Noise evaluation and optimization for a cryogenic sapphire oscillator with 10⁻¹⁵ level stability

Cryogenic sapphire oscillators (CSOs) simultaneously achieve ultra-low phase noise and outstanding frequency stability, making them widely used in precision measurement applications. In this study, performance evaluation and noise analysis are conducted on a home-built CSO. When compared with an optically generated microwave (OGM) reference, its synthesized 100 Hz signal demonstrates a relative frequency instability (Allan deviation) of 2.1 × 10⁻¹⁵ at an averaging time of 70 s. After evaluation of the dominant noise sources, it is shown that the short-term frequency stability is limited by the 1.4 Hz vibrational noise from the pulse cryocooler, resulting in a limitation of 1.2 × 10⁻¹⁵τ⁻¹. At an averaging time of 100 s, the contribution of temperature fluctuation noise becomes prominent, limiting the frequency stability to 10⁻¹⁶. In the long term, the stability of the voltage reference in the microwave power servo becomes the limiting factor. This research provides guidelines for the development of improved CSOs and their further applications in precision measurement physics.