NIST Technical Note 1337: Characterization of Clocks and Oscillators

Reprinted, with permission, from P. Lesage and C Audoin in Radio Science, VoL 14,No.4, pp. 521-539, 1979, Copyright © by the American Geophysical Union.Characterization and measurement of time and frequency stabilityP. Lesage and C. A udoin*Laboratoire de f'Horloge Atomique, Equipe de Recherche du CNRS, Universili Paris-Sud, Orsay, France(Received February I, 1979.)The roles which spectral density of fractional frequency fluctuations, two-sample variance, andpower spectra play in different pans of the electromagnetic spectrum are introduced. Their relationshipis discussed. Data acquisition in the frequency and the time domain is considered, and examplesare given throughout the spectrum. Recently proposed methods for the characterization ,of a singlehigh-quality frequency source are briefly described. Possible difficulties and limitations in theinterpretation of measurement results are specified, mostly in the presence of a dead time betweenmeasurements. The link between past developments in the field, such as two-sample variance andspectral analysis from time domain measurement, and recently introduced structure functions isemphasized.I. INTRODUCTIONProgress in the characterization of time andfrequency stability has been initiated owing to thework of the various authors of papers deliveredat the IEEE-NASA Symposium on Short TermFrequency Stability [1964] and of articles publishedin a special issue of the Proceedings of the IEEE[1966J. Presently widespread defmitions of frequencystability have been given by Barnes et al.(l97IJ. Many of the most important articles onthe subject of time and frequency have been gatheredin the NBS Monograph 140 [1974]. Since thattime, many papers have been published whichoutline different aspects of the field. Owing to theextent of the subject, they will be only partlyreviewed here. We will emphasize recentlyproposed principles of measurements and recentdevelopments in the time domain characterizationof frequency stability. The subject of time predictionand modeling as well as its use for estimationofthe spectrum offrequency fluctuations [Percival,1978J are beyond the scope of this paper. Recentreviews which outline several different aspects ofthe field of time and frequency characterizationhave been published [Barnes, 1976; Winkler, 1976;Barnes, 1977; Rutman, 1978; Kartaschoff, 1978].2. DEFINITIONS: MODEL OF FREQUENCYFLUCTUAnONSThe instantaneous output voltage of a frequencygenerator can be written asCopyriahl Cl 1979 by the Americon Geophysical UDioa.V(I) = [Vo + AV(t») cos [2'1Tvol + '9(1»where V o and V o are constants which represent thenominal amplitude and frequency, respectively.tJ. V(t) and cp(t) denote time-dependent voltage andphase variations.Fractional amplitude fluctuations are defmed by(I)E(t) = AV(t)! V o (2)A power spectral density of fractional amplitudefluctuations S.if) can be introduced if amplitudefluctuations are random and stationary in the widesense. Usually, for high-quality frequency sources,one hasIE(t)1 « I (3)and amplitude fluctuations are neglected. However,it is known that amplitude fluctuations can beconverted into phase fluctuations in electronic circuitsused for frequency metrology [Barillet andAudoin, 1976; Bava et al., 1977a] and that theymay perturb measurement of phase fluctuations[Brendel et al., 1977]. It is then likely that amplitudefluctuations will become the subject of more detailedanalysis in the future.According to the conventional defmition of instantaneousfrequency we haveV(I) = "0 + (l /2'1T)cP(l) (4)In a stable frequency generator the conditionIcP(t)1I2'1Tvo « I (5)is generally satisfied.We will use the following notations [Barnes et'" See Appendix Note # 24 521TN-171