Analysis and equivalent circuit for accurate wideband calculations of the impedance for a piezoelectric transducer having loss

M J Hagmann

doi:10.1063/1.5118897

Abstract

Others have analyzed the operation of piezoelectric transducers by defining two complex parameters which have the units of frequency to allow for the effects of loss. The present paper presents an analysis in which this procedure is extended to include harmonics as well as the fundamental frequency. In this extension it is seen that both positive and negative extrema in both the resistance and the conductance occur at a series of harmonics. Equivalent circuits are also presented with examples for both high-Q and low-Q materials showing agreement with these simulations.

Highlights

Berlincourt et al.1 and Meeker2 derived expressions for the electrical impedance of a piezoelectric disk transducer in the thickness modes when the loss is negligible
Sherrit et al.3 wrote this equation in the following form, and Sherrit and Mukerjee4 presented other equations having a similar form for modes with other types of piezoelectric transducers
For clarity we use the symbol Fp which is defined in Table II instead of fp, where the symbols fp and fs are defined and used later in the present derivation

Summary

INTRODUCTION

Berlincourt et al. and Meeker derived expressions for the electrical impedance of a piezoelectric disk transducer in the thickness modes when the loss is negligible. Ω is the angular frequency, and the relevant material constants and calculated parameters for Eq (1) that were defined and evaluated for the first two examples by Sherrit et al. are given in Tables I and II. Berlincourt et al. and Meeker assumed zero loss so they used real values for all of the material parameters which requires that the impedance is purely reactive with singularities at frequencies that are odd integer multiples of Fp. Sherrit et al. used measured values for the material parameters and dimensions that are complex to include the effects of loss and are given in Table I which we have used in examples.

ANALYSIS SHOWING THE RESONANCES

Effect of parameter γ on the real part of the complex impedance

Effect of parameter α on the real part of the complex admittance

CONCLUSIONS