Experiment and Simulation Validated Analytical Equivalent Circuit Model for Piezoelectric Micro-Machined Ultrasonic Transducer

An analytical Mason equivalent circuit is derived for a circular, clamped plate piezoelectric micro-machined ultrasonic transducer (pMUT) design in 31 mode considering an arbitrary electrode configuration at any axisymmetric vibration mode. The explicit definition of lumped parameters based entirely on geometry, material properties and defined constants enables straightforward and wide ranging model implementation for future pMUT design and optimization. Beyond pMUTs, the acoustic impedance model is developed for universal application to any clamped, circular plate system and operating regimes including relevant simplifications are identified via the wave number-radius product ka. For the single electrode fundamental vibration mode case, sol-gel Pb (Zr0.52)T i0.48O3 (PZT) pMUT cells are micro-fabricated with varying electrode size to confirm the derived circuit model with electrical impedance measurements. For the first time, experiment and finite element simulation results are successfully applied to validate extensive electrical, mechanical and acoustic analytical modeling of a pMUT cell for wide ranging applications including medical ultrasound, non-destructive testing, and range finding.