Automated Resonance Matching for CMOS MEMS Micro-Resonators

Abstract

This paper reports the design and characterization of a phase-locked loop-based control scheme implemented in a complementary metal–oxide–semiconductor process for resonance matching between capacitive micro-resonators. The system-on-chip implementation can be utilized for calibrating individual resonance in a large sensor array or matching the drive and sense modes for micromachined vibratory gyroscopes. The target micro-resonator acts as a voltage-controlled oscillator in the control loop with the resonance being adjusted by the electrostatic spring-softening effect. Sinusoidal test inputs applied to the control loop are shown to provide better resonance matching than square-wave inputs. This paper successfully demonstrates automated matching by pulling the resonance of a target micro-resonator within $2.4\times 10^{-2}$ % of the reference resonance under atmospheric pressure.