Multi-Degree-of-Freedom Simulation of Micro-Machined Sensors Under Mixed-Signal Control

Abstract

A general method of modeling and simulating a micro-machined inertial sensor under closed-loop control by a sigma-delta modulator is presented. The model of the mechanical subsystem captures all 6 mechanical degrees of freedom and the complex electrostatic fields in electrostatic comb drives. A technique is presented that makes transient simulations of the sophisticated mechanical model in conjunction with a modulator more tractable. The benefits of the modeling and simulation approach are demonstrated on an example consisting of a single-axis accelerometer and a second-order sigma-delta modulator. The example shows that transient simulations of the complete system can be performed in relatively short time while capturing cross coupling between mechanical modes of the sensor.