Control systems for capacitive micromachined inertial sensors with high-order sigma-delta modulators

Abstract

This work, for the first time, systematically presents a design methodology of the control system for micromachined inertial sensors with a high-order electromechanical ΣΔM. The methodology is based on relatively mature design techniques for high-order SA ADC. Different loop topologies, including multi-feedback, multi-feedback with resonators and feed-forward with resonators, were investigated and the noise levels at different stages of the high-order ΣΔM was analyzed. The behaviour of noise shaping for Brownian noise, quantization noise and electronic noise was discussed in detail. Monte-Carlo analysis was performed to investigate the sensitivity to fabrication tolerances of the sensing element and circuits, which showed that the single loop ΣΔM had a good immunity to fabrication tolerances. Using a displacement dependent feedback, a linearization scheme was proposed to cancel the nonlinear conversion from the voltage to electrostatic feedback force and, as result the output signal harmonic distortion was considerably suppressed. The mechanical quality factor Q of the sensing element has a remarkable effect on noise shaping, and phase lead compensator influences the loop stability. In a high-order electromechanical ΣΔM, non-idealities due to dead-zone and idle tones were greatly alleviated compared with a second-order ΣΔM. Special issues in continuous-time ΣΔM were addressed, including inter-symbol effects and excess loop delay. Non-idealities in the interface and control circuits were investigated. Furthermore, the approach was extended to apply to vibratory gyroscopes. The control system using a high-order bandpass ΣΔM leads to a much lower oversampling frequency and more flat signal response. A high performance fully differential accelerometer is designed with a mechanical noise floor below 1μg/√Hz. Detailed FEM analysis were performed using CoventorWare to design key parameters. Two fabrication processes based on silicon on glass (SOG) and silicon on insulator (SOI) were explored. A preliminary prototype of a continuous-time fifth-order electromechanical ΣΔM was built using SMT components on a six-layer PCB. A SNR of the PCB prototype using fully differential circuits of about 90dB was achieved in a 1kHz signal band with a sampling frequency 125kHz.

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