A Direct Time-Domain Measure of Frequency Stability: The Modified Allan Variance

A simple filter is shown to closely approximate the procedure used to compute the "Allan variance," an often used measure of the short term frequency stability of oscillators. This modified Allan variance is obtained by measuring the rms value of the instantaneous frequency waveform after filtering. Some advantages of the modified Allan variance include ease of implementation for short averaging times and better behavior when the instabilities include periodic components. The effect of the bandwidth of the measuring process on the minimum usable averaging time is also discussed.