of Phase Noise Measurement - John Miles KE5FX

IIoThe "Arl" ofPhase Noisef,lleasurementDieter SchererMarch 1985oRf & MlcrowaveMeasurementSymposlumancltxhlbltlonftE'HF$|IfJJ

O 1. Why Measure Phase Noise?Phase noise causes . . .o Lower receiver sensitivity in multi-signal environmentTransmillerH q-Doppler SignalDecorrelated Clutler NoiseJ_o Glutter noise in Doppler Radar Systemsr Phase errors in digital communication systemsphase noise imposes fundamental limitations wherever a weak signal is processed in the presence of a.tiorrg interferini rij""r. In the above example, phase noise sidebands of the receiver local oscillator areti"".i"*"a to thI Ifpioduct of the strong interfering sjsnll and cover up the weak wanted signal.A similar situatio;exists with cohereit Doppler radar. The strong interferring signal in this case isp;;;;J ty reflections from large stationarl' f5;".ts. Phase noise side bands of this unwanted returnlien"i"r. ,iecorrelateJbv delav ind potentially cover as clutter noise the weak Doppler signal'b,,r"n in the world of d-igital iata tiansmission phase noise is a limiting faetor. Phase noise adds too*,"r^il system rroir. in.rJ"sing Bit Error Rate and may cause a cycle slip in the carrier or data clockrecovery.5

2. Basic Representation of Phase Noiseo2.1 In the Time Domain:v(t) : Signat with random phase fluctuation A ,0(t)v(t) : Vs cos f?rtsl+ J O (t)lOscilloscoPe DisPlaYV(t) = Vs cos 2rlslar ao(t)Frequency and Phase are related bYf(r):##In the time domain phase noise can be observed as phase jitter of the signal on an oscilloscope displal' ora time interval counter may detect the instantaneous time fluctuations of the zero crossings.phase or frequency fluctuations are the same physical phenomena. One can be derived from the other asangular frequency is the first derivative of phase with respect to time.6

O,, In the Frequency Domain:FJd(t):Jd(f)Spectral Density of Phase Fluctuations S4SO(f)-Jd2rms(f)f'3 Flicker FMI d2rmsf'2 Random Walk Phaset-t Flicker Phasefo White PhaseFourier FrequencY | -€spectral Density of Frequency Fluctuations s3Sr t(f) = Jf2rms(f) : l2J @2rms(l) : fzSO(f)Spectral density distributions describe frequency or phase noise in the frequency domain. Terms like.,White,,' ,,Flicker,' and ..Random Walk" refei to the slope of f , f-t, and f-2 of thd density distribution.rrluiiipri."tion by the Fourier frequency - conespond.rls to differentiation in the time domain -converti the spectral density of phasl noiie to the spectral density offrequency noise.7

2.3 Relation of Phase Noise to Carrier Sideband NoiseoThe modulari6n pf the signal phase manifests itself in modulation sidebands to the carrier at offsetfrequencies u.hich ar" muliiples of the modulation rate rFourier frequencyr. The sideband levels arerelated to the magnirucle of the phase deviation by Bessel terms. For small'angle modulation, onl5'the firstBessel term is signrficanr and the relation betu'een phase deviation and sideband level is approximated b1'For small angle modulalion( I ar. < l radian)?P = {-t d2rms(f) J d2rmsA common, though indirect. representation of phase noise is,7{f r, the ratio of the single sideband noisepo$.er in a I Hz band*'ldth to the total carrier power specified at a given offset, f of the carrier'This representation is applicable only for very small phase deviations, sufficiently small to producenegligible higher order sidebands.Definition ol Y (t)y(tt=ry+--fott-+fogl = |Refation between 2,5 5, Sl f:lor -\6

o 3 Phase Noise Measurement Techniqueso Direct Spectrum Analysis) o Two Sources and Phase Detectoro Frequency Discriminator) o Delay Line Frequency Discriminatoro Carrier Suppression (Ondria Bridge)o Heterodyne Period GounterFrom the multitude of techniques to measure phase orfrequency noisetwobasicmethods are singled outand explained in some detail onthe following pages: the "Two Sources and Phase Detector" technique andthe "Dela5' Line Frequency Discriminator" technique'Both methods are ielatively simple to implement and are broadband solutions.They also complimenteach other well. The first method rnl.rur"s phase noise;high sensitivity is obtainable and two sources areneeded. The second method measures frequency noise, has inherently lower sensitivity close in but nosecond source is required.

