A discussion on the significance of geometry in determining the resonant behavior of fractal and other non-Euclidean wire antennas

Fractal-shaped wire antennas have been shown to exhibit resonance compression and multi-band behavior that has primarily been attributed to the space-filling properties of the fractal geometry. Exhibiting a lower resonant frequency than a same-sized Euclidean antenna, fractal-shaped antennas can be made smaller than a Euclidean antenna that is resonant at the same frequency. While numerous fractal-shaped antennas - such as Minkowski Island fractal loops and Koch fractal monopoles -have been described in the literature, most discussions regarding these antennas have primarily focused on comparing their resonant behavior to those of simple Euclidean antennas. To understand the significance of any fractal geometry in determining the resonant behavior of the fractal-shaped antenna, it is also necessary to consider the other physical properties of the antenna. For the wire-loop antenna, these physical properties include the loop area, the total wire length, and the wire. diameter. For the wire monopole antenna, these physical properties include the monopole height, the total wire length, and the wire diameter. In the previous discussions of fractal-shaped antennas, there has been little or no comparison of the fractal antenna's performance properties with those of another wire antenna having a different non-Euclidean geometry, but otherwise having the same physical properties. While the antennas would have different geometries, they would have the same physical area or height, the same total wire length, and the same wire diameter. In this paper, the performance properties of the Minkowski Island fractal loop and the Koch fractal monopole are compared with those of other non-Euclidean-geometry antennas. It is demonstrated through numerical modeling and measurement that antennas having other non-Euclidean wire geometries offer similar and, in some cases, improved, performance over their fractal-antenna counterparts. From the analysis presented here, it is also demonstrated that antenna geometry alone - fractal or otherwise - is not the significant factor determining the resonant behavior of wire antennas.