NIST Technical Note 1337: Characterization of Clocks and Oscillators

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National Institute of Standards and Technology Technical Note 1337Natl. Inst. Stand. Techno!., Tech. Note 1337, 352 pages (Jan. 1990)CODEN:NTNOEFu.s. GOVERNMENT PRINTING OFFICEWASHINGTON: 1990For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, DC 20402·9325
PREFACEFor many years following its publication in 1974, "TIME AND FREQUENCY: Theoryand Fundamentals," a volume edited by Byron E. Blair and published as NBS Monograph 140,served as a common reference for those engaged in the characterization of very stable clocks andoscillators. Monograph 140 has gradually become outdated, and with the recent issuance of anew military specification, MIL-0-55310B, which covers general specifications for crystal oscillators,it has become especially clear that Monograph 140 no longer meets the needs it so ablyserved in earlier years. During development of the new military specification, a process involvingdiscussion and input from many quarters, a key author of the specification, John Vig of the USArmy Electronics Technology and Devices, urged the National Bureau of Standards (now theNational Institute of Standards and Technology, NIST) to issue a revised publication to serve asreference for the characterization of clocks and oscillators. With NIST having agreed to thistask, the framers of the military specification used the nomenclature "NBS Monograph 140R" intheir document, anticipating a revised (R) volume which had not yet been prepared.Considering the availability of a number of newer books in the time and frequency field,the rewriting of a major volume like Monograph 140 seemed inappropriate. The real need hasnot been for rework of everything in Monograph 140, but only for those parts which providereference to definitions and methods for measurement and characterization of clocks and oscillators,subjects which are fully covered in a number of papers distributed through a variety ofconference proceedings, books, and journals. For the near term, we concluded that the mosteffective procedure would be to collect a representative set of these papers into one referencesource with introductory comments which permit the reader to quickly access material requiredto meet particular needs. Thus, we arrived at this particular collection. The editors' challengehas been to select representative papers, to organize them in a convenient manner, and to dealwith errata and notation inconsistencies in a reasonable manner. In the longer term, the materialin this volume needs to be more completely integrated. This task would profitably awaitfurther deVelopments in the area of phase noise measurements.Donald B. SullivanDavid W. AllanDavid A. HoweFred L. WallsBoulder, ColoradoFebruary 28, 1990iii
Page 1: Characterization ofClocks and Oscil
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Page 9 and 10: TOPICAL INDEX TO ALL PAPERSThe foll
Page 11 and 12: of the wide range of measurement si
Page 13 and 14: The first of these (D.l) by Lesage
Page 15 and 16: Table 1. Guide to Selection of Meas
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Page 19 and 20: Table 2. Ratio of mod a~('r) to a~(
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Page 23 and 24: From: Proceedings of the 35th Annua
Page 25 and 26: where V0 ;: nomi na I peak vo Itage
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Page 29 and 30: fluctuations prior to the bias box
Page 31 and 32: up an interesting hierarchy of kind
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Page 35 and 36: Since each average of the fractiona
Page 37 and 38: Thus. with 9~ probability the calcu
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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
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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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228 SAMUEL R. STEIN9.3 GHzOSCILLATO
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230 SAMUEL R. STEINThe combination
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232 SAMUEl R STEINHowever, the spec
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400 CHAPTER BIBLIOGRAPHIESAllan. D.
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402 CHAPTER BIBLIOGRAPHIESBaugh. R.
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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 \
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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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