NIST Technical Note 1337: Characterization of Clocks and Oscillators

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28. P. Kartaschoff and J. Barnes, "Standard Timeand Frequency Generation," Proc. IEEE, vol.60, pp. 493-501, May 1972.29. A. L. Lance, W. D. Seal, F. G. Mendoza, andN. W. Hudson, "Automating Phase Noise Measurementsin the Frequency Qomai~," Proc. 31stAnnual Symposium on Frequency Control, 1977,pp. 347-358.30. D. B. Leeson, "A Simple Model of FeedbackOscillator Noise Spectrum, 'I Proc. IEEE L.,vol. 54, pp. 329-330, February 1966.31. P. Lesage and C. Audoin, "A Time DomainMethod for Measurement of the Spectral Densityof Frequency Fluctuations at Low FourierFrequencies," Proc. 29th Annual Symposium onFrequency Control, 1975, pp. 394-403.42. F. L. Walls, S. R. Stein, J. E. Gray, and D. J.Glaze, "Design Considerations in State-ofthe-ArtSignal Processing and Phase NoiseMeas urement Sys tems •" Proc. 30th Annua 1Symposium on Frequency Control, 1976, pp.269-274.43. F. Walls and A. Wainwright, "Measurement ofthe Short-Term Stability of Quartz CrystalResonators and the Imp 1i cations for QuartzOscillator Design and Applications," IEEETrans. on Instrum. and Meas., pp. 15-20,March 1975.44. G. M. R. WinKler, "A Brief Review of FrequencyStability Measures," Proc. 8th Annual PreciseTime and Time Interval (PITI) Appl icationsand Planning Meeting, Nov. 1976, pp. 489-527.32. P. Lesage and C. Audoin, "Estimation of theTwo-Sample Variance with Limited Number ofData," Proc. 31st Annual Symposium on FrequencyControl,1977, PP. 311-318.33. P. Lesage and C. Audotn, "Characterization ofFrequency Stabil tty: Uncertai nty due toFinite Number of Measurements," IEEE Trans onInstrum. and Meas. IM-22, pp. 157-161, June1973. -----III... ,I!AppendixDEGREES OF FREEDOM FOR ALLAN VARIANCE_34. W. C. Lindsey and C. M. Chie, "Specificationand Measurement of Oscillator Phase NoiseInstability," Proc. 31st Annual Symposium onFrequency Control, 1977, pp. 302-310.35. D. G. Meyer, "A Test Set for Measurement ofPhase Noi se on Hi gh Qual i ty Si gna 1 Sources,"Proc. IEEE Trans on Instrum. and Meas. IM-19,No.4, pp. 215-227, November 1970. -36. C. D. Motchenbacher and F. C. Fitchen,Low-Noise Electronic Desion, New York.: JohnWiley &Sons, 1973.37. D. Percival. "Prediction Error Analysis ofAtomi c Frequency Standards ," Proc. 31stAnnual Symposium on Frequency Control, 1977.pp. 319-326.38. D. Percival, "A Heuristic Model of Long-TermClock Behavi or," Proc. 30th Annua 1 Sympos i umon Frequency Control, 1976, pp. 414-419.39. J. Shoaf, "Specification and Measurement ofFrequency Stabi lity," NBS Internal Report74-396, November 1974.E..g= IIII.u......o 110--IIIIII= e,~....oI.III !"i I::l IZ_L._~lJTau (in unit. or data .pacing)---lIII40. J. L. Stewart, "Frequency MOdulation Noise inOscillators," Proc. IRE, vol. 44, pp. 372376, March 1956.41. R. F. C. Vessot, L. Mueller, and J. Vanier,"The Specification of Oscillator Characteristicsfrom Measurements in the FrequencyDomain," Proc. IEEE, pp. 199-206, February1966.44TN-57
"r---"-IDEGREES OF FREEDO~ FOR ALLAN VARIANCE~i_ '" ....1..1....] 1IftI! ........ fer !lhIU FN----r-------.-----,IIjDEGREES OF FREEDOM FOR ALLAN VARIANCESWhite Phe•• Noia."0-0OJOJI.........0l!)IIII'llI-enIIICl.....0IIlll>..0EO::l:z iIL.__. _ __---ḷ .E0-cIIIIIII.........0..IIIIIII-mIIIc.....0IIII.0EO::lZ"SJ• - :l. 11-513..II-2S'I...12llIIoe...33.•,~,~,-- LIIl1liJ. I..J_Tou (In unlta of data apecing)DEGREES OF FREEDOM FOR ALLM~VARIANCEDEGREES Of FREEDOM FOR ALLAN VARIANCES-..g"(IIIIII,.........0..._ .._'----IIIIIII-tilIIIC.«4- I0 IIl-III..cJI!J------j••Tau (in unit. of data .paeing)Eo-c • IIL.... l1li ----
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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
Page 15 and 16: Table 1. Guide to Selection of Meas
Page 17 and 18: 10- 1410- 15c-een10- 1610- 1710- 18
Page 19 and 20: Table 2. Ratio of mod a~('r) to a~(
Page 21 and 22: of the frequency measured in this m
Page 23 and 24: From: Proceedings of the 35th Annua
Page 25 and 26: where V0 ;: nomi na I peak vo Itage
Page 27 and 28: ports of the pair of double balance
Page 29 and 30: fluctuations prior to the bias box
Page 31 and 32: up an interesting hierarchy of kind
Page 33 and 34: is determi ned by the measurement s
Page 35 and 36: Since each average of the fractiona
Page 37 and 38: Thus. with 9~ probability the calcu
Page 39 and 40: in fact. Also for n=l the "experime
Page 41 and 42: 1n tenns of the typical performance
Page 43 and 44: and eq (1.1) we get2m>(t) = ~T(t) =
Page 45 and 46: varactor control in th@ reference o
Page 47: V nn5(45 Hz) = 100 nV por root hort
