NIST Technical Note 1337: Characterization of Clocks and Oscillators

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CHAPTER 12 415Van Straalen. J. (1979). A one-chip LSI frequency meier in Ihe I'L lechnology for FM and AMreceivers. IEEE Trails. COIUJIm. Elulroll. CE-2S. 134-143.Vessol. R.• Mueller. l.. and Vanier, J. (1966). The specificalion of oscillalor characlerislics frommeasuremenlS made in Ihe frequency domain. Proc. IEEE Sot. 199-206.Viles. R. S. (1972). SlIIepl frequency lechniques for aCCUrllle r.f. measuremenls. Moreolli IIIslT1Uf1.13.88-92.Voss, R. F. (\979). lifnoise. Proc. JJrd AMII. Frtq. COII/rol Symp.• pp. 40-46.Wamwrighl. A. E.• Walls. F. l.. and McCaa. W. D. (1974). Direcl measuremenl of the inherenlfrequency stabilily of quanz crystal resonalors. Proc. 281h AllnLl. Frtq. Conlrol Symp.• pp.177-180.Walls. f. l.. and DeMarchi. A. (1975). Rf spectrum of a signal after frequency multiplication;measurement and comparison wilh a simple calculalion.IEEE Trans. Inslrum. MtQS.IM-24.310-317. *W.alls. f. L.. and Stein. S. R. (1976). Servo lechniques in oscillators and measurementsystems. NBS Tech. No/e (CS.) 69:.Walls. f. L.. Stein. S. R.. Gray. J. A.. and Glaze. D. J. (1976). Design considerations in state-ofthe-artsignal processinl! and phase noise measurement systems. Proe. 30,h .-fMII. Freq.COnlrol Symp.. pp. 269-274.Ward. R. B. (1982). VH f /UHF frequency measurement using the surface acoustic wave delaydifference device. Appl. Phys. Ull. 40.1010-1012.Weiss. C 0 .. and Godone. A. (l98~). Extension offrequency measurements with Schonley diodesto the 4 THz ranl!e Appl. Phys. B 27, 167-168.Weiss. R. (1976). Time-signal and standard·frequency receiver for the DCF 77 wilh reserve. l.FLinksehoLi 48. 964-968. In Gennan.Wessel. R. (1973). A digital frequency meter. Eleklromeisler DIsch. Elektrohand..'erk 48.1066-1068. In Gennan.Westlund, R. C. (1978). Very short time interval measurements. Ne..· £lee/rOil. It 13-14. 18.Wheeler. K. G. (1976). An optimum solution for couming and timing. He .. Electron. 9. 24. 28. 3~.Whinaker. A. E.. and Westbury. P. R. (\976). Measuring low frequencies. Ne... Eleclron. 9. 36.Wiley. R. G. (977). A direct time-domain measure of frequency stability: the modified Allanvariance. IEEE Tro/'lS. 1/'ISlrum. Mea!. IM-26, 38-41.Woschni. E. G. (975). Errors in high-precision frequency measurements due to interactiveeffects. Wiss. Z. Tech. Hochseh. Karl-Marx-Suuft 17. 633-639. In GermanWoschni. E. G. (1976). On the optimum difference frequency in hi~ accuracy frequencymeasurements of industrial parameters. Mess.. St~ern. Rtgtln Alllomalisitrllllgsprax. 19.334-335. In Gennan.Woschni. E. G. (978). Application of microprocessors to the calculation of error correction forthe synchronisation effect in hil!hly accurate frequency measurements. Win. Z. Tuh.Hochsch. Karl-Marx-Slodt 20. 665-668. In Gennan.Wrzesien. M. (\976). Instantaneous frequency measuring circuit. Pomiory. Autom. Kontrolo 22.90-91. In Polish.Ya~uda. Y. (1974). Accuracy of estimating c10ckface and mean rate of the frequency standard bynormal regression theory. J. Radio Res. UJb. (Japan) 21. 39-60.Yoshimura. K. (1972). The generation of an accurate and uniform time scale with calibrationsand prediction. ""BS Tech. "'-ole lC.S.) 626.59 pp.Yoshimura. K. (1978). Characterization of frequency stability: uncertainty due to the autocor·relation of the frequency fluctuations. IEEE Trans. Inslrum. Meas. IM-27. 1-7.Yoshimura. K. (1980). Calculation of unbIased clock-variances in uncalibrated atomic time scaleal~orithms. Mnrologio 16. 133-139.• See Appendix Note # 10TN-119
416 CHAPTER BIBLIOGRAPHIESYoshimura. K. Harada. K.. and Kobayashi. M. (1971). Measuremenl of short-term frequencystability of frequency standards. Rrt·. Radio Rl!s. LiJbs. 17. 437-4·B. In Japanese.Yuva!. I. (1982). Frequency comparalor uses synchronous detel:tion. Elufronics ~~. 160.Zander. H. (19771. Measurement of low frequencies with short duration. Elrklronik (Munich) 26.6J-64. In German.Zelenlosov·. V. L Sulakshin. A. 5.. and Fedorov. K P. (1976). Meter for measurinl! the carrierfrequency of smgle ultrahigh-frequency pulses. Insfrum. E.tp. Tl!ch. (Ellgi. Trans!.) 19.476-4"77.Zhilin. No S. and Subbotin. l. S. (1977). Devices for reproducinl! reference time inter-als. .4Jl!as.Tl!ch. (Engl. Trans!.) 20. 995-999.Zhuk. A V.. KJZ3nlseli. E. M.. Klrianakl. ~. K.. and Mosieliich. P. M. 119771. Computerinvestil!ation 01 the metroIOl!1Cal charac!enstlcs of frequency meters ....·I\h digital positivef~dback and measures to improve them. albor Prrrdacha lrrf. 50. 110-115. In RussianTN-120
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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 MEASUREMENT19
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Page 80 and 81: 12 FREQUENCY AND TIME MEASUREMENT 2
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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 and 126: 412 CHAPTER BIBLIOGRAPHIESPaul. F.
Page 127: 414 CHAPTER BIBLIOGRAPHIESSorden. J
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
Page 177 and 178: 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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