The Equivalent Circuit Modeling and Optimization of Square PMUTs Arrays for Improving Acoustic Performance

With advancements in MEMS technology, piezoelectric micromachined ultrasonic transducers (PMUTs) have gained prominence due to their miniature size, favorable acoustic impedance matching with human tissue, ease of 2D array fabrication, and seamless IC integration. However, efficient simulation tools for large-scale arrays remain limited, with most studies focusing only on single-element. In this work, we propose a comprehensive analytical model that couples mechanical, electrical, and acoustic domains by incorporating mutual radiation impedance among elements. The model is validated via finite element simulations, with resonant frequency, output power, and vibration velocity errors all below 3%. A 784-element square PMUTs array (radius: 70 μm, spacing: 40 μm) was fabricated, achieving a measured resonant frequency of 2.85 MHz in air and 2.1 MHz in water, closely matching the theoretical prediction of 2.2 MHz. Based on the equivalent model, we analyzed the effects of element spacing and array size on key performance about sound field, transmission power, and focal length. Results show that reducing spacing intensifies acoustic crosstalk, which, while broadening the bandwidth, suppresses output power. Additionally, increasing array size from 1 mm to 3 mm improves transmitted power from 2 mW to 18 mW, extends focal length from 1 mm to 8 mm, and narrows beamwidth from 82° to 36°. This study offers a validated theoretical method for designing and optimizing PMUTs arrays, facilitating their application in advanced ultrasonic systems.