为了分析核磁共振陀螺中129Xe自旋振荡器的振幅和频率特性, 建立了相应的半经典模型, 其中分别采用密度矩阵和经典电磁理论描述核自旋系综和反馈系统。然后, 根据自激振荡的自洽条件推导了用于描述自旋振荡器的振荡方程。进一步, 利用旋转波近似和慢变振幅近似将振荡方程化简为自洽方程组, 它由分别用于描述自旋振荡器振幅和频率的振幅方程和频率方程构成。基于上述自旋振荡器的半经典模型, 研究了带通滤波器对自旋振荡器振幅和频率的影响。仿真结果表明, 对核磁共振陀螺的典型参量, 反馈环路设计不当导致的自旋振荡器频移可达亚μHz。该研究对提高基于自旋振荡器的核磁共振陀螺性能具有一定的参考价值。

In order to analyze the amplitude and frequency characteristics of the 129Xe spin oscillator in the nuclear magnetic resonance gyroscope (NMRG), a corresponding theoretical model was established. The density matrix and the classical electromagnetic theory were utilized to describe the nuclear spin ensemble and the feedback system, respectively. An oscillation equation with self-consistency condition was obtained. Furthermore, the oscillation equation was simplified and expanded to self-consistency equations with rotating-wave and slow-varying approximations, which described the amplitude and frequency of the oscillator simultaneously. Based on the semiclassical model, the influence of a band-pass filter on the amplitude and frequency of the spin oscillator was investigated. The simulation results indicate that the typical frequency shift caused by unsuitable feedback loop may reach the magnitude of sub-micro Hz. Proposed model offers the potential to improve the performance of NMRG based on spin oscillators.