MEMS gyroscope control by sixth-order continuous-time band-pass sigma-delta modulator (ΣΔM) with multi-feedback loops

This paper presents a sixth-order continuous-time force feedback band-pass sigma-delta modulator (BP-ΣΔM) with multi-feedback loops for the sense mode of MEMS gyroscope and a corresponding multi-objective parameter optimization method based on genetic algorithm (GA). Compared with previous low-pass ΣΔM control system, it has better noise shaping ability and can be easily implemented in print circuit board (PCB) using standard off-the-shelf electronic components. As the system is extremely complex and highly nonlinear, the genetic algorithm is used to perform multi-objective parameter optimization. The simulated power spectrum density (PSD) of the optimized design for the BP-2AM shows that the signal-to-noise ratio (SNR) is larger than 90 dB within a bandwidth of 64 Hz. 200°/s angular input; the noise floor can achieve -120 dBV/√Hz. A z-axis fully decoupled silicon-on-insulator (SOI) atmospheric MEMS gyroscope and all the other standard off-the-shelf electronic components are mounted on a four-layer PCB to verify the functionality of the optimized ΣΔM closed-loop system. Measurement of the PSD of the output bitstream shows an obvious band-pass noise shaping and a deep notch at the gyroscope drive mode resonant frequency and reveals a noise floor of -100 dBV/√Hz.