Abstrakt

The paper presents novel network equivalent circuit of piezoceramic circular disc transducer that takes into account thickness and ra dial 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. Th e approximate solution for harmonic case is represented in the form of 4x4 matrix, which is syn thesized and implemented in circuit analysis software. The network is extended with acoustical p ort that allows for pressure calculations in the similar manner as when measuring echo-sounder trans mitting and receiving parameters. The novel model uses Cauer LC ladder of the second form for implementation of radial part of vibrations. The values for its parameters are ob tained by expanding the quotient of zero and first order Bessel functions of the first kind into continued fraction representation and can be expressed directly by geometry of the piezoelectric disc (its radius and thickness) and its material properties (stiffness coefficient and density). As the ladder contains only lumped elements, the model is portable across different implementations of SPICE simulators. It has clear interpretation considering mechanical properties of vibrating disc when comparing to thickness vibration model. Presented equivalent circuit of wh ole transducer is especially useful for simulating complete electronic circuit of dual freq uency echo-sounders constructed using single circular disc transducer.

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