New Equivalent Circuit of a Cymbal Transducer Incorporating the Third Harmonic Mode of Vibration

Abstract

A cymbal transducer is composed of a pair of metal caps and a piezoceramic disk. Cymbal transducers arranged in an array exhibit broadband characteristics. Although the finite element method has been widely used for analyzing the transducer and its array, an equivalent circuit that allows efficient analysis was recently developed. However, this previously reported circuit was based solely on the fundamental vibration mode of the transducer, and is thus unsuitable for analyzing the broadband characteristics of the cymbal array. Therefore, to overcome this limitation, a new broadband equivalent circuit for the cymbal transducer was devised in the present study. The new circuit was constructed by incorporating terms related to the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$3^{\text {rd}}$ </tex-math></inline-formula> harmonic vibration mode of the cap and corresponding radiation impedance into the existing equivalent circuit. The validity of this novel circuit was verified by comparing the analysis results with those obtained from the measurement of acoustic characteristics exhibited by a cymbal-transducer specimen. Compared with the previous circuit, the new equivalent circuit allows more accurate analysis and design of a cymbal transducer over a wider frequency range.