Analytical modeling of k 33 mode partial electrode configuration for loss characterization

Accurate determination of three types of losses (dielectric, elastic, and piezoelectric) in piezoelectric materials is critical, since they are closely related to the performance of high-power piezoelectric devices. The standard k33 mode has a number of serious deficits that hinder researchers from determining accurate physical parameters and losses. In order to overcome such deficits, “partial electrode” has been devised and proposed. This study provides an analytical derivation process and proposes a parameter determination method by utilizing analytical solutions. Compared to finite element analysis, analytical solutions show a 0.1% difference in resonance frequencies and a 2% difference in mechanical quality factors, proving themselves as valid modeling. The analytical solutions are fitted to experimental data to determine physical parameters and losses. The k33 (electromechanical coupling factor) values were calculated with determined values from curve fitting in two different ways and show good agreement to each other.