Exact one-dimensional computation of ultrasonic transducers with several piezoelectric elements and passive layers using the transmission line analogy

We present a computation technique for one-dimensional piezoelectric transducers, resonators, or interferometers having an arbitrary number of layers and piezoelectric elements electrically in parallel. Explicit and exact expressions are derived for the electric impedance and acoustic velocities. This method is based upon a systematic use of the electrical transmission line analogy, each passive or active medium being represented by a line. It has successfully been applied to various structures, particularly a symmetrical resonator with an intermediate liquid medium and a total of 29 media.