Electromechanical ΔΣ modulation with high-Q micromechanical accelerometers and pulse density modulated force feedback

This paper presents a comprehensive analysis of force-balanced microelectromechanical ΔΣ modulators for inertial and force sensing applications, with the emphasis on the control of high-Q micromechanical accelerometers. High Q is desirable for reducing thermal-mechanical Brownian noise but makes the control more challenging. Linear multibit force feedback using nonlinear actuators based on pulse density modulation (PDM) is described. The characteristics of the modulators, including stability, quantization noise, dynamic range, and proof-mass position error, are studied by simulations. The effects of nonidealities such as proof-mass position offset, manufacturing variations and undesired vibration modes are investigated.