Numerical modeling of MEMS structures involving motion effected by the coupling of Maxwell´s and mechanical equations

The adaptive body fitted grid generation method for moving boundaries is applied to the analysis of MEMS-based variable devices with the combined effect of mechanical and electrical forces. MEMS technology is growing rapidly in the RF field and the accurate design of RF MEMS structures that can be used for phase shifting or reconfigurable tuners requires the computationally effective modeling of their transient and steady-state behavior including the accurate analysis of their time-dependent moving boundaries. The technique proposed in this paper is based on the finite-difference time-domain method with an adaptive implementation of grid generation. In this paper, this simulation method is applied to the analysis of a two-dimensional MEMS variable capacitor with nonuniform motions such as accelerated motions. The acceleration of the MEMS capacitor is derived under the equilibrium between the spring force and electrical force. By substituting this acceleration value into the transformation function, the relation between the capacitance and the motion characteristics is derived. The relation between the bias voltage and the displacement is shown.