Transfer of Frequency Stability from an Atomic Frequency Reference to a Quartz-Crystal Oscillator

This paper presents a study of the transfer of frequency stability from an atomic reference to a quartz-crystal oscillator. The study is done for the cases of active and passive atomic frequency standards in which one makes use of a phase-lock loop and of a frequency-lock loop, respectively. The analysis is made in both the frequency and time domains and covers the cases of the hydrogen and rubidium masers and the passive cesium-and rubidium-frequency standards. The results obtained from numerical calculations are presented under the form of graphs. These results include the fractional frequency spectral density Sy(f) as a function of the Fourier frequency f, and the two sample variance σ2(τ) as a function of τ, the sampling time.