Frequency-Domain Interpretation of Oscillator Phase Stability

A frequency-domain interpretation of the phase stability of an oscillator is discussed. From a knowledge of the time dependence of an oscillator phase during a time interval T* it is possible to give the characteristics of this oscillator, not only for this time interval, but also for subsequent time intervals. Since the use of a Fourier transform for the computation of a continuous power spectrum is unrealistic, a discrete-spectrum approach will be taken. Usually, in the calculation of power spectra, stationarity of the fluctuations is assumed, although experiment indicates that this is often not the case. A more realistic approach is adopted. Analytical phenomena and random walk are separated from white noise on the basis of statistical criteria using discrete Fourier transforms. The white noise is then interpreted in the frequency domain. Both random walk and specific signals are studied in the time domain and can be separated by digital filtering. Two different sets of experimental results are analyzed by this method, one derived from measurements on a quartz-crystal oscillator locked to a low-frequency transmitter and the second from measurements on an ammonia maser. In both cases, measurement precision and ease of prediction of the behavior of the oscillator are improved.