3.1 Two Sources and Phase Detector TechniqueoSourceUnder Testlsolation AmPl.Phase Detector(Double Balanced Mixer)lv't_tl^AlLow Pass FillerLow NoiseAmplifierlsolation AmPl.CalibrationAllenuatori+IL--,1!F=Fvsd (t)=Jdimsltl=1/zforld

O 31 1 The Mixer as Phase DetectorVg cos t,,11Vs cos (-nt - 6(l))v (t) = cos (t,n - ,L) t. O(t)15) +vB peakV (t) = VB peak cos ({rn - col 1t. O(t))for c,rL =

3.1 .2 Calibration withBeat SignaloJv(f) =Kd r O (f)Ko = vB peak: fvg 76s1 . 1 --J d76s(f):;; JV 765(f)- JV rms(f)ffi-,forJ 6

O 313System Noise FloorlVn MtXJvn t.t.trLow Noise Amplifiert system (f) =JV2ntlttx +JV2nLNev2g rmsThe noise floor of the measurement system is established by the equivalent amplifier and mixer noisetshot noise, flicher noiser at the IF port redueed by the phase detector gain K6 (VB peak for linearoperation r. System sensitivity is therefore maximized by using a high level mixer, selecting a mixer u'ithlow flicker noise and follou'ing the mixer with a low noise amplifier.dBc-80N.robF@urg9-et ^Y=\urOO-gEACE-tr6gU'EEo-100-120-140\-160-180lHzExample: 3047A Mixer-Amplifer 5 MHz - 1.6 GHz- Syslem Noise wlth High Level Double BalancedMixer and Low Noise Amplifier\\-10 Hz 100 Hz 1 kHz 10 kHz 100 kHzf [HzJl MHzt3

31.4 Potential Error Sourcesoo Suppression or peaking ol noise near or below the phaselock loop bandwidth.o Inieclion lockingr Deviation from phase quadrature (resulting in aneffectively lower K6)o Non-linear operalion of mixer (if linearity was assumedin calibration)o Distortion of RF-Signal (resultingin a deviation ol K6from VB peaf)o Saturation of thepreamplilieror spectrum analyzer incalibration or by high spurious signals (e.9. linespurious)o Change of impedance interface while going lromcalibration to measuremente lnsuflicient cancelation of common source noise in aresidual noise testr AM-noise (in particular AM noise of the commonsource in a residual noise tesl)o Closely spaced spurious (e.9. line multiples)misinterpreted as Phase noiseo Noise injected by peripheral circuitry (power supply,phase lock looP)o Noise injected by peripheral instrumentatioh (€.9.,oscilloscope, DVM)o Microphonic noise.

Os: Delay Line Frequency Discriminator TechniqueSourceunderTeslSrt(t) = lf2r|nr{f)PowerAmPlifierDelay Line ( r)tort=fi2JVrms = K62tr Jf *.Osrt(f) Jvtrms (t Hz)7 (f) derived from Srt(f)roro

