NIST Technical Note 1337: Characterization of Clocks and Oscillators

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above. The measured noise voltages are scaled usingthe measured gains and the spectral density of phasenoise calculated. The overlapping ranges of thevarious spectrum analyzers allows one the opportunityto compare the measurements on the three spectrumanalyzers, Typically one can obtain S.(f) of theoscillator pair to an accuracy of about ± 0.6 dB atFourier frequency above 100 Hz. The agreement withrepeat measurements is often of order ± 0.2 dE asshown in Fig. 15.7) The noise floor of the system is determined bydriving both sides of the measurement system with oneoscillator haVing a similar power and impedance levelas that used in these measurements. If the noisefloor is within 13 dB of that measured in step 7above, corrections are made to the measurement datato remove the bias generated by the noise floor.Measurements of the amplitude accuracy of the phasemodulation side bands generated by the prototypephase modulators are summarized in Fig. 15. The samemodulator was used for carrier frequencies from 5 to300 MHz. The error in the phase modulation amplitudeis less than 0.5 dB for modulation frequencies fromdc to 10' of the carrier. The 10 GHz modulator alsomaintains an accuracy of better than 0.5 dB out to500 KHz from the carrier. At 1 GHz the modulationamplitude is 1.5 dB high. Once this is measured itcan be taken into account in the calibrationprocedure. The 45 GHz modulator results shown inFig. 15 should be attainable over the entire WR22wavequide bandWidth.The performance that can be obtained with thismeasurement technique is illustrated by actual phasenoise data on oscillator pairs shown in Figs. 15 and16. Typical accuracies are ±0.6 dB with a noisefloor at about - 175 dB relative to 1 radian 2 /Hz.The corrections applied to the raw data at 10 GHz areshown in Fig. 17. At low frequencies the effect ofthe phase-locked loop is apparent while at the higherfrequencies the roll-off of the amplifiers areimportant. These effects have been emphasized herein order to examine the ability of the calibrationprocess to correct for instrumentation gainvariations.V, ConclusionWe have analyzed several traditional approaches tomaking phase measurements and found that they alllacked some element necessary for making phase noisemeasurements from essentially dc out to 10, of thecarrier frequency with good phase noise floors and anaccuracy of order 1 dB. By combining several of thetechniques and adding a phase modulator which isexceptionally flat from dc to about lOt of thecarrier frequency, we have been able to achieveexcellent phase noise floors, bandwidths of at leastlOt of the carrier, and accuracies of order ±0.6 dB.1.5m Ll 1.0.!:...g 0.5wc:.Q oI--__.::=----------=:iii"5-g -0.5:ECDtil~ -1.011.-1.5!::--1-_~~-I-_...J--;!;-..l_-L-:_.L---l~:I::-....L._.L-~0,001 0.01 0.1 1 10 100Modulation Frequency (I) in % of Carrier FrequencyFig. 14 Measurement of the amplitude error ofmodulation signal versus Fourier frequencies f. forthese prototype phase modulators. Curves labeled 5,100, and 300 KHz were obtained with the modulatorused in 5 to 1,300 KHz test set. The curve labeled10 GHz was obtained with the modulator for the 2 to26 GHz test set. The curve labeled 45 GHz wasobtained with the WR22 test set.N -136I-NU~2 -138IV.... 11dBal'Uc::- ":9--140tf)Two Oscillator Calibration Test @ 5MHz• System Ax System BA System B + M410 Hz 100 Hz 1kHzI...og Fourier Frequency (HzlFig. 15 Demonstration of calibration accuracy fortwo oscillator concept. The curve labeled System Ashows the measured phase noise of a pair of 5 MHzOSCillators using the test set shown in Fig. 13. Thecurve labeled System B shows the measured phase noiseof the same pair of 5 MHz oscillators using a totallyseparate measurement system with the oscillators heldin phase quadrature with the measurement test set ofA. The curve labeled System B + ~/4 shows the phasenoise of the same pair of oscillators using test setB with and extra cable length of ~/4 inserted intoeach signal path. The agreement between the threecurves is in the worse case ± 0.15 dB.TN-137440
