Models of simple ultrasonic transducers

A mathematical description of the piezoelectric layer in a transducer was deduced, using the classical method of Mason. The mathematical Mason model is explained, and the resulting equivalent electrical circuits (lumped networks) of Mason for the transducer acting as emitter and as receiver are constructed. It is shown that a Krimboltz-Leedom-Matthaei scheme and a Mason scheme of a piezoelectric layer are mathematically equivalent in the case of even excitation. The transfer functions of the transducer, without adapting layers, are separately determined: as emitter and as receiver of an acoustic signal. The frequency response is numerically calculated for the combination of emitter and receiver, neglecting the damping of the acoustic signal in the transmission medium.