Shift in the Location of Resonant Frequencies Caused by Large Electromechanical Coupling in Thickness-Mode Resonators

Abstract

The frequencies of fundamental and overtone resonance in a thickness-mode piezoelectric resonator depart from an integral multiple relationship when the electromechanical coupling of the resonator material becomes large. This behavior can be explained by the fact that large electromechanical coupling significantly lowers the resonant frequency of the fundamental mode with respect to the overtones. The resonant frequencies have been calculated as a function of the electromechanical coupling coefficient and the mode number for thickness modes in poled ceramics. (The theoretical analysis for thickness-mode resonators is given in a separate paper by Tiersten.) The measured resonant frequencies of both thickness-dilatational and thickness-shear mode resonators made from BaTiO3, PZT-5, and PZT-7 ceramics were found to show good agreement with theory. An important practical application of this anharmonicity is in the determination of the shear coupling coefficient k13, direct measurement of which has hitherto been difficult. This coupling coefficient, along with k33 and kt, can now be obtained from the ratios of the resonant frequencies of the fundamental and overtone modes.