s.2.1 Theory of Delay Line Frequency Discriminatorord(r)(v(r) = Kd rd(r)t(t) = lo +Jt sin 2;ftV(t) = Ve cos (2;fst - f.ot 2nltlCarrier with sinusoidal FMDelay time rfs = Carrier frequencY| = FM rateJf = FMdeviationPhase Difference on Phase Detector JO(t)Jd(t) = Zrts(t - r)..*"ot2rrl(r- r) - 2ilsl-fJd(t) = -2rrls' ., (cos 2rrl (t - rl - cos 2iltl+JO(t) = - 2nls r * 2f sin zrf r sin p'r 1t - 7\"ot 2trltPhase Detector Output: V(t) = K6 -\@(t)lor 21116r = (2k+ 1)?(Phase Quadrature):V(f) = KO2f sin z:'lr sin 2trt (r -ilTransfer Function:Jv = Ko2{sin nlr = K62,..rlt #forr =fi:sin-zrfz = |tlrJV = K6 2nr Jlr_-Kp t#l= Frequency Discriminator Constant = K62nr

()szzSystem Noise FloorlVn urxJVn lxaLow Noise AmplifierDelay Line!'rt'PszSrt(f ) systemPhase Noise ol RF Amplitier (if used): Jdnr = ffi1t * f tKo (in linear operation): Kd = VB peak = fiffiottwith L = Conversion Loss (Power) of MixerMixer noise and baseband amplifier noise are interpreted by the systgm as frequency noise. This alsoholds for phaseuv un nr amplifier. The amplifier might have been added to boost thesignal level lowered "oir.l"tioJu."a b1' the lossy deial'line'':{:l;#- JV2n ..nlJr-l2pp(X5Z--1' (2;rl21(tt=++ srt(t)for J6

A different *.a5.of esrimating the s)'stem noise floor of the delal'line discriminator technique is to lumpall noise contributions into an equivalent phase noise perturbation J02r-tor "rrr' The delal' linediscriminator.interpreting Jc) as frequency rrbi.u enhancei this equivalent phase noise by a factor of| /2;f;.Example:Phase noise of the mixer at i kHz ! t 't kHz' = -160 dBc/Hz'with a 100 nsec dela5' time the resulting system noise floor isJ2=!tli|l'. 2rf; '= -160 dBc + 61 dB = -96 'Hz dBc-100-90-80-709 rttle, tnLosl-60-50*40-30-20Enhancemenl ofequivalent Phase noiseperturbation bY delaYt,tll=gxl=rll"r? (r) gr (t) \2; f ; rIrti+100100 Hz18

Os.2.3 Frequency Discriminator with ResonatorLow Noiseplifiert-r[r ro, r'h56(l) for t '*Cavity ResonalorCrystal FillerInside Resonator Bandwidth 1t . $ I'Equivalent Delay Time r=Eilfo=r[ ddl oKD= K52;r =*ri}Jvrms(f),?a= Kdfi rttmsltlAlthough not a broadband solution, it can be advantageous to replace the delay line with a cavityresonatoior crystal filter. Group delay td6/du\ produces an equivalent r of Q/ rfo for Fourier frequenciesless than half the bandwidth. Inside fo/zq, the system therefore measures the spectral density offrequency noise *'ith a discriminator constant of K6 2Q'/fo.Outside Resonator Bandwidth 1f ' $ t,Jvrms(Q = Kd Jdrms(f)Outside fot}Q,the system ma]' be vieg'ed as 2 signals applied to a phase ddtector u'ith the sidebandnoise of one"signal stripped off by the cavity resonator. The system then measures Jd216s with a phasedetector constant K6.19

4 HP Phase Noise Measurement Solutionso HP 11729C/8662A Phase Noise Test System(phase detector mode)o HP 11729 Carrier Noise Test Set(delay line discriminator mode)o HP 3047A Phase Noise Measurement Systemo HP 11740A Microwave Phase NoiseMeasurement SystemFollowing is a comparison of HP phase noise measurement solutions with particular focus on theLLTZ1 Carrier Noise Test Set, HP's most recent contribution to phase noise measurement.20

