Fractal antennas: A novel antenna miniaturization technique, and applications

Fractal geometry involves a recursive generating methodology that results in contours with infinitely intricate fine structures. This geometry, which has been used to model complex objects found in nature such as clouds and coastlines, has space-filling properties that can be utilized to miniaturize antennas. These contours are able to add more electrical length in less volume. In this article, we will look at miniaturizing wire and patch antennas using fractals. Fractals are profoundly intricate shapes that are easy to define, It will be seen that even though the mathematical foundations call for an infinitely complex structure, the complexity that is not discernible for the particular application can be truncated. For antennas, this means that we can reap the rewards of miniaturizing an antenna using fractals without paying the price of having to manufacture an infinitely complex radiator. In fact, it will be shown that the required number of generating iterations, each of which adds a layer of intricacy, is only a few. A primer on the mathematical bases of fractal geometry will also be given, focusing especially on the mathematical properties that apply to the analysis of antennas, Also presented will be an application of these miniaturized antennas to phased arrays. It will be shown how these fractal antennas can be used in tightly packed linear arrays, resulting in phased arrays that can scan to wider angles while avoiding grating lobes.