Spatially Distributed Transducers: Part II—Augmented Transmission Line Models

Transducer models are typically comprised of a finite number of discrete lumped elements connected using circuit conventions. Such models are inappropriate for transducers which explicitly depend upon the continuous nature of one or more system element. These transducers must be modeled as spatially distributed devices. In this article we present a class of models which is useful for spatially distributed transducers in which the response at one location is coupled to that at other locations. The models use a transmission line to describe the mechanical coupling between locations on the transducer, but have been augmented to include interaction with the environment and sources everywhere along the line. If only one element is used at every location to represent the interaction of the transducer and the environment, and only one type of source is present, then there are only four general models which need to be considered. These models are analyzed for the general case of spatially varying sources and physical parameters. It is shown that it is possible to prescribe up to four response characteristics of the transducer if the physical parameters are permitted to vary with space. Examples of spatially distributed transducers are presented and applications discussed.