NIST Technical Note 1337: Characterization of Clocks and Oscillators

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CHAPTER 12 413Rozwadowski. M. (1971). Modem frequency stabilisation methods. Pr:egl. Telekomun 44.335-338. In Polish.Ruderfer. M. (1979). One-way doppler effects in atomic timekeeping. Speculations Sci. Technol.2.387-404.Runyon. S. (1977). Focus on electronic.counters. Electron. Des. 25. 54-63.Rusconi. L.. and Sedmak. G. (1977). Estimates of the limiting standard deviation in the absolutetiming of periodic sources. Astrophys. Space Sci. 46. 301-308.Rutman. 1. (\972a). Comment on "Characterization of frequency stability," IEEE Trans.Instrum. Mea.>. 1~1-21. 85.Rutman. 1. (1972b). Short tenn frequency instability of signal generators. Onde Elecrr. 52.480-487. In French.Rutman. 1. (1974a). Characterization of frequency stability: a transfer function approach and itsapplication to measurements via filtering ofphase noise. I EEE Trans.lnsrrum. Meas.I:\
414 CHAPTER BIBLIOGRAPHIESSorden. J. L. (1974). A new generation in frequency and time measurements. Hew/ell-Packard J.25.2-8.Spapens. W. (1972). Accurate time measurements with a counter and an oscilloscope. Philips TeslMeas. NOI. (2l. 4-8.Speake. B. (1979). The accurate setting of microwave frequencies. Commun.Inl. 6.19.21.Stecher. R. (1973). Electronic time interval measurement with nanosecond resolution.Nachrichlenrech. Eleklron. 23.413-416. In German.Steele. 1. McA. (1967). Frequency measurement using standard frequency emissions. Conf. Freq.Generalion and Control Radio SySI.. lEE Conference Publication No. 31.Steer, G. (1973). A new UHF frequency measuring device. Fernme/de-Praxis SO. 571-600. InGerman.Stein. S.. Glaze, D .• Levine, J., Gray. L Hilliard. D., Howe. D .• and Erb, L. A. (1983). Automatedhigh-accuracy phase measurement system. IEEE Trans. Inslrum. Meas. IM-32. 227-231.Steiner. C. I. ( 1969). Electronic methods oftime measurement. E/ek Ironiker 8. 3-16. In German.Stoyko. A. (1967). Ephemeris time according to the revised lunar theory ofBrown. Bull. ASlron. 2,411-416. In French.Szata. R. (1968). New method of oscilloscopic frequency measurement. Pomiary. Au/om.,Kontro/a 14. 200--30 I. In Polish.Szepan. R. (1978). Determining accuracy ofreceiver-controlled frequency standards. Ne ....s Rohde& Sch ....ar: 18. 23-26.Taylor, D. (1968). Time measurement. Inslrum. Rn:. 15. 173-176.Taylor. G. W. (1977). Time-a precious commodity. E/eclron. Power 23, 61-64.Tolman. J. (1970). Accurate frequency and time measurement at the Institute of RadioEngineering and Electronics. S/aboproudy Db•. 31, 286-290. In Czech.Tooley. M. (1979). In-line crystal calibrator. Pracl. Wireless 55.49-50,55.Triplet. J. M. (1967). Ephemeris time determination by lunar photography. Bull. Astron. 2.465-527. In French.Trkal, V. (1968). A new definition of the second on a quantum basis. Cesk. Cas. Fy:. A. 18,641-669. In Czechoslavakian.Turrini, A. (1974). Heterodyne frequency meter No. 351C E.I.P. Antenna 46, 62-68. In Italian.Tyrsa, V. E., and Dyunyashev, V. V. (1981). Accuracy of frequency measurement based on thepulsed coincidence principle. Meas. Tech. (Eng/. Transl.) 24,308-312.Underhill. M. L Sarhadi. M .. and Aitchinson. C S. (1978). Fast-sampling frequency meter.Eleclron. Lell. 14, 366-367.Upton, R. (1977). An objective comparison of analog and digital methods of realtime frequencyanalysis. Brue/ Kjaer Tech. Rev. (Denmark) l. 18-26.Vakman, D. Yeo (1979). The evaluation of frequency stability. Te/ecommun. Radio Eng. (Eng/.Trans/.), ParI 2 34.49-53.Vakman. D. Yeo (1979). Measuring the frequency of an analytical signal. Radio Eng. Eleclron.Phys. (Engl. Trans/.) 24.63-69.Valaskova. E. (1971). Measuring the frequency of damped oscillations. Sdelol'aci Tech. 19.174-175. In Czech.Valverde. R. M. (1968). A digitallOstantaneous frequency-meter. AUloma:. Slrum. 16.216-221.In Italian.Van Blerkom. R.. Freeman, D. G .. and Crutchfield, R. C. Jr. (1968). Frequency measurement·techniques. IEEE Trans. InSlrum. Meas. IM-17. 133-145.Van Den Brock. H. G. 1. (1977). Two frequency counters for routine measurements. PolYlech.Tijdschr. E/eklrolech. Elektron. 32. 517-518. In Dutch.Van den Steen. L. (1979). A low frequency meter with instantaneous response. IEEE Trans.Biomed. Eng. B:\1E-26. 137-140.TN-118
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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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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
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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: 412 CHAPTER BIBLIOGRAPHIESPaul. F.
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 and 146: detail elsewhere [12]. The low pass
Page 147 and 148: NJ:",--0~.8~..(/)-110-1:20-130-140m
Page 149 and 150: is ~he preferred measure, since, un
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
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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 \
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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-
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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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