Effective Electromechanical Coupling for the Partially Electroded Ceramic Resonators of Different Geometries

Abstract

Effective electromechanical coupling factor (ECF) was studied on bar, disc and ring ceramic resonators partially covered by electrodes. ECFs were calculated theoretically and verified experimentally. Bar resonators (k31-mode) show maximum value of ECF keff = 0.26 at the electrode aspect ratio equal to 0.75 with calculated values fitting the experimental data for all aspect ratios. Calculations for bar resonators with embedded electrodes (k33-mode) show similar behavior like for k31- mode, but at higher ECFs. Maximum value of ECF for such a mode reaches keff = 0.67 for the electrode aspect ratio of 0.75. Partially electroded disc resonators (kpmode) are well described analytically by one-dimensional model only for the electrode aspect ratios up to 0.5. Maximum value keff = 0.58 for disc resonators was measured at the electrode aspect ratio equal to 0.80. Partially electroded ring resonators (kp-mode) show the same trend as discs without saturation of ECF values. Maximum ECF keff = 0.34 was measured for ring resonators with full electrode. The presented analytical formulae may serve as a guide for the optimum electrode pattern design for the partially electroded resonators.