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Performance Characteristics of the Minkowski Curve Fractal Antenna

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 احمد محمود عبد اللطيف الخفاجي 6/10/2011 4:58:08 PM
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  Introduction

 One of the prevailing trends in modern wireless mobile devices is a continuing decrease in physical size. In addition, as integration of multiple wireless technologies becomes possible, the wireless device will operate at multiple frequency bands. A reduction in physical size and multiband capability are thus important design requirements for antennas in future wireless devices. The geometry of the fractal antenna encourages its study both as a multiband solution [1-5] and also as a small physical size antenna [6-10]. First, because one should expect a self-similar antenna, which contains many copies of itself at several scales, to operate in a similar way at several wavelengths. That is, the antenna should keep similar radiation parameters through several bands. Second, because fractals are space filling contours, meaning electrically large features can be efficiently packed into small areas.The first application of fractals to antenna design was thinned fractal linear and planar arrays [11-15], i.e, arranging the elements in a fractal pattern to reduce the number of elements in the array and obtain wideband arrays or multiband performance. Cohen [6] was the first to develop an antenna element using the concept of fractals. He demonstrated that the concept of fractal could be used to significantly reduce the antenna size without degenerating the performance. Puente et al. [4] demonstrated the multiband capability of fractals by studying the behavior of the Sierpinski monopole and dipole. The Sierpinski monopole displayed a similar behavior at several bands for both the input return loss and radiation pattern. Other fractals have also been explored to obtain small size and multiband antennas such as the Hilbert curve fractal [16], the Minkowski island fractal [9], and the Koch fractal [17]. The majority of this paper will be focused upon the Minkowski curve fractal antenna and comparing its performance characteristics with those of the half-wavelength dipole (HWD) antenna. Analysis Method and Fractal Geometry  Modeling and numerical simulations were done using NEC4 program. This program is based upon the method of moments (MoM) in which the electromagnetic interaction between wire segments can be analyzed. The MoM simulation technique incorporates periodic boundary conditions [18]. This allows for only one element of the periodic array to be simulated. When studying intricate elements such as fractals, this saves time and allows wide frequency sweeps. From the NEC4 software, the input impedance, radiation patterns, gain,  voltage standing wave ratio (VSWR), and half power beamwidth (HPBW) could be obtained The geometry of the fractal is important because the effective length of the fractal antenna can be increased while keeping the total special area relatively the same. As the number of iterations of the fractal increases, the effective length increases. A simple way to build most fractal structures is using the concept of iterated function system (IFS) algorithm, which is based upon a series of affine transformations [19]. An affine transformation in the plane    can be written as:(1)where x1 and x2 are the coordinates of point x. if   with 0<rq<1, and  , the IFS transformation is a contractive similarity (angles are preserved) where rq is the scale factor and   is the rotation angle. The column matrix tq is just a translation on the plane. Applying these transformations, a Minkowski fractal of one iteration (M1) and Minkowski fractal of two iterations (M2) are obtained as shown in Fig. 1. It is interesting to mention that M1 geometry exhibits a 24% reduction in the length from the HWD geometry, whereas the M2 geometry exhibits a 44% reduction in the length from the HWD

 

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  • Minkowski Curve Fractal Antenna

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