Piezoelectric Disc Transformer Modeling Utilizing Extended Hamilton's Principle

Piezoelectric transformers (PTs) are resonant electromechanical voltage conversion devices used in a variety of applications including voltage boosting and galvanic isolation. They offer advantages over electromagnetic voltage transformers, including high energy density as well as the potential for monolithic fabrication, making them well suited to small-scale microelectromechanical applications. Among various PT topologies, circular discs lend themselves to microfabrication, and are considered here. In order to gain fundamental understanding of disc PT dynamics, this work applies the extended Hamilton's principle of variational calculus to the piezoelectric electric enthalpy, using cylindrical coordinates, in order to derive electromechanical constitutive equations for bulk disc transformers. The use of the Hamilton approach in this work supports the integration of mechanical tethers that physically support the disc, allowing the model to be applied to device designs that are compatible with monolithic microfabrication from sheets of bulk piezoelectric material. Using the integrated model, voltage gain (output voltage/input voltage) is predicted as a function of multiple variables including electrode area ratio, device size, tether stiffness, internal material damping, and output load impedance, and is compared against finite element numerical and experimental prototype results for verification. Prototype 4-mm diameter tethered disc PTs on the order of 0.002 cm
³
, two orders smaller than the bulk PT literature, were fabricated to validate the proposed model, and had peak voltage gains over 2.