Relationship between lacunarity and bandwidth of a koch-type wire antenna
Keywords:
Koch-type antenna, bandwidth, fraction bandwidth, lacunarity, regression analysis.
Abstract
A dipole wire antenna of the Koch type is considered. The antenna represents a wire dipole symmetrical with respect to the point of feeding. Arms of the dipole have a geometry similar to Koch's pre-fractal. The curves forming the arms differ from the classical Koch fractal only by the position of the central vertex. A family of antennas is singled out, in which the antennas differ from each other by coordinates of the central vertices. An algorithm for calculating lacunarity is described. A correlation analysis is provided with a correlation of bandwidth as well as relative bandwidth with lacunarity. Antennas having the geometry of the first three iterations of a Koch-type curve are chosen for the analysis. The calculated correlation coefficients are given in the tables. It is shown that increasing the iteration leads to a decrease in the correlation between the selected parameters. It is obtained that the correlation coefficients for the relative bandwidth are smaller than those for the bandwidth. Single-parameter regression models for the bandwidth and the relative bandwidth are constructed. The root-mean-square errors for the models are calculated. The proposed regression formulas can be used to design broadband wire antennas.
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References
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Li, Y., Mi, Y., Wang, Y., Li, G. (2012), The analysis and comparison of the electromagnetic radiation characteristic of the Koch fractal dipole, In: ISAPE, pp. 15-18.
Markina, A.G., Pleshchinskii, N.B., Tumakov, D.N. (2017), On electrical characteristics of comb-shaped microstrip antennas, in Proc. 2017 EIConRus, pp. 179-183.
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Markina, A.G., Tumakov, D.N., Pleshchinskii, N.B. (2018), Bandwidth enhancement of symmetrical fourth-teeth-shaped microstrip antenna, Helix, 8 (1), pp. 2275-2283.
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Plotnick, R.E., Gardner, R.E., Harqvore, W.W., Prestegaard, K., Perlmutters, M. (1996), Lacunarity analysis: A general technique for the analysis of spatial patterns, Physical review E, 53 (5), pp. 5461-5468.
Poole, S. (2011), Telenius-Lowe, Successful wire antennas, Radio Society of Great Britain, Abbey Court.
Rani, M. Haq, R.U., Verma, D.K. (2012), Variants of Koch curve: a review, International Journal of Computer Applications, 2 (4), pp. 20-24.
Sengupta, K., Vinoy, K.J. (2006), A new measure of lacunarity for generalized fractals and its impact in the electromagnetic behavior of Koch dipole antennas, Fractals, 14(4), pp. 271-282.
Singh, K., Grewal, V., Saxena, R. (2009), Fractal antennas: a novel miniaturization technique for wireless communications, International Journal of Recent Trends in Engineering, 2 (5), pp. 172-176.
Surutka, J.V., Velickivic, D.M. (2003), Symmetrical linear anntennas driven by two-wire lines, Serbian Jornal of Electrical Engineering, 1 (1), pp. 27-60.
Tumakov, D.N., Abgaryan, G.V., Chickrin, D.E. Kokunin, P.A. (2017), Modeling of the Koch-type wire dipole, Applied Mathematical Modelling, 51, pp. 341-360.
Vinoy, K.J., Abraham, J.K., Varadan, V.K. (2004), Generalized design of multi-resonant dipole antennas using Koch curves, ACES Journal, 19 (1a), pp. 22-31.
Wagh, K.H. (2015), A review on fractal antennas for wireless communication, International Journal of Review in Electronics and Communication Engineering, 32 (2), pp. 37-41.
Abgaryan, G.V., Tumakov, D.N. (2017), Relation between base frequency of the Koch-type wire dipole, fractal dimensionality and lacunarity, Journal of Fundamental and Applied Sciences, 9 (1S), pp. 1885-1898.
Baker, J.M., Iskander, M.F. (2015), Electrically small fractal antennas, In: IEEE International Symposium on Antennas and Propagation, pp. 1242-1243.
Balanis, C.A. (1997), Antenna theory: analysis and design, John Wiley & Sons, New Delhi.
Baliarda, C.P., Romeu, J., Cardama, A. (2000), The Koch monopole: a small fractal antenna,
IEEE Transactions on Antennas and Propagation, 48 (11), pp. 1773-1781.
Banerjee, P., Bezboruah, T., (2014), Theoretical study of radiation characteristics of short dipole antenna, Lecture Notes in Engineering and Computer Science, 2210 (1), pp. 785-790.
