Simulation of acoustic fields from arbitrary transducer stacks using a FEM transducer model and nonlinear wave propagation

Nonlinear acoustic field simulations can be useful for medical transducer design. An accurate estimation of the electro-mechanical transfer function of the acoustic stack, increases the accuracy of the predicted harmonic fields. In this study, we combined a 2D FEM model (using COMSOL) of the transducer stack, with a two-port model of the electrical transmit circuit, and the simulation program for nonlinear wave propagation Abersim. Example simulations showed the effect on the generated second harmonic field for simulated arrays with different elevation sizes, and different piezoelectric materials. Simulated arrays, (f_c = 3 MHz, 64 elements, elevation and azimuth focus = 60 mm) with elevation sizes of 9, 11, and 13 mm, were excited with a square wave 3-half-cycle pulse (f_c = 1.9 MHz, amplitude = 80 V_pp) through a transmit circuit consisting of a cable and inductive tuning. Nonlinear propagation through a tissue-like medium (attenuation = 0.3 dB/cm/MHz) resulted in maximum second harmonic pressures of 0.75, 0.93, and 1.1 MPa, for 9, 11 and 13 mm elevation, respectively. Simulations with different piezoelectric materials, showed that the single crystals PMN-33%PT and PZN-8%PT resulted in 7-8 dB higher second harmonic pressures than the PZT ceramics HD3202 and PZ21, for the same transmit conditions without tuning. Inductive tuning increased the efficiency for the PZT-ceramics by 6-8 dB, and for single crystals by 0-2 dB. These examples demonstrated how this comprehensive simulation tool could be used to optimize array design.