NIST Technical Note 1337: Characterization of Clocks and Oscillators

"'0 .. 0.87,"'-1 .. 0.77,"'-a" 0.75.As an example of the Gaussian model vith K~lOO, Q - -1(flickar frequency noise) and Oy(' % 1 second) .. 10- 13 ,ve Illay writll:vhich gives:Oy(' .. 1 second) .. (1 ± a.08) x 10- 12 •If M i. SMall, then the plus and minus confidencll intervalsbecome asymmetric and the "'. coefficients are notvalid: however, these confidence intervals can be calculated(Lesage and Audoin, 1973).If "overlapping" estimates are used, as outlined above,chen the confidence interval of the escimate can beshown to be less than or equal to I. as given above(Howe, Allan, Sarnes, 1981).5. Rc;ommendations for CbaIacterizini Qr RepQrtini~easurcments of frequencv and Phase Instabilitiesa. Nonrandom phenomena should be recognized, forexample:oooany observed time dependency of the Statisticalmeasures should be stated;the method of modeling systematicbehavior should be specified (for example.an estimate of the linear frequencydrift vas obtained from thecoefficients of a linear least-squaresregression to M frequency measurements,each with a specified averaging or sampletime. and measurement bandvidth f h);the environmental sensitivities should bestated (for example, che dependence offrequency and/or phase on temperature,magnetic field, barometric pres.ure,vibration, etc.):b. Relevant measurement or specificationparameters should be given:aa6. Referencuthe enviro~ent during measurement;if a passive alement. such as a cryatalfiltar, i. being mea.ured in contrast toa frequency and/or time generator.8arnes, J.A., Tables of bias functions, B 1end 8,. forvariances based on finite samples of procosses withpower law spectral densieie., N8S, Washington, DC,Tech. Note 375, (Jan. 1969).Barnes, J.A. and Allan, D.W .. ·Variances 8ased on Datawith Dead Time Between the Measurements: Theoryand Table.," NBS Tech Note 1318 (1988).Same., J.A., Chi, A.R., Cutlor. L.S., Healey, O.J.,Leeson, D.S., McGunigal, T.E., Mullen, J.A.,Smith,~.L., Sydnor, R., Vessot, R.F. and Winkler,C.M.R., Characterization of frequency stability,IEEE Trans. Instr. and Meas., Vol. ~, 105-120,(May 1971).cela Report 898, Dubrovnik, (1986).Draper, N.R. and Smith, H., Applied Regression Analy.i.,John Wiley and Sons,(1966).Howe, D. A., Allan, D. W., and Barnes, J.A., Propertiesof signal sources and measurement methods. Proc.35th Annual Symposium on Frequency Control, 669­117, (May 1981).Karcaschoff, P., Frequency and Time, Academic Press, NewYork (1978).Lesage, P., and Audoin, C. Characterization of frequencystability: uncertainty due to the finiee number ofmeasurements. IEEE Trans. Instr. and Meas., Vol.ll1:ll. 157-161, (June 1913).Lesage, P., Characteri~ation of Frequency Stability:Sias due to the juxtaposition of time intervalmeasurements. IEEE Trans. on Inser. and Meas, ~12..204-207, (1983).Scein. S. R, Frequency and Time: Their measurement andcharacterization. Precision Frequency Control,Vol. Z, Academic Press, ~ew York, 191-232, (1985).oaaoooothe method of ~easurements:the characteristics of the referencesignal;the nominal signal frequency va:the measurement .•ystem bandwidth f o andthe corresponding lov pass filterresponse;the total measurement time and the numberof measurem~nCs M;the calculation techniques (for example,detail. of the windo~ f'~ction ~henestimacing power spectral densities fromtime domain data, or the assumptions~bo~t effects of dead-time when estimatingthe tva-sample deviation eyer»~;the confidence of the estimate (or errorbar) and ies statistical probability(.e.-s.- "t:.hree.-.s:lgma. II );APP;"'fOIX I1. Pover-Law Speceral pensi=iesPower-law spectral densities are often employed as reasonabl~a~d accurate mod~Ls of ~he random f~uc~ua:ionsin precision oscillators. In practice. these randomfluctuations can often be re?resented by the sum of fiveindependent noise processes, and hence:{+2L ha~cr--2for 0 < f < f h~here h~'s are con5tan~$, Q'S are incegers. a~d f b isthe high frequency cut-off of a iow pa.s filter. Highfrequency divergence is eliminated by the res~riceionson f in this equation. The identification and characterizationof the five noise processes are given inTabie 1, and sho~ in Fig. 1.4211N-141