xMasonV2: An Open-Source Model Extension for Cascaded Transducer Arrays

Flexible polymer piezoelectrics such as P(VDF-TrFE) are increasingly employed in wearable ultrasound transducers, yet their high dielectric and elastic losses, together with the complexity of multilayer architectures, demand accurate and accessible design tools. We present xMasonV2, an open-source Python framework that translates a previously published state-space formulation of the Mason equivalent circuit into a practical simulation tool. This extension supports cascaded transducers with arbitrary layer configurations and incorporates dielectric and mechanical losses, thereby bridging the gap between theoretical models and design needs. Validation was performed against custom-fabricated P(VDF-TrFE) and PZT double-stack transducers as well as published single-layer datasets. Across four modes of the P(VDF-TrFE) stack, predicted resonance frequencies deviated by less than ±0.5MHz, corresponding to a mean absolut error (MAE) of 0.3MHz and a mean relative error (MRE) of 2.1%. For the PZT stack, errors remained within 1.3MHz, with an MAE of 0.7MHz and an MRE of 3.5%. Single-layer P(VDF-TrFE) elements exhibited higher deviations, with an MAE of 7.0MHz and an MRE of 11.0%, primarily due to manual fabrication variability. While the model reliably predicts resonance frequencies, impedance magnitudes remain less accurate because of unmodelled nonlinearities, temperature effects, and frequency-dependent losses. The openly released code provides a lightweight, browser-accessible tool to accelerate transducer prototyping and design exploration.