Equivalent Circuit Models for Micromechanical Inertial Sensors

Numerical simulation models for capacitive, micromechanical inertial sensors are presented. These dynamic, nonlinear models include the contributions of electrical, mechanical, and fluidic energy domains by means of electrical equivalent circuits consisting of lumped, frequency-independent components. The mechanical resonance modes, gap capacitances, gas film damping forces and the electrostatic actuation forces are accounted for in the model. Special attention is paid to modelling the rarefied gas flow in narrow air-gaps, including the effect of gas-surface interaction. These gas-rarefaction effects are included in the effective gas viscosity. Novel, compact design equations are presented for the effective viscosity in narrow air-gaps, valid in viscous, transitional and molecular flow regions. Inertial sensor models for an accelerometer and an angular rate sensor have been built from electrical equivalent circuit blocks that consist of elementary voltage-controlled current and charge sources. The verification show very good agreement with the simulated and measured frequency responses over a wide pressure range. The gas-surface interaction model has been tested by extracting a numerical value of the surface accommodation coefficient. Compact equivalent circuit models allow both sensor and sensor system simulations with any general purpose circuit simulation program. The models derived have been implemented and simulated with the circuit simulation program APLAC.