Circuit Theory Laboratory Report Series Equivalent Circuit Models for Micromechanical Inertial Sensors

Thesis for the degree of Doctor of Technology to be presented with due permission for public examination and debate in Abstract Numerical simulation models for capacitive, micromechanical inertial sensors are presented. These dynamic, nonlinear models include the contributions of electrical, mechanical, and uidic energy domains by means of electrical equivalent circuits consisting of lumped, frequency-independent components. The mechanical resonance modes, gap capacitances, gas lm damping forces and the electrostatic actuation forces are accounted for in the model. Special attention is paid to modelling the rareeed gas ow in narrow air-gaps, including the eeect of gas-surface interaction. These gas-rarefaction eeects are included in the eeective gas viscosity. Novel, compact design equations are presented for the eeective viscosity in narrow air-gaps, valid in viscous, transitional and molecular ow 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 veriication 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 coeecient. 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.