A 27 $\mu \text{W}$ 0.06 mm2 Background Resonance Frequency Tuning Circuit Based on Noise Observation for a 1.71 mW CT- $\Delta \Sigma $ MEMS Gyroscope Readout System With 0.9 °/h Bias Instability

Abstract

This paper presents the implementation of a bandpass filter tuning circuit solely based on noise observation for a continuous-time (CT) delta–sigma modulator gyroscope readout system. By evaluating the noise at the electronic filter input, a filter frequency deviation of less than 50 Hz or approximately 0.5% of the gyroscope’s drive resonance frequency is achieved, which minimizes the angular rate noise floor. The automatic tuning works in the background during normal angular rate readout with input signals up to the full scale, over a temperature range of 115 °C, and with interference signals of up to −27.2 dBFS. The power (27 $\mu \text{W}$ ) and area (0.06 mm2) overhead to the overall system is less than 2%. The overall CT readout system achieves a noise floor of 0.002 °/s/ $\sqrt {\mathrm {Hz}}$ and a bias instability of 0.9 °/h while consuming only 1.71 mW.