Page 50 and 51: We can use the convolution theorem
Page 52 and 53: though the concept of harmonics in
Page 54 and 55: and wz(t) is now the si!npled versi
Page 56 and 57: 10.7 Time Domain-Frequency Domain T
Page 58 and 59: o/(t). In the table, the left colum
Page 60 and 61: Weean make the following general re
Page 62 and 63: -flO• r.1OSP1 t(f2-,~ 1Ci~-/'10 f
Page 64 and 65: frequency extent of the analysis ba
Page 68 and 69: _--_._~--~II..gIIIIII1.......oIIIII
Page 70 and 71: From: Precision FrequenC)' Control,
Page 72 and 73: 12 FREQUENCY AND TIME MEASUREMENT 1
Page 74 and 75: 12 FREQUENCY AND TIME MEASUREMENT19
Page 80 and 81: 12 FREQUENCY AND TIME MEASUREMENT 2
Page 82 and 83: 12 FREOU::NCY AND TIME MEASUREMENT2
Page 90 and 91: 12 FREQUENCY AND TIME MEASUREMENTI~
Page 94 and 95: 12 FREOUENCV AND TIME MEASUREMENT21
Page 96: 12 FREQUENCY AND TIME MEASUREMENT21
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
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406 CHAPTER BIBLIOGRAPHIESGardner.
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408 CHAPTER BIBLIOGRAPHIESJackisch.
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410 CHAPTER BIBLIOGRAPHIESlesage. P
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412 CHAPTER BIBLIOGRAPHIESPaul. F.
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414 CHAPTER BIBLIOGRAPHIESSorden. J
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416 CHAPTER BIBLIOGRAPHIESYoshimura
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648IEEE TRANSACTIONS ON ULTRASONICS
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650 IEEE TRANSACTIONS ON ULTRASONIC
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652 IEEE TRANSACTIONS ON ULTRASONIC
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IEEE TRANSACTIONS ON ULTRASONICS. F
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Powet spectral analysis of the outp
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major difficulty is designing a mix
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The phase noise in the source can c
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detail elsewhere [12]. The low pass
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NJ:",--0~.8~..(/)-110-1:20-130-140m
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is ~he preferred measure, since, un
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2. Copy.r,ion Beeween Frequency and
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All.n, D. Y., .nd D...s, H., Picose
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105Characterization of Frequency St
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B'R:sES et ai.: ClHR.,CTY.RIZHIO:-r
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e4.RNES et al.: CH."R.ACTERrZ.4.TIO
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MII.NES et al.. CHAIl.ACfERlZATlO:-
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:l frequcllcy ~eparatioll froll1 th
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MRNES et al.: CHARACTERIZATION OF F
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B\R~f:S eL al.: CIHRACTERIZ.,TIOI<
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8IR:-IES et al.: CH.'R.'CTER[Z.
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142 Rep. 580--2Reprinted, with perm
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i44 Rep. 580-2If the initial sampli
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146 Rep. 580-2The values of ha are
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148 Rep. SSO-2TABLE II - Translalio
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ISO Rep. 580-2, 738-2BIBLIOGRAPHYAL
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522 LESAGE AND AUDOIN01., 1971J:S,I
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524 LESAGE AND AUDOINKl- 1410- 11 \
Page 185 and 186:
526LESAGE AND AUDOINQuartz ClJstalF
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528 LESAGE AND AUDOINMinrFrequent,r
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530 LESAGE AND AUOOINsuch as c:r;(T
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532 LESAGE AND AUDOINl.l-TEquations
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534 LESAGE AND AUDOINof measurement
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LESAGE AND AUDOIN2 - Vo )]53610- 1
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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-
Page 279 and 280:
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
Page 313 and 314:
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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