A novel triangular-electrode based capacitive sensing method for MEMS resonant devices

This paper reports a novel capacitive sensing method, enabling accurate and self-calibrated measurements for both the amplitude and phase information in sinusoidal motion. The approach constructively utilizes the inherent nonlinearity of a triangular-electrode based (TEB) variable-area sense capacitor. In the case of TEB detection signal, two harmonics exist and each carries information about the motional amplitude and phase. The TEB method robustly extracts the motional amplitude from the ratio of two sideband amplitudes and extracts the motional phase from the subtraction of two sideband phases. This technique is especially valuable for capacitive detection of periodic motion in MEMS resonant devices, such as the resonant accelerometer and Coriolis vibratory gyroscope. The paper presents detailed theoretical analysis and proposes a real-time measurement algorithm implemented in an FPGA device. Experimental results manifest that, compared with the traditional linear method, the sensitivity of the measured amplitude and phase to system parameter variations is highly suppressed up to 95%. Furthermore, an oscillation control system with TEB capacitive detection is introduced for micro-machined vibratory gyroscopes. First measurement results show the amplitude variance of the drive displacement is 120 ppm in an hour while the phase variance is 80 ppm. Allan variance analysis indicates a bias instability of 6.5°/h for the gyroscope output.