Micromachined vibratory gyroscopes controlled by a high-order bandpass sigma-delta modulator

This work reports on the design of novel closed-loop control systems for the sense mode of a vibratory-rate gyroscope based on a high-order sigma-delta modulator (SigmaDeltaM). A low-pass and two distinctive bandpass topologies are derived, and their advantages discussed. So far, most closed-loop force-feedback control systems for these sensors were based on low-pass SigmaDeltaM's. Usually, the sensing element of a vibratory gyroscope is designed with a high quality factor Q to increase the sensitivity and, hence, can be treated as a mechanical resonator. Furthermore, the output characteristic of vibratory rate gyroscopes is narrowband amplitude-modulated signal. Therefore, a bandpass SigmaDeltaM is a more appropriate control strategy for a vibratory gyroscope than a low-pass SigmaDeltaM. Using a high-order bandpass SigmaDeltaM, the control system can adopt a much lower sampling frequency compared with a low-pass SigmaDeltaM while achieving a similar noise floor for a given oversampling ratio (OSR). In addition, a control system based on a high-order bandpass SigmaDeltaM is superior as it not only greatly shapes the quantization noise, but also alleviates tonal behavior, as is often seen in low-order SigmaDeltaM control systems, and has good immunities to fabrication tolerances and parameter mismatch. These properties are investigated in this study at system level