Optimisation of the design of the resonators using the new materials: application to gallium phosphate and langasite

The coupling coefficient, the frequency constants and the temperature coefficients of the resonance frequencies of gallium phosphate and langasite thickness mode resonators were determined for all the crystalline orientations using a one dimensional model. It appears that both materials possess compensated orientations leading to a coupling coefficient (k²) nearly four times that of AT quartz. For these orientations the properties of energy trapping resonators were determined for two electrode geometries as a function of the mass loading and of the electrode dimensions. Designs optimising the capacitance ratio, the size of the plates and the unwanted responses were found. A comparison is made between computed and experimental results. It is concluded that nearly all the theoretical potential of these materials can be attained by well designed resonators