NIST Technical Note 1337: Characterization of Clocks and Oscillators

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CONTENTSPagePREFACE "" "."" .. " IIITOPICAL INDEX TO ALL PAPERS , , .. " .. xABSTRACT "TN-IA. INTRODUCTIONA.l OVERVIEWTN-IA.2 COMMENTS ON INTRODUCTORY AND TUTORIAL PAPERS , TN-2A.3 COMMENTS ON PAPERS ON STANDARDS AND DEFINmONS TN-3A.4 COMMENTS ON SUPPORTING PAPERS " " 1N-3A.5 GUIDE TO SELECTION OF MEASUREMENT METHODS TN-5A.6 RELATIONSHIP OF THE MODIFIED ALLAN VARIANCE TO THE ALLAN VARIANCE. " TN-9A.7 SUPPLEMENTARY READING LIST " 1N-BB. INTRODUcrORY AND TUTORIAL PAPERS8.1 Properties of Signal SOlJlrces and Measurement MethodsDA. Howe, D.W. Allan, and JA. Barnes35th Annual Symposium on Frequency Control, 1981 Proceedings 1N-14I. The Sine Wave and Stability . TN-14II. Measurement Methods Comparison " . TN-20III. Characterization . TN-22IV. Analysis of Time Domain Data . TN-23V. Confidence of the Estimate and Overlapping Samples . TN-26VI. Maximal Use of the Data and Determination of the Degrees of Freedom . TN-2BVII. Example of Time Domain Signal Processing and Analysis . TN-3DVIII. Spectrum Analysis ....................".................................. TN-32IX. Power-Law Noise Processes . TN-38X. Pitfalls in Digitizing the Data " " " " . TN-39XI. Translation From Frequency Domain Stability Measurement to Time Domain StabilityMeasurement and Vice-Versa . . " " " . TN-48XII. Causes of Noise Properties in a Signal Source . TN-50XIII. Conclusion " . TN-55IU Frequency and Time - Their Measurement and CharacterizationSamuel R. SteinPrecision Frequency Control, Volume 2, Chapter 12, 1985 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . TN-6112.1 Concepts, Definitions, and Measures of Stability TN-6312.1.1 Relationship Between the Power Spectrum and the Phase Spectrum TN-6512.1.2 The IEEE Recommended Measures of Frequency Stability TN-6512.1.3 The Concepts of the Frequency Domain and the Time Domain TN-7312.1.4 Translation Between the Spectral Density of Frequency and the Allan Variance """"" TN-7312.1.5 The Modified Allan Variance " TN-7512.1.6 Detennination of the Mean Frequency and Frequency Drift of an Oscillator TN-7712.1.7 Confidence of the Estimate and Overlapping Samples TN-SO12.1.8 Efficient Use of the Data and Determination of the Degrees of Freedom. . . . . . . . . . . . . . . TN-8312.1.9 Separating the Variances of an Oscillator and the Reference" " " TN-86v
0 • • • • • • • • • • • • • • • • •0 • • • • • • • • • • • • • • • • • • • • • • • •0 • 0 •••••••••••• 0 • • • • • • • • • • • • • • • • • • • •0 0 •••••••••••••• _ • • • •12.2 Direct Digital Measurement IN-B712.2.1 Time-Interval Measurements IN-8712.2.2 Frequency Measurements IN-8912.2.3 Period Measurements IN-8912.3 Sensitivity-Enhancement Methods IN-9012.3.1 Heterodyne Techniques IN-9012.3.2 Homodyne Techniques IN-9112.3.3 Multiple Conversion Methods IN-9712.4 Conclusion - - . . . . . . _. . . . . _. . . . . . . . . . . _. . . . . . . . . . _. . . . . . _. . . . . . . . . . . . __ TN-WIB.3 Time and Frequency (Time-Domain) Characterization, Estimation, and Prediction of PrecisionClocks and OscillatorsDavid W. AllanIEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 1987 _ o. TN-121Page0 ••••••• 0 _ ••• _ ••• 0 •• 0 •••••••••••••• _ •••••••• lli-1210L Introduction _ 0 _2. Systematic Models for Clocks and Oscillators .. _. 0 ••••••••••••• _ • • • • • • • • • • • • • • •• TN-1213. Random Models for Clocks and Oscillators _ 0 ••••••••••••••••••••••••••• _. TN-I234. Time-Domain Signal Characterization _ _ __ ••••••• lli-l235. Time and Frequency Estimation and Prediction _ TN-l266. Conclusions _ ••••••0 0 ••••••••••• 0 •••••• TN-127BA Extending the Range and Accuracy of Phase Noise MeasurementsF.L. Walls, AJ.D. Clements, C.M. Felton, MAo Lombardi and M.D. Vanek42nd Annual Symposium 011 Frequency Control, 1988 Proceedings _ _ lli-1290 •••••••••• 0 •••• _ • • • • • • • • • • • • • • • • • • • • • • • • ••L Introduction TN-129II. Model of a Noisy Signal TN-l290 •••••••••••••••••••••••• 0 •••••••••••HI. Two Oscillator Method TN-130IV. The New NBS Phase Noise Measurement Systems , TN-135V. Conclusion __ _ _. TN-l37C. PAPERS ON STANDARDS AND DEFINmONSCol Standard Terminology for Fundamental Frequency and Time MetrologyDavid Allan, Helmut Hellwig, Peter Kartaschoff, Jacques Vanier, John Vig, Gernot M.R. Winkler,and Nicholas Yannoni42nd Annual Symposium on Frequency Control, 1988 Proceedings _ 0• 0 TN-1390 ••••••••••••• _. lli-1390 ••••••••• 0 ••••••••••••1. Introduction _2. Measures of Frequency and Phase Instability TN-1393. Characterization of Frequency and Phase Instabilities _. TN-1394. Confidence Limits of Measurements 0 • 0 0 •• 0 •••••••••••• _ TN-l405. Recommendations for Characterizing or Reporting Measurements of Frequency andPhase Instabilities __. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. IN-141vi
Page 1 and 2: Characterization ofClocks and Oscil
Page 3: PREFACEFor many years following its
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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
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
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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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