanop-amp. OneofthetroubleshootingtechniquesIrecommendis<br />
tosimplifyandrebuild. Supposethatyouarebuildingacircuitusingoneormoreop-amps<br />
toperformsomeadvancedfunction. Ifoneofthoseop-ampsseemstobecausingaproblem<br />
andyoususpectitmaybefaulty,tryre-connectingitasasimplevoltagefollowerandseeifit<br />
functionsinthatcapacity. Anop-ampthatfailstoworkasavoltagefollowercertainlywon’t<br />
workasanythingmorecomplex!<br />
COMPUTERSIMULATION<br />
SchematicwithSPICEnodenumbers:<br />
1<br />
2<br />
−<br />
E 1<br />
2<br />
+<br />
V input<br />
0 0<br />
R bogus<br />
R load<br />
Netlist(makeatextfilecontainingthefollowingtext,verbatim):<br />
Voltage follower<br />
vinput 1 0<br />
rbogus 1 0 1meg<br />
e1 2 0 1 2 999meg
6.3. PRECISIONVOLTAGEFOLLOWER 297<br />
rload 2 0 10k<br />
.dc vinput 5 5 1<br />
.print dc v(1,0) v(2,0) v(1,2)<br />
.end<br />
AnidealoperationalamplifiermaybesimulatedinSPICEusingadependentvoltagesource<br />
(e1inthenetlist).Theoutputnodesarespecifiedfirst(2 0),thenthetwoinputnodes,noninvertinginputfirst(1<br />
2).Open-loopgainisspecifiedlast(999meg)inthedependentvoltage<br />
sourceline.<br />
BecauseSPICEviewstheinputimpedanceofadependentsourceasinfinite,somefinite<br />
amountofresistancemustbeincludedtoavoidananalysiserror.ThisisthepurposeofR bogus :<br />
toprovideDCpathtogroundfortheV input voltagesource.Such”bogus”resistancesshouldbe<br />
arbitrarilylarge.InthissimulationIchose1MΩforanR bogus value.<br />
Aloadresistorisincludedinthecircuitformuchthesamereason:toprovideaDCpathfor<br />
currentattheoutputofthedependentvoltagesource.Asyoucansee,SPICEdoesn’tlikeopen<br />
circuits!
298 CHAPTER6. ANALOGINTEGRATEDCIRCUITS<br />
6.4 Noninvertingamplifier<br />
PARTSANDMATERIALS<br />
• Operationalamplifier,model1458or353recommended(RadioShackcatalog#276-038<br />
and900-6298,respectively)<br />
• Three6voltbatteries<br />
• Two10kΩpotentiometers,lineartaper(RadioShackcatalog#271-1715)<br />
CROSS-REFERENCES<br />
LessonsInElectricCircuits,Volume3,chapter8:”OperationalAmplifiers”<br />
LEARNINGOBJECTIVES<br />
• Howtouseanop-ampasasingle-endedamplifier<br />
• Usingdivided,negativefeedback<br />
SCHEMATICDIAGRAM<br />
6 V<br />
6 V<br />
R 1<br />
R 2<br />
−<br />
1 / 2 1458<br />
+<br />
6 V V input<br />
V output<br />
ILLUSTRATION
6.4. NONINVERTINGAMPLIFIER 299<br />
+ -<br />
+ -<br />
+ - 1458<br />
INSTRUCTIONS<br />
Thiscircuitdiffersfromthevoltagefollowerinonlyonerespect:outputvoltageis”fedback”<br />
totheinverting(-)inputthroughavoltage-dividingpotentiometerratherthanbeingdirectly<br />
connected. Withonlyafractionoftheoutputvoltagefedbacktotheinvertinginput,theopampwilloutputacorrespondingmultipleofthevoltagesensedatthenoninverting(+)inputin<br />
keepingtheinputdifferentialvoltagenearzero.Inotherwords,theop-ampwillnowfunction<br />
asanamplifierwithacontrollablevoltagegain,thatgainbeingestablishedbythepositionof<br />
thefeedbackpotentiometer(R 2 ).<br />
SetR 2 toapproximatelymid-position.Thisshouldgiveavoltagegainofabout2.Measure<br />
bothinputandoutputvoltageforseveralpositionsoftheinputpotentiometerR 1 .MoveR 2 toa<br />
differentpositionandre-takevoltagemeasurementsforseveralpositionsofR 1 .Foranygiven<br />
R 2 position,theratiobetweenoutputandinputvoltageshouldbethesame.<br />
Youwillalsonoticethattheinputandoutputvoltagesarealwayspositivewithrespectto<br />
ground.Becausetheoutputvoltageincreasesinapositivedirectionforapositiveincreaseof<br />
theinputvoltage,thisamplifierisreferredtoasnoninverting.Iftheoutputandinputvoltages<br />
wererelatedtooneanotherinaninversefashion(i.e.positiveincreasinginputvoltageresults<br />
inpositivedecreasingornegativeincreasingoutput),thentheamplifierwouldbeknownasan<br />
invertingtype.<br />
Theabilitytoleverageanop-ampinthisfashiontocreateanamplifierwithcontrollable<br />
voltagegainmakesthiscircuitanextremelyusefulone.Itwouldtakequiteabitmoredesign<br />
andtroubleshootingefforttoproduceasimilarcircuitusingdiscretetransistors.<br />
TryadjustingR 2 formaximumandminimumvoltagegain.Whatisthelowestvoltagegain<br />
attainablewiththisamplifierconfiguration?Whydoyouthinkthisis?<br />
COMPUTERSIMULATION
300 CHAPTER6. ANALOGINTEGRATEDCIRCUITS<br />
SchematicwithSPICEnodenumbers:<br />
R 1<br />
2 R 2<br />
3<br />
0<br />
1<br />
2<br />
−<br />
+<br />
E 1<br />
3<br />
V input<br />
0<br />
R bogus<br />
R load<br />
0<br />
Netlist(makeatextfilecontainingthefollowingtext,verbatim):<br />
Noninverting amplifier<br />
vinput 1 0<br />
r2 3 2 5k<br />
r1 2 0 5k<br />
rbogus 1 0 1meg<br />
e1 3 0 1 2 999meg<br />
rload 3 0 10k<br />
.dc vinput 5 5 1<br />
.print dc v(1,0) v(3,0)<br />
.end<br />
WithR 1 andR 2 setequallyto5kΩinthesimulation,itmimicsthefeedbackpotentiometer<br />
oftherealcircuitatmid-position(50%). Tosimulatethepotentiometeratthe75%position,<br />
setR 2 to7.5kΩandR 1 to2.5kΩ.
6.5. HIGH-IMPEDANCEVOLTMETER 301<br />
6.5 High-impedancevoltmeter<br />
PARTSANDMATERIALS<br />
• Operationalamplifier,modelTL082recommended(RadioShackcatalog#276-1715)<br />
• Operationalamplifier,modelLM1458recommended(RadioShackcatalog#276-038)<br />
• Four6voltbatteries<br />
• Onemetermovement,1mAfull-scaledeflection(RadioShackcatalog#22-410)<br />
• 15kΩprecisionresistor<br />
• Four1MΩresistors<br />
The1mAmetermovementsoldbyRadioShackisadvertisedasa0-15VDCmeter,butis<br />
actuallya1mAmovementsoldwitha15kΩ+/-1%tolerancemultiplierresistor. Ifyouget<br />
thisRadioShackmetermovement,youcanusetheincluded15kΩresistorfortheresistor<br />
specifiedinthepartslist.<br />
ThismeterexperimentisbasedonaJFET-inputop-ampsuchastheTL082.Theotheropamp(model1458)isusedinthisexperimenttodemonstratetheabsenceoflatch-up:aproblem<br />
inherenttotheTL082.<br />
Youdon’tneed1MΩresistors,exactly.Anyveryhighresistanceresistorswillsuffice.<br />
CROSS-REFERENCES<br />
LessonsInElectricCircuits,Volume3,chapter8:”OperationalAmplifiers”<br />
LEARNINGOBJECTIVES<br />
• Voltmeterloading:itscausesanditssolution<br />
• Howtomakeahigh-impedancevoltmeterusinganop-amp<br />
• Whatop-amp”latch-up”isandhowtoavoidit<br />
SCHEMATICDIAGRAM
302 CHAPTER6. ANALOGINTEGRATEDCIRCUITS<br />
6 V<br />
15 kΩ 0-1 mA<br />
- +<br />
1 MΩ<br />
TP3<br />
6 V<br />
6 V<br />
6 V<br />
−<br />
TL082<br />
+<br />
Test<br />
probe<br />
TP2<br />
TP1<br />
1 MΩ<br />
1 MΩ<br />
1 MΩ<br />
ILLUSTRATION<br />
+ - TL082<br />
TP3<br />
TP2<br />
TP1<br />
+ -<br />
+ -<br />
+ -<br />
0 to 1 mA<br />
meter<br />
movement<br />
- +<br />
INSTRUCTIONS<br />
Anidealvoltmeterhasinfiniteinputimpedance,meaningthatitdrawszerocurrentfrom<br />
thecircuitundertest. Thisway,therewillbeno”impact”onthecircuitasthevoltageis
6.5. HIGH-IMPEDANCEVOLTMETER 303<br />
beingmeasured.Themorecurrentavoltmeterdrawsfromthecircuitundertest,themorethe<br />
measuredvoltagewill”sag”undertheloadingeffectofthemeter,likeatire-pressuregauge<br />
releasingairoutofthetirebeingmeasured:themoreairreleasedfromthetire,themorethe<br />
tire’spressurewillbeimpactedintheactofmeasurement. Thisloadingismorepronounced<br />
oncircuitsofhighresistance,likethevoltagedividermadeof1MΩresistors,showninthe<br />
schematicdiagram.<br />
Ifyouweretobuildasimple0-15voltrangevoltmeterbyconnectingthe1mAmeter<br />
movementinserieswiththe15kΩprecisionresistor,andtrytousethisvoltmetertomeasure<br />
thevoltagesatTP1,TP2,orTP3(withrespecttoground),you’dencounterseveremeasurement<br />
errorsinducedbymeter”impact:”<br />
6 V<br />
6 V<br />
TP3 should be 9 volts<br />
TP2 should be 6 volts<br />
TP1 should be 3 volts<br />
15 kΩ<br />
0-1 mA<br />
- +<br />
However, the meter will fail to<br />
measure these voltages correctly<br />
due to the meter’s "loading" effect!<br />
TP3<br />
TP2<br />
TP1<br />
1 MΩ<br />
1 MΩ<br />
1 MΩ<br />
1 MΩ<br />
Tryusingthemetermovementand15kΩresistorasshowntomeasurethesethreevoltages.Doesthemeterreadfalselyhighorfalselylow?Whydoyouthinkthisis?<br />
Ifweweretoincreasethemeter’sinputimpedance,wewoulddiminishitscurrentdraw<br />
or”load”onthecircuitundertestandconsequentlyimproveitsmeasurementaccuracy. An<br />
op-ampwithhigh-impedanceinputs(usingaJFETtransistorinputstageratherthanaBJT<br />
inputstage)workswellforthisapplication.<br />
Notethatthemetermovementispartoftheop-amp’sfeedbackloopfromoutputtoinvertinginput.Thiscircuitdrivesthemetermovementwithacurrentproportionaltothevoltage<br />
impressedatthenoninverting(+)input,therequisitecurrentsupplieddirectlyfromthebatteriesthroughtheop-amp’spowersupplypins,notfromthecircuitundertestthroughthetest<br />
probe.Themeter’srangeissetbytheresistorconnectingtheinverting(-)inputtoground.<br />
Buildtheop-ampmetercircuitasshownandre-takevoltagemeasurementsatTP1,TP2,<br />
andTP3.Youshouldenjoyfarbettersuccessthistime,withthemetermovementaccurately<br />
measuringthesevoltages(approximately3,6,and9volts,respectively).<br />
Youmaywitnesstheextremesensitivityofthisvoltmeterbytouchingthetestprobewith<br />
onehandandthemostpositivebatteryterminalwiththeother.Noticehowyoucandrivethe<br />
needleupwardonthescalesimplybymeasuringbatteryvoltagethroughyourbodyresistance:<br />
animpossiblefeatwiththeoriginal,unamplifiedvoltmetercircuit.Ifyoutouchthetestprobe<br />
toground,themetershouldreadexactly0volts.
304 CHAPTER6. ANALOGINTEGRATEDCIRCUITS<br />
Afteryou’veproventhiscircuittowork,modifyitbychangingthepowersupplyfromdual<br />
tosplit. Thisentailsremovingthecenter-tapgroundconnectionbetweenthe2ndand3rd<br />
batteries,andgroundingthefarnegativebatteryterminalinstead:<br />
6 V<br />
15 kΩ 0-1 mA<br />
- +<br />
1 MΩ<br />
6 V<br />
6 V<br />
6 V<br />
−<br />
TL082<br />
+<br />
TP3<br />
TP2<br />
TP1<br />
1 MΩ<br />
1 MΩ<br />
1 MΩ<br />
ThisalterationinthepowersupplyincreasesthevoltagesatTP1,TP2,andTP3to6,12,<br />
and18volts,respectively.Witha15kΩrangeresistoranda1mAmetermovement,measuring<br />
18voltswillgently”peg”themeter,butyoushouldbeabletomeasurethe6and12volttest<br />
pointsjustfine.<br />
Trytouchingthemeter’stestprobetoground.Thisshoulddrivethemeterneedletoexactly<br />
0voltsasbefore,butitwillnot! Whatishappeninghereisanop-ampphenomenoncalled<br />
latch-up:wheretheop-ampoutputdrivestoapositivevoltagewhentheinputcommon-mode<br />
voltageexceedstheallowablelimit. Inthiscase,aswithmanyJFET-inputop-amps,neither<br />
inputshouldbeallowedtocomeclosetoeitherpowersupplyrailvoltage.Withasinglesupply,<br />
theop-amp’snegativepowerrailisatgroundpotential(0volts),sogroundingthetestprobe<br />
bringsthenoninverting(+)inputexactlytothatrailvoltage.ThisisbadforaJFETop-amp,<br />
anddrivestheoutputstronglypositive,eventhoughitdoesn’tseemlikeitshould,basedon<br />
howop-ampsaresupposedtofunction.<br />
Whentheop-ampranona”dual”supply(+12/-12volts,ratherthana”single”+24voltsupply),thenegativepowersupplyrailwas12voltsawayfromground(0volts),sogroundingthe<br />
testprobedidn’tviolatetheop-amp’scommon-modevoltagelimit.However,withthe”single”<br />
+24voltsupply,wehaveaproblem. Notethatsomeop-ampsdonot”latch-up”thewaythe<br />
modelTL082does.YoumayreplacetheTL082withanLM1458op-amp,whichispin-for-pin<br />
compatible(nobreadboardwiringchangesneeded).Themodel1458willnot”latch-up”when<br />
thetestprobeisgrounded,althoughyoumaystillgetincorrectmeterreadingswiththemeasuredvoltageexactlyequaltothenegativepowersupplyrail.<br />
Asageneralrule,youshould<br />
alwaysbesuretheop-amp’spowersupplyrailvoltagesexceedtheexpectedinputvoltages.
6.6. INTEGRATOR 305<br />
6.6 Integrator<br />
PARTSANDMATERIALS<br />
• Four6voltbatteries<br />
• Operationalamplifier,model1458recommended(RadioShackcatalog#276-038)<br />
• One10kΩpotentiometer,lineartaper(RadioShackcatalog#271-1715)<br />
• Twocapacitors,0.1 µFeach,non-polarized(RadioShackcatalog#272-135)<br />
• Two100kΩresistors<br />
• Three1MΩresistors<br />
Justaboutanyoperationalamplifiermodelwillworkfineforthisintegratorexperiment,<br />
butI’mspecifyingthemodel1458overthe353becausethe1458hasmuchhigherinputbias<br />
currents.Normally,highinputbiascurrentisabadcharacteristicforanop-amptohaveina<br />
precisionDCamplifiercircuit(andespeciallyanintegratorcircuit!).However,Iwantthebias<br />
currenttobehighinorderthatitsbadeffectsmaybeexaggerated,andsothatyouwilllearn<br />
onemethodofcounteractingitseffects.<br />
CROSS-REFERENCES<br />
LessonsInElectricCircuits,Volume3,chapter8:”OperationalAmplifiers”<br />
LEARNINGOBJECTIVES<br />
• Methodforlimitingthespanofapotentiometer<br />
• Purposeofanintegratorcircuit<br />
• Howtocompensateforop-ampbiascurrent<br />
SCHEMATICDIAGRAM<br />
6 V<br />
100 kΩ<br />
1 MΩ<br />
0.1 µF<br />
6 V<br />
6 V<br />
10 kΩ<br />
100 kΩ<br />
1 MΩ<br />
−<br />
1 / 2 1458<br />
+<br />
V output<br />
6 V
306 CHAPTER6. ANALOGINTEGRATEDCIRCUITS<br />
ILLUSTRATION<br />
+ -<br />
+ -<br />
1458<br />
+ -<br />
+ -<br />
INSTRUCTIONS<br />
Asyoucanseefromtheschematicdiagram,thepotentiometerisconnectedtothe”rails”<br />
ofthepowersourcethrough100kΩresistors,oneoneachend. Thisistolimitthespanof<br />
thepotentiometer,sothatfullmovementproducesafairlysmallrangeofinputvoltagesfor<br />
theop-amptooperateon. Atoneextremeofthepotentiometer’smotion,avoltageofabout<br />
0.5volt(withrespectthethegroundpointinthemiddleoftheseriesbatterystring)willbe<br />
producedatthepotentiometerwiper. Attheotherextremeofmotion,avoltageofabout-0.5<br />
voltwillbeproduced. Whenthepotentiometerispositioneddead-center,thewipervoltage<br />
shouldmeasurezerovolts.<br />
Connectavoltmeterbetweentheop-amp’soutputterminalandthecircuitgroundpoint.<br />
Slowlymovethepotentiometercontrolwhilemonitoringtheoutputvoltage.Theoutputvoltage<br />
shouldbechangingatarateestablishedbythepotentiometer’sdeviationfromzero(center)<br />
position.Tousecalculusterms,wewouldsaythattheoutputvoltagerepresentstheintegral<br />
(withrespecttotime)oftheinputvoltagefunction.Thatis,theinputvoltagelevelestablishes<br />
theoutputvoltagerateofchangeovertime. Thisispreciselytheoppositeofdifferentiation,<br />
wherethederivativeofasignalorfunctionisitsinstantaneousrateofchange.<br />
Ifyouhavetwovoltmeters,youmayreadilyseethisrelationshipbetweeninputvoltage<br />
andoutputvoltagerateofchangebymeasuringthewipervoltage(betweenthepotentiometer
6.6. INTEGRATOR 307<br />
wiperandground)withonemeterandtheoutputvoltage(betweentheop-ampoutputterminal<br />
andground)withtheother.Adjustingthepotentiometertogivezerovoltsshouldresultinthe<br />
slowestoutputvoltagerate-of-change. Conversely,themorevoltageinputtothiscircuit,the<br />
fasteritsoutputvoltagewillchange,or”ramp.”<br />
Tryconnectingthesecond0.1 µFcapacitorinparallelwiththefirst. Thiswilldoublethe<br />
amountofcapacitanceintheop-amp’sfeedbackloop.Whataffectdoesthishaveonthecircuit’s<br />
integrationrateforanygivenpotentiometerposition?<br />
Tryconnectinganother1MΩresistorinparallelwiththeinputresistor(theresistorconnectingthepotentiometerwipertotheinvertingterminaloftheop-amp).Thiswillhalvethe<br />
integrator’sinputresistance.Whataffectdoesthishaveonthecircuit’sintegrationrate?<br />
Integratorcircuitsareoneofthefundamental”building-block”functionsofananalogcomputer.<br />
Byconnectingintegratorcircuitswithamplifiers,summers,andpotentiometers(dividers),almostanydifferentialequationcouldbemodeled,andsolutionsobtainedbymeasuringvoltagesproducedatvariouspointsinthenetworkofcircuits.Becausedifferentialequationsdescribesomanyphysicalprocesses,analogcomputersareusefulassimulators.Before<br />
theadventofmoderndigitalcomputers,engineersusedanalogcomputerstosimulatesuch<br />
processesasmachineryvibration,rockettrajectory,andcontrolsystemresponse.Eventhough<br />
analogcomputersareconsideredobsoletebymodernstandards,theirconstituentcomponents<br />
stillworkwellaslearningtoolsforcalculusconcepts.<br />
Movethepotentiometeruntiltheop-amp’soutputvoltageisasclosetozeroasyoucan<br />
getit,andmovingasslowlyasyoucanmakeit. Disconnecttheintegratorinputfromthe<br />
potentiometerwiperterminalandconnectitinsteadtoground,likethis:<br />
6 V<br />
100 kΩ<br />
1 MΩ<br />
0.1 µF<br />
6 V<br />
6 V<br />
10 kΩ<br />
100 kΩ<br />
−<br />
+<br />
1 MΩ<br />
1 / 2 1458<br />
V output<br />
6 V<br />
Connect integrator input directly to ground
308 CHAPTER6. ANALOGINTEGRATEDCIRCUITS<br />
+ - Connect integrator input directly to ground<br />
+ -<br />
1458<br />
+ -<br />
+ -<br />
Applyingexactlyzerovoltagetotheinputofanintegratorcircuitshould,ideally,causethe<br />
outputvoltagerate-of-changetobezero.Whenyoumakethischangetothecircuit,youshould<br />
noticetheoutputvoltageremainingataconstantlevelorchangingveryslowly.<br />
Withtheintegratorinputstillshortedtoground,shortpastthe1MΩresistorconnecting<br />
theop-amp’snoninverting(+)inputtoground.Thereshouldbenoneedforthisresistorinan<br />
idealop-ampcircuit,sobyshortingpastitwewillseewhatfunctionitprovidesinthisvery<br />
realop-ampcircuit:
6.6. INTEGRATOR 309<br />
6 V<br />
100 kΩ<br />
1 MΩ<br />
0.1 µF<br />
6 V<br />
6 V<br />
10 kΩ<br />
100 kΩ<br />
−<br />
+<br />
1 MΩ<br />
1 / 2 1458<br />
V output<br />
6 V<br />
Connect integrator input directly to ground<br />
Short past the "grounding" resistor<br />
+ - Connect integrator input directly to ground<br />
+ -<br />
1458<br />
+ -<br />
+ -<br />
Short past the "grounding" resistor<br />
Assoonasthe”grounding”resistorisshortedwithajumperwire,theop-amp’soutput<br />
voltagewillstarttochange,ordrift. Ideally,thisshouldnothappen,becausetheintegrator
310 CHAPTER6. ANALOGINTEGRATEDCIRCUITS<br />
circuitstillhasaninputsignalofzerovolts. However,realoperationalamplifiershavea<br />
verysmallamountofcurrententeringeachinputterminalcalledthebiascurrent.Thesebias<br />
currentswilldropvoltageacrossanyresistanceintheirpath. Sincethe1MΩinputresistor<br />
conductssomeamountofbiascurrentregardlessofinputsignalmagnitude,itwilldropvoltage<br />
acrossitsterminalsduetobiascurrent,thus”offsetting”theamountofsignalvoltageseenat<br />
theinvertingterminaloftheop-amp.Iftheother(noninverting)inputisconnecteddirectlyto<br />
groundaswehavedonehere,this”offset”voltageincurredbyvoltagedropgeneratedbybias<br />
currentwillcausetheintegratorcircuittoslowly”integrate”asthoughitwerereceivingavery<br />
smallinputsignal.<br />
The”grounding”resistorisbetterknownasacompensatingresistor,becauseitactsto<br />
compensateforvoltageerrorscreatedbybiascurrent. Sincethebiascurrentsthrougheach<br />
op-ampinputterminalareapproximatelyequaltoeachother,anequalamountofresistance<br />
placedinthepathofeachbiascurrentwillproduceapproximatelythesamevoltagedrop.<br />
Equalvoltagedropsseenatthecomplementaryinputsofanop-ampcanceleachotherout,<br />
thusnullingtheerrorotherwiseinducedbybiascurrent.<br />
Removethejumperwireshortingpastthecompensatingresistorandnoticehowtheopampoutputreturnstoarelativelystablestate.Itmaystilldriftsome,mostlikelyduetobias<br />
voltageerrorintheop-ampitself,butthatisanothersubjectaltogether!<br />
COMPUTERSIMULATION<br />
SchematicwithSPICEnodenumbers:<br />
1<br />
1 MΩ 2 0.1 µF<br />
3<br />
0 0<br />
−<br />
+<br />
Netlist(makeatextfilecontainingthefollowingtext,verbatim):<br />
DC integrator<br />
vinput 1 0 dc 0.05<br />
r1 1 2 1meg<br />
c1 2 3 0.1u ic=0<br />
e1 3 0 0 2 999k<br />
.tran 1 30 uic<br />
.plot tran v(1,0) v(3,0)<br />
.end
6.7. 555AUDIOOSCILLATOR 311<br />
6.7 555audiooscillator<br />
PARTSANDMATERIALS<br />
• Two6voltbatteries<br />
• Onecapacitor,0.1 µF,non-polarized(RadioShackcatalog#272-135)<br />
• One555timerIC(RadioShackcatalog#276-1723)<br />
• Twolight-emittingdiodes(RadioShackcatalog#276-026orequivalent)<br />
• One1MΩresistor<br />
• One100kΩresistor<br />
• Two510 Ωresistors<br />
• Audiodetectorwithheadphones<br />
• Oscilloscope(recommended,butnotnecessary)<br />
Aoscilloscopewouldbeusefulinanalyzingthewaveformsproducedbythiscircuit,butit<br />
isnotessential.Anaudiodetectorisaveryusefulpieceoftestequipmentforthisexperiment,<br />
especiallyifyoudon’thaveanoscilloscope.<br />
CROSS-REFERENCES<br />
LessonsInElectricCircuits,Volume4,chapter10:”Multivibrators”<br />
LEARNINGOBJECTIVES<br />
• Howtousethe555timerasanastablemultivibrator<br />
• Workingknowledgeofdutycycle<br />
SCHEMATICDIAGRAM<br />
1 MΩ<br />
V cc<br />
Disch<br />
555<br />
RST<br />
Out<br />
510 Ω<br />
6 V<br />
100 kΩ<br />
Thresh<br />
Trig<br />
Ctrl<br />
510 Ω<br />
6 V<br />
0.1 µF<br />
Gnd
312 CHAPTER6. ANALOGINTEGRATEDCIRCUITS<br />
ILLUSTRATION<br />
+ -<br />
+ -<br />
555<br />
INSTRUCTIONS<br />
The”555”integratedcircuitisageneral-purposetimerusefulforavarietyoffunctions.In<br />
thisexperiment,weexploreitsuseasanastablemultivibrator,oroscillator. Connectedtoa<br />
capacitorandtworesistorsasshown,itwilloscillatefreely,drivingtheLEDsonandoffwith<br />
asquare-waveoutputvoltage.<br />
Thiscircuitworksontheprincipleofalternatelycharginganddischargingacapacitor.The<br />
555beginstodischargethecapacitorbygroundingthe DischterminalwhenthevoltagedetectedbytheThreshterminalexceeds2/3thepowersupplyvoltage(V<br />
cc ).Itstopsdischarging<br />
thecapacitorwhenthevoltagedetectedbytheTrigterminalfallsbelow1/3thepowersupply<br />
voltage. Thus,whenboth Threshand Trigterminalsareconnectedtothecapacitor’spositiveterminal,thecapacitorvoltagewillcyclebetween1/3and2/3powersupplyvoltageina<br />
”sawtooth”pattern.<br />
Duringthechargingcycle,thecapacitorreceiveschargingcurrentthroughtheseriescombinationofthe1MΩand100kΩresistors.AssoonastheDischterminalonthe555timergoes<br />
togroundpotential(atransistorinsidethe555connectedbetweenthatterminalandground<br />
turnson),thecapacitor’sdischargingcurrentonlyhastogothroughthe100kΩresistor.The<br />
resultisanRCtimeconstantthatismuchlongerforchargingthanfordischarging,resulting<br />
inachargingtimegreatlyexceedingthedischargingtime.<br />
The555’s Outterminalproducesasquare-wavevoltagesignalthatis”high”(nearlyV cc )<br />
whenthecapacitorischarging,and”low”(nearly0volts)whenthecapacitorisdischarging.<br />
Thisalternatinghigh/lowvoltagesignaldrivesthetwoLEDsinoppositemodes:whenoneis<br />
on,theotherwillbeoff.Becausethecapacitor’scharginganddischargingtimesareunequal,<br />
the”high”and”low”timesoftheoutput’ssquare-wavewaveformwillbeunequalaswell.This<br />
canbeseenintherelativebrightnessofthetwoLEDs: onewillbemuchbrighterthanthe<br />
other,becauseitisonforalongerperiodoftimeduringeachcycle.<br />
Theequalityorinequalitybetween”high”and”low”timesofasquarewaveisexpressed<br />
asthatwave’sdutycycle. Asquarewavewitha50%dutycycleisperfectlysymmetrical:its<br />
”high”timeispreciselyequaltoits”low”time.Asquarewavethatis”high”10%ofthetime
6.7. 555AUDIOOSCILLATOR 313<br />
and”low”90%ofthetimeissaidtohavea10%dutycycle.Inthiscircuit,theoutputwaveform<br />
hasa”high”timeexceedingthe”low”time,resultinginadutycyclegreaterthan50%.<br />
Usetheaudiodetector(oranoscilloscope)toinvestigatethedifferentvoltagewaveforms<br />
producedbythiscircuit. Trydifferentresistorvaluesand/orcapacitorvaluestoseewhat<br />
effectstheyhaveonoutputfrequencyorcharge/dischargetimes.
