  In this paper, we present an analytical modeling technique for circularly
symmetric piezoelectric transducers, also called as Fresnel Lens. We also
present the design of a flat/piston transducer that can generate unique
acoustic wave patterns, having both converging and vortexing effects. The
converging effect is generated by designing the transducer electrodes in the
shapes of circular rings using Fresnel formula and exciting it with an RF
signal of resonant frequency. The vortexing effect is achieved by cutting the
rings to different sector angles: 90, 120, 180 and 270 degrees. We use the
analytical model to simulate the performance of these transducers.
