A spice equivalent circuit for modeling the performance of dual frequency echo-sounder

The paper presents novel network equivalent circuit of piezoceramic circular disc transducer that takes into account thickness and radial mode of vibrations. The starting point of the analysis is 4-port description of circular disc element representing the solution of wave equation set in radial and thickness directions. The approximate solution for harmonic case is represented in the form of 4x4 matrix, which is synthesized and implemented in circuit analysis software. The network is extended with acoustical port that allows for pressure calculations in the similar manner as when measuring echo-sounder transmitting and receiving parameters. The model is especially useful for simulating complete electronic circuit of dual frequency echo-sounders based on single circular disc transducer.