A lumped-parameter model of the free-flooded ring transducer array

The free-flooded ring (FFR) transducer is an extensively used ring-type acoustic transducer in underwater environments owing to its broad operating frequency bandwidth and small size. However, achieving high sound pressure levels with a single FFR transducer is often difficult, thus necessitating the construction of vertically arranged FFR transducer arrays. This study presents a comprehensive analysis of the electrical and acoustic characteristics of an FFR transducer array by considering the mutual radiation load and the effects of gaps between adjacent piezoelectric rings. The lumped-parameter models of the piezoelectric ring, cylindrical cavity, cylindrical gap, and radiation impedance constitute an entire impedance matrix. The radiation impedance matrix for the FFR transducer array is calculated using the Helmholtz-Kirchhoff integral formula by considering the interaction of the FFR surfaces with the surrounding fluid medium. The proposed model predicts the resonance peaks in the admittance and transmitted voltage response (TVR) with a relative error of 5%, and the TVR level within a 3 dB range. Detailed analyses of a four-FFR transducer array reveal that a wider gap between each FFR leads to a decreased chance of negative conductance and broader operating bandwidth. The proposed model offers valuable insights into the design of FFR transducer arrays.