Design and Implementation of a MASH2-0 Electromechanical Sigma–Delta Modulator for Capacitive MEMS Sensors Using Dual Quantization Method

Abstract

In this paper, a new control structure based on the dual quantization technique is presented for an electromechanical sigma–delta modulator (EM- $\Sigma \Delta \text{M}$ ) applied to a microelectromechanical system (MEMS) accelerometer. The modulator adopts a 2-0 multistage noise shaping structure (MASH2-0), taking the advantage of the intrinsic linearity of single-bit quantization and the reduced quantization error of multibit quantization in a single modulator. The sensor system is studied by the system-level modeling and the hardware implementation based on the field-programmable gate array technology. The study shows that, MASH2-0 shares the benefits of a MASH2-2 architecture of having an inherent stability, a high overload input level, and a high dynamic range compared with single-loop EM- $\Sigma \Delta \text{M}$ . However, the MASH2-0 architecture benefits from a considerably simpler implementation, while achieving a higher dynamic range and a higher signal-to-noise ratio compared with a MASH2-2 and a fourth-order single-loop $\Sigma \Delta \text{M}$ architecture. A capacitive MEMS accelerometer was designed and employed with this control system. Within a bandwidth of 1 kHz, the sensor achieved a noise floor level of −130 dB and a bias instability as low as $20~\mu \text{g}$ at an integration time of 40 s. Simulation estimated a full scale of ±20 g acceleration. The investigation confirms the concept of the MASH2-0 structure and shows its potential as a closed-loop interface for high-performance capacitive MEMS accelerometers. [2015-0071]