314 CHAPTER6. ANALOGINTEGRATEDCIRCUITS<br />
6.8 555rampgenerator<br />
PARTSANDMATERIALS<br />
• Two6voltbatteries<br />
• Onecapacitor,470 µFelectrolytic,35WVDC(RadioShackcatalog#272-1030orequivalent)<br />
• Onecapacitor,0.1 µF,non-polarized(RadioShackcatalog#272-135)<br />
• One555timerIC(RadioShackcatalog#276-1723)<br />
• TwoPNPtransistors–models2N2907or2N3906recommended(RadioShackcatalog#<br />
276-1604isapackageoffifteenPNPtransistorsidealforthisandotherexperiments)<br />
• Twolight-emittingdiodes(RadioShackcatalog#276-026orequivalent)<br />
• One100kΩresistor<br />
• One47kΩresistor<br />
• Two510 Ωresistors<br />
• Audiodetectorwithheadphones<br />
Thevoltageratingonthe470 µFcapacitorisnotcritical,solongasitgenerouslyexceeds<br />
themaximumpowersupplyvoltage. Inthisparticularcircuit,thatmaximumvoltageis12<br />
volts.Besureyouconnectthiscapacitorinthecircuitproperly,respectingpolarity!<br />
CROSS-REFERENCES<br />
LessonsInElectricCircuits,Volume1,chapter13:”Capacitors”<br />
LessonsInElectricCircuits,Volume4,chapter10:”Multivibrators”<br />
LEARNINGOBJECTIVES<br />
• Howtousethe555timerasanastablemultivibrator<br />
• Apracticaluseforacurrentmirrorcircuit<br />
• Understandingtherelationshipbetweencapacitorcurrentandcapacitorvoltagerate-ofchange<br />
SCHEMATICDIAGRAM
6.8. 555RAMPGENERATOR 315<br />
100 kΩ<br />
TP2<br />
+<br />
A<br />
-<br />
TP1<br />
47 kΩ<br />
TP3<br />
V cc<br />
555<br />
Disch<br />
Thresh<br />
Trig<br />
RST<br />
Out<br />
Ctrl<br />
510 Ω<br />
510 Ω<br />
6 V<br />
6 V<br />
470 µF<br />
Gnd<br />
ILLUSTRATION<br />
+ - CBE<br />
TP3<br />
TP2<br />
CBE<br />
-<br />
-<br />
555<br />
+ -<br />
TP1<br />
INSTRUCTIONS<br />
Again,weareusinga555timerICasanastablemultivibrator,oroscillator. Thistime,<br />
however,wewillcompareitsoperationintwodifferentcapacitor-chargingmodes:traditional<br />
RCandconstant-current.<br />
Connectingtestpoint#1(TP1)totestpoint#3(TP3)usingajumperwire. Thisallows<br />
thecapacitortochargethrougha47kΩresistor. Whenthecapacitorhasreached2/3supply<br />
voltage,the555timerswitchesto”discharge”modeanddischargesthecapacitortoalevelof<br />
1/3supplyvoltagealmostimmediately.Thechargingcyclebeginsagainatthispoint.Measure<br />
voltagedirectlyacrossthecapacitorwithavoltmeter(adigitalvoltmeterispreferred),and<br />
notetherateofcapacitorchargingovertime.Itshouldrisequicklyatfirst,thentaperoffasit<br />
buildsupto2/3supplyvoltage,justasyouwouldexpectfromanRCchargingcircuit.<br />
RemovethejumperwirefromTP3,andre-connectittoTP2. Thisallowsthecapacitorto<br />
bechargedthroughthecontrolled-currentlegofacurrentmirrorcircuitformedbythetwo<br />
PNPtransistors.Measurevoltagedirectlyacrossthecapacitoragain,notingthedifferencein<br />
chargingrateovertimeascomparedtothelastcircuitconfiguration.
316 CHAPTER6. ANALOGINTEGRATEDCIRCUITS<br />
ByconnectingTP1toTP2,thecapacitorreceivesanearlyconstantchargingcurrent.Constantcapacitorchargingcurrentyieldsavoltagecurvethatislinear,asdescribedbytheequationi=C(de/dt).Ifthecapacitor’scurrentisconstant,sowillbeitsrate-of-changeofvoltage<br />
overtime.Theresultisa”ramp”waveformratherthana”sawtooth”waveform:<br />
Sawtooth waveform (RC circuit)<br />
Ramp waveform (constant current)<br />
Thecapacitor’schargingcurrentmaybedirectlymeasuredbysubstitutinganammeterin<br />
placeofthejumperwire.Theammeterwillneedtobesettomeasureacurrentintherangeof<br />
hundredsofmicroamps(tenthsofamilliamp).ConnectedbetweenTP1andTP3,youshould<br />
seeacurrentthatstartsatarelativelyhighvalueatthebeginningofthechargingcycle,and<br />
tapersofftowardtheend.ConnectedbetweenTP1andTP2,however,thecurrentwillbemuch<br />
morestable.<br />
Itisaninterestingexperimentatthispointtochangethetemperatureofeithercurrent<br />
mirrortransistorbytouchingitwithyourfinger.Asthetransistorwarms,itwillconductmore<br />
collectorcurrentforthesamebase-emittervoltage.Ifthecontrollingtransistor(theoneconnectedtothe100kΩresistor)istouched,thecurrentdecreases.Ifthecontrolledtransistoris<br />
touched,thecurrentincreases.Forthemoststablecurrentmirroroperation,thetwotransistorsshouldbecementedtogethersothattheirtemperaturesneverdifferbyanysubstantial<br />
amount.<br />
Thiscircuitworksjustaswellathighfrequenciesasitdoesatlowfrequencies. Replace<br />
the470 µFcapacitorwitha0.1 µFcapacitor,anduseanaudiodetectortosensethevoltage<br />
waveformatthe555’soutputterminal.Thedetectorshouldproduceanaudiotonethatiseasy<br />
tohear.Thecapacitor’svoltagewillnowbechangingmuchtoofasttoviewwithavoltmeterin<br />
theDCmode,butwecanstillmeasurecapacitorcurrentwithanammeter.<br />
WiththeammeterconnectedbetweenTP1andTP3(RCmode), measurebothDCmicroampsandACmicroamps.<br />
Recordthesecurrentfiguresonpaper. Now,connecttheammeterbetweenTP1andTP2(constant-currentmode).<br />
MeasurebothDCmicroampsandAC<br />
microamps,notinganydifferencesincurrentreadingsbetweenthiscircuitconfigurationand<br />
thelastone. MeasuringACcurrentinadditiontoDCcurrentisaneasywaytodetermine<br />
whichcircuitconfigurationgivesthemoststablechargingcurrent. Ifthecurrentmirrorcircuitwereperfect–thecapacitorchargingcurrentabsolutelyconstant–therewouldbezero<br />
ACcurrentmeasuredbythemeter.
6.9. PWMPOWERCONTROLLER 317<br />
6.9 PWMpowercontroller<br />
PARTSANDMATERIALS<br />
• Four6voltbatteries<br />
• Onecapacitor,100 µFelectrolytic,35WVDC(RadioShackcatalog#272-1028orequivalent)<br />
• Onecapacitor,0.1 µF,non-polarized(RadioShackcatalog#272-135)<br />
• One555timerIC(RadioShackcatalog#276-1723)<br />
• Dualoperationalamplifier,model1458recommended(RadioShackcatalog#276-038)<br />
• OneNPNpowertransistor–(RadioShackcatalog#276-2041orequivalent)<br />
• Three1N4001rectifyingdiodes(RadioShackcatalog#276-1101)<br />
• One10kΩpotentiometer,lineartaper(RadioShackcatalog#271-1715)<br />
• One33kΩresistor<br />
• 12voltautomotivetail-lightlamp<br />
• Audiodetectorwithheadphones<br />
CROSS-REFERENCES<br />
LessonsInElectricCircuits,Volume3,chapter8:”OperationalAmplifiers”<br />
LessonsInElectricCircuits,Volume2,chapter7:”Mixed-FrequencyACSignals”<br />
LEARNINGOBJECTIVES<br />
• Howtousethe555timerasanastablemultivibrator<br />
• Howtouseanop-ampasacomparator<br />
• HowtousediodestodropunwantedDCvoltage<br />
• Howtocontrolpowertoaloadbypulse-widthmodulation<br />
SCHEMATICDIAGRAM<br />
0.1 µF<br />
33 kΩ<br />
V cc<br />
555<br />
Disch<br />
Thresh<br />
Trig<br />
Gnd<br />
RST<br />
Out<br />
Ctrl<br />
+<br />
1 / 2 1458<br />
−<br />
1<br />
+<br />
/ 2 1458<br />
−<br />
Load<br />
Power<br />
transistor<br />
6 V<br />
6 V<br />
6 V<br />
6 V
318 CHAPTER6. ANALOGINTEGRATEDCIRCUITS<br />
ILLUSTRATION<br />
E<br />
B<br />
C<br />
+ -<br />
+ -<br />
555<br />
+ - + -<br />
1458<br />
INSTRUCTIONS<br />
Thiscircuitusesa555timertogenerateasawtoothvoltagewaveformacrossacapacitor,<br />
thencomparesthatsignalagainstasteadyvoltageprovidedbyapotentiometer,usinganopampasacomparator.<br />
Thecomparisonofthesetwovoltagesignalsproducesasquare-wave<br />
outputfromtheop-amp,varyingindutycycleaccordingtothepotentiometer’sposition.This<br />
variabledutycyclesignalthendrivesthebaseofapowertransistor,switchingcurrentonand<br />
offthroughtheload.The555’soscillationfrequencyismuchhigherthanthelampfilament’s<br />
abilitytothermallycycle(heatandcool),soanyvariationindutycycle,orpulsewidth,hasthe<br />
effectofcontrollingthetotalpowerdissipatedbytheloadovertime.
6.9. PWMPOWERCONTROLLER 319<br />
E C<br />
Output (low power to load)<br />
Control<br />
voltage<br />
E C<br />
Output (high power to load)<br />
Controllingelectricalpowerthroughaloadbymeansofquicklyswitchingitonandoff,<br />
andvaryingthe”on”time,isknownaspulse-widthmodulation,orPWM.Itisaveryefficient<br />
meansofcontrollingelectricalpowerbecausethecontrollingelement(thepowertransistor)<br />
dissipatescomparativelylittlepowerinswitchingonandoff,especiallyifcomparedtothe<br />
wastedpowerdissipatedofarheostatinasimilarsituation.Whenthetransistorisincutoff,<br />
itspowerdissipationiszerobecausethereisnocurrentthroughit. Whenthetransistoris<br />
saturated,itsdissipationisverylowbecausethereislittlevoltagedroppedbetweencollector<br />
andemitterwhileitisconductingcurrent.<br />
PWMisaconcepteasierunderstoodthroughexperimentationthanreading. Itwouldbe<br />
nicetoviewthecapacitorvoltage,potentiometervoltage,andop-ampoutputwaveformsall<br />
onone(triple-trace)oscilloscopetoseehowtheyrelatetooneanother,andtotheloadpower.<br />
However,mostofushavenoaccesstoatriple-traceoscilloscope,muchlessanyoscilloscopeat<br />
all,soanalternativemethodistoslowthe555oscillatordownenoughthatthethreevoltages<br />
maybecomparedwithasimpleDCvoltmeter. Replacethe0.1 µFcapacitorwithonethat<br />
is100 µForlarger. Thiswillslowtheoscillationfrequencydownbyafactorofatleasta<br />
thousand,enablingyoutomeasurethecapacitorvoltageslowlyriseovertime,andtheopampoutputtransitionfrom”high”to”low”whenthecapacitorvoltagebecomesgreaterthan<br />
thepotentiometervoltage. Withsuchaslowoscillationfrequency,theloadpowerwillnotbe<br />
proportionedasbefore.Rather,thelampwillturnonandoffatregularintervals.Feelfreeto<br />
experimentwithothercapacitororresistorvaluestospeeduptheoscillationsenoughsothe<br />
lampneverfullyturnsonoroff,butis”throttled”byquickon-and-offpulsingofthetransistor.<br />
Whenyouexaminetheschematic,youwillnoticetwooperationalamplifiersconnectedin<br />
parallel. Thisisdonetoprovidemaximumcurrentoutputtothebaseterminalofthepower<br />
transistor.Asingleop-amp(one-halfofa1458IC)maynotbeabletoprovidesufficientoutput<br />
currenttodrivethetransistorintosaturation,sotwoop-ampsareusedintandem.Thisshould<br />
onlybedoneiftheop-ampsinquestionareoverload-protected,whichthe1458seriesofopampsare.Otherwise,itispossible(thoughunlikely)thatoneop-ampcouldturnonbeforethe<br />
other,anddamageresultfromthetwooutputsshort-circuitingeachother(onedriving”high”<br />
andtheotherdriving”low”simultaneously). Theinherentshort-circuitprotectionofferedby<br />
the1458allowsfordirectdrivingofthepowertransistorbasewithoutanyneedforacurrent-
320 CHAPTER6. ANALOGINTEGRATEDCIRCUITS<br />
limitingresistor.<br />
Thethreediodesinseriesconnectingtheop-amps’outputstothetransistor’sbasearethere<br />
todropvoltageandensurethetransistorfallsintocutoffwhentheop-ampoutputsgo”low.”<br />
Becausethe1458op-ampcannotswingitsoutputvoltageallthewaydowntogroundpotential,<br />
butonlytowithinabout2voltsofground,adirectconnectionfromtheop-amptothetransistor<br />
wouldmeanthetransistorwouldneverfullyturnoff. Addingthreesilicondiodesinseries<br />
dropsapproximately2.1volts(0.7voltstimes3)toensurethereisminimalvoltageatthe<br />
transistor’sbasewhentheop-ampoutputsgo”low.”<br />
Itisinterestingtolistentotheop-ampoutputsignalthroughanaudiodetectorasthe<br />
potentiometerisadjustedthroughitsfullrangeofmotion.Adjustingthepotentiometerhasno<br />
effectonsignalfrequency,butitgreatlyaffectsdutycycle.Notethedifferenceintonequality,<br />
ortimbre,asthepotentiometervariesthedutycyclefrom0%to50%to100%. Varyingthe<br />
dutycyclehastheeffectofchangingtheharmoniccontentofthewaveform,whichmakesthe<br />
tonesounddifferent.<br />
Youmightnoticeaparticularuniquenesstothesoundheardthroughthedetectorheadphoneswhenthepotentiometerisincenterposition(50%dutycycle–50%loadpower),versus<br />
akindofsimilarityinsoundjustaboveorbelow50%dutycycle. Thisisduetotheabsence<br />
orpresenceofeven-numberedharmonics. Anywaveformthatissymmetricalaboveandbelowitscenterline,suchasasquarewavewitha50%dutycycle,containsnoeven-numbered<br />
harmonics,onlyodd-numbered. Ifthedutycycleisbeloworabove50%,thewaveformwill<br />
notexhibitthissymmetry,andtherewillbeeven-numberedharmonics.Thepresenceofthese<br />
even-numberedharmonicfrequenciescanbedetectedbythehumanear,assomeofthemcorrespondtooctavesofthefundamentalfrequencyandthus”fit”morenaturallyintothetone<br />
scheme.
6.10. CLASSBAUDIOAMPLIFIER 321<br />
6.10 ClassBaudioamplifier<br />
PARTSANDMATERIALS<br />
• Four6voltbatteries<br />
• Dualoperationalamplifier,modelTL082recommended(RadioShackcatalog#276-1715)<br />
• OneNPNpowertransistorinaTO-220package–(RadioShackcatalog#276-2020or<br />
equivalent)<br />
• OnePNPpowertransistorinaTO-220package–(RadioShackcatalog#276-2027or<br />
equivalent)<br />
• One1N914switchingdiode(RadioShackcatalog#276-1620)<br />
• Onecapacitor,47 µFelectrolytic,35WVDC(RadioShackcatalog#272-1015orequivalent)<br />
• Twocapacitors,0.22 µF,non-polarized(RadioShackcatalog#272-1070)<br />
• One10kΩpotentiometer,lineartaper(RadioShackcatalog#271-1715)<br />
Besuretouseanop-ampthathasahighslewrate.AvoidtheLM741orLM1458forthis<br />
reason.<br />
Theclosermatchedthetwotransistorsare,thebetter.Ifpossible,trytoobtainTIP41and<br />
TIP42transistors,whicharecloselymatchedNPNandPNPpowertransistorswithdissipation<br />
ratingsof65wattseach.IfyoucannotgetaTIP41NPNtransistor,theTIP3055(availablefrom<br />
RadioShack)isagoodsubstitute.Donotuseverylarge(i.e.TO-3case)powertransistors,as<br />
theop-ampmayhavetroubledrivingenoughcurrenttotheirbasesforgoodoperation.<br />
CROSS-REFERENCES<br />
LessonsInElectricCircuits,Volume3,chapter4:”BipolarJunctionTransistors”<br />
LessonsInElectricCircuits,Volume3,chapter8:”OperationalAmplifiers”<br />
LEARNINGOBJECTIVES<br />
• Howtobuilda”push-pull”classBamplifierusingcomplementarybipolartransistors<br />
• Theeffectsof”crossoverdistortion”inapush-pullamplifiercircuit<br />
• Usingnegativefeedbackviaanop-amptocorrectcircuitnonlinearities<br />
SCHEMATICDIAGRAM
322 CHAPTER6. ANALOGINTEGRATEDCIRCUITS<br />
+V<br />
Audio<br />
signal<br />
in<br />
0.22 µF<br />
−<br />
1 / 2 TL082<br />
+<br />
1 MΩ<br />
-V<br />
6 V<br />
+V<br />
Volume<br />
10 kΩ<br />
+V<br />
−<br />
1 / 2 TL082<br />
+<br />
-V<br />
47 µF<br />
10 kΩ<br />
0.22 µF<br />
1N914<br />
+V<br />
TIP41<br />
or<br />
TIP3055<br />
TIP42<br />
8 Ω<br />
speaker<br />
Power<br />
supply<br />
6 V<br />
6 V<br />
-V<br />
6 V<br />
-V<br />
ILLUSTRATION<br />
Volume<br />
control<br />
+ - + -<br />
TL082<br />
NPN<br />
BCE<br />
PNP<br />
BCE<br />
+ -<br />
-<br />
-<br />
+ -<br />
Audio<br />
input<br />
Speaker<br />
INSTRUCTIONS<br />
Thisprojectisanaudioamplifiersuitableforamplifyingtheoutputsignalfromasmall<br />
radio,tapeplayer,CDplayer,oranyothersourceofaudiosignals. Forstereooperation,two
6.10. CLASSBAUDIOAMPLIFIER 323<br />
identicalamplifiersmustbebuilt,onefortheleftchannelandotherfortherightchannel.To<br />
obtainaninputsignalforthisamplifiertoamplify,justconnectittotheoutputofaradioor<br />
otheraudiodevicelikethis:<br />
Amplifier circuit<br />
Radio<br />
Audio<br />
input<br />
. . .<br />
. . .<br />
phones<br />
"Phono" plug<br />
"Mono" headphone<br />
plug<br />
Thisamplifiercircuitalsoworkswellinamplifying”line-level”audiosignalsfromhighquality,modularstereocomponents.<br />
Itprovidesasurprisingamountofsoundpowerwhen<br />
playedthroughalargespeaker,andmayberunwithoutheatsinksonthetransistors(though<br />
youshouldexperimentwithitabitbeforedecidingtoforegoheatsinks,asthepowerdissipationvariesaccordingtothetypeofspeakerused).<br />
Thegoalofanyamplifiercircuitistoreproducetheinputwaveshapeasaccuratelyaspossible.<br />
Perfectreproductionisimpossible,ofcourse,andanydifferencesbetweentheoutput<br />
andinputwaveshapesisknownasdistortion.Inanaudioamplifier,distortionmaycauseunpleasanttonestobesuperimposedonthetruesound.Therearemanydifferentconfigurations<br />
ofaudioamplifiercircuitry,eachwithitsownadvantagesanddisadvantages.Thisparticular<br />
circuitiscalleda”classB,”push-pullcircuit.<br />
Mostaudio”power”amplifiersuseaclassBconfiguration,whereonetransistorprovides<br />
powertotheloadduringone-halfofthewaveformcycle(itpushes)andasecondtransistor<br />
providespowertotheloadfortheotherhalfofthecycle(itpulls). Inthisscheme,neither<br />
transistorremains”on”fortheentirecycle,givingeachoneatimeto”rest”andcoolduringthe<br />
waveformcycle.Thismakesforapower-efficientamplifiercircuit,butleadstoadistincttype<br />
ofnonlinearityknownas”crossoverdistortion.”<br />
Shownhereisasine-waveshape,equivalenttoaconstantaudiotoneofconstantvolume:
324 CHAPTER6. ANALOGINTEGRATEDCIRCUITS<br />
Inapush-pullamplifiercircuit,thetwotransistorstaketurnsamplifyingthealternate<br />
half-cyclesofthewaveformlikethis:<br />
Transistor #1 Transistor #1 Transistor #1<br />
Transistor #2 Transistor #2 Transistor #2<br />
Ifthe”hand-off”betweenthetwotransistorsisnotpreciselysynchronized,though,the<br />
amplifier’soutputwaveformmaylooksomethinglikethisinsteadofapuresinewave:<br />
Transistor #1 Transistor #1 Transistor #1<br />
Transistor #2 Transistor #2 Transistor #2<br />
Here,distortionresultsfromthefactthatthereisadelaybetweenthetimeonetransistorturnsoffandtheothertransistorturnson.<br />
Thistypeofdistortion,wherethewaveform<br />
”flattens”atthecrossoverpointbetweenpositiveandnegativehalf-cycles,iscalledcrossover<br />
distortion. Onecommonmethodofmitigatingcrossoverdistortionistobiasthetransistors<br />
sothattheirturn-on/turn-offpointsactuallyoverlap,sothatbothtransistorsareinastateof<br />
conductionforabriefmomentduringthecrossoverperiod:<br />
Transistor #1 Transistor #1 Transistor #1<br />
both both both both both<br />
Transistor #2 Transistor #2 Transistor #2<br />
ThisformofamplificationistechnicallyknownasclassABratherthanclassB,because<br />
eachtransistoris”on”formorethan50%ofthetimeduringacompletewaveformcycle.The<br />
disadvantagetodoingthis,though,isincreasedpowerconsumptionoftheamplifiercircuit,becauseduringthemomentsoftimewherebothtransistorsareconducting,thereiscurrentconductedthroughthetransistorsthatisnotgoingthroughtheload,butismerelybeing”shorted”<br />
fromonepowersupplyrailtotheother(from-Vto+V).Notonlyisthisawasteofenergy,but<br />
itdissipatesmoreheatenergyinthetransistors. Whentransistorsincreaseintemperature,<br />
theircharacteristicschange(V be forwardvoltagedrop, β,junctionresistances,etc.),making<br />
properbiasingdifficult.<br />
Inthisexperiment,thetransistorsoperateinpureclassBmode. Thatis,theyarenever<br />
conductingatthesametime. Thissavesenergyanddecreasesheatdissipation,butlends<br />
itselftocrossoverdistortion.Thesolutiontakeninthiscircuitistouseanop-ampwithnegativefeedbacktoquicklydrivethetransistorsthroughthe”dead”zoneproducingcrossover<br />
distortionandreducetheamountof”flattening”ofthewaveformduringcrossover.
