Linear parametric amplification/attenuation for MEMS vibratory gyroscopes based on triangular area-varying capacitors

Abstract

This paper presents the linear parametric resonance for MEMS vibratory gyroscopes using triangular area-varying capacitors. Compared to parametric resonance using gap-varying capacitors, the electrostatic stiffness using triangular capacitors is completely linear and independent of the motion displacement. A pump voltage in the square-rooted form consisting of both DC tuning voltage and AC signal with twice the drive resonance frequency is applied to the triangular capacitors in gyroscope sense mode for both mode matching and parametric amplification of Coriolis signal simultaneously. Parametric amplification or attenuation is realized by choosing specific phase and amplitude of the pump voltage. Experimental results show a maximum parametric gain of 13 times in gyroscope sense mode and the open-loop scale factor amplification of 4.8 times compared with the case where no pump voltage is applied. For one-hour zero-rate-output data, an improvement factor of 5.74 is achieved for angle random walk from 0.1745 ° √h−1 to 0.0304 ° √h−1. Meanwhile, an improvement factor of 9.73 for bias instability is achieved from 3.609 ° h−1 (occurring at integration time 40 s) to 0.371 ° h−1 (at 52 s). The quadrature error due to stiffness coupling is reduced from 9 ° s−1 to 1 ° s−1 which agrees well with our analysis that Coriolis force is mechanically amplified while quadrature error is dampened.