Design study of piezoelectric micro-machined mechanically coupled cantilever filters using a combined finite element and microwave circuit analysis.

A new mechanical filter structure is presented which comprises two silicon cantilevers mechanically coupled by a silicon linkage with thin film piezoelectric transducers providing electrical input and output signals. The resonance behaviour of such a structure results in a band-pass filter response, having a band-width determined by the frequency separation between the closely spaced in-phase and out-of-phase vibrational modes of the two coupled cantilevers. A detailed configuration design analysis, filter simulation and optimisation of performance is undertaken using a new modelling approach combining microwave circuit theory and finite element analysis to evaluate the generalised (A, B, C and D) and scattering (S) circuit parameters of the filter. Two significant features of the filters have emerged from the derived analyses and simulations: (1) with correct design filter Q-values can reach several thousand which is much higher than the Q-values (80) of uncoupled cantilevers, (2) the Q-value is determined by the configuration of the silicon linkage and so is under the designer's control. The position and length of the linkage that give optimum Q and minimum insertion loss are determined.