Study of Fractal Antennas and Characterization

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1 Study of Fractal Antennas and Characterization Department of Physics M.M.P.G. College, Fatehabad (Haryana) Abstract-Fractal geometry involves a repetitive generating methodology that results in contours with infinitely intricate fine structures. This geometry, which has been used to model complex natural objects such as clouds and coastlines, has space-filling properties that can be utilized to miniaturize the antennas size. Fractal technology has great potential in antenna miniaturization, multifrequency and UWB & mobile communication applications. The purpose of this article is to introduce the concept of the fractal technology, review the progress in fractal antenna study and implementation, comparison of different types of fractal antenna elements and arrays and discuss the challenges and future scope of this type of antenna. Fractal antenna technology in communication field has become the research area. Keywords: Fractals, Fractal technology, Sierpinski triangle, Fractal geometry, Antenna arrays. I. INTRODUCTION Wireless communication technology has been developed to the broadband and integration; the requirement for portable mobile communication is higher. This requires antenna development corresponding broadband spectrum, multifrequency technology and miniaturization. Multi-band and ultra-wideband antennas are desirable in personal communication systems, compact satellite communication terminals, and other wireless applications. Future communications technology will put more serious challenges for antenna design, demanding a miniaturized structure to complete antenna design objectives. With the use of Fractal antenna can achieve the antenna requirements of modern communication such as compact size, which is being easy to manufacture and low cost. In general, a wideband antenna in the low frequency wireless bands can only be achieved with heavily loaded wire antennas, which usually means different antennas, are needed for different frequency spectrum. The study of fractal antennas provides attractive solutions for using a single small antenna operating in a number of frequency bands. Fractals represent a class of geometry with very unique properties that can be used for antenna design. Fractals are space-filling configurations, meaning electrically large features can be efficiently integrated into small areas. Since the electrical lengths of antenna have an important role in antenna design, this efficient integration can be used as a viable miniaturization technique. Fractal antenna solved two limitations of the traditional antenna: (1). In general antenna performance is highly dependent upon the electrical size of antenna. This means that antenna parameters (gain, input impedance, and orientation graph and side lobe patterns) will changes as the working frequency for fixed antenna size. Fractal self-similarity feature provides the broadband characteristics. (2) Fractal complex shapes make some antenna s size get reduced. The research of fractal antenna in military and communication field have a wide application prospect. II. CONCEPT OF FRACTALS The term fractal, which means irregular fragments [1] used to describe a family of complex structures that have an inherent self-similarity in their geometrical structure. The Euclidean geometries are limited to points, lines, sheets and volumes of integer dimensionality, fractal structures have its extension between these Euclidean classifications having noninteger dimensionality. Fractal geometries accurately characterize many non-euclidean features of the natural including the length of coastline, density of clouds, and the branching of trees [2] and also have its application in many areas of science and engineering including antenna design. Most fractal objects have self-similar shapes although there some fractal objects exist that are hardly self-similar at all. Most fractals also have infinite complexity that is, the complexity of the fractals remains. Most fractals antenna has fractional dimensions. The original inspiration for the 169

$development of fractal geometry came basically from the study of the natural patterns.$ Fractals can be divided into many different types.

$1Mathematically generated plants, are good examples of how fractals can be used to model complex geometries found in nature. Fig.2Fractal Landscape III.$

2 development of fractal geometry came basically from the study of the natural patterns. Fractals have been successfully used to model such complex natural objects such as cloud boundaries, mountain ranges, coastlines, snowflakes, trees, leaves, ferns etc. Fractals can be divided into many different types. Fractals concepts have been applied in image compression, in the creation of music from pink noise, and in the analysis of high altitude lightning phenomena. Fig.1Mathematically generated plants, are good examples of how fractals can be used to model complex geometries found in nature. Fig.2Fractal Landscape III. BRIEF OVERVIEW OF FRACTAL GEOMETRIES This section presents a brief overview of some of the more common fractal geometries that have been found to be more useful in developing new and innovative antenna designs. The geometric forms used for building man-made objects belong to Euclidean geometry; they are comprised of lines, planes, rectangular volumes, arcs, cylinders, spheres, etc. Fractal geometries are generated in an iterative fashion, leading to self-similar structures. The example of fractal shown is a Minkowski island fractal [5]. The starting geometry of the fractal, called the initiator, is a Euclidean square. Each of the four straight segments of the starting structure is replaced with the generator. Fig.3 The iterative-generation procedure for a Minkowski island fractal. This iterative generating procedure of fractal continues for an infinite number of times. The final result is a curve with an infinitely intricate underlying structure that is not differentiable at any point. The iterative generation process creates a geometry that has intricate details on an evershrinking scale. In a fractal, no matter how closely the structure is studied, there never comes a point where the fundamental building blocks can be observed. The reason for this intricacy is that the fundamental building blocks of fractals are scaled versions of the fractal shape [3]. This can be compared to it not being possible to see the ending reflection when standing between two mirrors. Closer inspection only reveals another mirror with an infinite number of mirrors reflected inside. Sierpinski triangle: Sierpinski triangle [4] is established by a triangle. The process is continuously removed the small inverted triangle in the center of the original triangle. This process will produce 3 k smaller triangle, and the area is (3/4) k, where k is the number of iterations. The side length of the triangle of each level is 1/2 of the side length of the top grade triangle.the final Sierpinski triangle contains numerous small triangular, and have maintained self-similarity at any scale. Fig. 4 Sierpinski triangle generating process 170

