Development and validation of a 2D Mason model for ultrasonic transducer arrays: A simplified approach simulating crosstalk and dissipation mechanisms

Piezoelectric elements arranged in 1D or 2D configurations are commonly used in ultrasonic transducer arrays for medical imaging and non-destructive testing (NDT) applications. These arrays are usually modeled using complex 2D or 3D numerical methods. Based on the equivalent circuit approach previously developed in our paper One-dimensional equivalent circuit for ultrasonic transducer arrays” (Bybi. et al. Applied Acoustics 2019) [1], this work proposes a novel and accurate two-dimensional equivalent circuit to model and simulate the electromechanical behavior of piezoelectric transducer arrays. The model consists of a lossy 2D Mason circuit taking into account the width and thickness modes and also the modes coupling, the crosstalk phenomenon, and various dissipation mechanisms, including dielectric, piezoelectric, and mechanical losses. The model is tested on a fabricated seven elements transducer array made of PZ27 and its results (electrical impedance, displacement, and crosstalk curves) are validated by comparison with experimental data. A good agreement is obtained between simulation results and measurements, confirming the validity of the model. Key advantages of the proposed model include its simplicity, ease of implementation, and a significant reduction in computation time compared to traditional numerical methods. Furthermore, this approach allows for the analysis of the crosstalk between array elements without the need for expensive experiments, such as laser vibrometer displacement measurements. Finally, the model will be extended to a 64-element piezoelectric array, with individual matching layers, backing, and its associated electronics, to deepen the study of the crosstalk phenomenon and propose solutions to reduce it.