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 reciprocity calibration methods[Ge, JASA, 97(1):324-330, 1995] and micromachined electrostatic or capacitive ultrasonic transducers stimulates further the interest in the subject [Ge, Science in China, A, 29(11), 1308-1315, 1999]. In this work, the space operator is not used. A complex transformation factor is introduced and 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. The input voltage and current equations are derived further, and the expressions for the two are identical, demonstrating their common properties also. Then, a unified impedance-type equivalent circuit for electromechanical transducers is given.