On the performance properties of the Koch fractal and other bent wire monopoles

Koch fractal monopole antennas are known to exhibit lower resonant frequencies than Euclidean monopoles of the same height. It has been concluded that there exists a unique relationship between the antennaʹs fractal geometry and its electromagnetic behavior. Here, the performance properties of the Koch fractal monopole are examined and compared with the performance properties of other bent wire geometry monopoles having the same total wire length and overall height. It is demonstrated that monopoles with less complex shapes exhibit lower resonant frequencies because they are more effective at increasing the electrical volume of the antenna. When these antennas are made to be resonant at the same frequency, they exhibit virtually identical performance properties independent of differences in their geometric shape and total wire length. It is also demonstrated that the effective height of these monopoles converge to that of an electrically small Euclidean monopole near the small antenna limit and they exhibit virtually identical radiation resistance properties at low frequencies. Finally, it is shown that the fractal limit in lowering of resonant frequency is related to the limit in the increase in the antennaʹs effective volume.