6.10. CLASSBAUDIOAMPLIFIER 325<br />
Thefirst(leftmost)op-ampshownintheschematicdiagramisnothingmorethanabuffer.<br />
Abufferhelpstoreducetheloadingoftheinputcapacitor/resistornetwork,whichhasbeen<br />
placedinthecircuittofilteroutanyDCbiasvoltageoutoftheinputsignal,preventingany<br />
DCvoltagefrombecomingamplifiedbythecircuitandsenttothespeakerwhereitmight<br />
causedamage. Withoutthebufferop-amp,thecapacitor/resistorfilteringcircuitreducesthe<br />
low-frequency(”bass”)responseoftheamplifier,andaccentuatesthehigh-frequency(”treble”).<br />
Thesecondop-ampfunctionsasaninvertingamplifierwhosegainiscontrolledbythe10<br />
kΩpotentiometer. Thisdoesnothingmorethanprovideavolumecontrolfortheamplifier.<br />
Usually,invertingop-ampcircuitshavetheirfeedbackresistor(s)connecteddirectlyfromthe<br />
op-ampoutputterminaltotheinvertinginputterminallikethis:<br />
Input<br />
−<br />
+<br />
+V<br />
-V<br />
Output<br />
Ifweweretousetheresultingoutputsignaltodrivethebaseterminalsofthepush-pull<br />
transistorpair,though,wewouldexperiencesignificantcrossoverdistortion,becausethere<br />
wouldbea”dead”zoneinthetransistors’operationasthebasevoltagewentfrom+0.7volts<br />
to-0.7volts:<br />
+V<br />
Audio<br />
signal<br />
in<br />
+V<br />
−<br />
1 / 2 TL082<br />
+<br />
-V<br />
V be<br />
8 Ω<br />
speaker<br />
Top transistor doesn’t turn<br />
on until V be exceeds +0.7 volts<br />
Bottom transistor doesn’t turn<br />
on until V be drops below -0.7 volts<br />
Ifyouhavealreadyconstructedtheamplifiercircuitinitsfinalform,youmaysimplifyitto<br />
thisformandlistentothedifferenceinsoundquality.Ifyouhavenotyetbegunconstructionof<br />
thecircuit,theschematicdiagramshownabovewouldbeagoodstartingpoint.Itwillamplify<br />
anaudiosignal,butitwillsoundhorrible!<br />
-V
326 CHAPTER6. ANALOGINTEGRATEDCIRCUITS<br />
Thereasonforthecrossoverdistortionisthatwhentheop-ampoutputsignalisbetween<br />
+0.7voltsand-0.7volts,neithertransistorwillbeconducting,andtheoutputvoltagetothe<br />
speakerwillbe0voltsfortheentire1.4voltsspanofbasevoltageswing. Thus,thereisa<br />
”zone”intheinputsignalrangewherenochangeinspeakeroutputvoltagewilloccur.Hereis<br />
whereintricatebiasingtechniquesareusuallyintroducedtothecircuittoreducethis1.4volt<br />
”gap”intransistorinputsignalresponse.Usually,somethinglikethisisdone:<br />
+V<br />
+<br />
1.4 volts<br />
-<br />
8 Ω<br />
speaker<br />
Input<br />
signal<br />
-V<br />
Thetwoseries-connecteddiodeswilldropapproximately1.4volts,equivalenttothecombinedV<br />
be forwardvoltagedropsofthetwotransistors,resultinginascenariowhereeach<br />
transistorisjustonthevergeofturningonwhentheinputsignaliszerovolts,eliminatingthe<br />
1.4volt”dead”signalzonethatexistedbefore.<br />
Unfortunately,though,thissolutionisnotperfect:asthetransistorsheatupfromconductingpowertotheload,theirV<br />
be forwardvoltagedropswilldecreasefrom0.7voltstosomething<br />
less,suchas0.6voltsor0.5volts.Thediodes,whicharenotsubjecttothesameheatingeffect<br />
becausetheydonotconductanysubstantialcurrent,willnotexperiencethesamechangein<br />
forwardvoltagedrop.Thus,thediodeswillcontinuetoprovidethesame1.4voltbiasvoltage<br />
eventhoughthetransistorsrequirelessbiasvoltageduetoheating. Theresultwillbethat<br />
thecircuitdriftsintoclassABoperation,wherebothtransistorswillbeinastateofconduction<br />
partofthetime.This,ofcourse,willresultinmoreheatdissipationthroughthetransistors,<br />
exacerbatingtheproblemofforwardvoltagedropchange.<br />
Acommonsolutiontothisproblemistheinsertionoftemperature-compensation”feedback”<br />
resistorsintheemitterlegsofthepush-pulltransistorcircuit:
6.10. CLASSBAUDIOAMPLIFIER 327<br />
+V<br />
R feedback<br />
R feedback<br />
8 Ω<br />
speaker<br />
Input<br />
signal<br />
-V<br />
Thissolutiondoesn’tpreventsimultaneousturn-onofthetwotransistors,butmerelyreducestheseverityoftheproblemandpreventsthermalrunaway.Italsohastheunfortunate<br />
effectofinsertingresistanceintheloadcurrentpath,limitingtheoutputcurrentoftheamplifier.<br />
ThesolutionIoptedforinthisexperimentisonethatcapitalizesontheprincipleof<br />
op-ampnegativefeedbacktoovercometheinherentlimitationsofthepush-pulltransistoroutputcircuit.Iuseonediodetoprovidea0.7voltbiasvoltageforthepush-pullpair.Thisisnot<br />
enoughtoeliminatethe”dead”signalzone,butitreducesitbyatleast50%:<br />
+V<br />
Audio<br />
signal<br />
in<br />
+V<br />
−<br />
1 / 2 TL082<br />
+<br />
-V<br />
8 Ω<br />
speaker<br />
-V
328 CHAPTER6. ANALOGINTEGRATEDCIRCUITS<br />
Sincethevoltagedropofasinglediodewillalwaysbelessthanthecombinedvoltagedrops<br />
ofthetwotransistors’base-emitterjunctions,thetransistorscanneverturnonsimultaneously,therebypreventingclassABoperation.Next,tohelpgetridoftheremainingcrossover<br />
distortion,thefeedbacksignaloftheop-ampistakenfromtheoutputterminaloftheamplifier<br />
(thetransistors’emitterterminals)likethis:<br />
+V<br />
Audio<br />
signal<br />
in<br />
+V<br />
−<br />
1 / 2 TL082<br />
+<br />
-V<br />
8 Ω<br />
speaker<br />
-V<br />
Theop-amp’sfunctionistooutputwhatevervoltagesignalithastoinordertokeepits<br />
twoinputterminalsatthesamevoltage(0voltsdifferential).Byconnectingthefeedbackwire<br />
totheemitterterminalsofthepush-pulltransistors,theop-amphastheabilitytosenseany<br />
”dead”zonewhereneithertransistorisconducting,andoutputanappropriatevoltagesignal<br />
tothebasesofthetransistorstoquicklydrivethemintoconductionagainto”keepup”withthe<br />
inputsignalwaveform.Thisrequiresanop-ampwithahighslewrate(theabilitytoproducea<br />
fast-risingorfast-fallingoutputvoltage),whichiswhytheTL082op-ampwasspecifiedforthis<br />
circuit. Slowerop-ampssuchastheLM741orLM1458maynotbeabletokeepupwiththe<br />
highdv/dt(voltagerate-of-changeovertime,alsoknownasde/dt)necessaryforlow-distortion<br />
operation.<br />
Onlyacoupleofcapacitorsareaddedtothiscircuittobringitintoitsfinalform: a47<br />
µFcapacitorconnectedinparallelwiththediodehelpstokeepthe0.7voltbiasvoltageconstantdespitelargevoltageswingsintheop-amp’soutput,whilea0.22<br />
µFcapacitorconnected<br />
betweenthebaseandemitteroftheNPNtransistorhelpsreducecrossoverdistortionatlow<br />
volumesettings:
6.10. CLASSBAUDIOAMPLIFIER 329<br />
+V<br />
Audio<br />
signal<br />
in<br />
0.22 µF<br />
−<br />
1 / 2 TL082<br />
+<br />
1 MΩ<br />
-V<br />
6 V<br />
+V<br />
Volume<br />
10 kΩ<br />
+V<br />
−<br />
1 / 2 TL082<br />
+<br />
-V<br />
47 µF<br />
10 kΩ<br />
0.22 µF<br />
1N914<br />
+V<br />
TIP41<br />
or<br />
TIP3055<br />
TIP42<br />
8 Ω<br />
speaker<br />
Power<br />
supply<br />
6 V<br />
6 V<br />
-V<br />
6 V<br />
-V
330 CHAPTER6. ANALOGINTEGRATEDCIRCUITS
Chapter7<br />
DIGITALINTEGRATED<br />
CIRCUITS<br />
Contents<br />
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .331<br />
7.2 Basicgatefunction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .333<br />
7.3 NORgateS-Rlatch. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .337<br />
7.4 NANDgateS-Renabledlatch . . . . . . . . . . . . . . . . . . . . . . . . . . .341<br />
7.5 NANDgateS-Rflip-flop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .343<br />
7.6 LEDsequencer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .347<br />
7.7 Simplecombinationlock . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .356<br />
7.8 3-bitbinarycounter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .359<br />
7.9 7-segmentdisplay. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .361<br />
7.1 Introduction<br />
Digitalcircuitsarecircuitsdealingwithsignalsrestrictedtotheextremelimitsofzeroand<br />
somefullamount. Thisstandsincontrasttoanalogcircuits,inwhichsignalsarefreeto<br />
varycontinuouslybetweenthelimitsimposedbypowersupplyvoltageandcircuitresistances.<br />
Thesecircuitsfindusein”true/false”logicaloperationsanddigitalcomputation.<br />
ThecircuitsinthischaptermakeuseofIC,orintegratedcircuit,components. Suchcomponentsareactuallynetworksofinterconnectedcomponentsmanufacturedonasinglewafer<br />
ofsemiconductingmaterial.Integratedcircuitsprovidingamultitudeofpre-engineeredfunctionsareavailableatverylowcost,benefittingstudents,hobbyistsandprofessionalcircuit<br />
designersalike.Mostintegratedcircuitsprovidethesamefunctionalityas”discrete”semiconductorcircuitsathigherlevelsofreliabilityandatafractionofthecost.<br />
CircuitsinthischapterwillprimarilyuseCMOStechnology,asthisformofICdesignallows<br />
forabroadrangeofpowersupplyvoltagewhilemaintaininggenerallylowpowerconsumption<br />
331
332 CHAPTER7. DIGITALINTEGRATEDCIRCUITS<br />
levels.ThoughCMOScircuitryissusceptibletodamagefromstaticelectricity(highvoltages<br />
willpuncturetheinsulatingbarriersintheMOSFETtransistors),modernCMOSICsarefar<br />
moretolerantofelectrostaticdischargethantheCMOSICsofthepast,reducingtheriskof<br />
chipfailurebymishandling.ProperhandlingofCMOSinvolvestheuseofanti-staticfoamfor<br />
storageandtransportofIC’s,andmeasurestopreventstaticchargefrombuildinguponyour<br />
body(useofagroundingwriststrap,orfrequentlytouchingagroundedobject).<br />
CircuitsusingTTLtechnologyrequirearegulatedpowersupplyvoltageof5volts,andwill<br />
nottolerateanysubstantialdeviationfromthisvoltagelevel.AnyTTLcircuitsinthischapter<br />
willbeadequatelylabeledassuch,anditwillbeexpectedthatyourealizeitsuniquepower<br />
supplyrequirements.<br />
Whenbuildingdigitalcircuitsusingintegratedcircuit”chips,”itishighlyrecommended<br />
thatyouuseabreadboardwithpowersupply”rail”connectionsalongthelength.Thesearesets<br />
ofholesinthebreadboardthatareelectricallycommonalongtheentirelengthoftheboard.<br />
Connectonetothepositiveterminalofabattery,andtheothertothenegativeterminal,and<br />
DCpowerwillbeavailabletoanyareaofthebreadboardviaconnectionthroughshortjumper<br />
wires:<br />
+ - These points electrically common<br />
These points electrically common<br />
Withsomanyoftheseintegratedcircuitshaving”reset,””enable,”and”disable”terminals<br />
needingtobemaintainedina”high”or”low”state,nottomentiontheV DD (orV CC )and<br />
groundpowerterminalswhichrequireconnectiontothepowersupply,havingbothterminals<br />
ofthepowersupplyreadilyavailableforconnectionatanypointalongtheboard’slengthis<br />
veryuseful.<br />
MostbreadboardsthatIhaveseenhavethesepowersupply”rail”holes,butsomedonot.<br />
Upuntilthispoint,I’vebeenillustratingcircuitsusingabreadboardlackingthisfeature,<br />
justtoshowhowitisn’tabsolutelynecessary.However,digitalcircuitsseemtorequiremore<br />
connectionstothepowersupplythanothertypesofbreadboardcircuits,makingthisfeature<br />
morethanjustaconvenience.
7.2. BASICGATEFUNCTION 333<br />
7.2 Basicgatefunction<br />
PARTSANDMATERIALS<br />
• 4011quadNANDgate(RadioShackcatalog#276-2411)<br />
• Eight-positionDIPswitch(RadioShackcatalog#275-1301)<br />
• Ten-segmentbargraphLED(RadioShackcatalog#276-081)<br />
• One6voltbattery<br />
• Two10kΩresistors<br />
• Three470 Ωresistors<br />
Caution!The4011ICisCMOS,andthereforesensitivetostaticelectricity!<br />
CROSS-REFERENCES<br />
LessonsInElectricCircuits,Volume4,chapter3:”LogicGates”<br />
LEARNINGOBJECTIVES<br />
• Purposeofa”pulldown”resistor<br />
• Howtoexperimentallydeterminethetruthtableofagate<br />
• Howtoconnectlogicgatestogether<br />
• HowtocreatedifferentlogicalfunctionsbyusingNANDgates<br />
SCHEMATICDIAGRAM<br />
1 / 4 4011<br />
6 V<br />
10 kΩ 10 kΩ<br />
470 Ω<br />
ILLUSTRATION
334 CHAPTER7. DIGITALINTEGRATEDCIRCUITS<br />
+ - 4011<br />
INSTRUCTIONS<br />
Tobegin,connectasingleNANDgatetotwoinputswitchesandoneLED,asshown. At<br />
first,theuseofan8-positionswitchanda10-segmentLEDbargraphmayseemexcessive,<br />
sinceonlytwoswitchesandoneLEDareneededtoshowtheoperationofasingleNANDgate.<br />
However,thepresenceofthoseextraswitchesandLEDsmakeitveryconvenienttoexpand<br />
thecircuit,andhelpmakethecircuitlayoutbothcleanandcompact.<br />
Itishighlyrecommendedthatyouhaveadatasheetforthe4011chipavailablewhenyou<br />
buildyourcircuit. Don’tjustfollowtheillustrationshownabove! Itisimportantthatyou<br />
developtheskillofreadingdatasheets,especially”pinout”diagrams,whenconnectingICterminalstoothercircuitelements.<br />
Thedatasheet’sconnectiondiagramisanessentialpieceof<br />
informationtohave.Shownhereismyownrenditionofwhatany4011datasheetshows:<br />
"Pinout," or "connection" diagram for<br />
the 4011 quad NAND gate<br />
V DD<br />
14 13 12 11 10 9 8<br />
1<br />
2<br />
3<br />
4<br />
5<br />
6<br />
7<br />
Gnd<br />
Inthebreadboardillustration,I’veshownthecircuitbuiltusingthelower-leftNANDgate:<br />
pin#’s1and2aretheinputs,andpin#3istheoutput.Pin#’s14and7conductDCpowertoall<br />
fourgatecircuitsinsidetheICchip,”V DD ”representingthepositivesideofthepowersupply<br />
(+V),and”Gnd”representingthenegativesideofthepowersupply(-V),orground.Sometimes<br />
thenegativepowersupplyterminalwillbelabeled”V SS ”insteadof”Gnd”onadatasheet,but<br />
itmeansthesamething.
7.2. BASICGATEFUNCTION 335<br />
Digitallogiccircuitrydoesnotmakeuseofsplitpowersuppliesasop-ampsdo.Likeop-amp<br />
circuits,though,groundisstilltheimplicitpointofreferenceforallvoltagemeasurements.If<br />
Iweretospeakofa”high”signalbeingpresentonacertainpinofthechip,Iwouldmeanthat<br />
therewasfullvoltagebetweenthatpinandthenegativesideofthepowersupply(ground).<br />
Notehowallinputsoftheunusedgatesinsidethe4011chipareconnectedeithertoV DD<br />
orground.Thisisnotamistake,butanactofintentionaldesign.Sincethe4011isaCMOS<br />
integratedcircuit,andCMOScircuitinputsleftunconnected(floating)canassumeanyvoltage<br />
levelmerelyfrominterceptingastaticelectricchargefromanearbyobject,leavinginputs<br />
floatingmeansthatthoseunusedgatesmayreceiveanyrandomcombinationsof”high”and<br />
”low”signals.<br />
Whyisthisundesirable,ifwearen’tusingthosegates?Whocareswhatsignalstheyreceive,<br />
ifwearenotdoinganythingwiththeiroutputs?Theproblemis,ifstaticvoltagesignalsappear<br />
atthegateinputsthatarenotfully”high”orfully”low,”thegates’internaltransistorsmay<br />
begintoturnoninsuchawayastodrawexcessivecurrent.Atworst,thiscouldleadtodamage<br />
ofthechip. Atbestitmeansexcessivepowerconsumption. Itmatterslittleifwechooseto<br />
connecttheseunusedgateinputs”high”(V DD )or”low”(ground),solongasweconnectthem<br />
tooneofthosetwoplaces.Inthebreadboardillustration,Ishowallthetopinputsconnected<br />
toV DD ,andallthebottominputs(oftheunusedgates)connectedtoground. Thiswasdone<br />
merelybecausethosepowersupplyrailholeswerecloseranddidnotrequirelongjumper<br />
wires!<br />
PleasenotethatnoneoftheunusedgateoutputshavebeenconnectedtoV DD orground,<br />
andforgoodreason! IfIweretodothat,Imaybeforcingagatetoassumetheopposite<br />
outputstatethatitstryingtoachieve,whichisacomplicatedwayofsayingthatIwouldhave<br />
createdashort-circuit. Imagineagatethatissupposedtooutputa”high”logiclevel(fora<br />
NANDgate,thiswouldbetrueifanyofitsinputswere”low”). Ifsuchagateweretohave<br />
itsoutputterminaldirectlyconnectedtoground,itcouldneverreacha”high”state(being<br />
madeelectricallycommontogroundthroughthejumperwireconnection).Instead,itsupper<br />
(P-channel)outputtransistorwouldbeturnedoninvain,sourcingmaximumcurrenttoa<br />
nonexistentload. Thiswouldverylikelydamagethegate! Gateoutputterminals,bytheir<br />
verynature,generatetheirownlogiclevelsandnever”float”inthesamewaythatCMOSgate<br />
inputsdo.<br />
Thetwo10kΩresistorsareplacedinthecircuittoavoidfloatinginputconditionsonthe<br />
usedgate. Withaswitchclosed,therespectiveinputwillbedirectlyconnectedtoV DD and<br />
thereforebe”high.”Withaswitchopen,the10kΩ”pulldown”resistorprovidesaresistive<br />
connectiontoground,ensuringasecure”low”stateatthegate’sinputterminal.Thisway,the<br />
inputwillnotbesusceptibletostraystaticvoltages.<br />
WiththeNANDgateconnectedtothetwoswitchesandoneLEDasshown,youarereadyto<br />
developa”truthtable”fortheNANDgate.EvenifyoualreadyknowwhataNANDgatetruth<br />
tablelookslike,thisisagoodexerciseinexperimentation:discoveringacircuit’sbehavioral<br />
principlesbyinduction.Drawatruthtableonapieceofpaperlikethis:
336 CHAPTER7. DIGITALINTEGRATEDCIRCUITS<br />
A B<br />
0 0<br />
0 1<br />
1 0<br />
1 1<br />
Output<br />
The”A”and”B”columnsrepresentthetwoinputswitches,respectively.Whentheswitch<br />
ison,itsstateis”high”or1.Whentheswitchisoff,itsstateis”low,”or0,asensuredbyits<br />
pulldownresistor.Thegate’soutput,ofcourse,isrepresentedbytheLED:whetheritislit(1)<br />
orunlit(0).Afterplacingtheswitchesineverypossiblecombinationofstatesandrecordingthe<br />
LED’sstatus,comparetheresultingtruthtablewithwhataNANDgate’struthtableshould<br />
be.<br />
Asyoucanimagine,thisbreadboardcircuitisnotlimitedtotestingNANDgates. Any<br />
gatetypemaybetestedwithtwoswitches,twopulldownresistors,andanLEDtoindicate<br />
outputstatus.Justbesuretodouble-checkthechip’s”pinout”diagrambeforesubstitutingit<br />
pin-for-pininplaceofthe4011.Notall”quad”gatechipshavethesamepinassignments!<br />
AnimprovementyoumightwanttomaketothiscircuitistoassignacoupleofLEDsto<br />
indicateinputstatus,inadditiontotheoneLEDassignedtoindicatetheoutput.Thismakes<br />
operationalittlemoreinterestingtoobserve,andhasthefurtherbenefitofindicatingifa<br />
switchfailstoclose(oropen)byshowingthetrueinputsignaltothegate,ratherthanforcing<br />
youtoinferinputstatusfromswitchposition:<br />
+ - 4011
7.3. NORGATES-RLATCH 337<br />
7.3 NORgateS-Rlatch<br />
PARTSANDMATERIALS<br />
• 4001quadNORgate(RadioShackcatalog#276-2401)<br />
• Eight-positionDIPswitch(RadioShackcatalog#275-1301)<br />
• Ten-segmentbargraphLED(RadioShackcatalog#276-081)<br />
• One6voltbattery<br />
• Two10kΩresistors<br />
• Two470 Ωresistors<br />
• Two100 Ωresistors<br />
Caution!The4001ICisCMOS,andthereforesensitivetostaticelectricity!<br />
CROSS-REFERENCES<br />
LessonsInElectricCircuits,Volume4,chapter3:”LogicGates”<br />
LessonsInElectricCircuits,Volume4,chapter10:”Multivibrators”<br />
LEARNINGOBJECTIVES<br />
• Theeffectsofpositivefeedbackinadigitalcircuit<br />
• Whatismeantbythe”invalid”stateofalatchcircuit<br />
• Whataraceconditionisinadigitalcircuit<br />
• Theimportanceofvalid”high”CMOSsignalvoltagelevels<br />
SCHEMATICDIAGRAM<br />
1 / 4 4001<br />
6 V<br />
10<br />
kΩ<br />
1 / 4 4001<br />
470<br />
Ω<br />
ILLUSTRATION
338 CHAPTER7. DIGITALINTEGRATEDCIRCUITS<br />
+ - 4001<br />
INSTRUCTIONS<br />
The4001integratedcircuitisaCMOSquadNORgate,identicalininput,output,and<br />
powersupplypinassignmentstothe4011quadNANDgate. Its”pinout,”or”connection,”<br />
diagramisassuch:<br />
"Pinout," or "connection" diagram for<br />
the 4001 quad NOR gate<br />
V DD<br />
14 13 12 11 10 9 8<br />
1<br />
2<br />
3<br />
4<br />
5<br />
6<br />
7<br />
Gnd<br />
WhentwoNORgatesarecross-connectedasshownintheschematicdiagram,therewillbe<br />
positivefeedbackfromoutputtoinput.Thatis,theoutputsignaltendstomaintainthegate<br />
initslastoutputstate. Justasinop-ampcircuits,positivefeedbackcreateshysteresis. This<br />
tendencyforthecircuittoremaininitslastoutputstategivesitasortof”memory.”Infact,<br />
therearesolid-statecomputermemorytechnologiesbasedoncircuitrylikethis!<br />
Ifwedesignatetheleftswitchasthe”Set”inputandtherightswitchasthe”Reset,”theleft<br />
LEDwillbethe”Q”outputandtherightLEDthe”Q-not”output.WiththeSetinput”high”<br />
(switchon)andtheResetinput”low,”Qwillgo”high”andQ-notwillgo”low.”Thisisknown<br />
asthesetstateofthecircuit.MakingtheResetinput”high”andtheSetinput”low”reverses<br />
thelatchcircuit’soutputstate:Q”low”andQ-not”high.”Thisisknownastheresetstateof<br />
thecircuit.Ifbothinputsareplacedintothe”low”state,thecircuit’sQandQ-notoutputswill<br />
remainintheirlaststates,”remembering”theirpriorsettings. Thisisknownasthelatched<br />
stateofthecircuit.