$V. HOW FRACTALS CAN BE USED AS ANTENNAS AND WHY FRACTALS ARE SPACE-FILLING GEOMETRIES The Euclidean geometries are limited to points, lines, sheets, and volumes, fractals include the geometries that$

3 V. HOW FRACTALS CAN BE USED AS ANTENNAS AND WHY FRACTALS ARE SPACE-FILLING GEOMETRIES The Euclidean geometries are limited to points, lines, sheets, and volumes, fractals include the geometries that fall between these distinctions. Therefore, a fractal can be a line that approaches a sheet. The line can be in such a way as to effectively almost fill the entire sheet. These space-filling properties lead to curves that are electrically very long, but fit into a compact physical space. This property can lead to the miniaturization of antenna elements. A prefractal [6] drops the complexity in the geometry of a fractal that is not distinguishable for a particular application. For fractal antennas, this can mean that the intricacies that are much smaller than a wavelength in the band of frequencies can be dropped out. This now makes this infinitely complex structure, which could only be analyzed mathematically. It will be shown that the band of generating iterations required to have the benefits of miniaturization is only a few before the additional complexities become indistinguishable. VI. FRACTAL ANTENNA ELEMENTS In general the concepts of fractals can be applied to develop various antenna elements. The use of fractals concept to antenna elements allows for compact, resonant antennas that are multiband and may be optimized to achieve the gain requirements. When antenna elements or arrays are designed with the concept of self-similarity for most fractals, they can achieve multiple frequency bands because different parts of the antenna are similar to each other at different scales. Fractal concept could be used to significantly reduce the antenna size without degenerating the performance. The multiband capability of fractals can be achieved with the Sierpinski monopole and dipole. The Sierpinski monopole displayed a similar behavior at several bands for both the input return loss and radiation pattern. The fractal concept can be used to reduce antenna size, such as the Koch dipole, Koch monopole, Koch loop, and Minkowski loop [7] or, it can be used to achieve multiple bandwidth and increase bandwidth of each single band due to the self-similarity in the geometry, such as the Sierpinski dipole, and Cantor slot patch. 171 A. Sierpinski monopole and dipole: The original gasket is generated by subtracting a central inverted triangle from a main triangle shape. The Sierpinski gasket is a self-similar structure. In such an ideal Sierpinski gasket, each one of its three main parts is exactly equal to the whole object, but scaled by a factor of two and so are each of the three gaskets that compose any of those parts. The selfsimilarity properties of the fractal shape are translated into its electromagnetic behavior and results in a multiband antenna. (a) (b) Fig. 5 Sierpinski monopole and dipole B. Koch monopole and dipole: The Koch curve has been used to construct a monopole and a dipole in order to compact the antenna size. 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. The miniaturization of the antennas specifies a greater degree of effectiveness for the first several iterations. The amount of scaling required for each iteration reduces as the number of iterations increase. (a) (b) Fig. 6 Koch antenna (a) Relative height of a resonant Koch monopole for different fractal iterations, (b) Dipole. C. Koch loop and Minkowski loop: Loop antennas are well understood and can be expressed effectively using a variety of Euclidean geometries. They have different limitations[8], however. Resonant loop antennas require a large amount of space and small loops have very low input

