Atomic timekeeping and the statistics of precision signal generators

TLDR: In this paper, a detailed analysis of the calibration procedure showed that the third finite difference of the phase is closely related to the clock errors and that quartz crystal oscillators exhibit a "flicker" or |ω|-1type of noise modulating the frequency of the oscillator.

Abstract: Since most systems that generate atomic time employ quartz crystal oscillators to improve reliability, it is essential to determine the effect on the precision of time measurements that these oscillators introduce. A detailed analysis of the calibration procedure shows that the third finite difference of the phase is closely related to the clock errors. It was also found, in agreement with others, that quartz crystal oscillators exhibit a "flicker" or |ω|-1type of noise modulating the frequency of the oscillator. The method of finite differences of the phase is shown to be a powerful means of classifying the statistical fluctuations of the phase and frequency for signal generators in general. By employing finite differences it is possible to avoid divergences normally associated with flicker noise spectra. Analysis of several cesium beam frequency standards have shown a complete lack of the |ω|-1type of noise modulation.