Modeling, design, and optimization of radiofrequency micromechanical structures

Abstract

This dissertation develops two and three-dimensional coupled electrostatic-mechanical models for RF MEMS switches. The electrostatic solution is obtained either by applying Laplace's equation in the homogenous regions and Gauss's law at the interface nodes or by applying Gauss's law in the whole regions. In case of applying Laplace's equation, a system of equations is generated and solved using the band matrix method, while in case of applying Gauss's law in the whole region an updating equation for the potential is generated then an efficient iterative technique is employed to compute it. The mechanical model is based on solving the mechanical equation that describes the movement of the switch's bridge either analytically or numerically. The interaction between the electrostatic and mechanical models is considered iteratively. The shape of the bridge, as a function of applied voltage, and the pull down voltage have been calculated and are found to be in close agreement with published measurement data for similar switches geometries. The models are implemented with a numerical simulation program (MATLAB). This thesis covers also the design and optimization aspects of RF MEMS switches using full-wave 3-D EM simulators. Two designs have been proposed. One is a pi-configuration MEMS switch for wideband and high-isolation applications. Second is a single-pole, three-throw switch. Both switches are designed on a high resistivity Si substrate and are based on fixed-fixed membrane architecture. An equivalent circuit model for each switch is proposed to describe the switch RF-performance very well. Additionally, a two-dimensional periodic and an L-shaped defected ground structures (DGS) in the coplanar waveguide technology are proposed. A criterion that determines the dependence of the equivalent circuit elements on the design parameters of the defect is demonstrated. The proposed DGS structures are efficient to design high-performance bandstop filters. All theoretical results are verified experimentally and results agree very well. Last, as an application for the DGS and MEMS switches, an RF MEMS reconfigurable DGS resonator is designed using a 2-D periodic DGS and RF MEMS switches to control the resonant frequency. A new equivalent circuit model for the resonator is proposed and the method to extract the circuit element values is derived as well. The proposed structure can be used in automotive and transceiver applications.