Barnsley, M.F., Harrington, A.N. (1989), The calculus of fractal interpolation functions, Journal of Approximation Theory, 57 (1), pp. 14-34.
Beigi, P., Mohammadi, P. (2016), A novel small triple-band monopole antenna with crinkle fractal-structure, International Journal of Electronics and Communications, 70 (10), pp. 1382-1387.
Gianvittorio, J.P., Rahmat-Samii, Y. (2002), Fractal antennas: a novel antenna miniaturization technique, and applications, IEEE Antennas and Propagation Magazine, 44 (1), pp. 20-36.
Igudesman, K., Davletbaev, M. Shabernev, G. (2015), New Approach to Fractal Approximation of Vector-Functions, Abstract and Applied Analysis, pp. 278-313.
Karim, M.N.A., Rahim, M.K.A., Majid, H.A., Ayop, O., Abu, M., Zubir, F. (2010), Log periodic fractal Koch antenna for UHF band applications, PIER, pp. 100 201-218.
Karpukov, L.M., Onufrienko, V.M., Romanenko, S.N. (2002), The properties of the fractal wire antennas, In: MMET International Conference, 1, pp. 310-312.
Krzysztofik, W.J. (2013), Fractal geometry in electromagnetics applications - from antenna to metamaterials, Microwave Review, 19 (2), pp. 3-14.
Li, Y., Mi, Y., Wang, Y., Li, G. (2012), The analysis and comparison of the electromagnetic radiation characteristic of the Koch fractal dipole, In: ISAPE, pp. 15-18.
Markina, A.G., Pleshchinskii, N.B., Tumakov, D.N. (2017), On electrical characteristics of comb-shaped microstrip antennas, in Proc. 2017 EIConRus, pp. 179-183.
Markina, A.G., Tumakov, D.N., Pleshchinskii, N.B. (2017), On base frequency for the symmetrical four comb-tooth-shaped microstrip antenna, Journal of Fundamental and Applied Sciences, 9 (1S), pp. 1534-1547.
Markina, A.G., Tumakov, D.N., Pleshchinskii, N.B. (2018), Bandwidth enhancement of symmetrical fourth-teeth-shaped microstrip antenna, Helix, 8 (1), pp. 2275-2283.
Milligan, T.A. (2005), Modern Antenna Design, John Wiley & Sons, New Jersey.
Nasr, M.H.A. (2013), Z-shaped dipole antenna and its fractal iterations, International Journal of Network Security & Its Applications, 5 (5), pp. 139-151.
Plotnick, R.E., Gardner, R.E., Harqvore, W.W., Prestegaard, K., Perlmutters, M. (1996), Lacunarity analysis: A general technique for the analysis of spatial patterns, Physical review E, 53 (5), pp. 5461-5468.
Poole, S. (2011), Telenius-Lowe, Successful wire antennas, Radio Society of Great Britain, Abbey Court.
Rani, M. Haq, R.U., Verma, D.K. (2012), Variants of Koch curve: a review, International Journal of Computer Applications, 2 (4), pp. 20-24.
Sengupta, K., Vinoy, K.J. (2006), A new measure of lacunarity for generalized fractals and its impact in the electromagnetic behavior of Koch dipole antennas, Fractals, 14(4), pp. 271-282.
Singh, K., Grewal, V., Saxena, R. (2009), Fractal antennas: a novel miniaturization technique for wireless communications, International Journal of Recent Trends in Engineering, 2 (5), pp. 172-176.
Surutka, J.V., Velickivic, D.M. (2003), Symmetrical linear anntennas driven by two-wire lines, Serbian Jornal of Electrical Engineering, 1 (1), pp. 27-60.
Tumakov, D.N., Abgaryan, G.V., Chickrin, D.E. Kokunin, P.A. (2017), Modeling of the Koch-type wire dipole, Applied Mathematical Modelling, 51, pp. 341-360.
Vinoy, K.J., Abraham, J.K., Varadan, V.K. (2004), Generalized design of multi-resonant dipole antennas using Koch curves, ACES Journal, 19 (1a), pp. 22-31.
Wagh, K.H. (2015), A review on fractal antennas for wireless communication, International Journal of Review in Electronics and Communication Engineering, 32 (2), pp. 37-41.
Published
2018-08-30
How to Cite
Abgaryan, G., & Tumakov, D. (2018). Relationship between lacunarity and bandwidth of a koch-type wire antenna. Amazonia Investiga, 7(15), 88-98. Retrieved from https://amazoniainvestiga.info/index.php/amazonia/article/view/405
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