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.
Fractional Frequency Synthesizers With Low Order Time-Variant Digital Sigma-Delta Modulator
