The use of fractal geometry in the design of piezoelectric ultrasonic transducers

The geometry of composite piezoelectric ultrasonic transducers is typically regular and periodic with one dominant length scale. In many applications there is motivation to design transducers that operate over a wide bandwidth so that, for example, signals containing a broad frequency content can be received. The device's length scale will dictate the central operating frequency of the device and so, in order to construct a wide bandwidth device, it would seem natural to design a device that contains a range of length scales. The objective of this article therefore is to consider one such transducer design and build a theoretical model to assess its performance. For the composite geometry a fractal medium is chosen as this contains a wide range of length scales. Numerical results of a theoretical model are presented. They suggest that this device would have a three-fold improvement in the reception sensitivity bandwidth as compared to a conventional composite design. Finite-element analysis provides information on the effect of poling on the device's performance. A preliminary experimental investigation was undertaken, with a Sierpinski gasket fractal transducer design, and good correlation between the simulated and experimentally measured operation was observed.