Aspect ratio dependence of electromechanical coupling coefficient of piezoelectric resonators

The most important parameter characterizing a piezoelectric material is the electromechanical coupling coefficient, which specifies the conversion efficiency between electrical and mechanical energies for a given vibration mode. For the resonance along the poling direction, there are two coupling coefficients defined, i.e., kt and k33, which are for resonators of the same mode but two extreme aspect ratios and they differ substantially. We have derived a unified formula for this coupling coefficient as a function of the vibrator aspect ratio. The unified formula can provide more accurate description to the effective coupling coefficient of resonators not satisfying the extreme aspect ratio requirements.