7.3. NORGATES-RLATCH 339<br />
Becausetheoutputshavebeendesignated”Q”and”Q-not,”itisimpliedthattheirstates<br />
willalwaysbecomplementary(opposite).Thus,ifsomethingweretohappenthatforcedboth<br />
outputstothesamestate,wewouldbeinclinedtocallthatmodeofthecircuit”invalid.”This<br />
isexactlywhatwillhappenifwemakebothSetandResetinputs”high:”bothQandQ-not<br />
outputswillbeforcedtothesame”low”logicstate.Thisisknownastheinvalidorillegalstate<br />
ofthecircuit,notbecausesomethinghasgonewrong,butbecausetheoutputshavefailedto<br />
meettheexpectationsestablishedbytheirlabels.<br />
Sincethe”latched”stateisahystereticconditionwherebythelastoutputstatesare”remembered,”onemightwonderwhatwillhappenifthecircuitpowersupthisway,withno<br />
previousstatetohold.Toexperiment,placebothswitchesintheiroffpositions,makingboth<br />
SetandResetinputslow,thendisconnectoneofthebatterywiresfromthebreadboard.Then,<br />
quicklymakeandbreakcontactbetweenthatbatterywireanditsproperconnectionpointon<br />
thebreadboard,notingthestatusofthetwoLEDsasthecircuitispoweredupagainandagain:<br />
make and break contact!<br />
+ - 4011<br />
Whenalatchcircuitsuchasthisispoweredupintoits”latched”state,thegatesrace<br />
againsteachotherforcontrol.Giventhe”low”inputs,bothgatestrytooutput”high”signals.<br />
Ifoneofthegatesreachesits”high”outputstatebeforetheother,that”high”statewillbefed<br />
backtotheothergate’sinputtoforceitsoutput”low,”andtheraceiswonbythefastergate.<br />
Invariably,onegatewinstherace,duetointernalvariationsbetweengatesinthechip,<br />
and/orexternalresistancesandcapacitancesthatacttodelayonegatemorethantheother.<br />
Whatthisusuallymeansisthatthecircuittendstopowerupinthesamemode,overandover<br />
again. However,ifyouarepersistentinyourpowering/unpoweringcycles,youshouldseeat<br />
leastafewtimeswherethelatchcircuitpowersuplatchedintheoppositestatefromnormal.<br />
Raceconditionsaregenerallyundesirableinanykindofsystem,astheyleadtounpredictableoperation.Theycanbeparticularlytroublesometolocate,asthisexperimentshows,<br />
becauseoftheunpredictabilitytheycreate.Imagineascenario,forinstance,whereoneofthe<br />
twoNORgateswasexceptionallyslow-acting,duetoadefectinthechip.Thishandicapwould<br />
causetheothergatetowinthepower-upraceeverytime. Inotherwords,thecircuitwillbe<br />
verypredictableonpower-upwithbothinputs”low.”However,supposethattheunusualchip<br />
weretobereplacedbyonewithmoreevenlymatchedgates,orbyachipwheretheotherNOR<br />
gatewereconsistentlyslower.Normalcircuitbehaviorisnotsupposedtochangewhenacomponentisreplaced,butifraceconditionsarepresent,achangeofcomponentsmayverywell<br />
dojustthat.
340 CHAPTER7. DIGITALINTEGRATEDCIRCUITS<br />
DuetotheinherentracetendencyofanS-Rlatch,oneshouldnotdesignacircuitwiththe<br />
expectationofaconsistentpower-upstate,butratheruseexternalmeansto”force”theraceso<br />
thatthedesiredgatealways”wins.”<br />
Aninterestingmodificationtotryinthiscircuitistoreplaceoneofthe470 ΩLED”dropping”resistorswithalower-valueunit,suchas100<br />
Ω.Theobviouseffectofthisalterationwill<br />
beincreasedLEDbrightness,asmorecurrentisallowedthrough.Anot-so-obviouseffectwill<br />
alsoresult,anditisthiseffectwhichholdsgreatlearningvalue.Tryreplacingoneofthe470 Ω<br />
resistorswitha100 Ωresistor,andoperatetheinputsignalswitchesthroughallfourpossible<br />
settingcombinations,notingthebehaviorofthecircuit.<br />
Youshouldnotethatthecircuitrefusestolatchinoneofitsstates(eitherSetorReset),but<br />
onlyintheotherstate,whentheinputswitchesarebothset”low”(the”latch”mode).Whyis<br />
this?Takeavoltmeterandmeasuretheoutputvoltageofthegatewhoseoutputis”high”when<br />
bothinputsare”low.”Notethisvoltageindication,thensettheinputswitchesinsuchaway<br />
thattheotherstate(eitherResetorSet)isforced,andmeasuretheoutputvoltageoftheother<br />
gatewhenitsoutputis”high.”Notethedifferencebetweenthetwogateoutputvoltagelevels,<br />
onegateloadedbyanLEDwitha470 Ωresistor,andtheotherloadedbyanLEDwitha100 Ω<br />
resistor.Theoneloadeddownbythe”heavier”load(100 Ωresistor)willbemuchless:somuch<br />
lessthatthisvoltagewillnotbeinterpretedbytheotherNORgate’sinputasa”high”signal<br />
atallasitisfedback! Alllogicgateshavepermissible”high”and”low”inputsignalvoltage<br />
ranges,andifthevoltageofadigitalsignalfallsoutsidethispermissiblerange,itmightnot<br />
beproperlyinterpretedbythereceivinggate.Inalatchcircuitsuchasthis,whichdependson<br />
asolid”high”signalfedbackfromtheoutputofonegatetotheinputoftheother,a”weak”<br />
signalwillnotbeabletomaintainthepositivefeedbacknecessarytokeepthecircuitlatched<br />
inoneofitsstates.<br />
ThisisonereasonIfavortheuseofavoltmeterasalogic”probe”fordeterminingdigital<br />
signallevels,ratherthananactuallogicprobewith”high”and”low”lights.Alogicprobemay<br />
notindicatethepresenceofa”weak”signal,whereasavoltmeterdefinitelywillbymeansof<br />
itsquantitativeindication.Thistypeofproblem,commonincircuitswheredifferent”families”<br />
ofintegratedcircuitsaremixed(TTLandCMOS,forexample),canonlybefoundwithtest<br />
equipmentprovidingquantitativemeasurementsofsignallevel.
7.4. NANDGATES-RENABLEDLATCH 341<br />
7.4 NANDgateS-Renabledlatch<br />
PARTSANDMATERIALS<br />
• 4011quadNANDgate(RadioShackcatalog#276-2411)<br />
• Eight-positionDIPswitch(RadioShackcatalog#275-1301)<br />
• Ten-segmentbargraphLED(RadioShackcatalog#276-081)<br />
• One6voltbattery<br />
• Three10kΩresistors<br />
• Two470 Ωresistors<br />
Caution!The4011ICisCMOS,andthereforesensitivetostaticelectricity!<br />
CROSS-REFERENCES<br />
LessonsInElectricCircuits,Volume4,chapter3:”LogicGates”<br />
LessonsInElectricCircuits,Volume4,chapter10:”Multivibrators”<br />
LEARNINGOBJECTIVES<br />
• Principleandfunctionofanenabledlatchcircuit<br />
SCHEMATICDIAGRAM<br />
Set<br />
Enable Reset<br />
(power connections to gates not<br />
shown for simplicity)<br />
1 / 4 4011<br />
Q<br />
Q<br />
1 / 4 4011<br />
6 V<br />
10<br />
kΩ<br />
10<br />
kΩ<br />
1 / 4 4011<br />
1 / 4 4011<br />
470<br />
Ω<br />
ILLUSTRATION
342 CHAPTER7. DIGITALINTEGRATEDCIRCUITS<br />
+ - 4011<br />
INSTRUCTIONS<br />
AlthoughthiscircuitusesNANDgatesinsteadofNORgates,itsbehaviorisidenticalto<br />
thatoftheNORgateS-Rlatch(a”high”SetinputdrivesQ”high,”anda”high”Resetinput<br />
drivesQ-not”high”),exceptforthepresenceofathirdinput: theEnable. Thepurposeof<br />
theEnableinputistoenableordisabletheSetandResetinputsfromhavingeffectoverthe<br />
circuit’soutputstatus.WhentheEnableinputis”high,”thecircuitactsjustliketheNORgate<br />
S-Rlatch.WhentheEnableinputis”low,”theSetandResetinputsaredisabledandhaveno<br />
effectwhatsoeverontheoutputs,leavingthecircuitinitslatchedstate.<br />
Thiskindoflatchcircuit(alsocalledagatedS-Rlatch),maybeconstructedfromtwoNOR<br />
gatesandtwoANDgates,buttheNANDgatedesigniseasiertobuildsinceitmakesuseofall<br />
fourgatesinasingleintegratedcircuit.<br />
E<br />
R<br />
S<br />
Q<br />
Q<br />
E<br />
0<br />
0<br />
0<br />
0<br />
1<br />
1<br />
1<br />
1<br />
S R<br />
0 0<br />
0 1<br />
1 0<br />
1 1<br />
0 0<br />
0 1<br />
1 0<br />
1 1<br />
Q Q<br />
latch latch<br />
latch latch<br />
latch latch<br />
latch latch<br />
latch latch<br />
0 1<br />
1 0<br />
0 0
7.5. NANDGATES-RFLIP-FLOP 343<br />
7.5 NANDgateS-Rflip-flop<br />
PARTSANDMATERIALS<br />
• 4011quadNANDgate(RadioShackcatalog#276-2411)<br />
• 4001quadNORgate(RadioShackcatalog#276-2401)<br />
• Eight-positionDIPswitch(RadioShackcatalog#275-1301)<br />
• Ten-segmentbargraphLED(RadioShackcatalog#276-081)<br />
• One6voltbattery<br />
• Three10kΩresistors<br />
• Two470 Ωresistors<br />
Caution!The4011ICisCMOS,andthereforesensitivetostaticelectricity!<br />
Althoughthepartslistcallsforaten-segmentLEDunit,theillustrationshowstwoindividualLEDsbeingusedinstead.<br />
Thisisduetolackofroomonmybreadboardtomountthe<br />
switchassembly,twointegratedcircuits,andthebargraph. Ifyouhaveroomonyourbreadboard,feelfreetousethebargraphascalledforinthepartslist,andasshowninpriorlatch<br />
circuits.<br />
CROSS-REFERENCES<br />
LessonsInElectricCircuits,Volume4,chapter3:”LogicGates”<br />
LessonsInElectricCircuits,Volume4,chapter10:”Multivibrators”<br />
LEARNINGOBJECTIVES<br />
• Thedifferencebetweenagatedlatchandaflip-flop<br />
• Howtobuilda”pulsedetector”circuit<br />
• Learntheeffectsofswitchcontact”bounce”ondigitalcircuits<br />
SCHEMATICDIAGRAM
344 CHAPTER7. DIGITALINTEGRATEDCIRCUITS<br />
Set<br />
Clock<br />
Reset<br />
(power connections to gates not<br />
shown for simplicity)<br />
1 / 4 4011<br />
Q<br />
Q<br />
1 / 4 4011<br />
6 V<br />
10<br />
kΩ<br />
10<br />
kΩ<br />
1 / 4 4011<br />
1 / 4 4011<br />
470<br />
Ω<br />
1 / 4 4001<br />
1 / 4 4001<br />
1 / 4 4001<br />
1 / 4 4001<br />
ILLUSTRATION<br />
+ - 4001 4011<br />
INSTRUCTIONS<br />
Theonlydifferencebetweenagated(orenabled)latchandaflip-flopisthataflip-flopis<br />
enabledonlyontherisingorfallingedgeofa”clock”signal,ratherthanfortheentireduration<br />
ofa”high”enablesignal. Convertinganenabledlatchintoaflip-flopsimplyrequiresthata<br />
”pulsedetector”circuitbeaddedtotheEnableinput,sothattheedgeofaclockpulsegenerates<br />
abrief”high”Enablepulse:
7.5. NANDGATES-RFLIP-FLOP 345<br />
Input<br />
Output<br />
Delayed input<br />
Input<br />
Delayed input<br />
Output<br />
Brief period of time when<br />
both inputs of the NOR gate<br />
are low<br />
ThesingleNORgateandthreeinvertergatescreatethiseffectbyexploitingthepropagationdelaytimeofmultiple,cascadedgates.<br />
Inthisexperiment,IusethreeNORgateswith<br />
paralleledinputstocreatethreeinverters,thususingallfourNORgatesofa4001integrated<br />
circuit:<br />
Pulse detector circuit<br />
Input<br />
1 / 4 4001<br />
Output<br />
1 / 4 4001<br />
1 / 4 4001<br />
1 / 4 4001<br />
Normally,whenusingaNORgateasaninverter,oneinputwouldbegroundedwhilethe<br />
otheractsastheinverterinput,tominimizeinputcapacitanceandincreasespeed. Here,<br />
however,slowresponseisdesired,andsoIparalleltheNORinputstomakeinvertersrather<br />
thanusethemoreconventionalmethod.<br />
Pleasenotethatthisparticularpulsedetectorcircuitproducesa”high”outputpulseat<br />
everyfallingedgeoftheclock(input)signal. Thismeansthattheflip-flopcircuitshouldbe<br />
responsivetotheSetandResetinputstatesonlywhenthemiddleswitchismovedfrom”on”<br />
to”off,”notfrom”off”to”on.”<br />
Whenyoubuildthiscircuit,though,youmaydiscoverthattheoutputsrespondtoSetand<br />
ResetinputsignalsduringbothtransitionsoftheClockinput,notjustwhenitisswitchedfrom<br />
a”high”statetoa”low”state. Thereasonforthisiscontactbounce:theeffectofamechanicalswitchrapidlymaking-and-breakingwhenitscontactsarefirstclosed,duetotheelastic<br />
collisionofthemetalcontactpads.InsteadoftheClockswitchproducingasingle,cleanlowto-highsignaltransitionwhenclosed,therewillmostlikelybeseverallow-high-low”cycles”<br />
asthecontactpads”bounce”uponoff-to-onactuation.Thefirsthigh-to-lowtransitioncaused<br />
bybouncingwilltriggerthepulsedetectorcircuit,enablingtheS-Rlatchforthatmomentin<br />
time,makingitresponsivetotheSetandResetinputs.<br />
Ideally,ofcourse,switchesareperfectandbounce-free.Intherealworld,though,contact<br />
bounceisaverycommonproblemfordigitalgatecircuitsoperatedbyswitchinputs,andmust
346 CHAPTER7. DIGITALINTEGRATEDCIRCUITS<br />
beunderstoodwellifitistobeovercome.
7.6. LEDSEQUENCER 347<br />
7.6 LEDsequencer<br />
PARTSANDMATERIALS<br />
• 4017decadecounter/divider(RadioShackcatalog#276-2417)<br />
• 555timerIC(RadioShackcatalog#276-1723)<br />
• Ten-segmentbargraphLED(RadioShackcatalog#276-081)<br />
• OneSPSTswitch<br />
• One6voltbattery<br />
• 10kΩresistor<br />
• 1MΩresistor<br />
• 0.1 µFcapacitor(RadioShackcatalog#272-135orequivalent)<br />
• Couplingcapacitor,0.047to0.001 µF<br />
• Ten470 Ωresistors<br />
• Audiodetectorwithheadphones<br />
Caution!The4017ICisCMOS,andthereforesensitivetostaticelectricity!<br />
Anysingle-pole,single-throwswitchisadequate.Ahouseholdlightswitchwillworkfine,<br />
andisreadilyavailableatanyhardwarestore.<br />
Theaudiodetectorwillbeusedtoassesssignalfrequency.Ifyouhaveaccesstoanoscilloscope,theaudiodetectorisunnecessary.<br />
CROSS-REFERENCES<br />
LessonsInElectricCircuits,Volume4,chapter3:”LogicGates”<br />
LessonsInElectricCircuits,Volume4,chapter4:”Switches”<br />
LessonsInElectricCircuits,Volume4,chapter11:”Counters”<br />
LEARNINGOBJECTIVES<br />
• Useofa555timercircuittoproduce”clock”pulses(astablemultivibrator)<br />
• Useofa4017decadecounter/dividercircuittoproduceasequenceofpulses<br />
• Useofa4017decadecounter/dividercircuitforfrequencydivision<br />
• Usingafrequencydividerandtimepiece(watch)tomeasurefrequency<br />
• Purposeofa”pulldown”resistor<br />
• Learntheeffectsofswitchcontact”bounce”ondigitalcircuits<br />
• Useofa555timercircuitto”debounce”amechanicalswitch(monostablemultivibrator)
348 CHAPTER7. DIGITALINTEGRATEDCIRCUITS<br />
SCHEMATICDIAGRAM<br />
1 MΩ<br />
V cc<br />
555<br />
Disch<br />
RST<br />
Out<br />
Clk ClkEn Rst Carry<br />
V DD 4017 Gnd<br />
0 1 2 3 4 5 6 7 8 9<br />
6 V<br />
0.1 µF<br />
Thresh<br />
Trig<br />
Gnd<br />
Ctrl<br />
Ten-segment<br />
LED bargraph<br />
470 Ω each<br />
ILLUSTRATION<br />
+ - 555 4017<br />
INSTRUCTIONS<br />
Themodel4017integratedcircuitisaCMOScounterwithtenoutputterminals. Oneof<br />
thesetenterminalswillbeina”high”stateatanygiventime,withallothersbeing”low,”<br />
givinga”one-of-ten”outputsequence. Iflow-to-highvoltagepulsesareappliedtothe”clock”<br />
(Clk)terminalofthe4017,itwillincrementitscount,forcingthenextoutputintoa”high”<br />
state.<br />
Witha555timerconnectedasanastablemultivibrator(oscillator)oflowfrequency,the<br />
4017willcyclethroughitsten-countsequence,lightingupeachLED,oneatatime,and”recycling”backtothefirstLED.Theresultisavisuallypleasingsequenceofflashinglights.Feel<br />
freetoexperimentwithresistorandcapacitorvaluesonthe555timertocreatedifferentflash<br />
rates.<br />
Trydisconnectingthejumperwireleadingfromthe4017’s”Clock”terminal(pin#14)tothe<br />
555’s”Output”terminal(pin#3)whereitconnectstothe555timerchip,andholditsendin<br />
yourhand.Ifthereissufficient60Hzpower-line”noise”aroundyou,the4017willdetectitas<br />
afastclocksignal,causingtheLEDstoblinkveryrapidly.<br />
Twoterminalsonthe4017chip,”Reset”and”ClockEnable,”aremaintainedina”low”state<br />
bymeansofaconnectiontothenegativesideofthebattery(ground).Thisisnecessaryifthe<br />
chipistocountfreely. Ifthe”Reset”terminalismade”high,”the4017’soutputwillbereset
7.6. LEDSEQUENCER 349<br />
backto0(pin#3”high,”allotheroutputpins”low”).Ifthe”ClockEnable”ismade”high,”the<br />
chipwillstoprespondingtotheclocksignalandpauseinitscountingsequence.<br />
Ifthe4017’s”Reset”terminalisconnectedtooneofitstenoutputterminals,itscounting<br />
sequencewillbecutshort,ortruncated. Youmayexperimentwiththisbydisconnectingthe<br />
”Reset”terminalfromground,thenconnectingalongjumperwiretothe”Reset”terminalfor<br />
easyconnectiontotheoutputsattheten-segmentLEDbargraph. Noticehowmany(orhow<br />
few)LEDslightupwiththe”Reset”connectedtoanyoneoftheoutputs:<br />
touch end of long jumper wire<br />
to an LED terminal<br />
disconnect<br />
+ - 555 4017<br />
Counterssuchasthe4017maybeusedasdigitalfrequencydividers,totakeaclocksignal<br />
andproduceapulseoccurringatsomeintegerfactoroftheclockfrequency.Forexample,ifthe<br />
clocksignalfromthe555timeris200Hz,andthe4017isconfiguredforafull-countsequence<br />
(the”Reset”terminalconnectedtoground,givingafull,ten-stepcount),asignalwithaperiod<br />
tentimesaslong(20Hz)willbepresentatanyofthe4017’soutputterminals.Inotherwords,<br />
eachoutputterminalwillcycleonceforeverytencyclesoftheclocksignal: afrequencyten<br />
timesasslow.<br />
Toexperimentwiththisprinciple,connectyouraudiodetectorbetweenoutput0(pin#3)of<br />
the4017andground,throughaverysmallcapacitor(0.047 µFto0.001 µF).Thecapacitoris<br />
usedfor”coupling”ACsignalsonly,tothatyoumayaudiblydetectpulseswithoutplacinga<br />
DC(resistive)loadonthecounterchipoutput.Withthe4017”Reset”terminalgrounded,you<br />
willhaveafull-countsequence,andyouwillheara”click”intheheadphoneseverytimethe<br />
”0”LEDlightsup,correspondingto1/10ofthe555’sactualoutputfrequency:
350 CHAPTER7. DIGITALINTEGRATEDCIRCUITS<br />
+ - 555 4017<br />
headphones<br />
Sensitivity<br />
plug<br />
Infact,knowingthismathematicalrelationshipbetweenclicksheardintheheadphone<br />
andtheclockfrequencyallowsustomeasuretheclockfrequencytoafairdegreeofprecision.<br />
Usingastopwatchorothertimepiece,countthenumberofclicksheardinonefullminute<br />
whileconnectedtothe4017’s”0”output. Usinga1MΩresistorand0.1 µFcapacitorinthe<br />
555timingcircuit,andapowersupplyvoltageof13volts(insteadof6),Icounted79clicksin<br />
oneminutefrommycircuit.Yourcircuitmayproduceslightlydifferentresults.Multiplythe<br />
numberofpulsescountedatthe”0”outputby10toobtainthenumberofcyclesproducedby<br />
the555timerduringthatsametime(mycircuit:79x10=790cycles). Dividethisnumber<br />
by60toobtainthenumberoftimercycleselapsedineachsecond(mycircuit:790/60=13.17).<br />
ThisfinalfigureistheclockfrequencyinHz.<br />
Now,leavingonetestprobeoftheaudiodetectorconnectedtoground,taketheothertest<br />
probe(theonewiththecouplingcapacitorconnectedinseries)andconnectittopin#3ofthe<br />
555timer.Thebuzzingyouhearistheundividedclockfrequency:
7.6. LEDSEQUENCER 351<br />
+ - 555 4017<br />
headphones<br />
Sensitivity<br />
plug<br />
Byconnectingthe4017’s”Reset”terminaltooneoftheoutputterminals,atruncatedsequencewillresult.<br />
Ifweareusingthe4017asafrequencydivider,thismeanstheoutput<br />
frequencywillbeadifferentfactoroftheclockfrequency:1/9,1/8,1/7,1/6,1/5,1/4,1/3,or1/2,<br />
dependingonwhichoutputterminalweconnectthe”Reset”jumperwireto. Re-connectthe<br />
audiodetectortestprobetooutput”0”ofthe4017(pin#3),andconnectthe”Reset”terminal<br />
jumpertothesixthLEDfromtheleftonthebargraph. Thisshouldproducea1/5frequency<br />
divisionratio:
352 CHAPTER7. DIGITALINTEGRATEDCIRCUITS<br />
+ - 555 4017<br />
headphones<br />
4017 output frequency is<br />
1/5 of input (clock) frequency<br />
Sensitivity<br />
plug<br />
Countingthenumberofclicksheardinoneminuteagain,youshouldobtainanumber<br />
approximatelytwiceaslargeaswhatwascountedwiththe4017configuredfora1/10ratio,<br />
because1/5istwiceaslargearatioas1/10. Ifyoudonotobtainacountthatisexactly<br />
twicewhatyouobtainedbefore,itisbecauseoferrorinherenttothemethodofcountingcycles:<br />
coordinatingyoursenseofhearingwiththedisplayofastopwatchorothertime-keepingdevice.<br />
Tryreplacingthe1MΩtimingresistorinthe555circuitwithoneofgreatlylesservalue,<br />
suchas10kΩ. Thiswillincreasetheclockfrequencydrivingthe4017chip. Usetheaudio<br />
detectortolistentothedividedfrequencyatpin#3ofthe4017,notingthedifferenttones<br />
producedasyoumovethe”Reset”jumperwiretodifferentoutputs,creatingdifferentfrequency<br />
divisionratios.Seeifyoucanproduceoctavesbydividingtheoriginalfrequencyby2,thenby<br />
4,andthenby8(eachdescendingoctaverepresentsone-halfthepreviousfrequency).Octaves<br />
arereadilydistinguishedfromotherdividedfrequenciesbytheirsimilarpitchestotheoriginal<br />
tone.<br />
Afinallessonthatmaybelearnedfromthiscircuitisthatofswitchcontact”bounce.”For<br />
this,youwillneedaswitchtoprovideclocksignalstothe4017chip,insteadofthe555timer.<br />
Re-connectthe”Reset”jumperwiretogroundtoenableafullten-stepcountsequence,and<br />
disconnectthe555’soutputfromthe4017’s”Clock”inputterminal.Connectaswitchinseries<br />
witha10kΩpulldownresistor,andconnectthisassemblytothe4017”Clock”inputasshown:
7.6. LEDSEQUENCER 353<br />
Clk<br />
ClkEn Rst<br />
V DD 4017<br />
Carry<br />
Gnd<br />
0 1 2 3 4 5 6 7 8 9<br />
6 V<br />
10 kΩ<br />
Ten-segment<br />
LED bargraph<br />
470 Ω each<br />
+ - 555 4017<br />
connect<br />
disconnect<br />
connect<br />
connect<br />
Thepurposeofa”pulldown”resistoristoprovideadefinite”low”logicstatewhentheswitch<br />
contactopens. Withoutthisresistorinplace,the4017’s”Clock”inputwirewouldbefloating<br />
whenevertheswitchcontactwasopened,leavingitsusceptibletointerferencefromstraystatic<br />
voltagesorelectrical”noise,”eitheronecapableofmakingthe4017countrandomly. With<br />
thepulldownresistorinplace,the4017’s”Clock”inputwillhaveadefinite,albeitresistive,<br />
connectiontoground,providingastable”low”logicstatethatprecludesanyinterferencefrom<br />
staticelectricityor”noise”coupledfromnearbyACcircuitwiring.<br />
Actuatetheswitchonandoff,notingtheactionoftheLEDs. Witheachoff-to-onswitch<br />
transition,the4017shouldincrementonceinitscount.However,youmaynoticesomestrange<br />
behavior: sometimes,theLEDsequencewill”skip”oneorevenseveralstepswithasingle<br />
switchclosure. Whyisthis? Itisduetoveryrapid,mechanical”bouncing”oftheswitch<br />
contacts.Whentwometalliccontactsarebroughttogetherrapidlyasdoeshappeninsidemost<br />
switches,therewillbeanelasticcollision. Thiscollisionresultsinthecontactsmakingand<br />
breakingveryrapidlyasthey”bounce”offoneanother. Normally,this”bouncing”ismuchto<br />
rapidforyoutoseeitseffects,butinadigitalcircuitsuchasthiswherethecounterchipisable
354 CHAPTER7. DIGITALINTEGRATEDCIRCUITS<br />
torespondtoveryquickclockpulses,these”bounces”areinterpretedasdistinctclocksignals,<br />
andthecountincrementedaccordingly.<br />
Onewaytocombatthisproblemistouseatimingcircuittoproduceasinglepulseforany<br />
numberofinputpulsesignalsreceivedwithinashortamountoftime. Thecircuitiscalled<br />
amonostablemultivibrator,andanytechniqueeliminatingthefalsepulsescausedbyswitch<br />
contact”bounce”iscalleddebouncing.<br />
The555timercircuitiscapableoffunctioningasadebouncer,ifthe”Trigger”inputis<br />
connectedtotheswitchassuch:<br />
Using the 555 timer to "debounce" the switch<br />
1 MΩ<br />
V cc<br />
555<br />
Disch<br />
RST<br />
Out<br />
Clk ClkEn Rst Carry<br />
V DD 4017 Gnd<br />
0 1 2 3 4 5 6 7 8 9<br />
6 V<br />
Thresh<br />
Trig<br />
Ctrl<br />
0.1 µF<br />
Gnd<br />
10 kΩ<br />
+ - 555 4017<br />
Pleasenotethatsinceweareusingthe555onceagaintoprovideaclocksignaltothe4017,<br />
wemustre-connectpin#3ofthe555chiptopin#14ofthe4017chip!Also,ifyouhavealtered<br />
thevaluesoftheresistororcapacitorinthe555timercircuit,youshouldreturntotheoriginal<br />
1MΩand0.1 µFcomponents.<br />
Actuatetheswitchagainandnotethecountingbehaviorofthe4017. Thereshouldbe<br />
nomore”skipped”countsastherewerebefore,becausethe555timeroutputsasingle,crisp<br />
pulseforeveryon-to-offactuation(noticetheinversionofoperationhere!)oftheswitch.Itis
7.6. LEDSEQUENCER 355<br />
importantthatthetimingofthe555circuitbeappropriate:thetimetochargethecapacitor<br />
shouldbelongerthanthe”settling”periodoftheswitch(thetimerequiredforthecontacts<br />
tostopbouncing),butnotsolongthatthetimerwould”miss”arapidsequenceofswitch<br />
actuations,iftheyweretooccur.
