Measuring the Allan Variance by Sinusoidal Fitting

Abstract

The Allan variance of signal and reference frequencies is measured by a least-squares fit of the output of two analog-to-digital converters (ADC's) to ideal sine waves. The difference in the fit phase of the two channels generates the timing data needed for the Allan variance. The fits are performed at the signal frequency ($\approx 10 $ MHz) without the use of heterodyning. Experimental data from a modified digital oscilloscope yields a residual Allan deviation of $3 \times 10^{-13}/\tau $, where $\tau$ is the observation time in sec. This corresponds to a standard deviation in time of $<$ 300 fs or 20 $\mu$Rad in phase. The experimental results are supported by statistical theory and Monte Carlo simulations which suggest that optimized devices may have one or two orders of magnitude better performance.