NIST Technical Note 1337: Characterization of Clocks and Oscillators

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282 A. L. LANCE, W. D. SEAL, AND F. LABAARA,.....---., IISIGNALIGENERATOR(FREQ.-MOD.CAPABILITY)IIIADELAY LINEHEWLETT-PACKARD5420ADIGITAL SIGNALANALYZERDUALCHANNELdeSCOPEDELAY LINEFIG. 24 A dual delay-line phase noise measurement system. (Courtesy Instrument Societyof America.)two differential delay-line systems. The single-oscillator signal is appliedto both systems and cross-spectrum analysis is performed on the signaloutput from the two delay-line systems. Signal processing is performed withthe Hewlett-Packard 5420A digital signal analyzer. The cross spectrum isobtained by taking the product of the Fourier transform of one signal andthe complex conjugate of the Fourier transform of a second signal. It isa phase-sensitive characteristic resulting in a complex product that servesas a measurement of the relative phase of two signals. Cross spectrum givesa phase- and amplitude-sensitive measurement directly. By performingthe product Sy(f) . Sx(f)*, a certain signal-to-noise enhancement is achieved.TN-233
7. PHASE NOISE AND AM :>lOISE MEASUREMENTS 283The low-noise amplifiers preceding the digital signal analyzer are usedwhen performing measurements at Fourier frequencies from 1 Hz to 25 kHz.The amplifiers are not used when performing measurements below theFourier frequency of 1 Hz.2. Calibrating the Dual Delay-Line SystemEach delay line in the system is calibrated separately following the samebasic procedure set forth in Section IV.B. The Hewlett-Packard 5420measures the one-sided spectral density of frequency fluctuations in hertzsquared per hertz. The spectral density of phase fluctuation in radianssquared per hertz can be calculated asand(99)(l00)per hertz. The Hewlett-Packard 5420 measurement ofSJy(f) in Hz 2 /Hz must,therefore, be corrected by 1/2f2. However, the f2 correction must be enteredin terms of radian frequency (w = 2rr.j). This conversion is accomplished by5£(f) = SJy(f)(1/2f2)(4rr. 2 /4rr. 2 ) = [2rr. 2 SJy(f)]/(W)2per hertz since Eq. (100) can be stated in the following terms:[2rr. 1 SJy(f)]/4rr.2f 2.(LOllSignal-to-noise enhancement greater than 20 dB has been obtained usingthe dual-channel delay-line system.D. MILLIMETER-WAVE PHASE-NOISE MEASUREMENTSI. Spectral Density of Phase FluctuationsThe delay line used as an FM discriminator is based, in principle, on anondispersive delay line. However, a waveguide can be used as the delayline because the Fourier frequency range of interest is a small percentageof the operating bandwidth (seldom over 100 MHz), and the dispersion canbe considered negligible.The calibration and measurement are performed as set forth in SectionIV.B. The modulation index m is usually established using the carrier-tosidebandratio that uses amplitude modulation because millimeter sourcesare either unstable or cannot be modulated. The two approaches to measurementsat millimeter frequencies are shown in Figs. 25 and 26. Figure 25shows the direct measurement using a waveguide delay line. This systemoffers improved sensitivity if adequate input power is available. The rf bridgeand delay-line portion of the system differs from Fig. 18 because pre- andTN-234
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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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: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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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
Page 207 and 208: 7. PHASE ~OISE AND AM NOISE MEASURE
Page 211 and 212: 7. PHASE :'-iOrSE AND AM NOISE MEAS
Page 213 and 214: or, in rms radians,7. PHASE !'rOISE
Page 215 and 216: i. PHASE :-JOISE AND AM NOISE MEASU
Page 221 and 222: 7. PHASE ~OISE AND AM NOISE MEASVRE
Page 241: 7. PHASE NOISE AND AM NOISE MEASURE
Page 245 and 246: _~ ~A _7. PHASE NOISE AND AM NOISE
Page 251 and 252: average frequency over the interval
Page 253 and 254: and frequency stability of precisio
Page 255 and 256: PHASE P~OT Clook No. ~- e I"d,....
Page 257 and 258: BL-\5ES .-\.\D \·A.Rl.-\.\CES OF S
Page 259 and 260: to a g
Page 261 and 262: while the Hanning ""!Odo"" yIelds1.
Page 263 and 264: Proc. 35th Ann. Freq. Control Sympo
Page 265 and 266: N-3n+lEj=1Mod Oy2 (t) =0 2(t) {.! +
Page 267 and 268: (a)1SIMULATED NOISE(b)1-10- 2- --10
Page 269 and 270: IEEE TRANSACTIONS ON INSTRUMENTATlO
Page 271 and 272: IEEE TRANSACTIONS ON INSTRUYlENTATI
Page 273 and 274: From: Proceedings of the 15th Annua
Page 275 and 276: where c = Dr/2. In regression analy
Page 277 and 278: '" Dr 22 = -7.507E-16 (about -6.5E-
Page 279 and 280: Coefficient of simple determination
Page 281 and 282: 100%CUMULATIVE PERIODOGRAM ~50%(,
Page 283 and 284: 100%CUMULATIVE PER I ODOGRAM50%U'10
Page 285 and 286: TABLE 6.STANDARD DEVIATIONSPROCEDUR
Page 287 and 288: APPENDIX AREGRESSION ANALYSIS(Equal
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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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