A 10 mW, 0.4 $\mu \text{g}/\surd $ Hz, 700 Hz $\Sigma \Delta $ High-Order Electromechanical Modulator for a High-Q Micromechanical Capacitive Accelerometer

Abstract

A switched-capacitor sigma–delta ( $\Sigma \Delta $ ) CMOS interface circuit for the closed-loop operation of a micromechanical capacitive accelerometer is presented in this paper. A distributed-feedback and feedforward topology is proposed to combine with a high-Q sensor element to obtain a sub- $\mu \text{g}/\surd $ Hz noise floor. The loop stability is implemented by damping the high-Q sensor element in the operation of electrostatic feedback force and heavy phase compensation, which introduces an extra zero to compensate the loop. Besides, the low-frequency loop gain is controlled by off-chip adjusting of distributed-feedback factor to keep the balance between the loop stability and noise shaping ability. The interface circuit is designed and fabricated in a standard 0.5- $\mu \text{m}$ CMOS process. The chip consumes 10 mW from a single 5-V supply. The measurement results show that the noise level is lower than 400 ng/ $\surd $ Hz, and the average noise equivalent acceleration density is 200 ng/ $\surd $ Hz over a 700-Hz bandwidth. The input range of the accelerometer is ±0.7 g resulting in a dynamic range of 125 dB over 1-Hz bandwidth. The measured sensitivity of 2.5 V/g is shown with a dc nonlinearity of 0.17%, and the bias instability is $19~\mu \text{g}$ .