System-level KLM power model for therapeutic ultrasound transducers: Linear approximation validity up to 21.5 W/cm2 and a counterintuitive Qm threshold effect

Accurate prediction of the output acoustic power of an ultrasonic therapy system is critical to treatment safety and efficacy. Here, we systematically verify the accuracy of a system-level Krimholtz–Leedom–Matthaei power model that fully integrates the driving source, cable and tuning network, power ultrasonic transducer, and acoustic load using the transmission matrix method. Validated in three representative power transducers made of PZT-4 ceramic, PZT-4 composite, and PZT-5H ceramic up to an intensity-on-transducer-surface (ITS) of 21.5 W/cm2, the model achieves relative errors of only −6% to −10% without requiring nonlinear material parameters, a value limited by the current measurement setup rather than by the model's inherent capability. Moreover, a counterintuitive threshold effect was discovered: for thickness mode power transducers, once the mechanical quality factor Qm exceeds ∼90, further increase yields negligible gain in output efficiency. This finding provides new design guidelines for the selection of piezoelectric materials in high-power applications, showing that chasing ultrahigh Qm is unnecessary beyond this saturation point.