356 CHAPTER7. DIGITALINTEGRATEDCIRCUITS<br />
7.7 Simplecombinationlock<br />
PARTSANDMATERIALS<br />
• 4001quadNORgate(RadioShackcatalog#276-2401)<br />
• 4070quadXORgate(RadioShackcatalog#900-6906)<br />
• Two,eight-positionDIPswitches(RadioShackcatalog#275-1301)<br />
• Twolight-emittingdiodes(RadioShackcatalog#276-026orequivalent)<br />
• Four1N914”switching”diodes(RadioShackcatalog#276-1122)<br />
• Ten10kΩresistors<br />
• Two470 Ωresistors<br />
• Pushbuttonswitch,normallyopen(RadioShackcatalog#275-1556)<br />
• Two6voltbatteries<br />
Caution!Boththe4001and4070ICsareCMOS,andthereforesensitivetostaticelectricity!<br />
Thisexperimentmaybebuiltusingonlyone8-positionDIPswitch,buttheconceptiseasier<br />
tounderstandiftwoswitchassembliesareused.Theideais,oneswitchactstoholdthecorrect<br />
codeforunlockingthelock,whiletheotherswitchservesasadataentrypointfortheperson<br />
tryingtoopenthelock. Inreallife,ofcourse,theswitchassemblywiththe”key”codeset<br />
onitmustbehiddenfromthesightofthepersonopeningthelock,whichmeansitmustbe<br />
physicallylocatedelsewherefromwherethedataentryswitchassemblyis.Thisrequirestwo<br />
switchassemblies.However,ifyouunderstandthisconceptclearly,youmaybuildaworking<br />
circuitwithonlyone8-positionswitch,usingtheleftfourswitchesfordataentryandtheright<br />
fourswitchestoholdthe”key”code.<br />
Forextraeffect,choosedifferentcolorsofLED:greenfor”Go”andredfor”Nogo.”<br />
CROSS-REFERENCES<br />
LessonsInElectricCircuits,Volume4,chapter3:”LogicGates”<br />
LEARNINGOBJECTIVES<br />
• UsingXORgatesasbitcomparators<br />
• Howtobuildsimplegatefunctionswithdiodesandapullup/downresistor<br />
• UsingNORgatesascontrolledinverters<br />
SCHEMATICDIAGRAM
7.7. SIMPLECOMBINATIONLOCK 357<br />
Vdd "Key code"<br />
switch<br />
No go<br />
470 Ω<br />
470 Ω<br />
10 kΩ<br />
(all)<br />
Vdd<br />
10 kΩ<br />
Go<br />
Vdd<br />
Data entry<br />
switch<br />
10 kΩ<br />
Enter<br />
10 kΩ<br />
(all)<br />
ILLUSTRATION<br />
Data entry<br />
+ -<br />
+ - 4070 4001<br />
Enter<br />
"Key" code<br />
INSTRUCTIONS<br />
ThiscircuitillustratestheuseofXOR(Exclusive-OR)gatesasbitcomparators. Fourof<br />
theseXORgatescomparetherespectivebitsoftwo4-bitbinarynumbers,eachnumber”entered”intothecircuitviaasetofswitches.<br />
Ifthetwonumbersmatch,bitforbit,thegreen<br />
”Go”LEDwilllightupwhenthe”Enter”pushbuttonswitchispressed.Ifthetwonumbersdo<br />
notexactlymatch,thered”Nogo”LEDwilllightupwhenthe”Enter”pushbuttonispressed.
358 CHAPTER7. DIGITALINTEGRATEDCIRCUITS<br />
Becausefourbitsprovidesameresixteenpossiblecombinations,thislockcircuitisnotvery<br />
sophisticated.Ifitwereusedinarealapplicationsuchasahomesecuritysystem,the”Nogo”<br />
outputwouldhavetobeconnectedtosomekindofsirenorotheralarmingdevice,sothatthe<br />
entryofanincorrectcodewoulddeteranunauthorizedpersonfromattemptinganothercode<br />
entry. Otherwise,itwouldnottakemuchtimetotryallcombinations(0000through1111)<br />
untilthecorrectonewasfound!Inthisexperiment,Idonotdescribehowtoworkthiscircuit<br />
intoarealsecuritysystemorlockmechanism,butonlyhowtomakeitrecognizeapre-entered<br />
code.<br />
The”key”codethatmustbematchedatthedataentryswitcharrayshouldbehiddenfrom<br />
view,ofcourse. Ifthiswerepartofarealsecuritysystem,thedataentryswitchassembly<br />
wouldbelocatedoutsidethedoor,andthekeycodeswitchassemblybehindthedoorwiththe<br />
restofthecircuitry. Inthisexperiment,youwilllikelylocatethetwoswitchassemblieson<br />
twodifferentbreadboards,butitisentirelypossibletobuildthecircuitusingjustasingle<br />
(8-position)DIPswitchassembly.Again,thepurposeoftheexperimentisnottomakeareal<br />
securitysystem,butmerelytointroduceyoutotheprincipleofXORgatecodecomparison.<br />
ItisthenatureofanXORgatetooutputa”high”(1)signaliftheinputsignalsarenotthe<br />
samelogicstate.ThefourXORgates’outputterminalsareconnectedthroughadiodenetwork<br />
whichfunctionsasafour-inputORgate:ifanyofthefourXORgatesoutputsa”high”signal–<br />
indicatingthattheenteredcodeandthekeycodearenotidentical–thena”high”signalwill<br />
bepassedontotheNORgatelogic.Ifthetwo4-bitcodesareidentical,thennoneoftheXOR<br />
gateoutputswillbe”high,”andthepull-downresistorconnectedtothecommonsidesofthe<br />
diodeswillprovidea”low”signalstatetotheNORlogic.<br />
TheNORgatelogicperformsasimpletask: preventeitheroftheLEDsfromturningon<br />
ifthe”Enter”pushbuttonisnotpressed.Onlywhenthispushbuttonispressedcaneitherof<br />
theLEDsenergize.IftheEnterswitchispressedandtheXORoutputsareall”low,”the”Go”<br />
LEDwilllightup,indicatingthatthecorrectcodehasbeenentered. IftheEnterswitchis<br />
pressedandanyoftheXORoutputsare”high,”the”Nogo”LEDwilllightup,indicatingthat<br />
anincorrectcodehasbeenentered.Again,ifthiswerearealsecuritysystem,itwouldbewise<br />
tohavethe”Nogo”outputdosomethingthatdetersanunauthorizedpersonfromdiscovering<br />
thecorrectcodebytrial-and-error. Inotherwords,thereshouldbesomesortofpenaltyfor<br />
enteringanincorrectcode.Letyourimaginationguideyourdesignofthisdetail!
7.8. 3-BITBINARYCOUNTER 359<br />
7.8 3-bitbinarycounter<br />
PARTSANDMATERIALS<br />
• 555timerIC(RadioShackcatalog#276-1723)<br />
• One1N914”switching”diode(RadioShackcatalog#276-1122)<br />
• Two10kΩresistors<br />
• One100 µFcapacitor(RadioShackcatalog#272-1028)<br />
• 4027dualJ-Kflip-flop(RadioShackcatalog#900-4394)<br />
• Ten-segmentbargraphLED(RadioShackcatalog#276-081)<br />
• Three470 Ωresistors<br />
• One6voltbattery<br />
Caution!The4027ICisCMOS,andthereforesensitivetostaticelectricity!<br />
CROSS-REFERENCES<br />
LessonsInElectricCircuits,Volume4,chapter10:”Multivibrators”<br />
LessonsInElectricCircuits,Volume4,chapter11:”Counters”<br />
LEARNINGOBJECTIVES<br />
• Usingthe555timerasasquare-waveoscillator<br />
• HowtomakeanasynchronouscounterusingJ-Kflip-flops<br />
SCHEMATICDIAGRAM<br />
10 kΩ<br />
6 V<br />
10<br />
kΩ<br />
V cc<br />
555<br />
Disch<br />
Thresh<br />
Trig<br />
RST<br />
Out<br />
Ctrl<br />
J<br />
C<br />
K<br />
S<br />
Q<br />
Q<br />
J<br />
C<br />
K<br />
S<br />
Q<br />
Q<br />
0.1 µF<br />
Gnd<br />
R<br />
R<br />
(LSB)<br />
(MSB)<br />
470 Ω 470 Ω 470 Ω
360 CHAPTER7. DIGITALINTEGRATEDCIRCUITS<br />
ILLUSTRATION<br />
+ - 555 4027<br />
INSTRUCTIONS<br />
Inasense,thiscircuit”cheats”byusingonlytwoJ-Kflip-flopstomakeathree-bitbinary<br />
counter.Ordinarily,threeflip-flopswouldbeused–oneforeachbinarybit–butinthiscase<br />
wecanusetheclockpulse(555timeroutput)asabitofitsown.Whenyoubuildthiscircuit,<br />
youwillfindthatitisa”down”counter. Thatis,itscountsequencegoesfrom111to110to<br />
101to100to011to010to001to000andthenbackto111.Whileitispossibletoconstruct<br />
an”up”counterusingJ-Kflip-flops,thiswouldrequireadditionalcomponentsandintroduce<br />
morecomplexityintothecircuit.<br />
The555timeroperatesasaslow,square-waveoscillatorwithadutycycleofapproximately<br />
50percent.Thisdutycycleismadepossiblebytheuseofadiodeto”bypass”thelowerresistor<br />
duringthecapacitor’schargingcycle,sothatthechargingtimeconstantisonlyRCandnot<br />
2RCasitwouldbewithoutthediodeinplace.<br />
Itishighlyrecommended,inthisexperimentasinallexperiments,tobuildthecircuitin<br />
stages:identifyportionsofthecircuitwithspecificfunctions,andbuildthoseportionsoneata<br />
time,testingeachoneandverifyingitsperformancebeforebuildingthenext.Averycommon<br />
mistakeofnewelectronicsstudentsistobuildanentirecircuitatoncewithouttestingsections<br />
ofitduringtheconstructionprocess,andthenbefacedwiththepossibilityofseveralproblems<br />
simultaneouslywhenitcomestimetofinallyapplypowertoit.Rememberthatasmallamount<br />
ofextraattentionpaidtodetailnearthebeginningofaprojectisworthanenormousamount<br />
oftroubleshootingworkneartheend! Studentswhomakethemistakeofnottestingcircuit<br />
portionsbeforeattemptingtooperatetheentirecircuitoften(falsely)thinkthatthetimeit<br />
wouldtaketotestthosesectionsisnotworthit,andthenspenddaystryingtofigureoutwhat<br />
theproblem(s)mightbewiththeirexperiment.<br />
Followingthisphilosophy,buildthe555timercircuitfirst,beforeevenpluggingthe4027<br />
ICintothebreadboard.Connectthe555’soutput(pin#3)tothe”LeastSignificantBit”(LSB)<br />
LED,sothatyouhavevisualindicationofitsstatus.Makesurethattheoutputoscillatesina<br />
slow,square-wavepattern(LEDis”lit”foraboutaslongasitis”off”inacycle),andthatitis<br />
areliablesignal(noerraticbehavior,nounexplainedpauses).Ifthe555timerisnotworking<br />
properly,neitherwilltherestofthecountercircuit! Oncethetimercircuithasbeenproven<br />
good,proceedtoplugthe4027ICintothebreadboardandcompletetherestofthenecessary<br />
connectionsbetweenit,the555timercircuit,andtheLEDassembly.
7.9. 7-SEGMENTDISPLAY 361<br />
7.9 7-segmentdisplay<br />
PARTSANDMATERIALS<br />
• 4511BCD-to-7seglatch/decoder/driver(RadioShackcatalog#900-4437)<br />
• Common-cathode7-segmentLEDdisplay(RadioShackcatalog#276-075)<br />
• Eight-positionDIPswitch(RadioShackcatalog#275-1301)<br />
• Four10kΩresistors<br />
• Seven470 Ωresistors<br />
• One6voltbattery<br />
Caution!The4511ICisCMOS,andthereforesensitivetostaticelectricity!<br />
CROSS-REFERENCES<br />
LessonsInElectricCircuits,Volume4,chapter9:”CombinationalLogicFunctions”<br />
LEARNINGOBJECTIVES<br />
• Howtousethe45117-segmentdecoder/displaydriverIC<br />
• GainfamiliaritywiththeBCDcode<br />
• Howtouse7-segmentLEDassembliestocreatedecimaldigitdisplays<br />
• Howtoidentifyanduseboth”active-low”and”active-high”logicinputs<br />
SCHEMATICDIAGRAM<br />
6 V<br />
(LSB)<br />
(MSB)<br />
10 kΩ<br />
each<br />
V DD<br />
LT<br />
BI<br />
4511<br />
A<br />
a<br />
B<br />
b<br />
C<br />
c<br />
D d<br />
e<br />
f<br />
g<br />
LE<br />
Gnd<br />
470 Ω<br />
each<br />
f<br />
e<br />
Cathode<br />
a<br />
g<br />
d<br />
b<br />
c
362 CHAPTER7. DIGITALINTEGRATEDCIRCUITS<br />
ILLUSTRATION<br />
+ - 4511<br />
INSTRUCTIONS<br />
Thisexperimentismoreofanintroductiontothe4511decoder/displaydriverICthanitis<br />
alessoninhowto”buildup”adigitalfunctionfromlower-levelcomponents.Since7-segment<br />
displaysareverycommoncomponentsofdigitaldevices,itisgoodtobefamiliarwiththe<br />
”driving”circuitsbehindthem,andthe4511isagoodexampleofatypicaldriverIC.<br />
Itsoperatingprincipleistoinputafour-bitBCD(Binary-CodedDecimal)value,andenergizetheproperoutputlinestoformthecorrespondingdecimaldigitonthe7-segmentLED<br />
display.TheBCDinputsaredesignatedA,B,C,andDinorderfromleast-significanttomostsignificant.Outputsarelabeleda,b,c,d,e,f,andg,eachlettercorrespondingtoastandardized<br />
segmentdesignationfor7-segmentdisplays. Ofcourse,sinceeachLEDsegmentrequiresits<br />
owndroppingresistor,wemustuseseven470 Ωresistorsplacedinseriesbetweenthe4511’s<br />
outputterminalsandthecorrespondingterminalsofthedisplayunit.<br />
Most7-segmentdisplaysalsoprovideforadecimalpoint(sometimestwo!),aseparateLED<br />
andterminaldesignatedforitsoperation.AllLEDsinsidethedisplayunitaremadecommon<br />
toeachotherononeside,eithercathodeoranode. The4511displaydriverICrequiresa<br />
common-cathode7-segmentdisplayunit,andsothatiswhatisusedhere.<br />
Afterbuildingthecircuitandapplyingpower,operatethefourswitchesinabinarycounting<br />
sequence(0000to1111),notingthe7-segmentdisplay.A0000inputshouldresultinadecimal<br />
”0”display,a0001inputshouldresultinadecimal”1”display,andsoonthrough1001(decimal<br />
”9”).Whathappensforthebinarynumbers1010(10)through1111(15)?Readthedatasheet<br />
onthe4511ICandseewhatthemanufacturerspecifiesforoperationaboveaninputvalueof<br />
9.IntheBCDcode,thereisnorealmeaningfor1010,1011,1100,1101,1110,or1111.These<br />
arebinaryvaluesbeyondtherangeofasingledecimaldigit,andsohavenofunctioninaBCD<br />
system.The4511ICisbuilttorecognizethis,andoutput(ornotoutput!)accordingly.<br />
Threeinputsonthe4511chiphavebeenpermanentlyconnectedtoeitherV dd orground:<br />
the”LampTest,””BlankingInput,”and”LatchEnable.”Tolearnwhattheseinputsdo,remove<br />
theshortjumpersconnectingthemtoeitherpowersupplyrail(oneatatime!),andreplace<br />
theshortjumperwithalongeronethatcanreachtheotherpowersupplyrail. Forexample,<br />
removetheshortjumperconnectingthe”LatchEnable”input(pin#5)toground,andreplace<br />
itwithalongjumperwirethatcanreachallthewaytotheV dd powersupplyrail.Experiment<br />
withmakingthisinput”high”and”low,”observingtheresultsonthe7-segmentdisplayasyou<br />
altertheBCDcodewiththefourinputswitches.Afteryou’velearnedwhattheinput’sfunction
7.9. 7-SEGMENTDISPLAY 363<br />
is,connectittothepowersupplyrailenablingnormaloperation,andproceedtoexperiment<br />
withthenextinput(either”LampTest”or”BlankingInput”).<br />
Onceagain,themanufacturer’sdatasheetwillbeinformativeastothepurposeofeachof<br />
thesethreeinputs. Notethatthe”LampTest”(LT)and”BlankingInput”(BI)inputlabels<br />
arewrittenwithbooleancomplementationbarsovertheabbreviations.Barsymbolsdesignate<br />
theseinputsasactive-low,meaningthatyoumustmakeeachone”low”inordertoinvoke<br />
itsparticularfunction.Makinganactive-lowinput”high”placesthatparticularinputintoa<br />
”passive”statewhereitsfunctionwillnotbeinvoked. Conversely,the”LatchEnable”(LE)<br />
inputhasnocomplementationbarwrittenoveritsabbreviation,andcorrespondinglyitis<br />
shownconnectedtoground(”low”)intheschematicsoastonotinvokethatfunction. The<br />
”LatchEnable”inputisanactive-highinput,whichmeansitmustbemade”high”(connected<br />
toV dd )inordertoinvokeitsfunction.
364 CHAPTER7. DIGITALINTEGRATEDCIRCUITS
Chapter8<br />
555TIMERCIRCUITS<br />
Contents<br />
8.1 The555IC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .365<br />
8.2 555SchmittTrigger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .366<br />
8.3 555HYSTERETICOSCILLATOR . . . . . . . . . . . . . . . . . . . . . . . . .370<br />
8.4 555MONOSTABLEMULTIVIBRATOR. . . . . . . . . . . . . . . . . . . . . .374<br />
8.5 CMOS555LONGDURATIONMINIMUMPARTSREDLEDFLASHER .380<br />
8.6 CMOS555LONGDURATIONBLUELEDFLASHER. . . . . . . . . . . . .385<br />
8.7 CMOS555LONGDURATIONFLYBACKLEDFLASHER . . . . . . . . . .389<br />
8.8 HOWTOMAKEANINDUCTOR. . . . . . . . . . . . . . . . . . . . . . . . . .392<br />
8.9 CMOS555LONGDURATIONREDLEDFLASHER. . . . . . . . . . . . . .395<br />
Originalauthor:BillMarsden<br />
8.1 The555IC<br />
The555integratedcircuitisthemostpopularchipevermanufactured.Independentlymanufacturedbymorethan10manufacturers,stillincurrentproduction,andalmost40yearsold,<br />
thislittlecircuithaswithstoodthetestoftime.Ithasbeenredesigned,improved,andreconfiguredinmanyways,yettheoriginaldesigncanbeboughtfrommanyvendors.Thedesignof<br />
thischipwasrightthefirsttime.<br />
Originallyconceivedin1970andcreatedbyHansR.Camenzindin1971,over1billion<br />
oftheseICsweremadein2003withnoapparentreductionindemand. Ithasbeenusedin<br />
everythingfromtoystospacecraft.Duetoitsversatility,availability,andlowcostitremainsa<br />
hobbyistfavorite.<br />
Oneofthesecretstoitssuccessisitisatrueblackbox,itssymbolizedschematicissimple<br />
andaccurateenoughthatdesignsusingthissimplificationasareferencetendtoworkfirst<br />
time.Youdon’tneedtounderstandeverytransistorinthebaseschematictomakeitwork.<br />
365
366 CHAPTER8. 555TIMERCIRCUITS<br />
Ithasbeenusedtoderivethe556,adual555,eachindependentoftheotherinone14<br />
pinpackage,andistheinspirationofthe558,aquadtimerina16pinpackage. Whatfew<br />
weakpointstheoriginaldesignhashavebeenaddressedbyredesignsintoCMOStechnology,<br />
withitsdramaticallyreducedcurrentandexpandedvoltagerequirements,andyettheoriginal<br />
versionremains.<br />
Originallyconceivedasasimpletimer,the555hasbeenusedforoscillators,waveform<br />
generators,VCO’s,FMdiscrimination,andalotmore.Itreallyisanallpurposecircuit.<br />
SOURCES<br />
• The555TimerIC-AnInterviewwithHansCamenzind(http://semiconductormuseum<br />
.com/Transistors/LectureHall/Camenzind/Camenzind Index.htm)<br />
• 555Tutorial(http://www.sentex.ca/˜mec1995/gadgets/555/555.html)<br />
• 555TimerICEncyclopediaArticle(http://www.nationmaster.com/encyclopedia/<br />
555-timer-IC)<br />
8.2 555SchmittTrigger<br />
PARTSANDMATERIALS<br />
• One9VBattery<br />
• BatteryClip(RadioShackcatalog#270-325)<br />
• MiniHookClips(solderedtoBatteryClip,RadioShackcatalog#270-372)<br />
• OnePotentiometer,10KΩ,15-Turn(RadioShackcatalog#271-343)<br />
• One555timerIC(RadioShackcatalog#276-1723)<br />
• Oneredlight-emittingdiode(RadioShackcatalog#276-041orequivalent)<br />
• Onegreenlight-emittingdiode(RadioShackcatalog#276-022orequivalent)<br />
• Two1KΩResistors<br />
• OneDVM(DigitalVoltMeter)orVOM(VoltOhmMeter)<br />
CROSS-REFERENCES<br />
LessonsInElectricCircuits,Volume3,chapter8:“PositiveFeedback”<br />
LessonsInElectricCircuits,Volume4,chapter3:“LogicSignalVoltageLevels”<br />
LEARNINGOBJECTIVES<br />
• LearnhowaSchmittTriggerworks<br />
• Howtousethe555timerasanSchmittTrigger
8.2. 555SCHMITTTRIGGER 367<br />
SCHEMATICDIAGRAM<br />
SchmittTriggershaveaconventiontoshowagatethatisalsoaSchmittTrigger,shown<br />
below.<br />
Thesameschematicredrawntoreflectthisconventionlookssomethinglikethis:<br />
ILLUSTRATION
368 CHAPTER8. 555TIMERCIRCUITS<br />
INSTRUCTIONS<br />
The555timerisprobablyoneofthemoreversatile”blackbox”chips.Its3resistorvoltage<br />
divider,2comparators,andbuiltinsetresetflipfloparewiredtoformaSchmittTriggerinthis<br />
design.Itsinterestingtonotethattheconfigurationisntevenclosetotheopampconfiguration<br />
shownelsewhere,buttheendresultisidentical.<br />
Tryadjustingthepotentiometeruntilthelightsflipstates,thenmeasurethevoltage.Comparethisvoltagetothepowersupplyvoltage.<br />
Adjustthepotentiometertheotherwayuntil<br />
theLEDsflipstatesagain,andmeasurethevoltage.Howclosetothe1/3and2/3marksdid<br />
youget?<br />
Trysubstitutingthe9Vbatterywitha6voltbattery,ortwo6voltbatteries,andseehow<br />
closethethresholdsaretothe1/3and2/3marks.<br />
SchmittTriggersareafundamentalcircuitwithseveraluses. Oneissignalprocessing,<br />
theycanpulldigitaldataoutofsomeextremelynoisyenvironments. Otherbiguseswillbe<br />
showninfollowingprojects,suchasanextremelysimpleRCoscillator.<br />
THEORYOFOPERATION<br />
ThedefiningcharacteristicofanySchmittTriggerisitshysteresis.Inthiscaseitis1/3and<br />
2/3ofthepowersupplyvoltage,definedbythebuiltinresistorvoltagedivideronthe555.The<br />
builtincomparatorsC1andC2comparetheinputvoltagetothereferencesprovidedbythe<br />
voltagedividerandusethecomparisontotripthebuiltinflipflop,whichdrivestheoutput<br />
driver,anothernicefeatureofthe555. The555candriveupto200maoffeithersideofthe<br />
powersupplyrail,theoutputdrivercreatesaverylowconductionpathtoeithersideofthe<br />
powersupplyconnections.Thecircuit”shorts”eachsideoftheLEDcircuit,leavingtheother<br />
sidetolightup.
