Hybrid Method for Extend the Measured Average Time Range of Allan Deviation

The research of time domain stability is very important for crystal oscillator. As so far, large range of the average time from milliseconds to thousands of seconds to assess the oscillator's stability is still on the way. In this work, a hybrid method to measure the large range of the Allan deviation of an oscillator is described. This method combines the Allan deviation of short average time with the Allan deviation of long average time, the former is converted from the single sideband phase noise, and the latter is from the directly measured Allan deviation of the oscillator. In this paper, the explicit expression of the relationship between the frequency stability in the time domain and the frequency domain is given, and the accuracy of the conversion from phase noise to Allan deviation is analyzed. Finally, taking a low phase noise 10MHz oven-controlled crystal oscillator as an example, the Allan deviation of the average time from 1 microsecond to 10000 seconds is measured. And the experimental results are in good agreement with the theoretical analysis, which shows that the hybrid method can extend the average time range of the Allan deviation measurement effectively.