Modeling and Electrode Design Optimizations of Plano-Plano Langasite Crystal Resonator

The 3-D finite-element model (FEM) of a Y-cut plano-plano langasite crystal thickness shear mode (TSM) resonator is presented, and Mindlin's theory is used to investigate the optimal electrode shapes and sizes for langasite crystal resonator. Circular and elliptical electrodes of various arc lengths are studied to identify the most optimal electrode design configuration in order to achieve TSM vibration free from any anharmonic modes. Simulation results show that resonators with elliptical electrodes have noticeably better suppression of spurious modes compared to that of circular electrodes. Moreover, spurious mode suppression is accomplished for multiple electrode sizes for the same shape, which greatly differs from Mindlin's theory. Hence, three optimized designs are shortlisted and their mass loading sensitivities are investigated. Circular and elliptical electrodes of the same area show similar responses to added mass, indicating that elliptical electrodes have no apparent advantage over circular electrode in mass sensing applications.