A Straightforward Approach for Synthesizing Electromechanical Sigma-Delta MEMS Accelerometers

The EM-ΣΔ (electromechanical sigma-delta) approach is a concise and efficient way to realize the digital interface for micro-electromechanical systems (MEMS) accelerometers. However, including a fixed MEMS element makes the synthesizing of the EM-ΣΔ loop an intricate problem. The loop parameters of EM-ΣΔ can not be directly mapped from existing electrical ΣΔ modulator, and the synthesizing problem relies an experience-dependent trail-and-error procedure. In this paper, we provide a new point of view to consider the EM-ΣΔ loop. The EM-ΣΔ loop is analyzed in detail from aspects of the signal loop, displacement modulation path and digital quantization loop. By taking a separate consideration of the signal loop and quantization noise loop, the design strategy is made clear and straightforward. On this basis, a discrete-time PID (proportional integral differential) loop compensator is introduced which enhances the in-band loop gain and suppresses the displacement modulation path, and hence, achieves better performance in system linearity and stability. A fifth-order EM-ΣΔ accelerometer system was designed and fabricated using 0.35 μm CMOS-BCD technology. Based on proposed architecture and synthesizing procedure, the design effort was saved, and the in-band performance, linearity and stability were improved. A noise floor of 1 μg/Hz, with a bandwidth 1 kHz and a dynamic range of 140 dB was achieved.