04-05-2011, 12:19 PM
Abstract:
This report will describe the theories and techniques for shrinking the size of an antenna through the use of fractals. Fractal antennas can obtain radiation pattern and input impedance similar to a longer antenna, yet take less area due to the many contours of the shape. Fractal antennas are a fairly new research area and are likely to have a promising future in many applications.
Keywords: Numerical integration, Moments Method.
INTRODUCTION
In today world of wireless communications, there has been an increasing need for more compact and portable communications systems. Just as the size of circuitry has evolved to transceivers on a single chip, there is also a need to evolve antenna designs to minimize the size. Currently, many portable communications systems use a simple monopole with a matching circuit. However, if the monopole were very short compared to the wavelength, the radiation
resistance decreases, the stored reactive energy increases, and the radiation efficiency would decrease. As a result, the matching circuitry can become quite complicated. As a solution to minimizing the antenna size while keeping high
radiation efficiency, fractal antennas can be implemented. The fractal antenna not only has a large effective length, but the contours of its shape can generate a capacitance or inductance that can help to match the antenna to the circuit.
Fractal antennas can take on various shapes and forms. For example, a quarter wavelength monopole can be transformed into a similarly shorter antenna by the Koch fractal.
FRACTAL DIPOLE ANTENNAS- KOCH FRACTAL
The expected benefit of using a fractal as a dipole antenna is to miniaturize the total height of the antenna at resonance, where resonance means having no imaginary component in the input impedance. The geometry of how this antenna could be used as a dipole is shown in Fig 1.
Fig. 1- Geometry of Koch dipole
A Koch curve is generated by replacing the middle third of each straight section with a bent section of wire that spans the original third. Each iterations adds length to the total curve which results in a total length that is 4/3 the original geometry:
The miniaturization of the fractal antenna is exhibited by scaling each iteration to be resonant at the same frequency. The miniaturization of the antennas shows a greater degree of effectiveness for the first several iterations. The amount of scaling that is required for each iteration diminishes as the number of iterations increase. The total lenght of the fractals at resonance is increasing, while the height reduction is reaching an asymptote. Therefore, it can be concluded that ihe increased complexity of the higher iterations are not advantageous. The miniaturization benefits are achieved in the first several iterations ( Fig. 2).
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