14-02-2013, 12:31 PM
FRACTAL ANTENNAS: DESIGN, CHARACTERISTICS AND APPLICATION
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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.
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 (
Far field directivity pattern for Koch dipoles of
different fractal iterations is shown in Fig. 3.
Fig. 3- Far field directivity pattern for Koch dipole
FRACTAL LOOPS
Loop antenas are well understood and have been studied using a variety of Euclidean geometry. The have distinct limitations, howeever. Resonant loop antennas require a large amount of space and small loops have very low input resistance. A fractal island can be used as a loop antenna to overcome these drawbacks. Two possible fractals fed as loop antennas are depicted in Fig. 4.