A Subharmonic Resonance-Based MEMS Filter

Abstract

We present a novel micromechanical filter exploiting the subharmonic resonance of order one-half to obtain a center frequency twice the fundamental frequency of the primary resonators, an ideal stopband, and a sharp roll-off. The filter is made up of two clamped-clamped microbeam resonators connected by a coupling beam. We discretize the distributed-parameter system using the Galerkin procedure to obtain a reduced-order model composed of two nonlinear coupled ODEs. It accounts for geometrical and electrical nonlinearities as well as the coupling between these two fields. Using the method of multiple scales, we determine four first-order nonlinear ODEs describing the amplitudes and phases of the modes. We use these equations to determine closed-form expressions for the static and dynamic deflections of the filter. The basis functions in the discretization are the linear undamped global mode shapes of the unactuated filter. The filtering mechanism is based on the exploitation of the interval where the trivial response to subharmonic excitations is unstable. We found criteria to tune the effective nonlinearities of the filter to realize a bandpass filter of an ideal stopband rejection and a sharp roll-off. When these criteria are not met, multivalued responses appear and distort the filter performance.