Frequency Stability Measurement of Cryogenic Sapphire Oscillators with a Multichannel Tracking DDS and the Two-Sample Covariance

Abstract: This article shows the first measurement of three 100 MHz signals exhibiting fluctuations from 2E-16 to parts in 1E-15 for integration time tau between 1 s and 1 day. Such stable signals are provided by three Cryogenic Sapphire Oscillators (CSOs) operating at about 10 GHz, also delivering the 100 MHz output via a dedicated synthesizer. The measurement is made possible by a 6-channel Tracking DDS (TDDS) and the two-sample covariance tool, used to estimate the Allan variance. The use of two TDDS channels per CSO enables high rejection of the instrument background noise. The covariance outperforms the Three-Cornered Hat (TCH) method in that the background converges to zero "out of the box," with no need of the hypothesis that the instrument channels are equally noisy, nor of more sophisticated techniques to estimate the background noise of each channel. Thanks to correlation and averaging, the instrument background (AVAR) rolls off with a slope 1/sqrt(m), the number of measurements, down to 1E-18 tau = 1E4 s. For consistency check, we compare the results to the traditional TCH method beating the 10 GHz outputs down to the MHz region. Given the flexibility of the TDDS, our methods find immediate application to the measurement of the 250 MHz output of the FS combs.