Theoretical modelling and optimization design of PMUT arrays for enhanced acoustic performance

Theoretical models are essential for performance analysis and structure optimization design of large-scale piezoelectric micromachined ultrasonic transducers (PMUT) arrays. However, current models have rarely incorporated the inter-element crosstalk and oversimplified the electro-mechanical-acoustic coupling, leading serious discrepancies with experimental results and limiting the array optimization design and performance improvement. To address this, a novel electro-mechanical-acoustic coupling model and a spatial acoustic field modeling approach are proposed for PMUT arrays, incorporating distributed deformation functions of individual element and mutual acoustic impedance to analyse key performance metrics such as transmission power, frequency response, focal length, and beamwidth. Its accuracy is validated through finite element simulations, demonstrating small deviations of less than 3%. Parametric studies reveal that increasing the filling ratio from 20% to 60% improves transmission power and bandwidth but significantly increases crosstalk, reducing focusing efficiency. Enlarging the array size results in proportional increases in acoustic output power and focal pressure, while simultaneously reducing beamwidth, thereby improving directivity. As for array arrangements, circular array achieves higher focal pressure than square array, albeit with shorter focal lengths. Annular array, with its distinct mainlobe and ring-shaped sidelobes, demonstrates superior focal pressure at longer distances, ideal for extended-range applications. The theoretical models are further validated by experimental results from fabricated square, hexagonal, circular, and annular PMUT arrays. This study proposes an accurate theoretical model for PMUT arrays, enabling accurate and reliable prediction of key acoustic performance metrics in large-scale arrays, and facilitating the array structure optimization design and performance enhancement of PMUT.