Influence of the filter in feedback loop on the operation of the nuclear magnetic resonance gyroscope

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.