New M.E. Thesis Submitted from ECE Student

DESIGN OF FRACTAL ANTEENA By Namrata Lamba,Electronics

Abstract A fractal antenna is an antenna that uses a fractal, self-similar design to maximize the length, or increase the perimeter (on inside sections or the outer structure) of material that can receive or transmit electromagnetic radiation within a given total surface area or volume. A good example of a fractal antenna as a spacefilling curve which is in the form of a shrunken fractal helix. Here, each line of copper is just small fraction of a wavelength.A fractal is a rough or fragmented geometric shape that can be subdivided in parts, each of which is a reduced-size copy of the whole. Fractals are generally self-similar and independent of size scaling. Due to this we come upon the amazing realization that a fractal shaped metal element can be used as an antenna over a very large band of frequencies. 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. The terms fractal and fractal dimension are due to Mandelbrot, who is the person most often associated with the mathematics of fractals (Mandelbrot, 1983). We can trace the origins of fractal theory, though he did not name it, to Helge Von Koch. In 1904 von Koch devised a curve that does not have a tangent anywhere. The curve defined by Von Koch is the basis for a class of fractals that bears his name. Also of importance to the early development of fractals (even before they were named by Mandelbrot) is the work of the English meteorologist Lewis Fry Richardson, who studied the relation between the perimeter of an island and the scale of the measurement use to measure it. All of this work builds on the point-set theory put forth by George Cantor (1870) .Mandelbrot included a definition of fractal dimension (of a geometric object) when he first talked about the concept of fractal in 1977. This definition, based on one given by Hausdorff in 1919, involves a limit process. Basically, it is the change in object size vs. the change in measurement scale, as the measurement scale approaches zero. Logarithms are used for both size and scale. (a) Dragon curve (b) Mengersponge (c) Volcano

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