Multiphysics analysis for micro electromechanical systems based on electrical circuit simulator

Abstract

We report a newly developed equivalent electrical circuit for microelectromechanical systems (MEMS) based on a circuit simulator Qucs (Quite Universal Circuit Simulator). An analog computing solver for the equation of motion (EOM) has been interpreted to an electrical equivalent circuit by using an electrical capacitor as an ideal mathematic integrator. Viscoelastic suspension and electrostatic parallel‐plate actuator are modeled as equivalent subcircuits that can be cosolved with the EOM module. Those subcircuit models are used as building blocks to numerically simulate the behavior of various types of MEMS actuators. Thanks to the well‐prepared simulation toolbox of Qucs, multiphysics analysis of micromechanical and electrical quantities has become straightforward on a single platform. Equivalent circuit models for coupled oscillator and parallel‐plate electrostatic actuator (including mechanical contact after electrostatic pull‐in) are presented as a verification program to examine the simulation accuracy. © 2011 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.

An Equivalent Circuit Model for Semiparallel Plate Electrostatic Torsion Mirror

“…Figure (b) illustrates the representation using an EDD (Equation Defined Device), a nonlinear dependent current source in Qucs . The four boxes on the left are current sources with cross‐referenced input voltages, designated as 1, 2,…, 4 from top to bottom (up to 8 sources can be associated).…”

“…Similarly, Fig. 4(b) shows the induced charge obtained at a driving voltage of 1 V, using analytical solution (6) for the electrostatic capacitance and its approximate solution (7), plotted as a function of the mirror angle θ. Here again analytical solution (6) becomes zero at the horizontal position θ = 0, and approximation (7) should be applied at small angles.…”

“…4(b) shows the induced charge obtained at a driving voltage of 1 V, using analytical solution (6) for the electrostatic capacitance and its approximate solution (7), plotted as a function of the mirror angle θ. Here again analytical solution (6) becomes zero at the horizontal position θ = 0, and approximation (7) should be applied at small angles. As will be explained later, the electrostatic mirror considered in this study is operated in the angular range of θ = 0 to 0.45°, and therefore both the analytical solution and its Taylor approximation are used in the operating range.…”

Equivalent-circuit model for electrostatic micro-torsion mirror

“…There are problems on the integration of actuators and circuits. Then, seamless interface between micromechanics and electronics is needed to perform multi-physics simulation in a straightforward manner on a single simulation platform [5,6].…”

A Spice-based multi-physics simulation technique for integrated MEMS

“…A drawback of this method is, however, one may need to repeat the entire procedure from the beginning every time the MEMS structure dimensions are modified, and it takes large amount of computation power of PC to prepare the mechanical and electrical matrices. In contrast to this, we use a very simple method to simulate the behavior of a MEMS actuator or sensor by using an electrical circuit simulator as a platform for multi-physics analysis [2]. We parameterize a micro actuator with its dimensions to express the output force or torque by using a lumped equivalent circuit model.…”