Experiments with the Electrical Analog of a Piezoelectric Transducer

An electrical analog of a piezoelectric transducer has been built and used to demonstrate the generation and detection of acoustic waves and the electrical characteristics of a piezoelectric resonator. The circuit uses an artificial transmission line to represent the distributed-constant mechanical properties of the transducer, and is therefore capable of reproducing the behavior of a transducer under both transient- and continuous-wave conditions. The theory of the equivalent circuit of a transducer is first extended to facilitate interpretation of the physical processes of generation and detection. This is done by developing an “impulse sequence” that takes into account waves generated at both faces of a transducer, and the delay in time and reflections that they undergo in passing through the transducer. This analysis is used to discuss examples of waveforms obtained with the analog in the following situations (with various simulated combinations of backing and load impedance): (1) as a generator of acoustic waves when excited by an electrical signal in the form of (a) a short impulse, (b) a step, (c) short trains of sinusoidal oscillations of various lengths; (2) as a detector of acoustic waves when excited by an acoustic signal in the form of (a) a step, (b) a train of sinusoidal oscillations. In detection, the effect of terminating the transducer with high and low resistances is also demonstrated. Experiments concerning the continuous-wave response of the analog are also described.