Higher Order Noise-Shaping Filters for High-Performance Micromachined Accelerometers

Micromachined inertial sensors that have been incorporated in sigma–delta force-feedback loops have been proven to improve linearity, dynamic range, and bandwidth, and also provide a direct digital output. Previous work mainly focused on using the sensing element only to form a second-order single-loop sigma–delta modulator $(\Sigma\Delta\hbox{M})$; however, the advantages of higher order single-loop electromechanical $\Sigma\Delta\hbox{M}$ have not been fully explored. High-performance inertial sensors require higher signal-to-quantization noise ratio (SQNR). This paper presents topologies for higher order single-loop electromechanical $ \Sigma\Delta\hbox{M}$ with optimal stable coefficients that lead to a better SQNR. The topologies have good immunity to fabrication tolerances, which was verified by Monte Carlo analysis. The topologies are applicable not only to accelerometers but also to other inertial sensors such as gyroscopes.