8.2. 555SCHMITTTRIGGER 369<br />
The5KΩresistorsarenotveryaccurate.ItisinterestingtonotethatICfabricationdoesn’t<br />
generallyallowprecisionresistors,buttheresistorscomparedtoeachotherareextremelyclose<br />
invalue,whichiscriticaltothecircuitsoperation.
370 CHAPTER8. 555TIMERCIRCUITS<br />
8.3 555HYSTERETICOSCILLATOR<br />
PARTSANDMATERIALS<br />
• One9VBattery<br />
• BatteryClip(RadioShackcatalog#270-325)<br />
• MiniHookClips(solderedtoBatteryClip,RadioShackcatalog#270-372)<br />
• U1-555timerIC(RadioShackcatalog#276-1723)<br />
• D1-Redlight-emittingdiode(RadioShackcatalog#276-041orequivalent)<br />
• D2-Greenlight-emittingdiode(RadioShackcatalog#276-022orequivalent)<br />
• R1,R2-1KΩ1/4WResistors<br />
• R3-10KΩ,15-TurnPotentiometer(RadioShackcatalog#271-343)<br />
• R4-10 Ω1/4WResistor<br />
• C1-1µFCapacitor(RadioShackcatalog272-1434orequivalent)<br />
• C1-100 µFCapacitor(RadioShackcatalog272-1028orequivalent)<br />
CROSS-REFERENCES<br />
LessonsInElectricCircuitsVolume1,chapter16:Voltageandcurrentcalculations<br />
LessonsInElectricCircuits,Volume1,chapter16:Solvingforunknowntime<br />
LessonsInElectricCircuits,Volume4,chapter10:Multivibrators<br />
LessonsinElectricCircuits,Volume3,chapter8:PositiveFeedback<br />
LEARNINGOBJECTIVES<br />
• LearnhowtouseaSchmittTriggerforasimpleRCOscillator<br />
• LearnapracticalapplicationforaRCtimeconstant<br />
• Learnoneofseveral555timerAstableMultivibratorConfigurations<br />
SCHEMATICDIAGRAM<br />
Hereisonewayofdrawingtheschematic:
8.3. 555HYSTERETICOSCILLATOR 371<br />
Asmentionedinthepreviousexperiment,thereisalsoanotherconvention,shownbelow:<br />
ILLUSTRATION
372 CHAPTER8. 555TIMERCIRCUITS<br />
INSTRUCTIONS<br />
ThisisoneofthemostbasicRCoscillators. Itissimpleandverypredictable. AnyinvertingSchmittTriggerwillworkinthisdesign,althoughthefrequencywillshiftsomewhat<br />
dependingonthehysteresisofthegate.<br />
Thiscircuithasalowerendfrequencyof0.7Hertz,whichmeanseachLEDwillalternate<br />
andbelitforjustunderasecondeach. Asyouturnthepotentiometercounterclockwisethe<br />
frequencywillincrease,goingwellintothehighendaudiorange.Youcanverifythiswiththe<br />
AudioDetector(Vol. VI,Chapter3,Section12)orapiezoelectricspeaker,asyoucontinueto<br />
turnthepotentiometerthepitchofthesoundwillrise. Youcanincreasethefrequency100<br />
timesbyreplacingthecapacitorwiththe1Fcapacitor,whichwillalsoraisethemaximum<br />
frequencywellintotheultrasonicrange,around70Khz.<br />
The555doesnotgorailtorail(itdoesn’tquitereachtheuppersupplyvoltage)becauseof<br />
itsoutputDarlingtontransistors,andthiscausestheoscillatorssquarewavetobenotquite<br />
symmetrical.CanyouseethislookingattheLEDs?Thehigherthepowersupplyvoltage,the<br />
lesspronouncedthisasymmetryis,whileitgetsworsewithlowerpowersupplyvoltages. If<br />
theoutputweretruerailtorailitwouldbea50%squarewave,whichcanbeattainedifone<br />
usestheCMOSversionofthe555,suchastheTLC555(RadioShackP/N276-1718).<br />
R3wasaddedtopreventshortingtheICoutputthroughC1,asthecapacitorshortstheAC<br />
portionofthe555outputtoground. Onadischargedbatteryitisnotnoticeable,butwitha<br />
fresh9Vthe555ICwillgetveryhot.IfyoueliminatetheresistorandadjustR4formaximum<br />
frequencyyoucantestthis,itisnotgoodforthebatteryorthe555,buttheywillsurvivea<br />
shorttest.<br />
THEORYOFOPERATION
8.3. 555HYSTERETICOSCILLATOR 373<br />
Thisisahystereticoscillator,whichisatypeofrelaxationoscillator. Itisalsoanastable<br />
multivibrator.Itisalogicaloffshootofthe555SchmittTriggerexperimentshownearlier.<br />
Theformulatocalculatethefrequencywiththisconfigurationusinga555is:<br />
f = 0.7<br />
RC<br />
The555hysteresisisdependentonthesupplyvoltage,sothefrequencyoftheoscillator<br />
wouldberelativelyindependentofthesupplyvoltageifitweren’tforthelackofrailtorail<br />
output.<br />
Theoutputofa555eithergoestoground,orrelativelyclosetotheplusvoltage. This<br />
allowstheresistorandcapacitortochargeanddischargethroughtheoutputpin.Sincethisis<br />
adigitaltypesignal,theLEDsinteractverylittleinitsoperation. Thefirstpulsegenerated<br />
bytheoscillatorisabitlongerthantherest.Thisandthecharge/dischargecurvesareshown<br />
inthefollowingillustration,whichalsoshowswhytheasymmetricalsquarewaveiscreated.
374 CHAPTER8. 555TIMERCIRCUITS<br />
8.4 555MONOSTABLEMULTIVIBRATOR<br />
PARTSANDMATERIALS<br />
• One9VBattery<br />
• BatteryClip(RadioShackcatalog#270-325)<br />
• MiniHookClips(solderedtoBatteryClip,RadioShackcatalog#270-372)<br />
• AWatchwithasecondhand/displayoraStopWatch<br />
• Awire,11/2”to2”(3.8mmto5mm)long,foldedinhalf(shownasredwireinillustration)<br />
• U1-555timerIC(RadioShackcatalog#276-1723)<br />
• D1-Redlight-emittingdiode(RadioShackcatalog#276-041orequivalent)<br />
• D2-Greenlight-emittingdiode(RadioShackcatalog#276-022orequivalent)<br />
• R1,R2-1KΩ1/4WResistors<br />
• Rt-27KΩ1/4WResistor<br />
• Rt-270KΩ1/4WResistor<br />
• C1,C2-0.1FCapacitor(RadioShackcatalog272-1069orequivalent)<br />
• Ct-10FCapacitor(RadioShackcatalog272-1025orequivalent)<br />
• Ct-100FCapacitor(RadioShackcatalog272-1028orequivalent)<br />
CROSS-REFERENCES<br />
LessonsInElectricCircuits,Volume1,chapter13:“Electricfieldsandcapacitance”<br />
LessonsInElectricCircuits,Volume1,chapter13:“Capacitorsandcalculus”<br />
LessonsInElectricCircuits,Volume1,chapter16:“Voltageandcurrentcalculations”<br />
LessonsInElectricCircuits,Volume1,chapter16:“Solvingforunknowntime”<br />
LessonsInElectricCircuits,Volume4,chapter10:“Monostablemultivibrators”<br />
LEARNINGOBJECTIVES<br />
• LearnhowaMonostableMultivibratorworks<br />
• LearnapracticalapplicationforaRCtimeconstant<br />
• Howtousethe555timerasaMonostableMultivibrator
8.4. 555MONOSTABLEMULTIVIBRATOR 375<br />
SCHEMATICDIAGRAM<br />
ILLUSTRATION<br />
INSTRUCTIONS<br />
Thisisoneofthemostbasic555circuits.Thiscircuitispartofthischipsdatasheet,completewiththemathneededtodesigntospecification,andisoneofthereasonsa555isreferred<br />
toasatimer.ThegreenLEDshownontheillustrationlightswhenthe555outputishigh(i.e.,<br />
switchedtoVcc),andtheredLEDlightswhenthe555outputislow(switchedtoground).<br />
Thisparticularmonostablemultivibrator(alsoknownasamonostableortimer)isnota<br />
retriggerabletype. Thismeansoncetriggereditwillignorefurtherinputsduringatiming
376 CHAPTER8. 555TIMERCIRCUITS<br />
cycle,withoneexception,whichwillbediscussedinthenextparagraph. Thetimerstarts<br />
whentheinputgoeslow,orswitchedtothegroundlevel,andtheoutputgoeshigh. Youcan<br />
provethisbyconnectingtheredwireshownontheillustrationbetweengroundandpointB,<br />
disconnectingit,andreconnectingit.<br />
Itisanillegalconditionfortheinputtostaylowforthisdesignpasttimeout.Forthisreason<br />
R3andC1wereaddedtocreateasignalconditioner,whichwillallowedgeonlytriggeringand<br />
preventtheillegalinput.Youcanprovethisbyconnectingtheredwirebetweengroundand<br />
pointA.Thetimerwillstartwhenthewireisinsertedintotheprotoboardbetweenthesetwo<br />
points,andignorefurthercontacts. Ifyouforcethetimerinputtostaylowpasttimeoutthe<br />
outputwillstayhigh,eventhoughthetimerhasfinished.Assoonasthisgroundisremoved<br />
thetimerwillgolow.<br />
RtandCtwereselectedfor3secondstimingduration. Youcanverifythiswithawatch,<br />
3secondsislongenoughthatweslowhumanscanactuallymeasureit.TryswappingRtand<br />
Ctwiththe27KOresistorandthe100Fcapacitor. Sincetheanswertotheformulaisthe<br />
samethereshouldbenodifferenceinhowitoperates.NexttryswappingRtwiththe270KO<br />
resistor,sincetheRCtimeconstantisnow10timesgreateryoushouldgetcloseto30seconds.<br />
Theresistorandcapacitorareprobably5%and20%tolerancerespectively,sothecalculated<br />
timesyoumeasurecanvaryasmuchas25%,thoughitwillusuallybemuchcloser.<br />
Anothernicefeatureofthe555isitsimmunityfromthepowersupplyvoltage.Ifyouwere<br />
toswapthe9Vbatterywitha6Vor12batteryyoushouldgetidenticalresults,thoughthe<br />
LEDlightintensitywillchange.<br />
C2isn’tactuallynecessary. The555IChasthisoptionincasethetimerisbeingused<br />
inanenvironmentwherethepowersupplylineisnoisy. Youcanremoveitandnotnoticea<br />
difference.The555itselfisasourceofnoise,sincethereisaverybriefperiodoftimethatthe<br />
transistorsonbothsidesoftheoutputarebothconducting,creatingapowersurge(measured<br />
innanoseconds)fromthepowersupply.<br />
Figure15.PNG45015.pngFigure26.PNG45016.pngFigure37.PNG45017.pngFigure4<br />
8.PNG45018.pngFigure59.PNG45019.png<br />
THEORYOFOPERATION<br />
Lookingatthefunctionalschematicshown(Figure8.1),youcanseethatpin7isatransistor<br />
goingtoground.<br />
Thistransistorissimplyaswitchthatnormallyconductsuntilpin2(whichisconnected<br />
throughthecomparatorC1,whichfeedstheinternalflipflop)isbroughtlow,allowingthe<br />
capacitorCttostartcharging.Pin7staysoffuntilthevoltageonCtchargesto2/3ofthepower<br />
supplyvoltage,wherethetimertimesoutandpin7transistorturnsonagain,itsnormalstate<br />
inthiscircuit.<br />
Thefollowing(Figure8.2)willshowthesequenceofswitching,withredbeingthehigher<br />
voltagesandgreenbeingground(0volts),withthespectruminbetweensincethisisfundamentallyananalogcircuit.<br />
Figure8.3isthestartingandendingpointforthiscircuit,whereitiswaitingforatriggertostartatimingcycle.<br />
Atthispointthepin7transistorison,keepingthecapacitorCt<br />
discharged.<br />
Figure8.4showswhathappenswhenthe555receivesatrigger,startingthesequence.Ct<br />
hasn’thadtimetoaccumulatevoltage,butthecharginghasstarted.
8.4. 555MONOSTABLEMULTIVIBRATOR 377<br />
Figure8.1:<br />
Figure8.2:ThisgraphshowsthechargecurveacrosstheCt.<br />
Figure8.3:
378 CHAPTER8. 555TIMERCIRCUITS<br />
Figure8.4:<br />
Figure8.5:
8.4. 555MONOSTABLEMULTIVIBRATOR 379<br />
Figure8.6:<br />
Figure8.5showsthecapacitorcharging,duringthistimethecircuitisinastableconfigurationandtheoutputishigh.<br />
Figure8.6showsthecircuitinthemiddleofswitchingoffwhenithitstimeout.Thecapacitorhaschargedto67%,theupperlimitofthe555circuit,causingitsinternalflipfloptoswitch<br />
states.Asshown,thetransistorhasn’tswitchedyet,whichwilldischargeCtwhenitdoes.<br />
Figure8.7:<br />
Figure8.7showsthecircuitafterithassettleddown,whichisbasicallythesameasshown<br />
inFigure8.3.
380 CHAPTER8. 555TIMERCIRCUITS<br />
8.5 CMOS555LONGDURATIONMINIMUMPARTSRED<br />
LEDFLASHER<br />
PARTSANDMATERIALS<br />
• TwoAAABatteries<br />
• BatteryClip(RadioShackcatalog#270-398B)<br />
• OneDVMorVOM<br />
• U1-TOneCMOSTLC555timerIC(RadioShackcatalog#276-1718orequivalent)<br />
• D1-Redlight-emittingdiode(RadioShackcatalog#276-041orequivalent)<br />
• R1-1.5MΩ1/4W5%Resistor<br />
• R2-47KΩ1/4W5%Resistor<br />
• C1-1FTantalumCapacitor(RadioShackcatalog272-1025orequivalent)<br />
• C2-100FElectrolyticCapacitor(RadioShackcatalog272-1028orequivalent)<br />
CROSS-REFERENCES<br />
LessonsInElectricCircuits,Volume1,chapter16:“Voltageandcurrentcalculations”<br />
LessonsInElectricCircuits,Volume1,chapter16:“Solvingforunknowntime”<br />
LessonsInElectricCircuits,Volume3,chapter9:“ElectroStaticDischarge”<br />
LessonsInElectricCircuits,Volume4,chapter10:“Multivibrators”<br />
LEARNINGOBJECTIVES<br />
• LearnapracticalapplicationforaRCtimeconstant<br />
• Learnoneofseveral555timerAstableMultivibratorConfigurations<br />
• Workingknowledgeofdutycycle<br />
• LearnhowtohandleESDsensitiveparts<br />
SCHEMATICDIAGRAM
8.5. CMOS555LONGDURATIONMINIMUMPARTSREDLEDFLASHER 381<br />
ILLUSTRATION<br />
INSTRUCTIONS<br />
NOTE!Thisprojectusesastaticsensitivepart,theCMOS555.Ifyoudonotuseprotection<br />
asdescribedinVolume3,Chapter9,ElectroStaticDischarge,youruntheriskofdestroyingit.<br />
The555isnotapowerhog,butitisachildofthe1970’s,createdin1971. Itwillsucka<br />
batterydryindays,ifnothours. Fortunately,thedesignhasbeenreinventedusingCMOS<br />
technology.Thenewimplementationisn’tperfect,asitlacksthefantasticcurrentdriveofthe<br />
original,butforaCMOSdevicetheoutputcurrentisstillverygood. Themainadvantages<br />
includewidersupplyvoltagerange(powersupplyspecificationsare2Vto18V,anditwillwork
382 CHAPTER8. 555TIMERCIRCUITS<br />
usinga11/2Vbattery)andlowpower. ThisprojectusestheTLC555,aTexasInstruments<br />
design.ThereareotherCMOS555’soutthere,verysimilarbutwithsomedifferences.These<br />
chipsaredesignedtobedropinreplacements,anddoverywellaslongastheoutputisnot<br />
substantiallyloaded.<br />
Thisdesignturnsadeficitintoanadvantageasthecurrentdriveonlygetsworseatlower<br />
powersupplyvoltages,itsspecificationsarenotmorethan3mafor2VDC.Thisdesigntriesto<br />
makethebatterieslastasabsolutelylongaspossibleusingseveraldifferentapproaches.The<br />
CMOSICisextremelylowcurrent,andsendstheLEDapulseof30ms(whichisaveryshort<br />
timebutwithinpersistenceofhumanvision)aswellasusingaslowflashrate(1second)using<br />
reallylargeresistorstominimizecurrent.Withadutycycleof3%,thiscircuitspendsmostof<br />
itstimeoff,and(assuming20mafortheLED)theaveragecurrentis0.6ma.Thebigproblem<br />
isusingthebuiltincurrentlimitationofthisIC,asisitisnotratedforaspecificcurrent,and<br />
theLEDcurrentcanvaryalotbetweendifferentCMOSICs.<br />
Itispossibletorunintoproblemswithelectrolyticcapacitorswhendealingwithverylow<br />
currents(2ainthiscase)inthattheleakagecanbeexcessive,aborderlinefailurecondition.<br />
Ifyourexperimentseemstodothisitmightbefixedbychargingacrossthebattery,then<br />
dischargingthecapacitorC1acrossanyconductorseveraltimes.<br />
WhenyoucompletethiscircuittheLEDshouldstartflashing,andwouldcontinuetodo<br />
soforseveralmonths.Ifyouuselargerbatteries,suchasDcells,thisdurationwillincrease<br />
dramatically.<br />
TomeasurethecurrentdrawfeedingtheLED,connectC1+toVccwithajumper(shownin<br />
redontheIllustration),whichwillturntheTLC555on.Measuretheamperageflowingfrom<br />
thebatterytothecircuit.Thetargetcurrentis20ma,Imeasured9mato24mausingdifferent<br />
CMOS555s.Thisisn’tcritical,thoughitwillaffectthebatterylife.<br />
THEORYOFOPERATION<br />
Anobservantreaderwillnotethatthisisfundamentallythesamecircuitthatwasused<br />
inthe555AUDIOOSCILLATORexperiment.Manydesignsusethesamebasicdesignsand<br />
conceptsseveraldifferentways,thisissuchacase.Aconventional555ICwouldworkinthis<br />
designifthepowersupplyweren’tsolowandaLEDcurrentlimitingresistorisused.Other<br />
thanthetypeoftransistorsusedtheblockdiagramshowninFigure8.8isbasicallythesame<br />
asaconventional555.<br />
Thisparticularoscillatordependsonthepin7transistor,muchlikethe555Monostable<br />
Multivibratorshowninanearlierexperiment. Thestartupconditioniswiththecapacitor<br />
discharged,theoutputhigh,andpin7transistoroff.Thecapacitorstartschargingasshown<br />
inFigure8.9.<br />
Whenthevoltageacrosspins2and6reaches2/3ofthepowersupplytheflipflopisreset<br />
viainternalcomparatorC1,whichturnsonthePin7transistor,andstartsthecapacitorC1<br />
dischargingthroughR2asshowninFigure8.10.ThecurrentshownthroughR1isincidental,<br />
andnotimportantotherthanitdrainsthebattery.Thisiswhythisresistorvalueissolarge.<br />
Whenthevoltageacrosspins2and6reaches1/3ofthepowersupplytheflipflopisset<br />
viainternalcomparatorC2,whenturnsoffthepin7transistor,allowingthecapacitortostart<br />
chargingagainthroughR1andR2,asshowninFigure8.9.Thiscyclerepeats.<br />
CapacitorC2extendsthelifeofthebatteries,sinceitwillstorethevoltageduringthe97%<br />
oftimethecircuitisoff,andprovidethecurrentduringthe3%itison.Thissimpleaddition<br />
willtakethebatteriesbeyondtheirusefullifebyalargemargin.
8.5. CMOS555LONGDURATIONMINIMUMPARTSREDLEDFLASHER 383<br />
Figure8.8:<br />
Figure8.9:
384 CHAPTER8. 555TIMERCIRCUITS<br />
Figure8.10:<br />
InrunningthisexperimenttherewasafeedbackmechanismIhadn’tanticipated. The<br />
outputcurrentoftheTLC555isnotproportional,asthepowersupplyvoltagegoesdownthe<br />
outputcurrentreducesalotmore. Myflasherlastedfor6monthsbeforeIterminatedthe<br />
experiment.Itwasstillflashing,itwasjustverydim.
8.6. CMOS555LONGDURATIONBLUELEDFLASHER 385<br />
8.6 CMOS555LONGDURATIONBLUELEDFLASHER<br />
PARTSANDMATERIALS<br />
• TwoAAABatteries<br />
• BatteryClip(RadioShackcatalog#270-398B)<br />
• U1-1CMOSTLC555timerIC(RadioShackcatalog#276-1718orequivalent)<br />
• Q1-2N3906PNPTransistor(RadioShackcatalog#276-1604(15pack)orequivalent)<br />
• Q2-2N2222NPNTransistor(RadioShackcatalog#276-1617(15pack)orequivalent)<br />
• CR1-1N914Diode(RadioShackcatalog#276-1122(10pack)orequivalent,seeInstructions)<br />
• D1-Bluelight-emittingdiode(RadioShackcatalog#276-311orequivalent)<br />
• R1-1.5MΩ1/4W5%Resistor<br />
• R2-47KΩ1/4W5%Resistor<br />
• R3-2.2KΩ1/4W5%Resistor<br />
• R4-620 Ω1/4W5%Resistor<br />
• R5-82 Ω1/4W5%Resistor<br />
• C1-1FTantalumCapacitor(RadioShackcatalog272-1025orequivalent)<br />
• C2-100FElectrolyticCapacitor(RadioShackcatalog272-1028orequivalent)<br />
• C3-470FElectrolyticCapacitor(RadioShackcatalog272-1030orequivalent)<br />
CROSS-REFERENCES<br />
LessonsInElectricCircuits,Volume1,chapter16:“Voltageandcurrentcalculations“<br />
LessonsInElectricCircuits,Volume1,chapter16:“Solvingforunknowntime”<br />
LessonsInElectricCircuits,Volume3,chapter4:“BipolarJunctionTransistors”<br />
LessonsInElectricCircuits,Volume3,chapter9:“ElectroStaticDischarge”<br />
LessonsInElectricCircuits,Volume4,chapter10:“Multivibrators”<br />
LEARNINGOBJECTIVES<br />
• LearnapracticalapplicationforaRCtimeconstant<br />
• Learnoneofseveral555timerAstableMultivibratorConfigurations<br />
• Workingknowledgeofdutycycle<br />
• HowtohandleESDsensitiveparts
386 CHAPTER8. 555TIMERCIRCUITS<br />
• Howtousetransistorstoimprovecurrentgain<br />
• Howtouseacapacitortodoublevoltagewithaswitch<br />
SCHEMATICDIAGRAM<br />
ILLUSTRATION<br />
INSTRUCTIONS<br />
NOTE!Thisprojectusesastaticsensitivepart,theCMOS555.Ifyoudonotuseprotection<br />
asdescribedinVolume3,Chapter9,ElectroStaticDischarge,youruntheriskofdestroyingit.
