Energy trapping in bulk acoustic wave composite resonator

The analytical approach to the problem of energy trapping in bulk acoustic wave composite resonators is developed. It is based on a standard system of wave equations and boundary conditions for adjacent to resonator three layer structure-relatively thick layer of the substrate, thin metal electrode deposited onto its surface and the layer of piezoelectric film. The dispersion equation is solved to find small components of the wave vector in the direction in the plane of the structure outside the resonator. The obtained formula describes the attenuation of the wave in the region close to resonator. This expression is purely analytic and does not require matching procedure in calculations. The situation corresponding to microwave bulk acoustic wave resonators structures is discussed. In particular the developed approach at least qualitively explains surprisingly perfect energy trapping which exists in almost all microwave composite resonators