Energy Integration Method for Calculating keff and its Application in Design Optimization of Disk Resonators via Convex Edge

Abstract

Piezoelectric resonators have been extensively used as filters, actuator, and sensors. The effective electromechanical coupling coefficient (<inline-formula> <tex-math notation= LaTeX >${k}_{\\text {eff}}{)}$ </tex-math></inline-formula> is the most useful parameter to evaluate the electromechanical conversion efficiency of piezoelectric resonators. However, even for simple geometry piezoelectric resonators, such as disks, the coupling between different modes makes the resonant characteristics very complex. The coupling causes low electromechanical coupling efficiency of the intended mode. We propose a finite-element-based energy integration method to calculate <inline-formula> <tex-math notation= LaTeX >${k}_{\\text {eff}}$ </tex-math></inline-formula> of piezoelectric resonators. This method is more accurate than the conventional resonance-antiresonance method and provides a powerful tool for the design optimization of pure mode resonators. A special case studied here is the fundamental thickness extensional (TE) mode of PZT-8 disks in the aspect ratio range of 2–20. Our results showed that multimode coupling near this mode can be greatly suppressed by modifying the edge surface of the disk to a convex shape. Such an optimized design could enhance <inline-formula> <tex-math notation= LaTeX >${k}_{\\text {eff}}$ </tex-math></inline-formula> of the fundamental TE mode by as much as 10%–45% depending on the aspect ratio.