8.6. CMOS555LONGDURATIONBLUELEDFLASHER 387<br />
Thiscircuitbuildsontheprevioustwoexperiments,usingtheirfeaturesandaddingto<br />
them. BlueandwhiteLEDshaveahigherVf(forwarddroppingvoltage)thanmost,around<br />
3.6V.3Vbatteriescan’tdrivethemwithouthelp,soextracircuitryisrequired.<br />
Asinthepreviouscircuits,theLEDisgivena0.03second(30ms)pulse. C3isusedto<br />
doublethevoltageofthispulse,butitcanonlydothisforashorttime.Measuringthecurrent<br />
thoughtheLEDisimpracticalwiththiscircuitbecauseofthisshortduration,butblueLEDs<br />
aregenerallymorepredictablebecausetheywereinventedlater.<br />
Thisparticulardesigncanalsobeusedwithasingle11/2Vbattery.Thebaseconceptwas<br />
createdwithanowobsoleteIC,theLM3909,whichusedaredLED,theIC,andacapacitor.<br />
Aswiththiscircuit,itcouldflasharedLEDforoverayearwithasingleDcell.Whennewer<br />
redLEDsincreasedtheirVffrom1.5Vto2.5Vthisoldchipwasnolongerpractical,andisstill<br />
missedbymanyhobbyists.Ifyouwanttotrya11/2VbatterychangeR5to10Ωanduseared<br />
LEDwithabetterCR1(seenextparagraph).<br />
CR1isnotthebestchoiceforthiscomponent,itwasselectedbecauseitisacommonpart<br />
anditworks.Almostanydiodewillworkinthisapplication.Schottkyandgermaniumdiodes<br />
dropmuchlessvoltage,asilicondiodedrops0.6-0.7V,whileaSchottkydiodedrops0.1-0.2V,<br />
andagermaniumdiodedrops0.2V-0.3V.Ifthesecomponentsareusedthereducedvoltagedrop<br />
wouldtranslateintobrighterLEDintensity,asthecircuitsefficiencyisincreased.<br />
THEORYOFOPERATION<br />
Q2isaswitch,whichthiscircuituses.WhenQ2isoffC3ischargedtothebatteryvoltage,<br />
minusthediodedrop,asshowninFigure8.11. SincetheblueLEDVfis3.4Vto3.6Vitis<br />
effectivelyoutofthecircuit.<br />
Figure8.11:<br />
Figure8.12showswhathappenswhenQ2turnson.ThecapacitorC3+sideisgrounded,<br />
whichmovesthe-sideto-2.4V.ThediodeCR1isnowbackbiased,andisoutofthecircuit.<br />
The-2.4VisdischargedthroughR5andD1tothe+3.0Vofthebatteries. The5.4Vprovides<br />
lotsofextravoltagetolighttheblueLED.LongbeforeC3isdischargedthecircuitswitches<br />
backandC3startschargingagain.<br />
IntheLM3909CR1wasaresistor. Thediodewasusedtominimizecurrent,byallowing<br />
R4tobeitsmaximumvalue.<br />
YoumaynoticeadimblueglowintheblueLEDwhenitisoff. Thisdemonstratesthe<br />
differencebetweentheoryandpractice,3Visenoughtocausesomeleakagethroughtheblue
388 CHAPTER8. 555TIMERCIRCUITS<br />
Figure8.12:<br />
LED,eventhoughitisnotconducting. Ifyouweretomeasurethiscurrentitwouldbevery<br />
small.
8.7. CMOS555LONGDURATIONFLYBACKLEDFLASHER 389<br />
8.7 CMOS555LONGDURATIONFLYBACKLEDFLASHER<br />
PARTSANDMATERIALS<br />
• TwoAAABatteries<br />
• BatteryClip(RadioShackcatalog#270-398B)<br />
• U1,U2-CMOSTLC555timerIC(RadioShackcatalog#276-1718orequivalent)<br />
• Q1-2N3906PNPTransistor(RadioShackcatalog#276-1604(15pack)orequivalent)<br />
• Q2-2N2222NPNTransistor(RadioShackcatalog#276-1617(15pack)orequivalent)<br />
• D1-Redlight-emittingdiode(RadioShackcatalog#276-041orequivalent)<br />
• D2-Bluelight-emittingdiode(RadioShackcatalog#276-311orequivalent)<br />
• R1-1.5MΩ1/4W5%Resistor<br />
• R2-47KΩ1/4W5%Resistor<br />
• R3,R5-10KΩ1/4W5%Resistor<br />
• R4-1MΩ1/4W5%Resistor<br />
• R6-100KΩ1/4W5%Resistor<br />
• R7-1KΩ1/4W5%Resistor<br />
• C1-1FTantalumCapacitor(RadioShackcatalog#272-1025orequivalent)<br />
• C2-100pFCeramicDiscCapacitor(RadioShackcatalog#272-123)<br />
• C3-100FElectrolyticCapacitor(RadioShackcatalog272-1028orequivalent)<br />
• L1-200HChokeorInductor(Exactvaluenotcritical,seeendofchapter)<br />
CROSS-REFERENCES<br />
LessonsInElectricCircuits,Volume1,chapter16:Title”Inductortransientresponse”<br />
LessonsInElectricCircuits,Volume1,chapter16:Title”WhyL/RandnotLR?”<br />
LessonsInElectricCircuits,Volume3,chapter4:Title”Thecommon-emitteramplifier”<br />
LessonsInElectricCircuits,Volume3,chapter9:Title”ElectrostaticDischarge”<br />
LessonsInElectricCircuits,Volume4,chapter10:Title”Monostablemultivibrators”<br />
LEARNINGOBJECTIVES<br />
• Learnanothermodeofoperationforthe555<br />
• HowtohandleESDParts<br />
• Howtouseatransistorforasimplegate(resistortransistorinverter)
390 CHAPTER8. 555TIMERCIRCUITS<br />
• Howinductorscanconvertpowerusinginductiveflyback<br />
• Howtomakeaninductor<br />
SCHEMATICDIAGRAM<br />
ILLUSTRATION<br />
INSTRUCTIONS<br />
NOTE!Thisprojectusesastaticsensitivepart,theCMOS555.Ifyoudonotuseprotection<br />
asdescribedinVolume3,Chapter9,ElectroStaticDischarge,youruntheriskofdestroyingit.<br />
Thisparticularexperimentbuildsonanotherexperiment,”Commutatingdiode”(Volume6,<br />
chapter5).Itisworthreviewingthatsectionbeforeproceeding.<br />
ThisisthelastofthelongdurationLEDflasherseries. Theyhaveshownhowtousea<br />
CMOS555toflashanLED,andhowtoboostthevoltageofthebatteriestoallowanLEDwith
8.7. CMOS555LONGDURATIONFLYBACKLEDFLASHER 391<br />
morevoltagedropthanthebatteriestobeused.Herewearedoingthesamething,butwith<br />
aninductorinsteadofacapacitor.<br />
Thebasicconceptisadaptedfromanotherinvention,theJouleThief. Ajoulethiefisa<br />
simpletransistoroscillatorthatalsousesinductivekickbacktolightanwhitelightLEDfrom<br />
a11/2battery,andtheLEDneedsatleast3.6voltstostartconducting! Likethejoulethief,<br />
itispossibletouse11/2voltstogetthiscircuittowork.However,sinceaCMOS555israted<br />
for2voltsminimum11/2voltsisnotrecommended,butwecantakeadvantageoftheextreme<br />
efficiencyofthiscircuit.Ifyouwanttolearnmoreaboutthejoulethiefplentyofinformation<br />
canbefoundontheweb.<br />
Thiscircuitcanalsodrivemorethat1or2LEDsinseries. AsthenumbersofLEDsgo<br />
uptheabilityofthebatteriestolastalongdurationgoesdown,astheamountofvoltagethe<br />
inductorcangenerateissomewhatdependentonbatteryvoltage. Forthepurposesofthis<br />
experimenttwodissimilarLEDswereusedtodemonstrateitsindependenceofLEDvoltage<br />
drop.ThehighintensityoftheblueLEDswampstheredLED,butifyoulookcloselyyouwill<br />
findtheredLEDisatitsmaximumbrightness. Youcanuseprettymuchwhatevercolorof<br />
LEDsyouchooseforthisexperiment.<br />
Generallythehighvoltagecreatedbyinductivekickbackissomethingtobeeliminated.<br />
Thiscircuitusesit,butifyoumakeamistakewiththepolarityoftheLEDstheblueLED,<br />
whichismoreESDsensitive,willlikelydie(thishasbeenverified). Anuncontrolledpulse<br />
fromacoilresemblesanESDevent.ThetransistorandtheTLC555canalsobeatrisk.<br />
Theinductorinthiscircuitisprobablytheleastcriticalpartinthedesign. Theterminductorisgeneric,youcanalsofindthiscomponentcalledachokeoracoil.<br />
Asolenoidcoil<br />
wouldalsowork,sincethatisalsoatypeofinductor. Sowouldthecoilfromarelay. Ofall<br />
thecomponentsIhaveused,thisisprobablytheleastcriticalI’vecomeacross. Indeed,coils<br />
areprobablythemostpracticalcomponentyoucanmakeyourselfthatexists.I’llcoverhowto<br />
makeacoilthatwillworkinthisdesignaftertheTheoryofOperation,butthepartshownon<br />
theillustrationisa200HchokeIboughtfromalocalelectronicsretailer.<br />
THEORYOFOPERATION<br />
Bothcapacitorsandinductorsstoreenergy. Capacitorstrytomaintainconstantvoltage,<br />
whereasinductorstrytomaintainconstantcurrent. Bothresistchangetotheirrespective<br />
aspect. Thisisthebasisfortheflybacktransformer,whichisacommoncircuitusedinold<br />
CRTcircuitsandotheruseswherehighvoltageisneededwithaminimumoffuss. When<br />
youchargeacoilamagneticfieldexpandsaroundit,basicallyitisanelectromagnet,andthe<br />
magneticfieldisstoredenergy.Whenthecurrentstopsthismagneticfieldcollapses,created<br />
electricityasthefieldcrossesthewiresinthecoil.<br />
Thiscircuitusestwoastablemultivibrators. Thefirstmultivibratorcontrolsthesecond.<br />
Botharedesignedforminimumcurrent,aswellastheinvertermadeusingQ1. Boththe<br />
oscillatorsareverysimilar,thefirsthasbeencoveredinpreviousexperiments. Theproblem<br />
isitstayson,orishigh,97%ofthetime. Onthepreviouscircuitsweusedthelowstateto<br />
lighttheLED,inthiscasethehighiswhatturnsthesecondmultivibratoron.Usingasimple<br />
transistorinverterdesignedforextralowcurrentsolvesthisproblem.Thisisactuallyavery<br />
oldlogicfamily,RTL,whichisshortforresistortransistorlogic.<br />
Thesecondmultivibratoroscillatesat68.6KHz,withasquarewavethatisaround50%.<br />
ThiscircuitusestheexactsameprincipalsasisshownintheMinimumPartsLEDFlasher.<br />
Again,thelargestpracticalresistorsareusedtominimizecurrent,andthismeansareally
392 CHAPTER8. 555TIMERCIRCUITS<br />
smallcapacitorforC2. ThishighfrequencysquarewaveisusedtoturnQ2onandoffasa<br />
simpleswitch.<br />
Figure8.13showswhathappenswhentheQ2isconducting,andthecoilstartstocharge.<br />
IfQ2weretostayonthenaneffectiveshortacrossthebatterieswouldresult,butsincethis<br />
ispartofanoscillatorthiswon’thappen.Beforethecoilcanreachit’smaximumcurrentQ2<br />
switches,andtheswitchisopen.<br />
Figure8.13:<br />
Figure8.14showsQ2whenitopens,andthecoilischarged.Thecoiltriestomaintainthe<br />
current,butifthereisnodischargepathitcannotdothis. Iftherewerenodischargepath<br />
isthecoilwouldcreateahighvoltagepulse,seekingtomaintainthecurrentthatwasflowing<br />
throughit,andthisvoltagewouldbequitehigh. However,wehaveacoupleofLEDsinthe<br />
dischargepath,sothecoilspulsequicklygoestothevoltagedropofthecombinedLEDs,then<br />
dumpstherestofitschargeascurrent. Asaresultthereisnohighvoltagegenerated,but<br />
thereisaconversiontothevoltagerequiredtolighttheLEDs.<br />
Figure8.14:<br />
TheLEDsarepulsed,andthelightcurvefollowsthedischargecurveofthecoilfairly<br />
closely.However,thehumaneyeaveragesthislightoutputtosomethingweperceiveascontinuouslight.<br />
8.8 HOWTOMAKEANINDUCTOR<br />
PARTSANDMATERIALS
8.8. HOWTOMAKEANINDUCTOR 393<br />
• 26Feet(8Meters)of26AWGMagnetWire(RadioShackcatalog#278-1345orequivalent)<br />
• 6/32X1.5inchscrew,aM4X30mmscrew,oranailofsimilardiametercutdowntosize,<br />
steeloriron,butnotstainless<br />
• Matchinglocknut(optional)<br />
• TransparentTape(optional,neededifusingscrews)<br />
• SuperGlue<br />
• SolderingIron,Solder<br />
Ashasbeenmentionedbefore,thisisnotaprecisionpart. Inductorsingeneralcanhave<br />
alargevarianceformanyapplications,andthisonespecificallycanbeoffonthehighsidea<br />
largeamount.Thetargethereisgreaterthan220µH.<br />
Ifyouareusingascrew,useonelayerofthetransparenttapebetweenthethreadsandthe<br />
wire. Thisistopreventthethreadsofthescrewfromcuttingintothewireandshortingthe<br />
coilout.Ifyouareusingalocknutputitonthescrew1”(25mm)fromtheheadofthescrew.<br />
Startingaround1”fromoneendofthewire,usethegluetotackthewireontheheadofthe<br />
nailorscrewasshown.Lettheglueset.<br />
Figure8.15:<br />
Windthewireneatlyandtightly1”thelengthofscrew,againtackingitinplacewithsuper<br />
glue. (Figure8.15). Youcanuseavariablespeeddrilltohelpwiththis,aslongasyouare<br />
careful.Likeallpowerappliances,itcanbiteyou.Holdthewiretightuntilthegluesets,then<br />
startwindingasecondlayeroverthefirst. Continuethisprocessuntilallofthewireexcept<br />
thelast1”isused,usingthegluetooccasionallytackthewiredown.Arrangethewireonthe<br />
lastlayersothesecondinductorleadisontheotherendofthescrewawayfromthefirst.Tack<br />
thisdownforafinaltimewiththeglue.Letdrycompletely.<br />
Gentlytakeasharpbladeandscraptheenameloffeachendofthetwoleads. Tinthe<br />
exposedcopperwiththesolderingironandthesolder,andyounowhaveafunctionalinductor<br />
thatcanbeusedinthisexperiment.
394 CHAPTER8. 555TIMERCIRCUITS<br />
Figure8.16:<br />
HereiswhattheoneImadelookedlike:Figure8.16.<br />
Theconnectionsshownarebeingusedtomeasuretheinductance,whichworkedoutpretty<br />
closeto220H.
8.9. CMOS555LONGDURATIONREDLEDFLASHER 395<br />
8.9 CMOS555LONGDURATIONREDLEDFLASHER<br />
PARTSANDMATERIALS<br />
• TwoAAABatteries<br />
• BatteryClip(RadioShackcatalog#270-398B)<br />
• ADVMorVOM<br />
• U1-CMOSTLC555timerIC(RadioShackcatalog#276-1718orequivalent)<br />
• Q1-2N3906PNPTransistor(RadioShackcatalog#276-1604(15pack)orequivalent)<br />
• Q2-2N2222NPNTransistor(RadioShackcatalog#276-1617(15pack)orequivalent)<br />
• D1-Redlight-emittingdiode(RadioShackcatalog#276-041orequivalent)<br />
• R1-1.5MΩ1/4W5%Resistor<br />
• R2-47KΩ1/4W5%Resistor<br />
• R3-2.2KΩ1/4W5%Resistor<br />
• R4-27 Ω1/4W5%Resistor(ortestselectabettervalue)<br />
• C1-1FTantalumCapacitor(RadioShackcatalog272-1025orequivalent)<br />
• C2-100FElectrolyticCapacitor(RadioShackcatalog272-1028orequivalent)<br />
CROSS-REFERENCES<br />
LessonsInElectricCircuits,Volume1,chapter16:“Voltageandcurrentcalculations”<br />
LessonsInElectricCircuits,Volume1,chapter16:“Solvingforunknowntime”<br />
LessonsInElectricCircuits,Volume3,chapter4:“BipolarJunctionTransistors”<br />
LessonsInElectricCircuits,Volume3,chapter9:“ElectroStaticDischarge”<br />
LessonsInElectricCircuits,Volume4,chapter10:“Multivibrators”<br />
LEARNINGOBJECTIVES<br />
• LearnapracticalapplicationforaRCtimeconstant<br />
• Learnoneofseveral555timerAstableMultivibratorConfigurations<br />
• Workingknowledgeofdutycycle<br />
• HowtohandleESDsensitiveparts<br />
• Howtousetransistorstoimprovecurrentgain<br />
• HowtocalculatethecorrectresistorforaLED
396 CHAPTER8. 555TIMERCIRCUITS<br />
SCHEMATICDIAGRAM<br />
ILLUSTRATION<br />
INSTRUCTIONS<br />
NOTE!Thisprojectusesastaticsensitivepart,theCMOS555.Ifyoudonotuseprotection<br />
asdescribedinVolume3,Chapter9,ElectroStaticDischarge,youruntheriskofdestroyingit.<br />
Thecircuitshowninthepreviousexperiment,CMOS555LongDurationMinimumParts<br />
RedLEDFlasher,hasonebigdrawback,whichisalackofLEDcurrentcontrol.Thisexperimentusesthesamebasic555schematicandaddstransistorizeddriverstocorrectthis.
8.9. CMOS555LONGDURATIONREDLEDFLASHER 397<br />
Thepartsusedforthistransistordriverarenoncritical.ItisdesignedtoloadtheTLC555<br />
toanabsoluteminimumandstillturnonQ2fully. Thisisimportantbecauseasthebattery<br />
voltageapproaches2VthedrivefromtheTLC555isreducedtoitsminimumvalues.Bipolar<br />
transistorscanbegoodswitches.<br />
SinceLEDscanhavesomuchvariationR4shouldbetweakedtomatchthespecificLED<br />
used.Thecurrentislimitedto18.5mawith27ΩandaVf(LEDforwarddroppingvoltage)of<br />
2.5V,anLEDVfof2.1Vwilldraw33ma,andaLEDVfof1.5willdraw56ma.Thelatteristoo<br />
muchcurrent,nottomentionwhatthatwoulddoforthebatterylife.Tocorrectthisuse47Ω<br />
iftheVfis2.1V,and75ΩiftheVfis1.5V,assumingthetargetcurrentis20ma.<br />
YoucanmeasureVfbyusingthejumpershowninredintheillustration,whichwillturn<br />
theLEDonfulltime.YoucancalculatethevalueofR4byusingtheequation:<br />
R4=(3V-Vf)/0.02A<br />
ItwasmentionedinthepreviousexperimentthatcapacitorC2extendedthelifeofthe<br />
batteries.Aninterestingexperimentistoremovethispartperiodicallyandseewhathappens.<br />
AtfirstyouwillnoticeadimmingoftheLED,andafteraweekortwothecircuitwilldie<br />
withoutit,andresumeworkinginacoupleofsecondswhenitisreplaced. Thisflasherwill<br />
workfor3monthsusingfreshalkalineAAAbatteries.<br />
THEORYOFOPERATION<br />
TheCMOS555oscillatorwasexplainedfullyinthepreviousexperiment,sothetransistor<br />
driverwillbethefocusofthisexplanation.<br />
ThetransistordrivercombineselementsofacommoncollectorconfigurationonQ1,along<br />
withcommonemitterconfigurationonQ2. Thisallowsforveryhighinputresistancewhile<br />
allowingQ2toturnonfully.Theinputresistanceofthetransistoristhe β(gain)ofthetransistortimestheemitterresistor.<br />
IfQ1hasagainof50(aminimumvalue)thenthedriver<br />
loadstheTLC555withmorethan100KΩ.Transistorscanhavelargevariationsingain,even<br />
withinthesamefamily.<br />
WhenQ1turnson1maissenttoQ2.ThisismorethanenoughtoturnQ2fully,whichis<br />
referredtoassaturation.Q2isusedasasimpleswitchfortheLED.
398 CHAPTER8. 555TIMERCIRCUITS
AppendixA-1<br />
ABOUTTHISBOOK<br />
A-1.1 Purpose<br />
Theysaythatnecessityisthemotherofinvention.Atleastinthecaseofthisbook,thatadage<br />
istrue. Asanindustrialelectronicsinstructor,Iwasforcedtouseasub-standardtextbook<br />
duringmyfirstyearofteaching.Mystudentsweredailyfrustratedwiththemanytypographicalerrorsandobscureexplanationsinthisbook,havingspentmuchtimeathomestruggling<br />
tocomprehendthematerialwithin.Worseyetwerethemanyincorrectanswersinthebackof<br />
thebooktoselectedproblems.Addinginsulttoinjurywasthe$100+price.<br />
Contactingthepublisherprovedtobeanexerciseinfutility. Eventhoughtheparticular<br />
textIwasusinghadbeeninprintandinpopularuseforacoupleofyears,theyclaimedmy<br />
complaintwasthefirstthey’deverheard.Myrequesttoreviewthedraftforthenextedition<br />
oftheirbookwasmetwithdisinterestontheirpart,andIresolvedtofindanalternativetext.<br />
FindingasuitablealternativewasmoredifficultthanIhadimagined. Sure,therewere<br />
plentyoftextsinprint,butthereallygoodbooksseemedabittooheavyonthemathandthe<br />
lessintimidatingbooksomittedalotofinformationIfeltwasimportant. Someofthebest<br />
bookswereoutofprint,andthosethatwerestillbeingprintedwerequiteexpensive.<br />
ItwasoutoffrustrationthatIcompiledLessonsinElectricCircuitsfromnotesandideasI<br />
hadbeencollectingforyears.Myprimarygoalwastoputreadable,high-qualityinformation<br />
intothehandsofmystudents,butasecondarygoalwastomakethebookasaffordableas<br />
possible.Overtheyears,Ihadexperiencedthebenefitofreceivingfreeinstructionandencouragementinmypursuitoflearningelectronicsfrommanypeople,includingseveralteachers<br />
ofmineinelementaryandhighschool.Theirselflessassistanceplayedakeyroleinmyown<br />
studies,pavingthewayforarewardingcareerandfascinatinghobby. IfonlyIcouldextend<br />
thegiftoftheirhelpbygivingtootherpeoplewhattheygavetome...<br />
So,Idecidedtomakethebookfreelyavailable.Morethanthat,Idecidedtomakeit”open,”<br />
followingthesamedevelopmentmodelusedinthemakingoffreesoftware(mostnotablythe<br />
variousUNIXutilitiesreleasedbytheFreeSoftwareFoundation,andtheLinuxoperating<br />
399
400 APPENDIXA-1. ABOUTTHISBOOK<br />
system,whosefameisgrowingevenasIwrite).Thegoalwastocopyrightthetext–soasto<br />
protectmyauthorship–butexpresslyallowanyonetodistributeand/ormodifythetexttosuit<br />
theirownneedswithaminimumoflegalencumbrance. Thiswillfulandformalrevokingof<br />
standarddistributionlimitationsundercopyrightiswhimsicallytermedcopyleft.Anyonecan<br />
”copyleft”theircreativeworksimplybyappendinganoticetothateffectontheirwork,but<br />
severalLicensesalreadyexist,coveringthefinelegalpointsingreatdetail.<br />
ThefirstsuchLicenseIappliedtomyworkwastheGPL–GeneralPublicLicense–ofthe<br />
FreeSoftwareFoundation(GNU).TheGPL,however,isintendedtocopyleftworksofcomputer<br />
software,andalthoughitsintroductorylanguageisbroadenoughtocoverworksoftext,its<br />
wordingisnotasclearasitcouldbeforthatapplication. Whenother,lessspecificcopyleft<br />
Licensesbeganappearingwithinthefreesoftwarecommunity,Ichoseoneofthem(theDesign<br />
ScienceLicense,orDSL)astheofficialnoticeformyproject.<br />
In”copylefting”thistext,Iguaranteedthatnoinstructorwouldbelimitedbyatextinsufficientfortheirneeds,asIhadbeenwitherror-riddentextbooksfrommajorpublishers.I’msure<br />
thisbookinitsinitialformwillnotsatisfyeveryone,butanyonehasthefreedomtochangeit,<br />
leveragingmyeffortstosuitvariantandindividualrequirements.Forthebeginningstudent<br />
ofelectronics,learnwhatyoucanfromthisbook,editingitasyoufeelnecessaryifyoucome<br />
acrossausefulpieceofinformation.Then,ifyoupassitontosomeoneelse,youwillbegiving<br />
themsomethingbetterthanwhatyoureceived.Fortheinstructororelectronicsprofessional,<br />
feelfreetousethisasareferencemanual,addingoreditingtoyourheart’scontent. The<br />
only”catch”isthis:ifyouplantodistributeyourmodifiedversionofthistext,youmustgive<br />
creditwherecreditisdue(tome,theoriginalauthor,andanyoneelsewhosemodificationsare<br />
containedinyourversion),andyoumustensurethatwhoeveryougivethetexttoisawareof<br />
theirfreedomtosimilarlyshareandeditthetext.Thenextchaptercoversthisprocessinmore<br />
detail.<br />
ItmustbementionedthatalthoughIstrivetomaintaintechnicalaccuracyinallofthis<br />
book’scontent,thesubjectmatterisbroadandharborsmanypotentialdangers. Electricity<br />
maimsandkillswithoutprovocation,anddeservestheutmostrespect. Istronglyencourage<br />
experimentationonthepartofthereader,butonlywithcircuitspoweredbysmallbatteries<br />
wherethereisnoriskofelectricshock,fire,explosion,etc.High-powerelectriccircuitsshould<br />
belefttothecareoftrainedprofessionals! TheDesignScienceLicenseclearlystatesthat<br />
neitherInoranycontributorstothisbookbearanyliabilityforwhatisdonewithitscontents.<br />
A-1.2 TheuseofSPICE<br />
Oneofthebestwaystolearnhowthingsworkistofollowtheinductiveapproach:toobserve<br />
specificinstancesofthingsworkingandderivegeneralconclusionsfromthoseobservations.<br />
Inscienceeducation,labworkisthetraditionallyacceptedvenueforthistypeoflearning,althoughinmanycaseslabsaredesignedbyeducatorstoreinforceprinciplespreviouslylearned<br />
throughlectureortextbookreading,ratherthantoallowthestudenttolearnontheirown<br />
throughatrulyexploratoryprocess.<br />
HavingtaughtmyselfmostoftheelectronicsthatIknow,Iappreciatethesenseoffrustrationstudentsmayhaveinteachingthemselvesfrombooks.<br />
Althoughelectroniccomponents<br />
aretypicallyinexpensive,noteveryonehasthemeansoropportunitytosetupalaboratory<br />
intheirownhomes,andwhenthingsgowrongthere’snoonetoaskforhelp.Mosttextbooks
A-1.3. ACKNOWLEDGEMENTS 401<br />
seemtoapproachthetaskofeducationfromadeductiveperspective: tellthestudenthow<br />
thingsaresupposedtowork,thenapplythoseprinciplestospecificinstancesthatthestudent<br />
mayormaynotbeabletoexplorebythemselves.Theinductiveapproach,asusefulasitis,is<br />
hardtofindinthepagesofabook.<br />
However,textbooksdon’thavetobethisway. IdiscoveredthiswhenIstartedtolearna<br />
computerprogramcalledSPICE.Itisatext-basedpieceofsoftwareintendedtomodelcircuits<br />
andprovideanalysesofvoltage,current,frequency,etc.Althoughnothingisquiteasgoodas<br />
buildingrealcircuitstogainknowledgeinelectronics,computersimulationisanexcellentalternative.Inlearninghowtousethispowerfultool,Imadeadiscovery:SPICEcouldbeused<br />
withinatextbooktopresentcircuitsimulationstoallowstudentsto”observe”thephenomena<br />
forthemselves. Thisway,thereaderscouldlearntheconceptsinductively(byinterpreting<br />
SPICE’soutput)aswellasdeductively(byinterpretingmyexplanations). Furthermore,in<br />
seeingSPICEusedoverandoveragain,theyshouldbeabletounderstandhowtouseitthemselves,providingaperfectlysafemeansofexperimentationontheirowncomputerswithcircuit<br />
simulationsoftheirowndesign.<br />
Anotheradvantagetoincludingcomputeranalysesinatextbookistheempiricalverificationitaddstotheconceptspresented.<br />
Withoutdemonstrations,thereaderislefttotake<br />
theauthor’sstatementsonfaith,trustingthatwhathasbeenwrittenisindeedaccurate.The<br />
problemwithfaith,ofcourse,isthatitisonlyasgoodastheauthorityinwhichitisplacedand<br />
theaccuracyofinterpretationthroughwhichitisunderstood.Authors,likeallhumanbeings,<br />
areliabletoerrand/orcommunicatepoorly. Withdemonstrations,however,thereadercan<br />
immediatelyseeforthemselvesthatwhattheauthordescribesisindeedtrue.Demonstrations<br />
alsoservetoclarifythemeaningofthetextwithconcreteexamples.<br />
SPICEisintroducedearlyinvolumeI(DC)ofthisbookseries,andhopefullyinagentle<br />
enoughwaythatitdoesn’tcreateconfusion.Forthosewishingtolearnmore,achapterinthis<br />
volume(volumeV)containsanoverviewofSPICEwithmanyexamplecircuits. Theremay<br />
bemoreflashy(graphic)circuitsimulationprogramsinexistence,butSPICEisfree,avirtue<br />
complementingthecharitablephilosophyofthisbookverynicely.<br />
A-1.3 Acknowledgements<br />
First,Iwishtothankmywife,whosepatienceduringthosemanyandlongevenings(and<br />
weekends!)oftypinghasbeenextraordinary.<br />
Ialsowishtothankthosewhoseopen-sourcesoftwaredevelopmenteffortshavemadethis<br />
endeavorallthemoreaffordableandpleasurable.Thefollowingisalistofvariousfreecomputersoftwareusedtomakethisbook,andtherespectiveprogrammers:<br />
• GNU/LinuxOperatingSystem–LinusTorvalds,RichardStallman,andahostofothers<br />
toonumeroustomention.<br />
• Vimtexteditor–BramMoolenaarandothers.<br />
• Xcircuitdraftingprogram–TimEdwards.<br />
• SPICEcircuitsimulationprogram–toomanycontributorstomention.<br />
• TEXtextprocessingsystem–DonaldKnuthandothers.
