Design of a Dual Quantization Electromechanical Sigma–Delta Modulator MEMS Vibratory Wheel Gyroscope

Abstract

This paper presents a dual quantization lateral-axis capacitive electromechanical sigma–delta modulator (EM- $\Sigma \Delta {\mathrm{ M}}$ ) vibratory wheel gyroscope under mode-matched condition. A symmetric wheel gyroscope structure was designed, fabricated, and wafer-level packaged under vacuum. The EM- $\Sigma \Delta {\mathrm{ M}}$ interface loop adopts a fourth-order multifeedback and local resonator $\Sigma \Delta {\mathrm{ M}}$ noise shaping structure, taking advantage of single-bit and multibit quantization in a single-loop modulator. To evaluate the influence of quantization noise, various numbers of bits of the multibit quantizator were compared and the optimal number of bits was calculated. The interface circuit system was implemented in hardware based on a low-noise front-end application-specified integrated circuit and a back-end discrete-time EM- $\Sigma \Delta {\mathrm{ M}}$ realized in a field-programmable gate array chip. The system clock was generated using a self-clocking scheme, which allows interfacing to gyroscope with a wide range of drive frequencies. Experimental evaluation indicated that the digital gyroscope system achieved a scale factor of 2073LSB(4.1 mV)/deg/s, with a nonlinearity of 0.046%, a noise floor of 3.1 m°/s/ $\surd $ Hz within a bandwidth of 100 Hz, and a bias instability of 1.3 deg/hr. [2017-0081]