Tuning Micro-Electro-Mechanical Resonators for Maximum Dynamic Range
This research seeks to improve the linear dynamic range (LDR) of micro-electro-mechanical systems (MEMS) resonators, which are commonly used in sensing and timing applications. We address specifically the need for devices whose response is relatively large yet remains single-valued near resonance. We develop and analyze a model for a class of electrostatically actuated micro structures that includes higher order electrostatic effects, thereby allowing one to determine the LDR for devices that are tuned to eliminate cubic order nonlinear effects. The inclusion of the capacitive forces produces a model that is best solved by expanding the force in a Taylor series. Previous studies have shown that by keeping up through cubic terms in the expansion, improved drive conditions can be found by balancing mechanical and electrostatic nonlinearities at that order. However, the maximum amplitude and associated frequency were only found experimentally, since higher order effects were ignored. The goal of this thesis is to extend these models by including an additional term from the electrostatic force and use it to determine the LDR of the system balanced at cubic order. The Method of Averaging is employed to determine approximate expressions for the steady-state response, which allows for the closed form solution for the maximum response of the resulting model.