13-07-2012, 11:46 AM
DESIGN OF FRACTAL ANTENNA FOR MOBILE APPLICATIONS
[attachment=27526]
Fractal
A fractal is a rough or fragmented geometric shape that can be subdivided in parts, each of which is (at least approximately) a reduced-size copy of the whole.
Fractals are generally self-similar and independent of scale. There are many mathematical structures that are fractals; e.g. Sierpinski’s gasket, Cantor’s comb, von Koch’s snowflake, the Mandelbrot set, the Lorenz attractor, et al.
Fractals also describe many real-world objects, such as clouds, mountains, turbulence, and coastlines that do not correspond to simple geometric shapes.
2 Koch Fractal structure
Koch fractal geometry was originally introduced by a Helge von Koch in 1904.One starts with a straight line, called the initiator. This is partitioned into three equal parts, and the segment at the middle is replaced with two others of the same length. This is the first iterated version of the geometry and is called the generator. The process is reused in the generation of higher iterations. The number of iterations defines the order of the fractals.
Advantages
Miniaturization
Better input impedance matching wideband/multiband
Frequency independent
Reduced mutual coupling in fractal array structures.
Disadvantages
Gain loss
Complexity
Numerical limitations
Benefits diminish after few iterations
[attachment=27526]
Fractal
A fractal is a rough or fragmented geometric shape that can be subdivided in parts, each of which is (at least approximately) a reduced-size copy of the whole.
Fractals are generally self-similar and independent of scale. There are many mathematical structures that are fractals; e.g. Sierpinski’s gasket, Cantor’s comb, von Koch’s snowflake, the Mandelbrot set, the Lorenz attractor, et al.
Fractals also describe many real-world objects, such as clouds, mountains, turbulence, and coastlines that do not correspond to simple geometric shapes.
2 Koch Fractal structure
Koch fractal geometry was originally introduced by a Helge von Koch in 1904.One starts with a straight line, called the initiator. This is partitioned into three equal parts, and the segment at the middle is replaced with two others of the same length. This is the first iterated version of the geometry and is called the generator. The process is reused in the generation of higher iterations. The number of iterations defines the order of the fractals.
Advantages
Miniaturization
Better input impedance matching wideband/multiband
Frequency independent
Reduced mutual coupling in fractal array structures.
Disadvantages
Gain loss
Complexity
Numerical limitations
Benefits diminish after few iterations