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 2×10 −16 to parts in 10 −15 for integration time τ 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 twosample 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/ √ m, the number of measurements, down to 10 −18 at τ = 10 4 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.

KLTS: A Rigorous Method to Compute the Confidence Intervals for the Three-Cornered Hat and for Groslambert Covariance

“…These methods were applied to assess the confidence intervals for the GCov measurements of a set of 3 Cryogenic Sapphire Oscillators designed and made in FEMTO-ST. These measurements were carried out by the Tracking DDS designed and made in INRIM (for more details, see [10]). It may be noticed that, since the clocks are in the same room, we can not fully assume their total independence.…”

“…It may be noticed that, since the clocks are in the same room, we can not fully assume their total independence. Figure 5 presents the same measurements as the ones plotted in Figure 11 (below) of [10] but we have added the 95 % confidence intervals obtained by using KLTS (below 100 EDF, i.e. τ > 5000 s) and KLTG (above 100 EDF, i.e.…”

Physics of the sapphire whispering-gallery-mode solid-state MASER oscillator

“…The need for microwave sources exhibiting ultra-high spectral purity and high temporal stability is a key point highlighted by the performance limitations in major strategic applications such as radar, spatial communications, ultra-high accuracy navigation systems, and high bit rate optical telecommunications. The Cryogenic Sapphire Oscillator (CSO) is currently the only available technology able to provide a relative frequency stability better than 1×10 −15 for integration time between 1 s and 10 4 s [1,2,3,4,5,6]. The CSO is a classical transmission oscillator that uses as a frequency determining element a passive cryogenic high-Q sapphire resonator based on a cylindrical dielectric resonator made in a high purity sapphire monocrystal.…”

Magnetic sensitivity of the Microwave Cryogenic Sapphire Oscillator

“…As the CSO presents state-of-the-art short term frational frequency stability, its individual characterisation was only recently made possible by the implementation of the three-cornered-hat method 10 . By revealing the individual frequency stability of three independant CSOs, we demonstrated that residual temperature variations arising from a non-perfect resonator stabilisation can be responsible for a part in the CSO short term frequency instability 11 .…”