Spatially Distributed Transducers: Part I—Coupled Two-Port Models

Abstract

The process of modeling transducers generally involves the use of a finite number of discrete lumped elements connected using circuit-like conventions. However, such models are difficult to use for transducers which implicitly depend upon variation of a physical parameter with location since they view the transducer as existing only at points or discrete intervals in space. In this article a general modeling procedure is developed which views a transducer as a spatially distributed device. The model introduced here uses the theory of connected two-ports to determine the overall transfer matrix and scattering matrix representations. This directly yields the transducer sensitivities and efficiencies. The model is limited to transducers which may be thought of as being comprised of an infinite number of infinitesimal twoport elements, each of which is mechanically independent of the others. Coupling between the elements occurs through the input and output ports. The modeling procedure is demonstrated using an acoustic antenna, and shown to accurately predict the directional behavior.