Characterization of Frequency Stability

• Published in: IEEE transactions on instrumentation and measurement 1971-05, Vol.IM-20 (2), p.105-120
• Main Authors: Barnes, James A., Chi, Andrew R., Cutler, Leonard S., Healey, Daniel J., Leeson, David B., McGunigal, Thomas E., Mullen, James A., Smith, Warren L., Sydnor, Richard L., Vessot, Robert F. C., Winkler, Gernot M. R.
• Format: Article
• Language: English
• Subjects: Noise; Stability analysis; Thermal stability; Time frequency analysis; Time measurement
• ISSN: 0018-9456; 1557-9662
• DOI: 10.1109/TIM.1971.5570702

Consider a signal generator whose instantaneous output voltage V(t) may be written as V(t) = [V 0 + ??(t)] sin [2??v 0 t + s(t)] where V 0 and v 0 are the nominal amplitude and frequency, respectively, of the output. Provided that ??(t) and ??(t) = (d??/(dt) are sufficiently small for all time t, one may define the fractional instantaneous frequency deviation from nominal by the relation y(t) - ??(t)/2??v o A proposed definition for the measure of frequency stability is the spectral density S y (f) of the function y(t) where the spectrum is considered to be one sided on a per hertz basis. An alternative definition for the measure of stability is the infinite time average of the sample variance of two adjacent averages of y(t); that is, if y k = 1/t ??? tk+r = y(t k ) y(t) dt where ?? is the averaging period, t k+1 = t k + T, k = 0, 1, 2 ..., t 0 is arbitrary, and T is the time interval between the beginnings of two successive measurements of average frequency; then the second measure of stability is ?? y 2 (??) ??? (y k+1 - y k ) 2 /2 where denotes infinite time average and where T = ??. In practice, data records are of finite length and the infinite time averages implied in the definitions are normally not available; thus estimates for the two measures must be used. Estimates of S y (f) would be obtained from suitable averages either in the time domain or the frequency domain.