402 APPENDIXA-1. ABOUTTHISBOOK<br />
• Texinfodocumentformattingsystem–FreeSoftwareFoundation.<br />
• L A TEXdocumentformattingsystem–LeslieLamportandothers.<br />
• Gimpimagemanipulationprogram–toomanycontributorstomention.<br />
• Winscopesignalanalysissoftware–Dr. ConstantinZeldovich. (Freeforpersonaland<br />
academicuse.)<br />
AppreciationisalsoextendedtoRobertL.Boylestad,whosefirsteditionofIntroductory<br />
CircuitAnalysistaughtmemoreaboutelectriccircuitsthananyotherbook.Otherimportant<br />
textsinmyelectronicsstudiesincludethe1939editionofThe”Radio”Handbook,Bernard<br />
Grob’ssecondeditionofIntroductiontoElectronicsI,andForrestMims’originalEngineer’s<br />
Notebook.<br />
ThankstothestaffoftheBellinghamAntiqueRadioMuseum,whoweregenerousenough<br />
toletmeterrorizetheirestablishmentwithmycameraandflashunit.<br />
IwishtospecificallythankJeffreyElknerandallthoseatYorktownHighSchoolforbeing<br />
willingtohostmybookaspartoftheirOpen<strong>Book</strong>Project,andtomakethefirsteffortincontributingtoitsformandcontent.ThanksalsotoDavidSweet(website:<br />
(http://www.andamooka.org))<br />
andBenCrowell(website: (http://www.lightandmatter.com))forprovidingencouragement,constructivecriticism,andawideraudiencefortheonlineversionofthisbook.<br />
ThankstoMichaelStutzfordraftinghisDesignScienceLicense,andtoRichardStallman<br />
forpioneeringtheconceptofcopyleft.<br />
Lastbutcertainlynotleast,manythankstomyparentsandthoseteachersofminewho<br />
sawinmeadesiretolearnaboutelectricity,andwhokindledthatflameintoapassionfor<br />
discoveryandintellectualadventure.Ihonoryoubyhelpingothersasyouhavehelpedme.<br />
TonyKuphaldt,July2001<br />
”Acandlelosesnothingofitslightwhenlightinganother”<br />
KahlilGibran
A-1.3. ACKNOWLEDGEMENTS 403<br />
jrap@allaboutcircuits.com
404 APPENDIXA-1. ABOUTTHISBOOK
AppendixA-2<br />
CONTRIBUTORLIST<br />
A-2.1 Howtocontributetothisbook<br />
The Work is copyright the Author. All rights to the Work are reserved<br />
by the Author, except as specifically described below. This License<br />
describes the terms and conditions under which the Author permits you<br />
to copy, distribute and modify copies of the Work.<br />
In addition, you may refer to the Work, talk about it, and (as<br />
dictated by "fair use") quote from it, just as you would any<br />
copyrighted material under copyright law.<br />
Your right to operate, perform, read or otherwise interpret and/or<br />
execute the Work is unrestricted; however, you do so at your own risk,<br />
because the Work comes WITHOUT ANY WARRANTY -- see Section 7 ("NO<br />
WARRANTY") below.<br />
Asacopyleftedwork,thisbookisopentorevisionandexpansionbyanyinterestedparties.<br />
Theonly”catch”isthatcreditmustbegivenwherecreditisdue.Thisisacopyrightedwork:<br />
itisnotinthepublicdomain!<br />
Ifyouwishtociteportionsofthisbookinaworkofyourown,youmustfollowthesame<br />
guidelinesasforanyothercopyrightedwork. HereisasamplefromtheDesignScienceLicense:<br />
Ifyouwishtomodifythisbookinanyway,youmustdocumentthenatureofthosemodificationsinthe”Credits”sectionalongwithyourname,andideally,informationconcerninghow<br />
youmaybecontacted.Again,theDesignScienceLicense:<br />
Permission is granted to modify or sample from a copy of the Work,<br />
405
406 APPENDIXA-2. CONTRIBUTORLIST<br />
producing a derivative work, and to distribute the derivative work<br />
under the terms described in the section for distribution above,<br />
provided that the following terms are met:<br />
(a) The new, derivative work is published under the terms of this<br />
License.<br />
(b) The derivative work is given a new name, so that its name or<br />
title can not be confused with the Work, or with a version of<br />
the Work, in any way.<br />
(c) Appropriate authorship credit is given: for the differences<br />
between the Work and the new derivative work, authorship is<br />
attributed to you, while the material sampled or used from<br />
the Work remains attributed to the original Author; appropriate<br />
notice must be included with the new work indicating the nature<br />
and the dates of any modifications of the Work made by you.<br />
Giventhecomplexitiesandsecurityissuessurroundingthemaintenanceoffilescomprising<br />
thisbook,itisrecommendedthatyousubmitanyrevisionsorexpansionstotheoriginalauthor<br />
(TonyR.Kuphaldt). Youare,ofcourse,welcometomodifythisbookdirectlybyeditingyour<br />
ownpersonalcopy,butwewouldallstandtobenefitfromyourcontributionsifyourideaswere<br />
incorporatedintotheonline“mastercopy”wherealltheworldcanseeit.<br />
A-2.2 Credits<br />
Allentriesarrangedinalphabeticalorderofsurname.Majorcontributionsarelistedbyindividualnamewithsomedetailonthenatureofthecontribution(s),date,contactinfo,etc.Minor<br />
contributions(typocorrections,etc.)arelistedbynameonlyforreasonsofbrevity.PleaseunderstandthatwhenIclassifyacontributionas“minor,”itisinnowayinferiortotheeffort<br />
orvalueofa“major”contribution,justsmallerinthesenseoflesstextchanged.Anyandall<br />
contributionsaregratefullyaccepted.Iamindebtedtoallthosewhohavegivenfreelyoftheir<br />
ownknowledge,time,andresourcestomakethisabetterbook!<br />
A-2.2.1 DennisCrunkilton<br />
• Date(s)ofcontribution(s):January2006topresent<br />
• Natureofcontribution: Minitableofcontents,allchaptersexceptappedicies;html,<br />
latex,ps,pdf;SeeDevel/tutorial.html;01/2006.<br />
• Natureofcontribution: CH4,section:Inductionmotor,09/2007.<br />
• Natureofcontribution: CH4,section:Inductionmotor,large02/2010.<br />
• Contactat: dcrunkilton(at)att(dot)net
A-2.2. CREDITS 407<br />
A-2.2.2 TonyR.Kuphaldt<br />
• Date(s)ofcontribution(s):1996topresent<br />
• Natureofcontribution:Originalauthor.<br />
• Contactat: liec0@lycos.com<br />
A-2.2.3 BillMarsden<br />
• Date(s)ofcontribution(s):August2008<br />
• Natureofcontribution:Originalauthor:“555Schmidttrigger”Section,Chapter7.<br />
• Contactat: bill marsden2(at)hotmail(dot)com<br />
A-2.2.4 ForrestM.MimsIII<br />
• Date(s)ofcontribution(s):February2008<br />
• Natureofcontribution:Ch5;ClarificationconcerningLEDsasphotosensors.<br />
• Contactat: FMims(at)aol.com<br />
A-2.2.5 Yournamehere<br />
• Date(s)ofcontribution(s):Monthandyearofcontribution<br />
• Natureofcontribution:Inserttexthere,describinghowyoucontributedtothebook.<br />
• Contactat: my email@provider.net<br />
A-2.2.6 Typocorrectionsandother“minor”contributions<br />
• line-allaboutcircuits.com(June2005)TypographicalerrorcorrectioninVolumes1,2,3,5,<br />
variouschapters,(:s/visa-versa/viceversa/).<br />
• ThestudentsofBellinghamTechnicalCollege’sInstrumentationprogram.<br />
• ColinCreitz(May2007)Chapters:several,s/it’s/its.<br />
• JeffDeFreitas(March2006)Improveappearance:replace“/”and”/”Chapters:A1,A2.<br />
• DonStalkowski(June2002)TechnicalhelpwithPostScript-to-PDFfileformatconversion.<br />
• JosephTeichman(June2002)SuggestionandtechnicalhelpregardinguseofPNG<br />
imagesinsteadofJPEG.<br />
• MichaelWarner(April2002)Suggestionsforasectiondescribinghomelaboratorysetup.
408 APPENDIXA-2. CONTRIBUTORLIST<br />
• jut@allaboutcircuits.com(August2007)Ch1,s/starting/started.<br />
• Unregistered@allaboutcircuits.com(August2007)Ch6,s/andandoff/onandoff/.<br />
• TimothyUnregistered@allaboutcircuits.com(Feb2008)Changeddefaultromanfont<br />
tonewcent.<br />
• ImranullahSyed(Feb2008)Suggestedcenteringofuncaptionedschematics.<br />
• Sylverce@allaboutcircuits.com,Caveman@allaboutcircuits.com(May2008)Changed<br />
image05320.pngtoagreewithimage05321.png¡/item<br />
• sarwiz@allaboutcircuits.com(April2009)Ch4,s/Trychanged/Trychanging/¡/item<br />
• jrap@allaboutcircuits.com(August2009)added tagsto”555Schmitttrigger”,dic.sml.<br />
• Heavydoody@allaboutcircuits.com(August2009)correctiontoimage05198.eps&.png<br />
.<br />
• Dcrunkilton@allaboutcircuits.com(January2010)added tagto”555<br />
Schmitttrigger”.<br />
• Bereahorn@allaboutcircuits.com(January2010)Ch2,s/Thelessressistance/Themore<br />
resistance.<br />
• BillMarsden@allaboutcircuits.com(April2010)addednewCROSS-REFERENCEto<br />
”555Schmitttrigger”.<br />
• Dcrunkilton@allaboutcircuits.com(September2010)Ch6,s/useable/usable/.<br />
• D.Crunkilton(June2011)hi.latex,headerfile;updatedlinktoopenbookproject.net.
AppendixA-3<br />
DESIGNSCIENCELICENSE<br />
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Theideaof”copyleft”istowillfullyrevoketheexclusivityofthoserightsundercertain<br />
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Theintentofthislicenseistobeageneral”copyleft”thatcanbeappliedtoanykindofwork<br />
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Whereas”designscience”isastrategyforthedevelopmentofartifactsasawaytoreform<br />
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409
410 APPENDIXA-3. DESIGNSCIENCELICENSE<br />
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412 APPENDIXA-3. DESIGNSCIENCELICENSE<br />
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INGBUTNOTLIMITEDTOTHEIMPLIEDWARRANTIESOFMERCHANTABILITYOR<br />
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ENDOFTERMSANDCONDITIONS<br />
[$Id: dsl.txt,v 1.25 2000/03/14 13:14:14 m Exp m $]
Index<br />
βratio,257<br />
555timer,312,315,318<br />
555timerIC,365<br />
AC,145<br />
ACcoupling,oscilloscope,196,210<br />
Active-highinput,363<br />
Active-lowinput,363<br />
Alligatorclip,19<br />
Alternatingcurrent,145<br />
Alternator,164<br />
Amp,36<br />
Ampere,36<br />
Amplifiercircuit,134<br />
Amplifierimpedance,244<br />
Amplifier,inverting,247,299<br />
Amplifier,noninverting,299<br />
Amplifier,operational,252<br />
Amplitude,185<br />
Analog,289,331<br />
Analogcomputer,133,144<br />
Analogmultimeter,16<br />
Antiresonance,192<br />
Astablemultivibrator,275,312<br />
Audiotaperpotentiometer,87,117,155<br />
Autorangingmeter,18<br />
Bananaplugsandjacks,99<br />
Battery,19<br />
Betaratio,257<br />
Biascurrent,op-amp,309<br />
Bindingposts,99<br />
Bounce,switchcontact,345,353<br />
Breadboard,22<br />
Calculus,143,306<br />
Calibrationdrift—hyperpage,107<br />
Capacitor,decoupling,199<br />
Choke,191<br />
Choke,filter,225<br />
Circuit,29<br />
Circuit,short,32<br />
Common-modevoltage,267<br />
Commonality,electrical,24<br />
Computersimulation,76<br />
Computer,analog,133,144<br />
Constant-currentdiode,263<br />
Contactbounce,345,353<br />
Continuity,22<br />
Continuityvs.commonality,24<br />
Currentdivider,84<br />
Currentmirror,263,315<br />
Currentregulator,257<br />
Current,definition,36<br />
DC,59<br />
Debouncing,switch,354<br />
Decouplingcapacitor,199<br />
Derivative,calculus,143,306<br />
Detector,null,124<br />
Differentialamplifier,267,270<br />
Differentialpair,267,270<br />
Differentiation,calculus,143,306<br />
Digital,289,331<br />
Digitalmultimeter,16<br />
Diode,26<br />
Diodeequation,258<br />
Diode,constant-current,263<br />
Directcurrent,59<br />
Discontinuity,29<br />
Divider,current,84<br />
Divider,voltage,70<br />
Drift,calibration,107<br />
Dutycycle,312<br />
413
414 INDEX<br />
E,symbolforvoltage,44<br />
Effect,Seebeck,110<br />
<strong>Electrical</strong>continuity,22<br />
<strong>Electrical</strong>shockhazard,26<br />
<strong>Electrical</strong>lycommonpoints,24,64<br />
Electromagneticinduction,57<br />
Electromagnetism,56<br />
Equation,diode,258<br />
Experiment:3-bitbinarycounter,359<br />
Experiment:4-wireresistancemeasurement,<br />
127<br />
Experiment:555audiooscillator,311<br />
Experiment:555rampgenerator,314<br />
Experiment:555SchmittTrigger,366<br />
Experiment:7-segmentdisplay,361<br />
Experiment:ACpowersupply,147<br />
Experiment:Alternator,164<br />
Experiment:Ammeterusage,35<br />
Experiment:Audiodetector,155<br />
Experiment:Audiooscillator,274<br />
Experiment:Basicgatefunction,333<br />
Experiment:BJTswitch,230<br />
Experiment:Bridgerectifier,218<br />
Experiment:Capacitorcharginganddischarging,138<br />
Experiment:Center-taprectifier,213<br />
Experiment:ClassBaudioamplifier,321<br />
Experiment:Common-emitteramplifier,246<br />
Experiment:Commutatingdiode,203<br />
Experiment:Currentdivider,78<br />
Experiment:Currentmirror,255<br />
Experiment:Differentialamplifier,266<br />
Experiment:Electromagneticfieldsensor,AC,<br />
160<br />
Experiment:Electromagneticinduction,57<br />
Experiment:Electromagnetism,55<br />
Experiment:Electrostaticfieldsensor,AC,162<br />
Experiment:Half-waverectifier,205<br />
Experiment:High-impedancevoltmeter,301<br />
Experiment:Inductionmotor,170,174<br />
Experiment:Integrator,305<br />
Experiment:JFETcurrentregulator,261<br />
Experiment:Keyboardassignalgenerator,183<br />
Experiment:LEDsequencer,347<br />
Experiment:Multi-stageamplifier,251<br />
Experiment:Multimeter,112<br />
Experiment: NANDgateS-Renabledlatch,<br />
341<br />
Experiment:NANDgateS-Rflip-flop,343<br />
Experiment:Noninvertingamplifier,298<br />
Experiment:Nonlinearresistance,45<br />
Experiment:NORgateS-Rlatch,337<br />
Experiment:Ohm’sLaw,42<br />
Experiment:Ohmmeterusage,21<br />
Experiment:Oscilloscope,PC,186<br />
Experiment:Parallelbatteries,63<br />
Experiment:Phaseshift,177<br />
Experiment:Potatobattery,136<br />
Experiment:Potentiometerasrheostat,93<br />
Experiment:Potentiometerasvoltagedivider,<br />
87<br />
Experiment:Potentiometricvoltmeter,122<br />
Experiment:Powerdissipation,48<br />
Experiment:Precisionpotentiometer,99<br />
Experiment:Precisionvoltagefollower,294<br />
Experiment:Pulsed-lightsensor,238<br />
Experiment:PWMpowercontroller,317<br />
Experiment:Rate-of-changeindicator,142<br />
Experiment:Rectifier/filter,221<br />
Experiment:Rheostatrangelimiting,102<br />
Experiment:Seriesbatteries,60<br />
Experiment:Signalcoupling,194<br />
Experiment:Simplecircuit,28<br />
Experiment:Simplecombinationlock,356<br />
Experiment:Simpleop-amp,269<br />
Experiment:Soundcancellation,180<br />
Experiment:Staticelectricitysensor,235<br />
Experiment:Switchincircuit,53<br />
Experiment:Tankcircuit,191<br />
Experiment:Thermoelectricity,109<br />
Experiment:Transformer,homemade,151<br />
Experiment:Vacuumtubeaudioamplifier,277<br />
Experiment:Variableinductor,153<br />
Experiment:Voltageaverager,131<br />
Experiment:Voltagecomparator,291<br />
Experiment:Voltagedetector,sensitive,117<br />
Experiment:Voltagedivider,67<br />
Experiment:Voltagefollower,241<br />
Experiment:Voltageregulator,227<br />
Experiment:Voltmeterusage,15<br />
Experiment:Waveformanalysis,189
INDEX 415<br />
Feedback,290,295<br />
Feedback,negative,248<br />
Fieldwinding,alternator,164<br />
Filter,223<br />
Filterchoke,225<br />
Floatinginput,defined,335,353<br />
Frequency,185<br />
Frequencydomain,190<br />
Full-waverectification,214<br />
Functiongenerator,184<br />
Fundamentalfrequency,190<br />
Fuse,37<br />
Fuse,slow-blow,147<br />
Generator,19,164<br />
Generator,ACsignal,184<br />
Half-waverectification,206<br />
Harmonics,185<br />
Hazard,electricalshock,26<br />
Headphone,117<br />
Heatsink,223<br />
Hysteresis,338<br />
I,symbolforcurrent,44<br />
IC,202,289,331<br />
Illegalstate,338<br />
Impedancematching,120,158<br />
Impedance,amplifier,244<br />
Impedance,definition,120,158<br />
Induction,electromagnetic,57<br />
Inductivekickback—hyperpage,56,120,158<br />
Integratedcircuit,202,289,331<br />
Integration,calculus,306<br />
Interactiveadjustment,101<br />
Invalidstate,338<br />
Invertingamplifier,247,299<br />
Joule’sLaw,51<br />
Jumperwire,19<br />
KCL,84<br />
Kirchhoff’sCurrentLaw,84<br />
Kirchhoff’sVoltageLaw,70<br />
KVL,70<br />
Latch-up,304<br />
Latchedstate,338<br />
LED,18<br />
Light-EmittingDiode,18<br />
Lineartaperpotentiometer,87,117,155<br />
Magnetwire,55,151<br />
MaximumPowerTransferTheorem,120,158<br />
Megger,128<br />
Metermovement,112<br />
Meteroverrange,18<br />
Metricprefix,25,38<br />
Monostablemultivibrator,354<br />
Motor,induction,168<br />
Motor,synchronous,168<br />
Movement,meter,112<br />
Multimeter,16<br />
Multivibrator,275,312<br />
Multivibrator,monostable,354<br />
Negativefeedback,248<br />
Noninvertingamplifier,299<br />
Nulldetector,124<br />
Null-balancevoltmeter,124<br />
Ohm,22<br />
Ohm’sLaw,44<br />
Ohm’sLaw,ACversion,178<br />
Op-amp,267,270<br />
Operationalamplifier,252,267,270,290<br />
Operationalamplifier,programmable,273<br />
Oscilloscope,187<br />
Oscilloscopecoupling,196,210<br />
Overrange,meter,18<br />
Pair,differential,267,270<br />
Parallel,64,105<br />
Permeability,154<br />
Phaseshift,178<br />
Photocell,27<br />
Polarity,19,31<br />
Potentiometer,87<br />
Potentiometerasrheostat,94<br />
Potentiometer,linearvs.audiotaper,87<br />
Potentiometricvoltmeter,124<br />
Powersupply,145<br />
Power,definition,51
416 INDEX<br />
Programmableop-amp,273<br />
Pulldownresistor,352<br />
Pulse-widthmodulation,319<br />
PWMpowercontrol,319<br />
Q,inductorqualityfactor—hyperpage,192<br />
R,symbolforresistance,44<br />
Racecondition,339<br />
Railvoltage,296<br />
Rectification,full-wave,214<br />
Rectification,half-wave,206<br />
Rectifyingdiode,26<br />
Regulator,current,257<br />
Reluctance,magnetic,152<br />
Resetstate,338<br />
Resistance,definition,22<br />
Resistorcolorcode,24<br />
Resistor,pulldown,352<br />
Resistor,shunt,243<br />
Resonance,192<br />
Resonantfrequency,192<br />
Rheostat,94<br />
Ring-lugterminal,165<br />
Ripplevoltage,208,223<br />
Schmitttrigger,366<br />
Seebeckeffect,110<br />
Semiconductor,202<br />
Series,61,104<br />
Series-parallel,66<br />
Setstate,338<br />
Shielding,161,163<br />
Shockhazard,26<br />
Shortcircuit,32<br />
Shuntresistor,243<br />
Signalgenerator,184<br />
Simulation,computer,76<br />
Slipring,alternator,165<br />
Soldering,148<br />
Spancalibration,105<br />
SPICE,76<br />
Splitphase,219<br />
Statorwinding,alternator,164<br />
Strip,terminal,34<br />
Switch,53<br />
Switchdebouncing,354<br />
Tankcircuit,192<br />
Terminalstrip,34<br />
Terminal,ringlug,165<br />
Thermalrunaway,259,263<br />
Thermocouple,110<br />
Timeconstant,140<br />
Timedomain,190<br />
Transformer,117,145<br />
Transistor,96<br />
Transistor,junctionfield-effect,236<br />
Unit,ampere,36<br />
Unit,ohm,22<br />
Unit,volt,18<br />
Unit,watt,51<br />
Volt,18<br />
Voltagedivider,70<br />
Voltagefollower,242,270,295<br />
Voltage,common-mode,267<br />
Voltage,definition,18<br />
Voltage,polarity,19,31<br />
Voltage,ripple,208,223<br />
Watt,51<br />
Wire,magnet,55<br />
Z,symbolforimpedance,120,158<br />
Zerocalibration,105
INDEX 417<br />
.
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