Uniform behavior of the electromechanical coupling factor in piezoelectric resonators

Abstract

The coupling of mechanical and electrical energies in piezoelectric materials is a problem extensively studied by many researchers. A precise determination of this coupling is an essential aspect of the theory and performance evaluation of the piezoelectric transducers utilized in multiple medical and industrial applications. In this article, the derivation of the electromechanical coupling factor in dynamic regime, $k,$ of four of the most common piezoelectric resonators vibrating under lossless conditions is reviewed. It is explicitly demonstrated that the frequency spectrum of $k$ is uniform through the resonators with respect to their fundamental mechanical resonance frequencies, regardless the vibration mode considered. This uniformity can be described by a simple mathematic expression with the ‘same form’ for all the vibration modes studied. The outcomes presented are in the hope to shed some new light on the basic functional theory of the piezoelectric resonator.

Keywords

• electromechanical coupling factor
• quasistatic material coupling factor
• piezoelectric materials
• piezoelectric resonator
• ultrasound transducer