Fractal Shaped Antenna Elements for Wide-and Multi-band Wireless Applications

Open Access
Vinoy, Kalarickaparambil Joseph
Graduate Program:
Engineering Science and Mechanics
Doctor of Philosophy
Document Type:
Date of Defense:
March 11, 2002
Committee Members:
  • Vasundara V Varadan, Committee Chair
  • Vasundara V Varadan, Committee Member
  • Douglas Henry Werner, Committee Member
  • James Kenneth Breakall, Committee Member
  • Jose K Kollakompil, Committee Member
  • Fractals
  • Antennas
  • multifrequency antennas
  • Wire antennas
The use of fractal geometries has significantly impacted many areas of science and engineering; one of which is antennas. Antennas using some of these geometries for various telecommunications applications are already available commercially. The use of fractal geometries has been shown to improve several antenna features to varying extents. Yet a direct corroboration between antenna characteristics and geometrical properties of underlying fractals has been missing. This research work is intended as a first step to fill this gap. In terms of antenna performance, fractal shaped geometries are believed to result in multi-band characteristics and reduction of antenna size. Although the utility of different fractal geometries varies in these aspects, nevertheless they are primary motives for fractal antenna design. For example, monopole and dipole antennas using fractal Sierpinski gaskets have been widely reported and their multiband characteristics have been associated with the self-similarity of the geometry. However this qualitative explanation may not always be realized, especially with other fractal geometries. A quantitative link between multiband characteristics of the antenna and a mathematically expressible feature of the fractal geometry is needed for design optimization. To explore this, a Koch curve is chosen as a candidate geometry, primarily because its similarity dimension can be varied from 1 to 2 by changing a geometrical parameter (indentation angle). Extensive numerical simulations presented here indicate that this variation has a direct impact on the primary resonant frequency of the antenna, its input resistance at this frequency, and the ratio of the first two resonant frequencies. In other words, these antenna features can now be quantitatively linked to the fractal dimension of the geometry. This finding can lead to increased flexibility in designing antennas using these geometries. These results have been experimentally validated. The relationship between the fractal dimension and multiband characteristics of fractal shaped antennas has been verified using other fractal geometries as well. The physical appearance of fractal a binary tree can be varied by either changing the branching angle, or using different scale factors between the lengths of the stem and branches of the tree. While the change in angle does not affect its fractal dimension, the scale factor does. A similar trend is observed in the multiband characteristics of monopole antennas using these geometries. This confirms similar findings based on Koch curves. It may however be mentioned that this correlation between multiband nature of the antenna and the fractal dimension of the geometry could not yet be linked across different geometries having the same dimension. Apart from these theoretical findings, this research is also directed towards designing antennas with unconventional features. The multiband characteristic of the Sierpinski gasket antenna has been experimentally modified, for octave bandwidth using a ferroelectric substrate material along with an absorber layer. It has also been shown that these antennas can be converted to a conformal configuration with relative ease, without loosing much of its bandwidth. However the presence of absorbers cause some loss in energy, necessitating a compromise between bandwidth and efficiency of the antenna. The space filling nature of Hilbert curves lead to significant reduction in antenna size. This has been explored numerically and validated experimentally. One of the advantages of using fractal geometries in small antennas is the order associated with these geometries in contrast to an arbitrary meandering of random line segments (which may also result in small antennas). However this fact has not been used in antenna design thus far. In this work, approximate expressions for designing antennas with these geometries have been derived incorporating their fractal nature. Numerical simulations presented here also indicate that antenna size can be further reduced by superimposing one fractal geometry (Koch curve) along line segments of another (Hilbert curve). Due to the presence of a large number of closely placed line segments, antennas using Hilbert curves can be designed for reconfigurable radiation characteristics with the inclusion of few additional line segments and RF switches. Although these switch positions are not optimized for specific performance, they offer immense potential for designing antennas with novel characteristics. To conclude, the research work reported here is a numerical and experimental study in identifying features of fractal shaped antennas that could impart increased flexibility in the design of newer generation wireless systems.