Evolving Ideas. Study of Sierpinski Triangle Gasket. Computing, Communication and Networking

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1 588 Evolving Ideas Computing, Communication and Networking Publish by Global Vision Publishing House Edited by Jeetendra Pande Nihar Ranjan Pande Deep Chandra Joshi Study of Sierpinski Triangle Gasket Ashish A. Lale 1, Bhagwan V. Khiste 2, Guruprasad Burshe 3 and Sanjay Khobragade 4 ABSTRACT An investigation of the application for mobile communication, RADAR, WLAN, of uniform branch length ratios for sierpinski triangle designs is presented. An analysis is performed to examine the parameters of antenna with a frequency rang in between 1 GHz to 6 GHz, operating frequency 5.1GHz with a VSWR < 2 of similar antenna structures. This paper shows the design of sierpinski triangle, which uses unique fractal geometry. A common feeding structure based on coaxial probe coupling has been applied in order to compare a number of common fractal geometries. This reduces issues with other feed techniques such as choice of appropriate feed position and the small inherent bandwidth of direct contact. The single band behaviors of antenna are studied in this paper with an iterative method and try it to convert in multiband antenna. The behaviors of an antenna are investigated such as return loss, number of iterations, VSWR and radiation pattern. This geometry, which has been used to model complex objects found in nature such as clouds and coastlines, has space-filling properties that can be utilized to miniaturize antennas. These unique properties of fractals have been exploited to develop a new class of antenna-element designs to possess several highly desirable properties, including multi-band performance, low side lobe levels, and its ability to develop rapid beam forming algorithms based on the recursive nature of fractals. INTRODUCTION Antennas have been studied for about a hundred years and in use for as long. Fractal shaped antennas are used today for multi-frequency purposes which was not possible for traditional antennas. Common 1 Department of Electronics and Telecommunication, Dr. Babasaheb Ambedkar Technological University Lonere, Maharashtra, ashishlale@gmail.com 2 Department of Electronics and Telecommunication, Dr. Babasaheb Ambedkar Technological University Lonere, Maharashtra, bkhiste@gmail.com 3 Department of Electronics and Telecommunication, Dr. Babasaheb Ambedkar Technological University Lonere, Maharashtra, guru.burshe@gmail.com 4 Research Scholar, RU, Kurnool, AP and Sr. Lecturer, Dr. Babasaheb Ambedakar Technological University Lonere, svk2305@gmail.com

2 Study of Sierpinski Triangle Gasket 589 Fractals including the Hilbert Curve, Sierpinski Triangle and Koch Snowflake have been extensively researched in numerous basic forms including the loop, the dipole and in arrays 2. The term fractal, which means broken or irregular fragments, was originally coined by Mandelbrot to describe a family of complex shapes that possess an inherent self-similarity or self affinity in their geometrical structure. The original inspiration for the development of fractal geometry came largely from an in-depth study of the patterns of nature. For instance, fractals have been successfully used to model such complex natural objects as galaxies, cloud boundaries, mountain ranges, coastlines, snowflakes, trees, leaves, ferns and much more. The first frequency independent and multiband fractal antenna is the Sierpinski monopole. Such a monopole displayed a similar behavior at several bands from both the input return loss and radiation patterns points of view. The Sierpinski triangle also called the Sierpinski gasket or the Sierpinski Sieve is a fractal named after the Polish mathematician Waclaw Sierpiñski who described it in , 6, 7. Wireless applications at low frequencies are always a quite difficult task for engineers as the wavelength of the antenna is in direct proportion to its size. So, at low frequencies the antenna of smaller size is always a preference. The main aspect needed in today s Communication is the multiband behavior of the device as antenna, etc. Therefore, from engineering prospective, it is important to determine the resonant frequencies in different Sierpinski modes when other parameters are available. Also, it is equally important to find the side length of the generating triangle when all other parameters are available. CONSTRUCTION OF SIERPINSKI GASKET ANTENNA Sierpinski gasket antenna is a representative fractal antenna. Usually, it is inverse triangle configuration when its zero Proceedings stage and dug out a 1/2 side triangle of 2 3 cm of its length of side of triangle, when it s one stage. Fig. 1 shows a three stages Sierpinski gasket antenna which is decrease by degrees. In theory fractal antenna can be infinite stages, but the stages must be finite in practice. The material used for this synthesis is Roger RT/ duroid 6006(tm) with permittivity (6.15) and dielectric loss tangent (0.0019). Fig. 1: Scheme of Three Stages Sierpinski Gasket Antenna For construction of fractals of triangle there is an error of 3D modular, for limiting this we construct the next iteration so that it remains a gap between the main patch and next iteration. Fig. 2: Gap between Main and Next Iteration Patch

