A unified equivalent circuit of electromechanical transducers

Abstract

It has been interesting to find a unified equivalent circuit of electromechanical transducers for a long time. Hunt provided a method using a space operator to represent all transducer types with a single form of equivalent circuit [Hunt, Electroacoustics, 1954]. But, as indicated by Beranek, the space operator k does not commute with the time operator j, so that one must define jk=−kj [Beranek, JASA 77(4), 1309–1313, 1985]. During the last decades, the research on micromachined electrostatic or capacitive ultrasonic transducers stimulates further the interest in the subject [Ge, Sc. China, A 29(11), 1308–1315, 1999]. In this work, the space operator is not used. A transformation factor is defined as a ratio of blocked electrical-to-mechanical transfer impedance to blocked electrical impedance, thus, the factor is a real number for reciprocal transducers and imaginary for antireciprocal ones, which indicates the essential difference of the two types of transducers. Then, the corresponding driving-point electrical impedances are derived, and the expressions for the two are identical, demonstrating their common properties also. Thus, a unified impedance-type equivalent circuit for electromechanical transducers can be further obtained. [Work supported by NSFC (Grant Nos. 60374044 and 60774053).]