Design of Spring Coupling for High Q, High Frequency MEMS Filters

This paper presents the design optimization of the coupling beam of wine glass (WG) mode micromechanical disk filters using the simulated annealing algorithm. The filter under consideration consists of two identical wine-glass mode disk resonators, mechanically coupled by a flexural mode beam. Such coupled two-resonator system exhibits two mechanical resonance modes with closely spaced frequencies that define the filter passband. The frequencies of the constituent resonators determine the center frequency of the filter, while the bandwidth is determined by the stiffness and location of attachment of the coupling beam. The goal is to design a filter with a commonly used bandwidth, namely 100 kHz. The design variables that control the bandwidth value are the beam length, the beam width, and the location of attachment of the coupling beam from the center. The simulated annealing algorithm is used to solve the optimization problem, since the governing dynamic equations of the resonator-coupling system are highly nonlinear. The resulting optimum design is simulated using the finite element method, which confirms the achievement of the desired center frequency and bandwidth.