正弦振动条件下原子钟的频率稳定度分析

Analysis of frequency stability of atomic clock under sinusoidal vibration

振动对原子钟(原子频标)的影响可分为对原子谐振的影响、对伺服环路的影响和对晶体振荡器(晶振)的影响.在振动频率范围内,晶振的输出相位噪声只与晶振的加速度灵敏度、峰值加速度和振动频率有关,与静态相位噪声没有关系,但在振动频率范围之外,晶振的输出相位噪声就是其静态相位噪声.由原子钟的稳定性传递到输出晶振的频率稳定度公式,就可通过伺服环路把晶振的振动分析融入到原子钟的振动分析之中.利用相位噪声转换为阿仑方差的积分公式,根据留数定理推导出直接计算阿仑方差的解析表达式,得到增加伺服环路带宽可以有效抑制振动对原子钟频率稳定度影响的结论;分析了通过减振和选择加速度灵敏度较小的晶振这2种方法改善原子钟振动性能的问题.

Vibration effects on the atomic clock（atomic frequency standard） could be divided into three parts： atomic resonance effects, crystal oscillator effects and servo-loop effects. Within the vibration frequency, the phase noise of crystal oscillator under sinusoidal vibration was only related to acceleration sensitivity, peak acceleration and vibration frequency, and it has no concern with the phase noise in the static state. But above the vibration frequency, the phase noise of crystal oscillator was the same with the value in the static state. By the frequency stability transfer fornmlas from the atomic clock to crystal oscillator, vibration effects on crystal oscillator was combined with vibration effects on the atomic clock through servo loop. For computing Allan variance directly from integral equation of phase noise, the several analysis fornmlas were derived by residue theorem. With increased servo loop bandwidth, vibration effects on frequency stability of the atomic clock can be controlled effectively. Two other methods are analyzed to improve the performance of the atomic clock under vibration： reducing vibration frequency and choosing crystal oscillator with smaller acceleration sensitivity.