An exact solution to the problem of trapping of oscillation energy in microwave-band acoustic resonators based on cubic crystals

An exact solution is obtained to the problem of the oscillation spectrum in a microwave-band composite resonator structure that can work on longitudinal and transverse acoustic waves and contains a comparatively thick cubic-crystal plate and a piezoelectric film with electrodes deposited on the plate. The problem is solved for the resonator operating at high-order harmonics of the fundamental frequency of the plate in the case when the ratio between the thicknesses of the resonator and other layers of the structure is sufficiently large. The derived formulas can be used to analyze the possibility of achieving a high Q factor of a composite resonator structure at a desired frequency.