Theoretical Resonance Analysis of Langevin Transducers with Equivalent Circuit Models for Therapeutic Ultrasound

In this paper, the resonance characteristics of Langevin ultrasonic transducers is analyzed with equivalent circuit models. Transducer configuration is devised by half-wavelength principle and material properties used. Both resonance peak frequency and effective electromechanical coupling coefficient are simulated by calculating the transducer's input electrical impedance at given center frequencies, 30 kHz, 40 kHz, and 50 kHz. In case of a bare transducer, the relative errors derived from its expected resonance peaks are equal to be 0.3% at 30 kHz, 0.8% at 40 kHz, and 0.6% at 50 kHz. The corresponding coupling coefficients are found to be 0.20, 0.17, and 0.20, respectively. For a transducer coupled with a titanium rod, similar simulations are also carried out at the same frequencies. The model errors become 0.8%, 1.1%, and 0.7%, while their coupling coefficients are estimated to be 0.10, 0.07, and 0.10. The model is thus shown to be capable of predicting those resonance signatures within narrow margin under a variety of conditions. The results indicate that this approach may be taken advantage of to determine the design criteria of Langevin transducers for therapeutic procedures.