Theoretical and experimental studies of the force-frequency effect in BAW LGS and LGT resonators

It is well known that, for quartz crystal, mechanical and/or thermal stress sensitivities prevent the achievement of ultimate performances of bulk acoustic wave piezoelectric resonators. It is important to check these effects in newly developed Langasite (LGS) and Langatate (LGT) resonators. A theoretical and experimental study of the force-frequency effect (denoted by the K_f coefficient) in Y-cut LGS thickness-shear resonators, working at various overtone modes, is presented. Theoretical predictions are based on Tiersten theory of wave propagation in a pre-stressed medium. For LGS crystals, 3^rd order nonlinear elastic constants have been published and used here for modeling the behavior of thickness-shear resonators submitted to diametrical compression. A comparison between theoretical predictions and experimental measurements is presented. In the case of LGT crystal, numerical data of the third order elastic coefficients are not available at this time. Only experimental measurements of Kf coefficient are presented in order to compare the behaviors of LGS and LGT Y-cut resonators