Sigma-Delta Control of a Biased and Initially-Displaced MEMS Microphone

This paper extends an earlier work that achieved resonance damping of a micro-machined directional microphone by embedding it in a compensated sigma-delta modulator (Wu et al., 2004). The goal was to combat the quadratic nonlinearity in the electrostatic force. The new developments in this paper include the use of a different capacitive device that is also biased to allow more effective readout, and the consideration of the dependence of the electrostatic force on the displacement of the microphone diaphragm, which was ignored in the earlier work. This paper discusses signal level adjustment to correct the effect of the asymmetry due to the bias, and partial feedback linearization to mitigate the nonlinearity in the electrostatic force due to the membrane displacement. Background information is given on the microphone and the damping scheme is explained. Simulation results of the control loop using Simulink are presented, where the full nonlinear model of the electrostatic force transducer is included. In addition, preliminary results of simulated linear circuit implementation of the sigma-delta control loop Multisim are also presented. This paper also investigates the robustness of the damping scheme with respect to uncertainties in stiffness and mass in the design model.