NIST Technical Note 1337: Characterization of Clocks and Oscillators

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A.7 SUPPLEMENTARY READING LISTGerber, Eduard A. and Arthur Ballato (editors),IPreciSion Frequency Control, Volumes 1and 2 (Academic Press, New York, 1985).iJespersen, James and Jane Fitz-Randolph, Froim Sundials to Atomic Clocks, (DoverPublications, New York, 1982).,Kartaschoff, P., Frequency and Time, (Academic Press, New York, 1978).iIKruppa, Venceslav F. (editor), Frequency Stability:[Fundamentals and Measurement, (IEEEPress, New York, 1983).IRandall, R.B., Frequency Analysis, (Brliel and Kj~r, Denmark, 1987).IVanier, J. and C. Audoin, The Quantum Physics df Atomic Frequency Standards, Volumes1 and 2 (Adam Hilger, Bristol, England, 1989). IISpecial Issues of Journals devoted to Time and Frequen? TopicsIProceedings of the IEEE, Vol. 54, February, 1966. iiProceedings of the IEEE, VoL 55, June, 1967.Proceedings of the IEEE, Vol. 74, January, 1986.IEEE Transactions on Ultrasonics, Ferroelectrics, ~nd Frequency Control, Vol. UFFC-34,November, 1987. !IRegular Publications dealing with Time and Frequency TopicsIEEE Transactions on Ultrasonics, Ferrolectrics ami, Frequency Control.IProceedings of the Annual Symposium on FrequenGJ( Contro~IEEE.Proceedings of the Annual Precise Time and Time [Interval (PITI) Applications and PlanningMeeting, available from the U.S. Naval Obsertatory.Proceedings of the European Frequency and Time ~01um.IN-13
From: Proceedings of the 35th Annual Symposium on Frequency Control, 1981.PROPERTIES OF SIGNAL SDURCE~MEASUREMENT METHODSiANDD. A. Howe, D. W. Allan, and J.IA. BarnesSummaryThis paper is a review of frequency stabilitymeasurement techniques and of noise properties offrequency sources.First, a historical development of the usefulnessof spectrum analysis and time domain measurementswi 11 be presented. Then the rati ana1e wi 11be stated for the use of the two-sample (Allan)variance rather than the classical variance.Next, a range of measurement procedures wi 11 beoutlinea with the trade-offs given for the various,-echni ques emp 1oyed. Methods of i nte,,:lreti ng themeasurement results will be given. In particular,the five commonly used noise models (white PM,flicker PM, white FM, flicker FM, and random walkFM) and thei r causes wi 11 be di scussea. Methodsof characterizing systematics will also be given.Confidence intervals on the various measures willbe discussed. In addition, we will point outmethods of improving this confidence interval fora fixed number of data points.Topics will be treated in conceptual detail.Only light (fundamental) mathematical treatmentwi 11 be gi ven.Although traditional concepts. will be detailed, two new topi cs will be introduced in thi spaper: (1) accuracy limitations of digital andcomputer-based analysis and (2) optimizing theresults from a fixed set of input data.The final section will be devoted to fundamental(physical) causes of noise in commonly usedfrequency standards. Also transforms from time tofrequency domain and vice-versa will be given.Key Words. Frequency stabil ity; Oscill ator noi semodeling; Power law spectrum; Time-domain stabi1ity; Frequency-domain stabil ity; White noise;Flicker noise.IntroductionPrecision oscillators play an important rolein high speed communications, navigation, spacetracking, deep space probes and in numerous otherimportant applications. In this paper, we willrevi ew some preci sian methods or measuri ng thefrequency and frequency stability of precisionoscillators. Development of topics does not relyheavily on mathemati cs. The equipment and set-upfor stabi 1i ty measurements are out1i ned. Ex amp 1esand typical results are presented. PhysicalTime and Frequency Divis~onNational Bureau of Standa~dsBoulder, Colorado 8030B,interpre~ations of common noise processes arediscusseb. A table is provided by which typicalrrequencw domain stability characteristics may beitranslated to time domain stability characteristicsand vicetversa.L THEI SINE WAVE AND STABILITYA , Is i ne wave signal generator produces avoltage [that· changes in time in a sinusoidal wayas show~ in figure 1.1. The signal is an oscillatingsi;gna1 because the sine wave repeats itself.A cycle! of the oscillation is produced in oneperi ad 'rr". The phase is the ang1 e ""," wi thi n acycle c~rresonding to a particular time "t"..,,: FIGURE 1.1Itiis convenient for us to express angles inradians! rather than in units of degrees, andpositi\(~ zero-crossings will occur at even multip1es!orinumber iorrecipro~a1express{on!sine wa~en-radi ans. The frequency: "u" is thecycles in one second, which is theof period (seconds per cycle). Thedescribing the voltage "V" out of asignal generator is given by Vet) ::: V pis the peak voltage amplitUde.sin ["'(t)] where VipEquival+nt expressions are1TN-14
Page 1 and 2: Characterization ofClocks and Oscil
Page 3 and 4: PREFACEFor many years following its
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Page 9 and 10: TOPICAL INDEX TO ALL PAPERSThe foll
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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~(
Page 21: of the frequency measured in this m
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) =
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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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Page 56 and 57: 10.7 Time Domain-Frequency Domain T
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Page 64 and 65: frequency extent of the analysis ba
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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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