4 resistance. A fractal island can be used as a loop antenna to overcome these drawbacks. Both types of fractal loops have the similar characteristic that the perimeter increases to infinity while maintaining the volume of structure. This increase in length decreases the required volume occupied for the antenna at resonance. For a small loop, the increase in length improves the input resistance of antenna structure. By increasing the input resistance, the antenna can be more effectively matched to a feeding transmission line. Fig. 7 Koch loop and Minkowski loop D. Fractal Patch Elements: The concept of fractals can be used to miniaturize patch elements as well as wire elements. The fractal concept of increasing the electrical length of a radiator can be applied to a patch element. The patch antenna can be viewed as a microstrip transmission line. Therefore, if the current can be forced to travel along the convoluted path of a fractal to travel along the convoluted path of a fractal instead of a straight Euclidean path, the area occupy the resonant transmission line decreases. This technique of fractal has been applied to patch antenna in various forms [9].The torn-square fractal is used along the edge that determines the resonant length in a rectangular patch. The generating methodology is very similar to that of a Koch curve. The straight radiating edges of the patch are held constant in width while being brought closer to each other. This concept maintains the gain at the same level for the resonant linearly-polarized patch as for the resonant. VII. FRACTAL ANTENNA ARRAYS The term fractal antenna arrays generally used to denote a geometrical arrangement of antenna elements that is fractal. The different properties of random fractals are used [10] to develop a design 172 methodology for quasi-random arrays. In other words, random fractals were used to generate array configurations that were somewhere between completely ordered and completely disordered. The application of fractals concept is to antenna design with a compact size, high gain fractal linear and planar arrays [11]. The objective is achieved by arranging the elements in a fractal pattern to reduce the number of elements in the array and obtain wideband arrays or multiband performance. Another advantage of these fractal arrays is that the selfsimilarity in their geometric structure may be exploited in order to develop algorithms for rapid computation of their radiation patterns. VIII. CONCLUSION The concepts of fractals can be applied to the design of antenna elements and arrays. Fractals are spacefilling geometries that can be used as antennas to effectively fit long electrical lengths into small areas. Most fractals have self-similarity, so fractal antenna elements or arrays can also achieve multiple frequency bands due to the self-similarity between different parts of the antenna. The combination of the infinite complexity and the self-similarity makes it possible to design antennas with very wideband performance. Applications of fractal geometry are becoming increasingly widespread in the fields of science and wireless communication engineering. In the future, fractal antennas can be studied in several areas. One area of development is to implement fractal antennas into current technologies in practical situations, such as the expanding wireless technology. Fractal antenna technology which has broad application prospects can solve present antenna design, and some key techniques in the field of antenna, but there are still many aspects need further exploration of technology. REFERENCES [1] B. B. Mandelbrot, The Fractal Geometry of Nature, New York, W. H. Freeman, [2] D. H. Werner and S. Ganguly, An overview of fractal antennas engineering research, IEEE Antennas and Propagation Magazine, vol. 45, no. 1, pp , February [3] Carles Puente Baliarda, etal. An iterative model for fractal antenna: application on The Sierpinski gasket antenna, IEEE Transactions on Antennas and Propagation, vol. 48, No. 5, May pp

5 [4] Yuan-hai Yu and Chang-peng. Ji, Research of Fractal Technology in the Design of Multi-frequency Antenna, [5] J. Gianvitorio and Y. Rahmat "Fractal antennas: a novel antenna miniaturization technique and applications", IEEE Antennas and Propagation Magazine, vol. 44, No. 1, February [6] Douglas H. Wemer and Raj Mittra, Frontiers in Electromagnetics, New York, IEEE Press, [7] N. Cohen, Fractal antenna applications in wireless telecommunications, Proceedings of Electronics Industries Forum of New England, 1997, pp [8] C. Puente-Baliarda, J. Romeu, R. Pous, and A. Cardama, On the behavior of the Sierpinski multiband fractal antenna, IEEE Trans. on Antennas and prop., Vol. AP-46, 1998, pp [9] Xue-Xia Zhang and Fan Yang, Study of a Slit Cut on a Microstrip Antenna and Its Applications, Microwave and Optical TechnoIogy Letters, 18,4, 1998, pp [10] Y. Kim and D. L. Jaggard, The fractal random array, Proc. IEEE, vol. 74, Sept. 1986, pp [11] D. L. Jaggard and A. D. Jaggard Cantor ring arrays, Digest of IEEE AP-WRSI International Symposium, 1998, pp

Stacked Fractal Antenna Having Multiband With High Bandwidth

Conference on Advances in Communication and Control Systems 2013 (CAC2S 2013) Stacked Fractal Antenna Having Multiband With High Bandwidth Nikhil Kumar Gupta 1 Sahil Bhasin 2 Varun Pahuja 3 Abstract This