An analytical design methodology for microelectromechanical (MEM) filters

The design of coupling spring for a microelectromechanical (MEM) filter is driven by the requirements of bandwidth. A novel design aspect of the coupling spring design is presented which follows mechanical-electrical-mechanical domains in order. A designed second order MEM bandpass filter consists hereby of two laterally/vertically driven resonance structures, which are coupled by a mechanical spring. For these structures, an equivalent electrical representation can be obtained and in this paper, both the series and parallel electrical equivalent circuits are analyzed. The transfer function and the correlation between the bandwidth and the coupling spring for these filter equivalents are derived. The analysis yields a complete design procedure for MEM bandpass filters, which is presented along with simulation results. With changing design parameters the filter response has been demonstrated to be maximally flat as in the case of Butterworth-filters, or to have a response allowing a wider bandwidth (as much as double) than in the former case. Analytical studies of both the extreme responses are presented with simulation results.