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High-Q sensing element is desirable for high performance while makes the loop control a great challenge. This paper presents a closed-loop system for high-Q capacitive MEMS accelerometer which has achieved loop control effectively. The proportional-derivative(PD)control is developed in the system to improve the system stability. In addition, pulse width modulation (PWM) electrostatic force feedback is designed in the loop to overcome the nonlinearity. Furthermore, a sigma-delta (ΣΔ) modulator with noise shaping is built to realize digital output. System model is built in Matlab/Simulink. The simulation results indicate that equivalent Q value is reduced to 1.5 to ensure stability and responsiveness of the system. The effective number of bits of system output is 14.7 bits. The system nonlinearity is less than 5‰. The equivalent linear model including main noise factors is built, and then a complete theory of noise and linearity analysis is established to contribute to common MEMS accelerometer research.

Modeling and Analysis of a Closed-Loop System for High-Q MEMS Accelerometer Sensor