o4.1HP 11729C/8662A Phase Noise Test SystemPrinciple ol Operation(Phase Detector Method)x0EFCInpul640 MHzLow NoiseReferenceSignalHP 8662ASynthesizedSignal GeneratorOpl.003DCFMInpulHPr11729C Carrier Noise Tesl Setill*LiGeneration Selection5-1280 MHzRI5-1280 MHz IallF-AmpILow NoiseAmp I10 Hz-10 MHzIIIIIMicrowaveSourceUnder Test.01-18 GHzSpeclrumAnalyzerr IIllConlroller,lI IL .JJThe HP 86624 Synthesized signal Generatorprovides astateof'theartlownoieereferenesignal at640MHzto the Hp 11Z2gC Carrier Noise Test Set. This signal is applied to a step recovery diode multiplier which generatesa comb of signals spaced by 640 MHz ranging beyond 18 GHz. A switched in filter selects an_appropriatecombline. This microwavireference signal down converts themicrowavesourceutdertestinto an lFrange of 5to 1280 MHz.The double balanced mixer phase compares the IF signal with the output signal o{the HP 8662A (.01 to 1280MHz). phase quadrature is enforced by phase locking the HP 8662A to the signal rurder test either thru thelimited electronic control of the HP 8662A's 10 MHz crystal oseillator or thnr its DGFM port. The loop band'widths can be set over a 4 decade range.A firstorder phase lock loopis enabledby thecapturefeaturemaking lock acquisition easy. Then thesecondorder phase lock loop (with very high dc gain) maintains lock and phase quadr-ature. To enable phase noise-"".u".-.nts within the loop Larrd*idth, the phase noise suppression can be characterized via the loop testports.21

NNHP 11729C Carrier Noise Test Sel - - --'lI r 1 r--1 r---1 't 'i o

0411 Noise Floor of HP 11729C/8662A Phase Noise Test System(Phase Detector Method)NIoE\IFtrtr,gEtroFllJLozltJoIo.o@-24-40-60-80-10012A-140-160-180\ \\\\-86!\ \I\\I;2 in DC FMll\-640 MHz Reference Signal 'from HP 8662Atl\\\ rlpical Hp r'rz2eclaeize\ $ytt"m Noise @ 10 GHzt-.a\\\\_,rHz 10Hz 100 Hz 1 kHz 10 kHz 100 kHzOflset fromCarrier | [Hz]\---,-------MHz10 MHzJ1 Js ts/ system = 10 log (Nz r 'lQro - 1010 - 1010)N = Multiplicalion number of the 640 MHz signal/ r = Absolule SSB Phase Noise of lhe 640 MHzreference signal (dBclHz).? a = Absolute SSB Phase Noise of lhe 5 lo 640(1280) MH: lunable signal (dBc/Hz).,lg = Two-porl noise of HP 11729C (dBc/Hr).OllsetflomcarrierlHz10 Hz100H21 kHz10 kHz100 kHz1 IlHzTypical640 llHzlownoiseoulputTypical320-640llHz tunableE662AoulputTypicalTwo-porlnolse ofHP 11729C@5GHzTypicalTwo-porlnoise olHP 11729C@ 10 GHz-54 dBc -64 dBc -99 dBc -93 dBc-94 dBc -94 dBc -112 dBc -106 dBc-114 rlBc -1ltf dBc -125 dBc -119 dBc-126 dBc -125 dBc -132 dBc -126 dBc-149 dBc -136 d8c -137 dBc -131 dBc-159 dBc -136 rlBc -1t18 rlBc -142 dBc-159 dBc -146 dBc -153 dBc -147 dBcFor most microwave applications, 11, the SSB phase noise of the 640 MHz reference signal, is thedominating factor in setting the noise floor of the system as its phase noise is multiplied up to microwavefrequencies.23

