Definition and measurement of the normalized electrical impedance of lossy piezoelectric resonators for ultrasonic transducers

Relevant equivalent circuit parameters and values of material constants of a piezoelectric resonator can be determined from measurements of its electrical input impedance as a function of frequency. The complex electrical impedance curves and the associated critical frequencies are the basis of this characterization by the piezoelectric resonance method. In this paper, the previously introduced concept of normalized electrical impedance of the lossy resonator, extended to include piezoelectric losses, is applied to the analysis of the effects of different types of intrinsic losses on peak values, bandwidths and characteristic frequencies. The resulting impedance patterns depend solely on the electromechanical coupling coefficient and the loss tangents, providing a useful tool for the analysis of low-Q resonators. The normalized impedance is experimentally evaluated from the basic data provided by an HP 4194A impedance analyser by means of specifically developed ASP programs.