Phase noise modelling of MEMS resonant accelerometer with non-AGC-driven circuit

Abstract

Phase noise is an essential performance indicator for microelectromechanical system (MEMS) resonant accelerometers. The optimal resolution achievable is limited by the close-to-the carrier phase noise resulting from the modulation of noise sources by the mechanical resonator and driving circuit. Compared with the frequently used automatic gain control (AGC) circuit, the non-AGC scheme is more concise and can avoid the additional frequency flicker noise and 1/f 5 phase noise introduced by the AGC module. Although the mechanisms of these two kind of control loops are well-known by the communities, the phase noise modelling study on the non-AGC loop, especially compared with that of AGC loop is insufficient. This paper established a phase noise model for the AGC and non-AGC closed loop circuit of MEMS resonant accelerometer. The model includes the effects of resonator thermal noise, random loading noise of proof masses, front-circuit noise, comparator noise, AGC noise and amplitude stiffness coupling on the output noise spectrum of the resonant accelerometer. This paper carries the noise analysis through a behaviour level simulation with Simulink. The measured frequency power spectral density and Allan variance are very close to the theoretical predictions, which verifies the effectiveness of the phase noise model. The test results show that the white noise and the bias instability of the silicon resonant accelerometer are 837 ng (√Hz)−1 and 140 ng respectively, which are in good agreement with the model prediction results.