Multi stage noise shaping (MASH) sigma delta modulator for capacitive MEMS inertial sensors

This research discusses the theoretical investigation, simulation and hardware implementation of the ElectroMechanical Multi-stAge noise SHaping (EM-MASH) sigma delta modulator (ΣΔM). The potential advantages of an EM-? M MASH compared to single-loop high-order ΣΔMs applied to inertial MEMS sensors are its inherent stability and high overload input level due to the use of lower order ΣΔMs in its individual stages. Furthermore, MASH has the advantages of high dynamic range and high noise shaping performance because of its overall high-order ΣΔM architecture. So far, the EM-MASH has not been sufficiently explored. This study is expected to serve as solid basis for the application of EM-MASH. In this research, various EM-MASH architectures (MASH21, MASH22, MASH211, MASH221 and MASH222) were theoretically studied, and the results were validated with simulations. A fourth order EM-MASH22-ΣΔM was theoretically examined and successfully implemented with a capacitive MEMS accelerometer, which includes a second order EM-ΣΔM loop cascaded with a purely electronic second order ΣΔM. The quantization noise from the first loop is digitised by the second loop and then cancelled by digital filters, whereas the quantization noise from the second loop is shaped by the second loop filter and a digital filter, which together provide fourth order noise shaping. The performance of EM-MASH22 was compared with that of a single-loop fourth order EM-ΣΔM (SD4). Both architectures were investigated by system level modelling and hardware implementation using surface-mount PCB technology. The results show that (a) both architectures achieve the same noise floor level of 19 µg/√Hz; (b) MASH22 is unconditionally stable, whereas SD4 is only conditionally stable; and (c) MASH22 achieves a higher overload input level and a higher dynamic range than does SD4. Furthermore, the research presents a novel EM-MASH-ΣΔM that employs a dual quantization technique and adopts a 2-0 structure (EM-MASH20). With a simpler and configurable composition, MASH20 is aimed at exhibiting a performance higher than that achieved with the MASH22 structure. The MASH20 does not require a second-stage ΣΔM, which reduces the complexity of the digital filters compared to those required for the MASH22; thus, the digital filter matching is more easily achievable. The study shows that the MASH20, like the MASH22, has an inherent stability, high overload input level, and high dynamic range compared to single-loop ΣΔM. However, the MASH20, with its simpler implementation, achieved a higher dynamic range and signal-to-noise ratio than the MASH22 and the SD4. A capacitive MEMS accelerometer was designed and employed with MASH20. Within a bandwidth of 1 kHz, the sensor achieves a noise floor level of 15 µg/√Hz, a full-scale acceleration of ±20 g and a bias instability of 20 µg for a period of three hours. The EM-MASH-ΣΔM is sensitive to the variation of the sensing element parameters and other analogue parameters, both of which are subject to manufacturing tolerance and imperfections. This causes a leakage of the quantization noise in the final output and degrades the modulator performance. The research explored a calibration method to solve this problem by utilizing the digital domain capabilities. The method is based on the optimization algorithm which was investigated using MATLAB. The research confirms the concept of the EM-MASH structure and proves that it is applicable as a closed-loop interface for high-performance capacitive MEMS inertial sensors.