3 590 Ashish A. Lale, Bhagwan V. Khiste, Guruprasad Burshe and Sanjay Khobragade Fig. 3: Sierpinski Triangles ANTENNA FEED The probe feeding technique is used in this study to further minimize the effects of such variables in this comparative study. This kind of bandwidth enhancement technique includes the use of a thick air or foam substrate and the loading of a chip resistor on a micro strip antenna with a thin dielectric substrate. 6 The Coaxial feed or probe feed is a very common technique used for fractal antennas. As seen from Figure 2, the inner conductor of the coaxial connector extends through the dielectric and is soldered to the radiating patch, while the outer conductor is connected to the ground plane. The main advantage of this type of feeding scheme is that the feed can be placed at any desired location inside the patch in order to match with its input impedance. This feed method is easy to fabricate and has low spurious radiation. However, its major disadvantage is that it provides narrow bandwidth and is difficult to model since a hole has to be drilled in the substrate and the connector protrudes outside the ground plane, thus, not making it completely planar for thick substrates ( h > 0.02 d o ) 6, 7. Fig. 4: Construction of Probe Feeding Mechanism EXPERIMENTAL RESULTS AND DISCUSSION Here comparing the iterations of triangle patch with changing the material of substrate, r, changing the probe position and height, diameter the frequency of operation only in between 1 GHz to 6 GHz with a VSWR < 2.

4 Study of Sierpinski Triangle Gasket 591 Iteration 1 For the iteration 1 the length of side of each triangle is 3 cm, r = 6.15, probe height = 0.5cm, diameter = 0.32cm; the BW for VSWR <2(i.e ) is 210 MHz (4%) at the center frequency of GHz. And return loss is -30db. Gain=6.8985db. Fig. 5: VSWR of Iteration 1 Fig. 6: Return Loss of Iteration 1 Fig. 7: Radiation Pattern of Iteration 1

5 592 Ashish A. Lale, Bhagwan V. Khiste, Guruprasad Burshe and Sanjay Khobragade Iteration 2 For the iteration 2 the length of side of each triangle is 3 /2 cm, r = 6.15, probe height = 0.5cm, diameter = 0.32cm; the BW for VSWR <2(i.e. 1.28) is 110 MHz (2.2%) at the center frequency of 4.95 GHz. And return loss is -18db. Gain = 7.394db. Fig. 8: VSWR of iteration 2 Fig. 9: Return Loss of Iteration 2 Fig. 10: Radiation pattern of Iteration 2

6 Study of Sierpinski Triangle Gasket 593 Iteration 3 For the iteration 3 the length of side of each triangle is 3 /4cm, r = 6.15; probe height = 0.3cm, diameter = 0.14cm, position x = 0.19, y = 0.6; the BW for VSWR<2(i.e. 1.43) is 60 MHz (1%) at the center frequency of 5.55 GHz. And return loss is -14db. Gain = -0.67db. Fig. 11: VSWR of Iteration 3 Fig. 12: Return Loss of Iteration 3 Fig. 13: Radiation Pattern Iteration 3

7 594 Ashish A. Lale, Bhagwan V. Khiste, Guruprasad Burshe and Sanjay Khobragade TABLE I: Comparison between Different Parameter Iterations VSWR Bandwidth(MHz) Return Loss(db) Iteration (4%) -30 Iteration (2.2%) Iteration (1%) -15 CONCLUSION This paper proposes a novel multi-band fractal triangle antenna. Through changing the value of the height, the apex angles degree and the nesting number, the central frequency, return loss and the bandwidth of each pass band can be controlled. The symmetrical fractal triangle antenna is obtained and proved also to have multi-band characteristic and other merits. To research and experiment deeper, the results shows the single band antenna and we try to convert it into multi-band antenna. The concrete relation between the parameters and the performance of the antenna will be further given to precisely design the antenna. In sum, the multi-band fractal triangle antenna is a novel multi-band antenna with broad prospect of application. It used in mobile communication (2.4GHz), RADAR (3-30GHZ), WLAN, of uniform branch length ratios for a sierpinski triangle design is presented. An analysis is performed to examine the parameters of antenna with a frequency rang in between 1 GHz to 6 GHz. REFERENCES 1 R. Friedberg and O. Martin, Random walks on sierpinski gasket, IEEE, vol. 47, , Brigita Kutnjak-Urbank, Stefano Zapperi, Sava Milosepic, and H. Eugene Stanley, Sand pile Model on the Sierpinski gasket fractal, IEEE, vol. 54, Number 1, Ak, Cb, July C. Puente, J. Romeu, R. Pous, and A. Cardama, on the behavior of the Sierpinski multi-band fractal antenna, IEEE Trans. Antennas Propagation, vol. 46, pp , Sami He bib, Hervé Aubert, Olivier Pascal, Nelson, J.G.Fonseca, Lionel Ries, And Jean marc E. Lopez, Sierpinski Pyramidal Antenna Loaded with a Cutoff open-ended Waveguide, IEEE Antennas And Wireless Propagation Letters, Vol. 8, Thomas M. Tirpak, Sam M. Daniel, John D. Lalonde, and Wayne J. Davis, A Note on a Fractal Architecture for Modeling and Controlling Flexible Manufacturing Systems, IEEE Transactions on Systems, Man, And Cybernetics, Vol. 22, No. 3, May-June G. Kumar and K. P. Ray, Broad Band Micro Strip Antennas, TK M5 K85, Artech House Boston London 28-57, Y. T. La and S. W. Lee, Antenna Handbook, volume 1 Fundamentals and Mathematical Techniques, Thomson Publishing Company, 1993.