Effect of size and shape on the performances of BAW resonators: A model and its applications

The performances of BAW resonators depend on their size and shape. A model is presented that describes this dependence. The electrical behavior of the resonator is subdivided into two parts. The ideal resonator, composed of the piezoelectric layer sandwiched between two electrodes, provides an ideal response while parasitic elements are degrading it. The model deals with the performances of the ideal resonator only. It is shown that both k
_eff

²
and Q-factors depend on a single parameter, A/p, the ratio between the surface and perimeter of the resonator. Resonators with small A/p ratio show largely reduced coupling and Q-factors. The model also correctly predicts the variation of coupling and quality factors between triangular, rectangular, pentagonal, elliptical and circular resonators. Finally, it is shown that this model can successfully be used to design complex devices such as filters.