Analysis of an electromechanical ΣΔ modulator for MEMS sensors based on sliding mode control

Many MEMS sensors use a closed loop sensing interface to enhance their performances. ΣΔ modulation is often employed in such interfaces in order to simultaneously satisfy the requirements of performance enhancement and analog-to-digital conversion of the sensed quantity. Despite their simple structure, ΣΔ modulators have a complex dynamics that is not completely understood yet: thus, designers must resort to approximated, heuristic methods or extensive numerical simulations in order to assess stability or predict performances of such devices. In this paper we show that the condition for a correct mode of operation of a single-bit, low-pass ΣΔ modulator can be restated in terms of existence of a sliding mode in the system. We use this observation in order to design a ΣΔ modulation-based sensing interface for MEMS sensors, and to analyze its stability in a rigorous way, exploiting system-theoretical tools such as Lyapunov stability and passivity properties. Simulation results are provided to support the argumentation.