Rep. 580-2 149BLAIR, B. E. (Ed.) [May, 1974) Time <strong>and</strong> frequency: theory <strong>and</strong> fundamentals. NBS Monograph No. 140. (US GovernmentPrinting Office, Washington, D.C. 20402).BOILEAU, E. <strong>and</strong> PICINBONO, B. [March, 1976) Statistical study <strong>of</strong> phase nuctuations <strong>and</strong> oscillator stability. IEEE Trans.Insrr. Meas., Vol. 25, I, 66-75.BRANDENBERGER, H., HADORN, F., HALFORD, D. <strong>and</strong> SHOAF, J. H. (1971) High quality quartz crystal oscillators:frequency-domain <strong>and</strong> time-domain stability. Proc. 25th Annual Symposium on Frequency Control, 226-230.CHI, A. R. [December, 1977) The mechanics <strong>of</strong> translation <strong>of</strong> frequency stability measures between frequency <strong>and</strong> time-domainmeasurements. Proc. 9th Annual Precise Time <strong>and</strong> Time Interval (PTTI) Applications <strong>and</strong> Planning Meeting, Greenbelt,MD, USA.CUTLER, L. S. <strong>and</strong> SEARLE, C. L. [February, 1966] Some aspects <strong>of</strong> the theory <strong>and</strong> measurement <strong>of</strong> frequency Ouctuations infrequency st<strong>and</strong>ards. Proc. IEEE, Vol. 54, 136-154.DE PRINS, J. <strong>and</strong> CORNELISSEN, G. [October, 1971] Analyse spectrale discrete. Eurocon (Lausanne, Switzerl<strong>and</strong>).DE PRINS, J., DESCORNET, G., GORSKI, M. <strong>and</strong> TAMINE, J. [December, 1969] Frequency-domain interpretation <strong>of</strong>oscillator phase stability. IEEE Trans. Ins/r. <strong>and</strong> Meas., Vol. IM-18, 251-261.GROSLAMBERT, J., OLIVIER, M. <strong>and</strong> UEBERSFELD, J. [December, 1974] Spectral <strong>and</strong> short-term stability measurements.IEEE Trans. Ins/r. Meas., Vol. IM-23 4, 518-521.HOWE, D. A., ALLAN, D. W. <strong>and</strong> BARNES. J. A. [May, 1981] Properties <strong>of</strong> signal sources <strong>and</strong> measurement. Proc.35th Annual Symposium on Frequen,y Control, Philadelphia, PA, USA (US Army Electronics Comm<strong>and</strong>,Ft. Monmouth, NJ 07703), 669-717 (Electronics Industries Association, Washington, DC 20006, USA).IEEE [May, 1972J Special issue on time <strong>and</strong> frequency. Proc. IEEE, Vol. 60, 5.IEEE [1983J Frequency S/abili/y: Fundamen/als <strong>and</strong> Measurement, 77-80. Ed. V. F. Kroupa. IEEE Press Books.IEEE-NASA [1964] Proceedings <strong>of</strong> Symposium on short-term frequency stability. NASA Publication SP 80.JONES, R. H. <strong>and</strong> TRYON, P. V. [January-February, 1983] Estimating time from atomic clocks. NBS Res., Vol. 88, I, 17-24.LESAGE, P. [1983J <strong>Characterization</strong> <strong>of</strong> frequency stability: Bias due to the juxtaposition <strong>of</strong> time interval measurements. IEEETrans. Ins/r. Meas., Vol. IM-32, I, 204-207.LESAGE, P. <strong>and</strong> AUDOIN, F. [June, 1973J <strong>Characterization</strong> <strong>of</strong> frequency stability: uncertainty due to the finite number <strong>of</strong>measurements. IEEE Trans. Insrr. Meas., Vol. IM-22, I, 103.LESAGE, P. <strong>and</strong> AIJDOIN, C. [March, 1974J Correction to: <strong>Characterization</strong> <strong>of</strong> frequency stability: uncertainty due to finitenumber <strong>of</strong> measurements. IEEE Trans. Ins/r. Meas., Vol. IM-23, I, 103.LESAGE, P. <strong>and</strong> AUDOIN, F. [May, 1975J A time domain method for measurement <strong>of</strong> the spectral density <strong>of</strong> frequencyOuctuations at low Fourier frequencies. Proc. <strong>of</strong> the 29th Annual Symposium on Frequency Control, 394-403.LESAGE, P. <strong>and</strong> AUDOIN, C. [September, 1976J Correction to: <strong>Characterization</strong> <strong>of</strong> frequency stability: uncertainty due to thefinite number <strong>of</strong> measurements. IEEE Trans. Instr. Meas., Vol. IM-25, 3.LESAGE, P. <strong>and</strong> AYI, T. [December, 1984J <strong>Characterization</strong> <strong>of</strong> frequency stability: analysis <strong>of</strong> modified Allan variance <strong>and</strong>properties <strong>of</strong> its estimate. IEEE Trans. Insrr. Meas., Vol. IM-33, 4,332-336.LINDSEY, W. C. <strong>and</strong> CHIE, C. M. [De~mber,Proc. IEEE, Vol. 64, 1662-1666. 