NIST Technical Note 1337: Characterization of Clocks and Oscillators

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254 A. L. LANCE. W. D. SEAL, AND F. LABAARG. AM NOISE IN THE FREQUENCY DOMAINThe spectral density of AM fluctuations of a signal follows the samegeneral derivation previously given for the spectral density of phase f1uctations.Amplitude fluctuations & of the signal under test produces voltagefluctuations bA at the output of the mixer. Interpretating the mean-squarefluctuations & and 1> in spectal density fashion, we obtain S6,(f), the spectraldensity of amplitude fluctuations bE: of a signal in volts squared per hertz:(48)The term m(j) is the normalized version of the amplitude modulation (AM)portion of SJrf p( v), with its frequency parameter f referenced to the signal'saverage frequency vo, taken as the origin such that the difference frequencyf equals ~' - ~'o' The range of Fourier frequency difference f is from minusVo to plus infinity.Theterm men is defined as the ratio ofthe spectral density ofone amplitudemodulatedsideband to the total signal power, at Fourier frequency differencef from the signal's average frequency Va, for a single specified signal or device.The dimensionality is per hertz. !f(f) and m(f) are similar functions; theformer is a measure of phase-modulated (PM) sidebands, the later is a correspondingmeasure of amplitude-modulated (AM) sidebands. We introducethe symbol m(f) to have useful terminology for the important concept ofnormalized AM sideband power.For the types of signals under consideration, by definition the two amplitude-fluctuationsidebands (lower sideband and upper sideband, at - ff from \'0' respectively) of a signal are coherent with each other. Also, theyare of equal intensity. The operation of the mixer when it is driven at colinearphase is such that the amplitudes of the two AM sidebands are added linearlyin the output of the mixer, resulting in four times as much power in the outputas would be present if only one of the AM sidebands were allowed to contributeto the output of the mixer. Hence, for If I < VO,and, using the definitionwe find, in decibels (carrier) per hertz,(49)(50)m(f) = (l/2V6)S.ll f I). (51)TN-205
i. PHASE :-JOISE AND AM NOISE MEASUREMENTS 255III. Phase-Noise Measurements Using the Two-Oscillator *TechniqueA functional block diagram of the two-oscillator system for measuringphase noise is shown in Fig. 8. NBS has performed phase noise measurementssince 196i using this basic system. The signal level and sideband levels canbe measured in terms of voltage or power. The low-pass filter prevents localoscillator leakage power from overloading the spectrum analyzer whenbaseband measurements are performed at the Fourier (offset) frequenciesof interest. Leakage signals will interfere with autoranging and with thedynamic range of the spectrum analyzer.The low-noise, high-gain preamplifier provides additional system sensitivityby amplyfying the noise signals to be measured. Also, because spectrumanalyzers usually have high values of noise figure, this amplifier is very desirable.As an example, if the high-gain preamplifier had a noise figure of3 dB and the spectrum analyzer had a noise figure of 18 dB, the system sensitivityat this point has been improved by 15 dB. The overall system sensitivitywould not necessarily be improved 15 dB in all cases, because the limitingsensitivity could have been imposed by a noisy mixer.NOISY SIGNAL(THIS IS THE QUANTITYTO BE MEASURED)SMALLFLUCTUATIONSNOISE ONLYMIXERLOW-NOISEAMPLIFIERFIG. 8 The two-oscillator technique for measuring phase noise. Small fluctuations fromnominal voltage are equivalent to phase variations. The phase shifter adjusts the two signalsto quadrature in the mIxer, which cancels carriers and converts phase noise to fluctuating devoltage... See Appendix Note # 6TN-206
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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 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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Page 171 and 172: 142 Rep. 580--2Reprinted, with perm
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Page 175 and 176: 146 Rep. 580-2The values of ha are
Page 177 and 178: 148 Rep. SSO-2TABLE II - Translalio
Page 179 and 180: ISO Rep. 580-2, 738-2BIBLIOGRAPHYAL
Page 181 and 182: 522 LESAGE AND AUDOIN01., 1971J:S,I
Page 183 and 184: 524 LESAGE AND AUDOINKl- 1410- 11 \
Page 185 and 186: 526LESAGE AND AUDOINQuartz ClJstalF
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Page 193 and 194: 534 LESAGE AND AUDOINof measurement
Page 195 and 196: LESAGE AND AUDOIN2 - Vo )]53610- 1
Page 197 and 198: 538 LESAGE AND AUWINstability measu
Page 199 and 200: Copyright Ie) 1984 Academic Press.
Page 201 and 202: 7. PHASE NOISE AND AM NOISE MEASURE
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Page 251 and 252: average frequency over the interval
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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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