Methods for Calculating the Transfer Functions of Broadband Plate Piezoelectric Transducers with Transition Layers

The work considers broadband ultrasonic piezoelectric transducers for medical diagnostic echoscopes, ultrasonic therapeutic devices, which are widely used for the diagnosis and treatment of various diseases in medicine. Such piezoelectric transducers provide a bandwidth that covers almost the entire operating range of single-frequency electroacoustic transducers, specifically 1.4 to 18 MHz for diagnostic devices and 1 to 3 MHz for therapeutic devices. The use of broadband piezoelectric transducers significantly expands the capabilities of ultrasound devices. With the help of a 4.5-18 MHz band scanner, it becomes possible to obtain an image of the spinal canal, the possibility of which has not even been discussed before. Therapeutic devices become more effective, and at the same time, their safety increases by eliminating the possibility of the formation of standing waves in the broadband mode. In this work, a method was chosen for expanding the band of a piezoelectric transducer using acoustic layers and electrical circuits, and the features of their medical application were taken into account: the load of piezoelectric transducers on a medium with low impedance and high attenuation – biological tissue – and operation in the echo mode. In all of the above applications of broadband piezoelectric transducers, the transfer function parameter becomes important, that is, the ratio of the input action to the output one. The purpose of the work is to obtain expressions for the transfer functions of wideband piezoelectric transducers of various designs with one or two transition layers. The calculation of the piezoelectric transducer transfer functions was carried out by two methods: the wave equation method, which is characterized by the need to solve a system consisting of a large number of equations even with a small number of transition layers, and on the basis of A-matrices of the regular line segment. It is shown that these two methods give the same calculated ratios, but the second method is more convenient for calculations.