4.1.2 HP 11729C Operating in Discriminator Modeo--IL-HP 11729C Carrier NotseTesl SetComb Comb LineGeneralion SectionCalibrationsource,-6'rl--lf-It Signal al Carrier lreq. or lF wilhI Calibrated FM SidebandsIIIfcalibrationb Calibralioni I o.o1 to 18 GHzMicrowave Sourceunder TestlF-Amp5lo 1280 MHzExternal Delay LineIt_iox.to I'i"lBasebandSpectrumAnalyzeraaooLow noise down convercion of microwave signal under lestDelay line operating at lF (5-1500 MHz)Calibration signal provided by HP 8662APhase quadrature Indication.The HP LL729C may also be used in a delay line discriminator mode. The microwave reference signalgenerated by the 640 MHz signal down converts the Bource under test into the IF range.The power splitterind auxiliaiy IF output allows one to simply ineert an appropriate delay line ext*nally.Delaying t-he signal at IF means lower delay line losses and also a wider choice of delay devices, like e.g.SAW d;lav line. Any signal generator with FM sidebands at IF or RF can Eenle as a calibration tool.24

4.1.3Sensitivity of HP 11729C(Delay Line Frequency Discriminator Mode)o!oGcg-20-40-60C)-'*r(!ooo,9ozooG3r@o-trof-,..1--ruo L"^J./ \..'usclllalorat 10 GHzI1OO nst Delay\ Typical Free'Running- -y'Source at 10 GHz Io 1Hz 10 Hz tOO Hz 1 kHz 1O kHz lOO kHz 1 MHz 10 MHzOffset From Carrier (Hz)\\ \.\\\-\.-- L.-..-.

4.2.1Phase Noise Measurementon Pulsed RF SignalsoPulsed RF Source (DUT)t-APulse DriveIIIJAnti-aliasing FillerNarrow BandPhase Lock LooPThe baseband signal ofa pulsed RF signal phaselocked to a reference source equals the baseband signalof a. ut pulsed Rf signal jated by the pulse envelope (see Fig. A, B, C). The CW noise spectrum J (0 ismultiplied by the envelope function of the pulse,(-t)nnn n tSln -Itn2'rtcos -T\Observed in the frequency domain, this gating process means convolving the two spectra to obtain thepulsed baseband sp""tto- (see Fig. C). The resulting spectrum has J (f) folded around multiples of theiuise repetition frequency (PRF). The relevant part of this spectrum is yielded by the DC tcrm of the pulseenrrelopefunction, it"t.ttshowsthattheleveloftheunpulsedphasenoisespectrum.c(0isreducedbytheunPursrdrqu"r.'J the duty cycle.J $1,*o= (+)' Jl3por""aA lowpass filter, the antialiasing filter, with a corner frequency of

Time DomainFrequency DomainFig A: Pulse Envelope-+lPRFzParSpeclrum of Pulse EnveloPetcAcGsFig B: Unpulsed Baseband Signal(UnPulsed Phase Noise)Unpulsed Phase Noise SpectrumtGgA! gGGo!utpulsedl\/l\,\-\-2 \Fig C: Pulsed Baseband Signalbefore Low PassPulsed Phase Noise Speclrumbelore Low Passt GoAE3GaoG aFig D: Pulsed Baseband Signalafler Low PassPulsed Phase Noise Spectrumaller Low Pass

4.2.2. Pulsed Phase Noise Measurementswith the HP 11729C (Phase Detector Mode)HP 11729CLPFffiNoiseSpectrumOutput640Input5 to 1280lnputPLL GontrolVoltageOutputSelecting pulse mode (phase noise) on the HP 11729C applies an error cunent to the mixer/phasedetector and switches in a user-supplied low pass filter to remove the pulse repetition frequencyfeedthrough.