1976J Theory <strong>of</strong> oscillator instability based upon structure functions.MEYER, D.G. [November, 1970J A test set for the accurate measurements <strong>of</strong> phase noise on high-quality signal sources. IEEETrans. Ins". Meas., Vol. (M-19, 215-227.PERCIVAL, D. B. [June, 1976J A heuristic model <strong>of</strong> long-term atomic clock behavior. Proc. <strong>of</strong> the 30th Annual Symposium onFrequency Control.RICCI, D. W. <strong>and</strong> PEREGRINO, L. [June, 1976J Phase noise measurement using a high resolution counter with on-line dataprocessing. Proc. <strong>of</strong> the 30th Annual Symposium on Frequency Control.RUTMAN, J. [February, 1972J Comment on characterization <strong>of</strong> frequency stability. IEEE Trans. Ins". Meas., Vol. IM-21, 2, 85.RUTMAN, J. [March, 1974J <strong>Characterization</strong> <strong>of</strong> frequency stability: a transfer function approach <strong>and</strong> its application tomeasurements via filtering <strong>of</strong> phase noise. IEEE Trans. Insrr. Meas., Vol. (M-23, I, 40-48.RUTMAN, J. [September, 1978J <strong>Characterization</strong> <strong>of</strong> phase <strong>and</strong> frequency instabilities in precision frequency sources: fifteenyears <strong>of</strong> progress. Proc. IEEE, Vol. 66, 9, 1048-1075.RUTMAN, J. <strong>and</strong> SAUVAGE, G. [December, 1974J Measurement <strong>of</strong> frequency stability in the time <strong>and</strong> frequency domains viafiltering <strong>of</strong> phase noise. IEEE Trans. Ins/r. Meas., VoL (M-23, 4, 515, 518.SAUVAGE, G. <strong>and</strong> RUTMAN, J. [July· August, 1973] Analyse spectrale du bruit de frequence des oscillateurs par la variance deHadamard. Ann. des Telecom., Vol. 28, 7-8, 304-314.VON NEUMANN, J., KENT, R. H., BELLINSON, H. R. <strong>and</strong> HART, B. L [1941] The mean square successive difference. Ann.Math. S/ar., U, 153-162.WALLS, F. L., STEIN, S. R., GRAY, J. E. <strong>and</strong> GLAZE, D. J. [June, 1976] Design considerations in state-<strong>of</strong>-the·art signalprocessing <strong>and</strong> phase noise measurement systems. Proc. <strong>of</strong> the 30th Annual Symposium on Frequency Control.WINKLER, G. M. R. [December, 1976) A brief review <strong>of</strong> frequency stability measures. Proc. 8th Annual Precise Time <strong>and</strong> TimeInterval (PTTI) Applications <strong>and</strong> Planning Meeting (US Naval Research Laboratory, Washington, DC), 489-528.YOSHIMURA, K. [March, 1978] <strong>Characterization</strong> <strong>of</strong> frequency stability: Uncertainty due to the autocorrelation <strong>of</strong> the frequencyfluctuations. IEEE Trans. Ins/r. Meas., IM-27 I, 1-7.TN-169
ISO Rep. 580-2, 738-2BIBLIOGRAPHYALLAN, D. W., ~t at. (1913) Performance, modelling, <strong>and</strong> simulation <strong>of</strong> some caesium beam clocks. Proc. 21th AnnualSymposium on Frequency Control, 334-346.FISCHER, M. C. (December, 1916] Frequency stability measurement procedures. "Proc. 8th Annual Precise Time <strong>and</strong> TimeInterval (PTTI) Applications <strong>and</strong> Planning Meeting (US Naval Research Laboratory, Washington, DC), 515~18.HALFORD, D. (March, 1968J A general mechanical model for 1/1« spectral density noise with special reference to flicker noise1/1/1. hoc. IEEE (Corres.), Vol. 56,3, 2SI·2S8.MANDELBROT, B. [April, 1961] Some noises with II/spectrum, a bridge between direct current <strong>and</strong> white noise. IEEE TrailS.In! 17I~ory, Vol. IT·l3, 2, 289·298.RUTMAN, J. <strong>and</strong> UEBERSFELD, J. [February, 1972] A model for flicker frequency noise <strong>of</strong> oscillators. hoc. IEEE, Vol. 60, 1,233-235.VANIER, J. <strong>and</strong> TETU, M. (1918] Time domain measurement <strong>of</strong> frequency stability: a tutorial approach. Proc. 10th AnnualPrecise Time <strong>and</strong> Time Interval (PTTI) Applications <strong>and</strong> Planning Meeting, Washington, DC, USA, 247·291.VESSOT, R. (1916] Frequency <strong>and</strong> Time St<strong>and</strong>ards. Chap. 5.4 Methods <strong>of</strong> Experimental Physics, Academic Press, 198·221.VESSOT, R., MUELLER, L. <strong>and</strong> VANIER, J. (February, 1966] The specification <strong>of</strong> oscillator characteristics from measurementsmade in the frequency domain. hoc. IEEE, Vol. 54, 2, 199-201.WINKLER, G. M. R., HALL. R. G. <strong>and</strong> PERCIVAL, D. B. (October, 1970] The US Naval Observatory clock time reference <strong>and</strong>the performance <strong>of</strong> a sample <strong>of</strong> atomic clocks. Ml'lrotogia, Vol. 6, .., 126-134.TN-170
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Characterization ofClocks and Oscil
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PREFACEFor many years following its
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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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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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7. PHASE NOISE AND AM NOISE MEASURE
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7. PHASE NOISE AND AM NOISE MEASURE
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_~ ~A _7. PHASE NOISE AND AM NOISE
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7. PHASE NOISE AND AM NOISE MEASURE
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7. PHASE NOISE AND AM NOISE MEASURE
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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