Recent efforts by several researchers around the world to combine fractal geometry with electromagnetic theory have led to a plethora of new and innovative antenna designs. In this report, we provide a comprehensive overview of recent developments in the rapidly growing field of fractal antenna engineering. Fractal antenna engineering research has been primarily focused in two areas: the first deals with the analysis and design of fractal antenna elements, and the second concerns the application of fractal concepts to the design of antenna arrays. Fractals have no characteristic size, and are generally composed of many copies of themselves at different scales. These unique properties of fractals have been exploited in order to develop a new class of antenna-element designs that are multi-band and/or compact in size. On the other hand, fractal arrays are a subset of thinned arrays, and have been shown to possess several highly desirable properties, including multi-band performance, low sidelobe levels, and the ability to develop rapid beamforming algorithms based on the recursive nature of fractals. Fractal elements and arrays are also ideal candidates for use in reconfigurable systems. Finally, we provide a brief summary of recent work in the related area of fractal frequency-selective surfaces.

An overview of fractal antenna engineering research

The combination of fractal geometry with electromagnetic theory opens an interesting window for research to find new antenna designs and applications Fractal technology applications can be divided into six main groups: (1) multifrequency antenna elements, frequency-selective surfaces, and arrays; (2) electrically small antennas; (3) high-directivity radiating elements; (4) low-sidelobe arrays; (5) undersampled arrays; and (6) fast computational methods This article reviews most of the work done in the fractal technology field covering the last six fields


Keywords:

fractal;
antennas;
multifrequency;
arrays;
small antennas;
arrays;
microstrip antennas;
broadband;
high-directivity

Fractal Shaped Antennas: A Review

A new set of fractal multiband antennas called mod-p Sierpinski gaskets is presented. Mod-p Sierpinski fractal antennas derive from the Pascal triangle and present a log-periodic behavior, which is a consequence of their self-similarity properties. Mod-p Sierpinski fractal antennas constitute a generalization of the classical Sierpinski antenna.

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Generalized Sierpinski fractal multiband antenna

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.

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

The relationship between the Sierpinski gasket's self-similar fractal gap structure and its multiband behavior is considered. It is demonstrated that the majority of the self-similar fractal gap structure can be eliminated from the Sierpinski gasket without significantly affecting its multiband behavior. The analysis presented here demonstrates that the multiband behavior of the Sierpinski gasket is primarily a function of the periodic placement of the four gaps located along the central vertical axis of the antenna.

On the significance of self-similar fractal geometry in determining the multiband behavior of the Sierpinski gasket antenna

A simple model that explains the behavior of the Sierpinski fractal antenna is presented. This model shows that the multiband behavior of the Sierpinski fractal antenna is a consequence of its fractal nature. The model is applied to predict the behavior of the Sierpinski fractal antenna when the flare angle is modified and its validity is assessed by comparing its predictions with measured data.

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C.P. Baliarda

Papers

An iterative model for fractal antennas: application to the Sierpinski gasket antenna