عنوان البحث(Papers / Research Title)
On the Performance Properties of the Minkowski Island Fractal Antennas
الناشر \ المحرر \ الكاتب (Author / Editor / Publisher)
احمد محمود عبد اللطيف الخفاجي
Citation Information
احمد,محمود,عبد,اللطيف,الخفاجي ,On the Performance Properties of the Minkowski Island Fractal Antennas , Time 6/10/2011 4:52:36 PM : كلية العلوم
وصف الابستركت (Abstract)
The performance properties of Minkowski island have been investigated
الوصف الكامل (Full Abstract)
INTRODUCTION
With the widespread proliferation of telecommunication technology in recent years, the need for small-size multiband antennas has increased manifold. However, an arbitrary reduction in the antenna size would result in a large reactance and deterioration in the radiation efficiency. As a solution to minimizing the antenna size while keeping high radiation efficiency, fractal antennas can be implemented. 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 [Mandelbrot(1983), Barnsley et.al (1988), Peitgen et.al (1990), and Jones et.al (1990)]. Fractal are space filling contours, meaning electrically large features can be efficiently packed into small areas [Falconer (1990) and Lauwerier (1990)]. Since the electrical lengths play such an important role in antenna design, this efficient packing can be used as a viable miniaturization technique. Miniaturization of a loop antenna using fractals was shown by Cohen [Cohen (1995) and Cohen (1996)]. A first attempt to explore the multifrequency properties of fractals as radiating structures was done by Puente and Pous [Puente and Pous (1996)]. In many cases, the use of fractal antennas can simplify circuit design, reduce construction costs, and improve reliability. Because fractal antennas are self-loading, no antenna tuning coils or capacitors are necessary. Often they do not require any matching components to achieve multiband or broadband performance. Fractal antennas can take on various shapes and forms. Among those currently reported in the literature include koch fractal [Puente et.al (1998)], the Sierpinski gasket [Puente et.al (1998) and Werner et.al (1998)], Hilbert curve [Vinoy et.al (2001)], and the Minkowski island fractals [Gianvittorio and Sami (2002)]. Some of these geometries have recently been pursued for antenna applications because of their inherent multiband nature. However, incorporation of fractal geometries into the antenna structures, and various aspects of their optimization, are still in the incipient stages. The majority of this paper will be focused upon the Minkowski island fractal antennas.
MINKOWSKI ISLAND FRACTAL GEOMETRY
In order for an antenna to work equally well at all frequencies, it must satisfy two criteria: it must be symmetrical about a point, and it must be self-similar, having the same basic appearance at every scale: that is, it has to be fractal. The shape of the fractal is formed by an iterative mathematical process. This process can be described by an iterative function system (IFS) algorithm, which is based upon a series of affine transformations [Werner and Ganguly (2003)]. An affine transformation in the plane w can be written as:where x1 and x2 are the coordinates of point x. If r1=r2=r with 0<r<1, and q1=q2=q, the IFS transformation is a contractive similarity (angles are preserved) where r is the scale factor and q is the rotation angle. The column matrix t is just a translation on the plane.Applying several of these transformations in a recursive way, the Minkowski island fractals are obtained as depicted in Fig.1. The intiator is a square which can be regarded as a zeroth order of the Minkowski island fractal (MO). Each side of the square is modeled with 10 segments each of them has a length of 6 cm and a diameter of 2mm. The Minkowski island fractal of one iteration (M1) is formed by displacing the middle third of each side by some fraction of 1/3. By applying the same procedure on M1, the Minkowski island fractal of second iteration (M2) is obtained. It should be pointed out that the area of M1 is 37.4% smaller than that of MO, and the area of M2 is 54.5% smaller than that of MO.
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