On the relationship between fractal dimension and the performance of multi-resonant dipole antennas using koch curves

Abstract

This paper relates for the first time, multiple resonant frequencies of fractal element antennas using Koch curves to their fractal dimension. Dipole and monopole antennas based fractal Koch curves studied so far have generally been limited to certain standard configurations of the geometry. It is possible to generalize the geometry by changing its indentation angle, to vary its fractal similarity dimension. This variation results in self-similar geometry which can be generated by a recursive algorithm. Such a variation is found to have a direct influence on the input characteristics of dipole antennas. The primary resonant frequency, the input resistance at this resonance, and the ratio of first two resonant frequencies, have all been directly related to the fractal dimension. Curve-fit expressions can also be obtained for the performance of antennas at their primary resonance, in terms of fractal iteration and fractal dimension. The antenna characteristics have been studied using extensive numerical simulations and are experimentally verified. These findings underscore the significance of fractal dimension as an important mathematical property of fractals that can be used as a design parameter for antennas. The use of these ideas would not only reduce the computational intensity of optimization approaches for design of fractal shaped antennas, but also help antenna designers approach the problem systematically. Design formulation for antennas based on other fractal geometries can be similarly obtained after identifying suitable parameters of variation. This would therefore help analytical design of multiband and multifunctional antennas using fractal geometries.Index Terms-Fractals, multifrequency antennas, wire antennas.

On the Use of Dimension and Lacunarity for Comparing the Resonant Behavior of Convoluted Wire Antennas

“…On the other hand, for given values of n and L T , the measurement at scale δ and the average lacunarity currently provide a unique information that cannot hold, in general, simultaneously for all the three resonances. It is worth to notice that, for the particular case of the Von Koch geometry, an empirical formula that relates the first resonant frequency to the Hausdorff dimension has been derived in [11], while another one relating the first resonant frequency to the average lacunarity has been presented in [14]. Furthermore, in [15], an analytical model that provides the resonant frequencies of the Minkowski dipole as a function of D H has been described.…”

“…In many cases, the selection of the geometry satisfying the design specifications requires accurate electromagnetic simulations and the adoption of proper optimization techniques. In fact, usually the theoretical prediction of the resonant behavior of an antenna is a problem difficult to solve, even if some efforts have been made to better characterize the relationship between the antenna geometry and electromagnetic characteristics of the radiator [10][11][12][13][14][15][16]. In particular, in fractal antenna design, recent studies have investigated the possibility to relate the Hausdorff fractal dimension to the position of the resonant frequencies of a convoluted dipole [10,11].…”

Fractal-Shaped Reconfigurable Antennas

“…In the paper by (Krupenin, 2006), it was shown that self-similar fractals affect the electromagnetic properties of antennas created on the basis of these geometries, and that Koch fractal antennas are multiband structures. (Vinoy et al, 2003) related multiple resonant frequencies of Koch fractal antennas to their fractal dimension. (Krishna et al, 2008) proposed a dual wide-band CPW-fed modified Koch fractal printed slot antenna for WLAN and WiMAX operations.…”

Electromagnetic Transmission Through Fractal Apertures in Infinite Conducting Screen

“…In [26], a multiresonant dipole antenna based on Koch curve has been studied. It has been shown that by changing the indentation angle of the curve, which in turn changes the fractal dimension, the input characteristics of the Koch antennas can be changed.…”

“…It has been shown that by changing the indentation angle of the curve, which in turn changes the fractal dimension, the input characteristics of the Koch antennas can be changed. Iterated Function System (IFS) for a generalized Koch curve with a scale factor s and indentation angle θ can be expressed as [26],…”