l4.3 HP 3047A Phase Noise Measurement SystemApptication ExamPle:Two-por4 phase noise measurement on lrequency dividerHP 3047A Phase Noise llelcurement SyrlemHP 98il6A or9816ADerk Top ComPuter125 MllzComparisonDevice125 MHzt_The Hp 304?4. phase Noise Measurement system represents a high sensitivity phase detector systemwith controllable prr"". r""r, circuits. Extensive softwlre automates the calibration and measurementprocedures ri--!r^-^ i^ ^- ^oax-l^ ^f o -acidrrql nhecp measure-Determining the phase noise of frequency dividers is.an example of a residual phase noise ment. Here, the phase noise of the 8662;. i;t;;i;;".J"a and the svstem will measure the rms sum ofnoise of both dividers.Lr I i lLrLEr i F[rt]F+tstshrrPLES!,i i 5Et0lHZ-3S-.ig-59-Eg F-i6-BU-so t- .- r8g- ilBF.-ra6-t30-r{8- l5Ei-r661-.-r79lH=29

4.4 HP 11740A Microwave Phase NoiseMeasurement SystemHP 11729C Carrier NoiseTesl SelDevice under TestGunn VCO al '10.4 GHzHP 3(X7A Spectrum AnalYzer SYslemHP 9836A or 9815ADesk Top GomPuler800 MHz540 MHzRelerence SignalIn the Hp 11?40A Microwave Ncise Measurement System, the HP ll7290 provides a broadband andlo*, noise micro*'ave reference signal eliminating the need for a eecond comparable source'--The Hp gOaZe phase detector system then compares the IF output of the HP 11729C with either theb-12g0 MHz outfut of the HP 8662A or any other suitable and tunable IF eource.-\\l----T-\ --T:?''i".''rl. (. )lek tez< Ir'! reY.dBc./P.z r v's { !:12-l ?er.30

Iou-20Comparison of System Sensitivities-40NE(,tr l,-60l tP 11729CC;AW @\t,nza\ 00 nselay\oGELoLL-Go ooI02ooGao,o-100-120-140-160-'-aF.t\\\\\ -HP 117: l9c/8662A@10cHz\t.\= \\ -rHP 3047A @ 10 l--iGHz*\\*-:a;=-180iT; 10 Hz 100 Hz 1z 10 kHz 100 kHz 1 MHz 10MHzOtfset from Carrier (Hz).Performance shown requires a second, user supplied sourceof comparable Phase noise.31

Principle olOperalion46 Phase Noise Measurement Systems ComparisonHP 11729C/8662APhase NoiseTesl Systeml-tFha!' d€lector moo()- ;;;^-- IHP 8566A EHP 35854HP3582ASpectrum AnalYzerHP 11729CCarrier NoiseTest SelHP 8562ASynlhesizedSig Geni--I"r''Gl: lSource Under Tesl/a- \./ 6_@-'ReferenceHP 3047APhase NoiseMeasurementSystemHP 35854Speclrum AnalyzerHP 3582ASpectrum AnalyzerHP 35601AS.A. lnlerfaceJ--;,;;; - II Reference IHP 8662AI xp seesa iI HP 8340A I] xe aozza Ii_ _:':3: _ _lHP 11740AMicrowavePhase NoiseMeasuremenlSyslemHP 3585ASpectrum AnalYzerHP 3582ASpeclrum AnalYzerHP 35601AS.A. InlerfaceHP 11729CCanler NoiseTesl Setf .*..r^ "*t.*lI Synthesized IIsig Gen It HPrs36A-1816Al l-rP ,836 -rst6^ ISource Under TestSource Uncler TestReferenceHP 11729CCarrier NoiseTesl Set(trequencYdiscriminalof mode jHP 11729CCarrrer NoiseTesl SelHP 8556A/8HP 8568A'BHP 3561ASpectrum Analyzert-'- - - - - -'f "*'"-' ISource Under Tesl%G\r;RelerenceFrequency Range 10 MHz - 18 GHz 5 MHz - 18 GHz 5 llHz -'18 GHz 10 MHa - 18 GHzLow Noise MicrowaveRelerence SignalTypical SyslemNoiie al 10 GHryes no yes yes123 dBc al 10 kHz145 dBc noise lloor- 170 dBc al 10 kHz' - 123 dBc at 10 kHz- 170 ctBc noise floor - 145 dBc noise floot(with HP 1r729C)Itili.li-1't2 dBc al 10 kHz I- 145 dBc noise flooriOllsel FrequencY :10 MHz

