Piezoelectric Transducers: Complete Electromechanical Model with Parameter Extraction

This paper presents a complete electromechanical (EM) model of piezoelectric transducers (PTs) independent of high or low coupling assumptions, vibration conditions, and geometry. The PT's spring stiffness is modeled as part of the domain coupling transformer, and the piezoelectric EM coupling coefficient is modeled explicitly as a split inductor transformer. This separates the coupling coefficient from the coefficient used for conversion between mechanical and electrical domains, providing a more insightful understanding of the energy transfers occurring within a PT and allowing for analysis not previously possible. This also illustrates the role the PT's spring plays in EM energy conversion. The model is analyzed and discussed from a circuits and energy harvesting perspective. Coupling between domains and how loading affects coupled energy are examined. Moreover, simple methods for experimentally extracting model parameters, including the coupling coefficient, are provided to empower engineers to quickly and easily integrate PTs in SPICE simulations for the rapid and improved development of PT interface circuits. The model and parameter extractions are validated by comparing them to the measured response of a physical cantilever-style PT excited by regular and irregular vibrations. In most cases, less than a 5-10% error between measured and simulated responses is observed.