Parameter optimization for a high-order band-pass continuous-time sigma-delta modulator MEMS gyroscope using a genetic algorithm approach

Abstract

This paper describes a novel multiobjective parameter optimization method based on a genetic algorithm (GA) for the design of a sixth-order continuous-time, force feedback band-pass sigma-delta modulator (BP-ΣΔM) interface for the sense mode of a MEMS gyroscope. The design procedure starts by deriving a parameterized Simulink model of the BP-ΣΔM gyroscope interface. The system parameters are then optimized by the GA. Consequently, the optimized design is tested for robustness by a Monte Carlo analysis to find a solution that is both optimal and robust. System level simulations result in a signal-to-noise ratio (SNR) larger than 90 dB in a bandwidth of 64 Hz with a 200° s−1 angular rate input signal; the noise floor is about −100 dBV Hz−1/2. The simulations are compared to measured data from a hardware implementation. For zero input rotation with the gyroscope operating at atmospheric pressure, the spectrum of the output bitstream shows an obvious band-pass noise shaping and a deep notch at the gyroscope resonant frequency. The noise floor of measured power spectral density (PSD) of the output bitstream agrees well with simulation of the optimized system level model. The bias stability, rate sensitivity and nonlinearity of the gyroscope controlled by an optimized BP-ΣΔM closed-loop interface are 34.15° h−1, 22.3 mV °−1 s−1, 98 ppm, respectively. This compares to a simple open-loop interface for which the corresponding values are 89° h−1, 14.3 mV °−1 s−1, 7600 ppm, and a nonoptimized BP-ΣΔM closed-loop interface with corresponding values of 60° h−1, 17 mV °−1 s−1, 200 ppm.