GLOSSARY OF SYMBOLSFKTBfefsIf(t)rf(t)K6Kp9tttPgPssbosrt(f )s6(f)tY(t)vB peaka0(r)Ao(t)TlmwlIHz]lHzllHzlIHzJIHzlIvolt/radJlvolVHzl[dBc/HzJlmwllmwltllzzttlz!lrad2lHzlIsec]IvoltlIvoltJlradllradllseclAvailable noise power in bandwidth BCarrier lrequencYCorner lrequencY of flicker noiseFourier frequency (sideband-, olfset-, modulation'baseband-f requency)I nstanta neous lreguencYI nstantaneous frequency lluctuationPhase detector constantFrequency discriminator constantRatio of single sideband phase noise to total signalpower in a 1 Hz bandwidth I Hertz from the carrierSignal powerPower of single sidebandQuality factor of resonatorSpectral density of lrequency fluctuationsSpeclral density of phase fluctuationsTimeInstantaneous voltagePeak voltage of sinusoldal beat signalInslantaneous Phase fluctuationInstantaneous Phase PerlurbanceDelay time

REFERENCES1r Ashler'. J.R.. et al. "The l\leasurement of Noise in Microu'ave Transmilters." IEEE Transactiorts ctnMierouat'c Theorl'and Technigues, Vol. MTT-25, No. 4, pp. 29a'318, tApril, 19ii t.0rJ}4)D)Fischer. M.. "An Overvieu' of Modern Techniques for Measuring Spectral Purity", Microu'aves, Vol. 16.No. 7, pp. 66-75, July 1979.Hewlett-Packard staff. "Understanding and Measuring Phase Noise in the Frequency Domain,"Application Note 207, October 1976.Hewlett-Packard staff, "Measuring Phase Noise with the HP 35854 Spectrum Analyzer", ApplicationNote 246-2, IMay 1981.Hewlett-Packard staff, "Applications and Measurements of Low Phase Noise Signals Using the 8662ASynthesized Signal Generator", Application Note 283'1, November 1981.6t Howe, D.A., "Frequenc]'Domain Stability Measurements: A Tutorial Introduction", NBS TechnicalNote 679, March 1976.1tLance, A.L., Seal, \\'.D., Hudson, N.W., Mendoza, F.G., and Donald Halford. "Phase Noise MeasurementsUsing Cross-Spectrum Analysis," Conference on Precision Electromagnetic Measurements.Ottawa, Canada, June 1978.8t Ondria F.G., "A lMicrowave System for Measurements of AM and FM Noise Spectra", IEEE Transactionson Microu'aue Theorl'and Techniques, Vol. MTT-16,pp.767-781, September 1968.9tl0)lltScherer, Dieter, "Design Principles and Test Methods for l,ow Phase Noise RF and Microwave Sources",Hewlett-Packard RF and Microu'ave Measurement Symposium, October 1978. (Also edited versionin Microwaves, "Today's Lesson - Learn about Low-Noise Design", part 1, pp. 116-122, April1979, part 2,pp.72-77, May 1979r.Shoal J.H., Halford, D., Risley, A.S., "Frequency Stability Specification and Measurement: HighFrequency and Microwave Signals", NBS Technical Note 632, January 1973.Temple, R., "Choosing a Phase Noise Measurement Technique - Concepts and Implementation",Hewlett-Packard RF and Microwave Measurement Symposium, February 1983.34

HP ArchiveThis vintage Hewlett-Packard document waspreserved and distributed bywww.hparchive.comPlease visit us on the web!The HP Archive thanks George Pontisfor his contribution of this material.On-line curator: John Miles, KE5FXjmiles@pop.net