NJ:",--0~.8~..(/)-110-1:20-130-140m -150-0cc -160-170-180Phase Noise at X Band2 3 4 567Lng Fourier Frequency (Hz)--_ .. .. -~.--4 5 6 7 aI-Dg Fourier Frequency (Hz).. - .8 9Fig. 16 Phase noise measurement on a pair of 10.6GHz sources using the new NBS measurement technique.a::I"0 0£:tJjc:.2 -513~00c:0:;:;~.0~0-103Calibration CorrectionFig. 17 Correction factor applied to the measurementdata made to obtain the results of Fig. 16.ACknowled~ement~The authors are grateful to many colleagues,especially David W. Allan, James C. Bergquist, AndreaDeMarchi, David J. Glaze, James E. Gray, David A.Howe, John P. Lowe, Samuel R. Stein and Charles Stonefor many fruitful discussions on this topic and theCalibration Coordination Group for the funding toimprove the accuracy and bandwidth of phase noisemetrology.References1. J. A. Barnes, A. R. Chi, L. S. Cutler, D. J.Healey, D. B. Leeson, T. E. McGunigal, J. A. Mullen,Jr., W. L. Smith R. L. Sydnor, R. F. C. Vessot, G. M.Winkler, Characterization of Frequency Stability,Proc. IEEE Trans. on I &M 22, 105-120 (1971).3. D.W. Allan, H. Hellwig, P. Kartaschoff, J.Vanier, J. Vig, G.M.R. Winkler, and N.F. Yannoni,Standard Terminology for Fundamental Frequency andTime Metrology, to be published in the Proe. of the42nd Symposium on Frequency Control, Baltimore. MD.June 1-4, 1988.4. F. L. Walls, and S. R. Stein, AccurateMeasurements of Spectral Density of Phase Noise inDevices, Proc. of 31st SFC, 335-343, (1977).(National Technical Information Service, SillsBuilding, 5825 Port Royal Road, Springfield, VA22161).5. F. L. Walls, S. R. Stein, J. E. Gray, and D. J.Glaze, Design Considerations in State-of-the-ArtSignal Processing and Phase Noise MeasurementSystems, Proc. 30th Ann. SFC, 269-274 (1976).(National Technical Information Service, SillsBuilding, 5285 Port Royal Road. Springfield, VA22161).6. R. L.. Barger, M. S. Soren. and J. L. Hall,Frequency Stabilization of a cw Dye Laser, Appl.Phys. Lett. 22. 573 (1973).7. F. L. Walls and A. E. Wainwright, Measurement ofthe Short-Term Stability of Quartz Crystal Resonatorsand the Implications for Crystal Oscillator Designand Applications, IEEE Trans. on I & M~, 15-20(1975).8. A. S. Risley, J. H. Shoaf, and J. R. Ashley,Frequency Stabilization of X-Band Sources for Use inFrequency Synthesis into the Infrared, IEEE Trans. onI & M, n, 187-195 (1974).9. J. R. Ashley, T. A. Barley, and G. J. Rast, TheMeasurement of Noise in Microwave Transmitters, IEEETrans. on Microwave Theory and Techniques, SpecialIssue on Low Noise Technology, (1977).10. A. L. Lance. ~. D. Seal, F. G. Mendoza, and N. W.Hudson, Automating Phase Noise Measurements in theFrequency Domain, Proc. 31st Ann. Symp. On Freq.Control, 347-358 (1977).11. A. L. Lance and W. D. Seal, Phase Noise and AMNoise Measurements in the Frequency Domain atMillimeter Wave Frequencies, from Infrared andMillimeter Waves, Ken Bucton Ed., Academic Press, NY1985.12. F. L. Walls and A. DeMarchi, RF Spectrum of aSignal After Frequency Multiplication Measurement andComparison with a Simple Calculation, IEEE Trans. onI & M~, 210-217 (1975).13. F.L. Walls, A New Phase Modulator for WidebandPhase Noise Measurement Systems, to be submiCted toIEEE Transactions on Ultrasonics, Ferroelectrics andFrequency Concrol.2. J. H. Shoaf, D. Halford, and A. S. Risley,Frequency Stability Specifications and Measurement,NBS Technical Note 632, (1973). Document availablefrom US Government printing office. Order SD at#CI3.46:632.441TN-13B
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Characterization ofClocks and Oscil
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PREFACEFor many years following its
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0 • • • • • • • •
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0 •• 0 •• 0 •• 0 •
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TOPICAL INDEX TO ALL PAPERSThe foll
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of the wide range of measurement si
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The first of these (D.l) by Lesage
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Table 1. Guide to Selection of Meas
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10- 1410- 15c-een10- 1610- 1710- 18
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Table 2. Ratio of mod a~('r) to a~(
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of the frequency measured in this m
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From: Proceedings of the 35th Annua
