Modeling miniaturized piezoelectric ultrasound transducers: comparison of lumped and finite element models

In the quest to develop wirelessly-powered implantable medical devices (IMD), ultrasonic power transfer has received significant attention due to its distinct advantages (sub-mm wavelength, lower attenuation, higher allowed power intensity by the FDA) compared to other alternatives such as radio frequency-based approaches. A typical power link structure for US-based IMDs consists of a piezoelectric cube (PC) and an easy to use modeling technique would provide value insights for design of such wireless power systems. Equivalent circuit modeling (ECM) is the most common method utilized to model piezoelectric acoustic devices. In this work, a detailed analysis of two commonly used ECM models, KLM and Leach are developed specifically for a PC resonator. Then, a 3D finite element model is developed and the results of the developed ECM are compared with the finite element model results for a PC as well as other aspect ratios of the transducer. The two ECM models yielded similar results with a difference of less than 0.5%. The Leach model does not utilize frequency-dependent elements, its implementation in conventional circuit analysis software is more straightforward. Through ECM, the effect of each design parameter on transducer characteristics could be determined. However, to achieve more accurate results as the aspect ratio converges to one, the use FEM or experimental data to perform modification on ECM is necessary.