A Frequency-Dependent Dynamic Electric–Mechanical Network for Thin-Wafer Piezoelectric Transducers Polarized in the Thickness Direction: Physical Model and Experimental Confirmation

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Abstract
This paper is concerned with electric–acoustic/acoustic–electric conversions of thin-wafer piezoelectric transducers polarized in the thickness direction. By introducing two mechanical components with frequency-dependent values, i.e., radiation resistance and radiation mass, into the equivalent circuit of the thin-wafer piezoelectric transducer, we established a frequency-dependent dynamic mechanic-electric equivalent network with four terminals for an arbitrary given frequency, an enhancement from the conventional circuit networks. We derived the analytic expressions of its electric–acoustic and acoustic–electric conversion impulse responses using the four-terminal equivalent circuit to replace the traditional six-terminal equivalent circuit for a thin-wafer transducer with harmonic vibrational motion. For multifrequency electrical/acoustic signals acting on the transducer, we established parallel electric–acoustic/acoustic–electric conversion transmission networks. These two transmission network models have simple structures and clear physical and mathematical descriptions of thin-wafer transducers for electric–acoustic/acoustic–electric conversion when excited by a multifrequency electric/acoustic signal wavelet. The calculated results showed that the transducer’s center frequency shift relates to its mechanical load and vibration state. The method reported in this paper can be applied to conventional-sized and small-sized piezoelectric transducers with universal applicability.
Funding Information
  • National Natural Science Foundation of China (41974130)
  • Xi’an Fanyi University (41974130)
  • Xi’an University of Posts and Telecommunications (41974130)
  • Physical Sciences Division at The University of Chicago (41974130)

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