Exploring and Identifying Bias-Instability Noise Sources in Mode-Split MEMS Gyroscopes Based on Electrostatic Frequency Tuning

In this article, bias instability induced by phase noise via electrostatic frequency tuning is first investigated. We propose a noise model that reveals the transfer mechanism of electrostatic frequency tuning on scale factor (SF) instability noise and demodulated phase noise in an open-loop sense system of gyroscopes to analyze the relationship between frequency split and noise performances. The 1/f noise sources are the electrostatic frequency-tuning voltage noise and drive amplitude noise. By varying the frequency split and monitoring the instability of gyro’s quadrature output and rate output, it is possible to identify these noise sources and contributions to bias instability (BIS) of zero-rate output. This identification also indicates the low bias-instability design criteria from both mechanical and circuit aspects, for example, the needed quadrature coupling rate, Q-factor, and frequency split. According to the proposed noise model, including amplitude and phase conversion processes, the lower limit of frequency split can be determined considering the bias-instability deterioration effect. A frequency-tuning criterion of open-loop MEMS mode-split gyroscopes for different noise requirement is hence established. Angle random walk (ARW) and BIS together define the adjustable range of frequency split in MEMS gyroscopes. The upper limit of frequency split is set by suppression of the white noise from the interface circuit. The experimental result indicates that an MEMS mode-split gyroscope has achieved an ARW of 0.009°/ $\surd $ h and a BIS of 0.17°/h under the quadrature of 40°/s and the frequency split of critical value (110 Hz).