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where V0 ;: nomi na I peak vo Itage
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ports of the pair of double balance
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fluctuations prior to the bias box
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up an interesting hierarchy of kind
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is determi ned by the measurement s
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Since each average of the fractiona
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Thus. with 9~ probability the calcu
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in fact. Also for n=l the "experime
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1n tenns of the typical performance
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and eq (1.1) we get2m>(t) = ~T(t) =
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varactor control in th@ reference o
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V nn5(45 Hz) = 100 nV por root hort
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We can use the convolution theorem
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though the concept of harmonics in
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and wz(t) is now the si!npled versi
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10.7 Time Domain-Frequency Domain T
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o/(t). In the table, the left colum
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Weean make the following general re
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-flO• r.1OSP1 t(f2-,~ 1Ci~-/'10 f
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frequency extent of the analysis ba
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28. P. Kartaschoff and J. Barnes, "
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_--_._~--~II..gIIIIII1.......oIIIII
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From: Precision FrequenC)' Control,
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12 FREQUENCY AND TIME MEASUREMENT 1
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12 FREQUENCY AND TIME MEASUREMENT19
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12 FREQUENCY AND TIME MEASUREMENT 2
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12 FREOU::NCY AND TIME MEASUREMENT2
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12 FREQUENCY AND TIME MEASUREMENTI~
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12 FREOUENCV AND TIME MEASUREMENT21
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Page 107 and 108: 228 SAMUEL R. STEIN9.3 GHzOSCILLATO
Page 109 and 110: 230 SAMUEL R. STEINThe combination
Page 111 and 112: 232 SAMUEl R STEINHowever, the spec
Page 113 and 114: 400 CHAPTER BIBLIOGRAPHIESAllan. D.
Page 115 and 116: 402 CHAPTER BIBLIOGRAPHIESBaugh. R.
Page 117 and 118: 404 CHAPTER BIBLIOGRAPHIESConway. A
Page 119 and 120: 406 CHAPTER BIBLIOGRAPHIESGardner.
Page 121 and 122: 408 CHAPTER BIBLIOGRAPHIESJackisch.
Page 123 and 124: 410 CHAPTER BIBLIOGRAPHIESlesage. P
Page 125 and 126: 412 CHAPTER BIBLIOGRAPHIESPaul. F.
Page 127 and 128: 414 CHAPTER BIBLIOGRAPHIESSorden. J
Page 129 and 130: 416 CHAPTER BIBLIOGRAPHIESYoshimura
Page 131 and 132: 648IEEE TRANSACTIONS ON ULTRASONICS
Page 133 and 134: 650 IEEE TRANSACTIONS ON ULTRASONIC
Page 135 and 136: 652 IEEE TRANSACTIONS ON ULTRASONIC
Page 137 and 138: IEEE TRANSACTIONS ON ULTRASONICS. F
Page 139 and 140: Powet spectral analysis of the outp
Page 141 and 142: major difficulty is designing a mix
Page 143 and 144: The phase noise in the source can c
Page 145: detail elsewhere [12]. The low pass
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Page 151 and 152: 2. Copy.r,ion Beeween Frequency and
Page 153 and 154: All.n, D. Y., .nd D...s, H., Picose
Page 155 and 156: 105Characterization of Frequency St
Page 157 and 158: B'R:sES et ai.: ClHR.,CTY.RIZHIO:-r
Page 159 and 160: e4.RNES et al.: CH."R.ACTERrZ.4.TIO
Page 161 and 162: MII.NES et al.. CHAIl.ACfERlZATlO:-
Page 163 and 164: :l frequcllcy ~eparatioll froll1 th
Page 165 and 166: MRNES et al.: CHARACTERIZATION OF F
Page 167 and 168: B\R~f:S eL al.: CIHRACTERIZ.,TIOI<
Page 169 and 170: 8IR:-IES et al.: CH.'R.'CTER[Z.
