The design of quarter-wavelength impedance matching layers for cylindrical transducers.

Abstract

Impedance matching layers are commonly used in piezoelectric underwater acoustic projectors. The layer maximizes transmitted power from the ceramic into the water and also increases the bandwidth of the projector. For the design of cylindrical transducers, it is common in practice to utilize the familiar plane wave formulation of the quarter-wavelength impedance matching layer as a starting point for the design of the cylindrical layer. Material properties and thickness are then modified by trial and error, heuristic, or empirical methods to optimize the design. This practice is undertaken because, apparently, the quarter-wavelength impedance matching layer formulation is not readily available in the acoustics literature for the cylindrical coordinate system. To address this deficiency, the reflection and transmission coefficients for the cylindrical three-medium problem were derived. No general zero-reflection, perfect transmission condition was found, but the equations can be used to find the material properties and layer thickness required to maximize transmission at a given frequency. The results of the derivation are shown and used in the design of a layered cylindrical piezoelectric transducer.