NIST Technical Note 1337: Characterization of Clocks and Oscillators

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Chapter 12399Ablowich. D .. Jr. (1966) Some observations conccrnin~ frcqucncy and tlmc standardization.Proc. lis/Ins/rum. Soc. Am. Con! 21. 20Al:imochkin. I. K .. Dcnisov. V. P.• and Chcrcnl:ova. E. M (1973). Lon~·tcrm frcquencycomparator. M~as. Tech (Eng/. Trans/.) 16. 83-85Aldridl!c. D. (1975).5 MHz dll!ital frcqucncy mctcr. Eltc/ron (8~1. 61. 63-64. 66, 68Aldridl!c, D. (1978).5 MHz dil!ital frequcncy mcasurinJ! instrumcnt EI~k/ron. An: 10. 15-18. InGcrmanAllan. D W. (1966). Statistics of atomic frcqucncy standards. Proc.IEEE S4. 2.21-~30Allan. D (1975). "The Mcasurcmcnt of Frcquency and Frequency Slabillty of PreCIsionOscillators." NBS Technical Note 669. National Bureau of Standards. Boulder. Colorad0Allan. D. W .• and Barnes. J. A. (19811. A modificd .. Allan vanancc" .....ith Increased OSCillatorcharactcriution ability Proc. jJ/h Ann" Fr~q Control Symp.. pp 4~O-4'3TN-I03
400 CHAPTER BIBLIOGRAPHIESAllan. D. W.. and Daams. H. I 1975). Picosecond time difference measurement system. Proc.191JrAnnu. Freq. Concrol Symp .• pp. 404-411. .Allan. D. W .. and Hellwig. H. (\978). Time deviation and the prediction error for clockspecification, characterization and application. Proc. Position Localion and NQt:igalionSymp.. pp. 29-36.Allan. D. W .. Gray. 1. E.. and Machlan. H. E. (1972). The National Bureau of Standards atomictime scales~ generation. dissemination. stability, and accuracy. IEEE Trans. Instrum . .\feas.IM-21.388-391.Allan. D. W.. Gray. J. E.. and Machlan, H. E. (\974). The National Bureau of Standards atomictime scales: generation. stability. accuracy and accessibility. In "Time and Frequency:Theory and Fundamentals" (B. E. Blair. ed.), NBS Monogr. NO. pp. 205-231.Allan. D. W .. Hellwig, H.. and Glaze. D. J. (1975). An accuracy algorithm for an atomic timescale. Merrologia 11. 133-138.Andres. I. (1977). Straight talk on frequency counters. Communications 504. 56-60.Andriyanov. A. V., Glebovich. G. V., Krylov. V. V.. Korsakov. S. Ya.. and Ponomarev, D. M.(1980). Automated measurements in the time domain and a method of increasing theiraccuracy I:mer. TekJr. 23,42-44. In Russian.Anonymous (1967). Definition. realisation and use of time and frequency. Colloq. Dig. lEE.Paper no. I J·8 7.Anon~mous (1975a l. Electromagnetic radiation in frequency' measurements. Electron. AlLSr. 37,31. nAnonymous (\975b). Analogue frequency meter (rev. counter). Elektor (GB) I. 737.Anon~mous 11975c). l'ni"ersal frequency reference. Elektor (GB) 1. 715.Anonymous (l975d). A programmable counter type frequency meter. Elecrron. Microelectron.Ind. (2131. 45-49. In French.Anonymous (l976a). High accuracy timing devices. Elektron. Elekrroll!ch. 31. 9-11. In Dutch.Anon~mous (\976b). Time and frequency; two important quantilies 10 modem measurements.Tl!cnol. Eleltr. (\2), 66-69. In Italian.Anon~mous (\977a). 50 MHz counter 'timer. CSIO Commun. I/ndial4. 3~.Anonymous (1977b). A un"'ersal counting and time measuring device. Elekron Inc. IS). 167-169.In German.Anonymous (1977c). Precision timebase for frequency counter. Elekror 1GB) 3.22-25..-\nonymous (1977d). Which counter' Auromation 12. 21. 23. 25Anonymous (1978a). Time measurement where are we? M1!5. Regul. Autom. 43. 19-23. InFrench.Anonymous (1978b). A universal counter on one chip. Elekrronikschau 504. ~8. In German.Anonymous (1978c). Yaesu ~Iusen YC·500S frequency counter. Electron. AlLSt. 40. 103.Anon~mous (1979a). A system of measurement and display of frequency for a AM FM receiver.Electron. Appl. Ind. 271. 55-56. In French...t.nonymous (l979b). A frequency counter for radio receivers. Elekrronikschau 55. 56-57. InGerman.Anonymous (19~9c '. A speciallC revolutionizes the design of universal counters. Elekron. Pra.t.14. 14-18. In German.Anon~mous \ 1979d). Microprocessor and lSI: two features of a universal 100 MHz count~r.Electron Appl. Ind. 270. :23-26. In French.Anonymous (197ge). Time frequency measurements in radJr equipment-which technique?Onde Elecrr. 59. 47-5·t In FrenchAntyufee.... V. I.. Breslavets. V. P.. Fedulov. V. M.. and Fertik. N. S. (19801. Application ofdigitalliltratlon for measuring instability R
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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
Page 62 and 63: -flO• r.1OSP1 t(f2-,~ 1Ci~-/'10 f
Page 64 and 65: frequency extent of the analysis ba
Page 66 and 67: 28. P. Kartaschoff and J. Barnes, "
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: 232 SAMUEl R STEINHowever, the spec
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 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:-
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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 \
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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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