Page 171 and 172: 142 Rep. 580--2Reprinted, with perm
Page 173 and 174: i44 Rep. 580-2If the initial sampli
Page 175 and 176: 146 Rep. 580-2The values of ha are
Page 177 and 178: 148 Rep. SSO-2TABLE II - Translalio
Page 179 and 180: ISO Rep. 580-2, 738-2BIBLIOGRAPHYAL
Page 181 and 182: 522 LESAGE AND AUDOIN01., 1971J:S,I
Page 183 and 184: 524 LESAGE AND AUDOINKl- 1410- 11 \
Page 185 and 186: 526LESAGE AND AUDOINQuartz ClJstalF
Page 187 and 188: 528 LESAGE AND AUDOINMinrFrequent,r
Page 189 and 190: 530 LESAGE AND AUOOINsuch as c:r;(T
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538 LESAGE AND AUWINstability measu
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Copyright Ie) 1984 Academic Press.
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7. PHASE NOISE AND AM NOISE MEASURE
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7. PHASE ~OISE AND AM NOISE MEASURE
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7. PHASE :'-iOrSE AND AM NOISE MEAS
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or, in rms radians,7. PHASE !'rOISE
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i. PHASE :-JOISE AND AM NOISE MEASU
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7. PHASE ~OISE AND AM NOISE MEASVRE
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7. PHASE NOISE AND AM :>lOISE MEASU
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_~ ~A _7. PHASE NOISE AND AM NOISE
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average frequency over the interval
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and frequency stability of precisio
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PHASE P~OT Clook No. ~- e I"d,....
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BL-\5ES .-\.\D \·A.Rl.-\.\CES OF S
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to a g
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while the Hanning ""!Odo"" yIelds1.
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Proc. 35th Ann. Freq. Control Sympo
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N-3n+lEj=1Mod Oy2 (t) =0 2(t) {.! +
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(a)1SIMULATED NOISE(b)1-10- 2- --10
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IEEE TRANSACTIONS ON INSTRUMENTATlO
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IEEE TRANSACTIONS ON INSTRUYlENTATI
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From: Proceedings of the 15th Annua
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where c = Dr/2. In regression analy
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'" Dr 22 = -7.507E-16 (about -6.5E-
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Coefficient of simple determination
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100%CUMULATIVE PERIODOGRAM ~50%(,
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100%CUMULATIVE PER I ODOGRAM50%U'10
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TABLE 6.STANDARD DEVIATIONSPROCEDUR
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APPENDIX AREGRESSION ANALYSIS(Equal
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andG == N (N - 1) (N - 2)Also, the
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APPENDIX BREGRESSIONS ON LINEAR AND
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REFERENCES1. D.W. Allan, "The Measu
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5.12 )( 10 - 7 SEC
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100%CUMULATIVE PERIODOGRAM -50%U'
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100%CUMULATIVE PERIODOGRAM50%(J'l..
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FREQUENCY DRIFT AND WHITESTANDARD D
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MR. McCASKILL:Well, let me go furth
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NIST Technical Note 1318, 1990.VARI
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By definition, white noise has a po
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where aZ(N,T,r) is the expected sam
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Some useful asymptotic forms of B 3
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Since the time-domain definition fo
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Stability Using Non-zero Dead-Time
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I!II.....I~I.....cIQ)IEQ) I~I~(J)
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-2,THE BIAS FUNCTION, 8 2 (r,p.)Fig
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AppendixWith reference to figure 1,
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8lIN,r,lll) for r = .011\1\ N= ~ 81
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BUN,r,IItJI for r =/tl\ !'I= 8 16 3
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81 (N,r,lIUl for r =ItJ \ IF 4 8 16
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__ ....... ~...........__ .........
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BllN,r,kl) for r = 1024It! \ N= 4 B
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B2(r,llU)It! \ r = .0001 .0003 .001
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B3( 2, P1,I", IIU) far r '" .01~\ ~
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83(2,I'f,r,~)for r '"""'III \ 2 4 B
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B312.I'I,r,llU) for r " 4I\J \ pt::
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B3(2,I'I,r,lIJ) Fer r ~ MI\J\ PI::
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B3(2,"',r,ail for r = 1024MIl \ I'l
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E. APPENDIX - Notes and ErrataThe n
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Influence of Pressure and Humidity
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22. page TN-160In eqs (101), (102),
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29. page TN-180If the ratio of T/ T
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NIST-114A(REV. 3-89)4. TITLE AND SU
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NIST Technical Note 1337: Characterization of Clocks and Oscillators

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