An Equivalent Circuit Model of PMUTs with Clamped and Simply-Supported Plates

Transducer development depends upon analytical equivalent-circuit models for device analysis and simulation. While mature models of bulk piezoelectric transducers exist, models of piezoelectric bending-plate transducers like PMUTs (piezoelectric micromachined ultrasonic transducers) are still evolving to meet the needs of advancing piezoelectric MEMS (microelectromechanical systems) technology. This work builds upon existing PMUT models by deriving equivalent circuit model parameters for a general plate-velocity profile. This derivation applies energy conservation starting from the e-parameter form of the piezoelectric constitutive equations and a two-port description of the PMUT. Assuming a thin plate, circular symmetry, and a thin electrode for the PMUT reduces the nine constitutive equations to three and yields an expression for the transducer's total energy in terms of deflection, charge, and voltage. Applying the Jacobian matrix to this energy expression and equating it to the Z-parameters of the conventional PMUT equivalent circuit yields expressions for the transducer's equivalent circuit parameters. FEM (finite-element model) simulations of a 200-kHz PMUT design verify the model for clamped and simply supported plates. Furthermore, they show that the simply supported transducer outperforms the clamped-plate transducer.