Article 8118

Title of the article

ON THE ANALYSIS AND SYNTHESIS OF FRACTAL ANTENNAS 

Authors

Boykov Il'ya Vladimirovich, Doctor of physical and mathematical sciences, professor, head of the sub-department of higher and applied mathematics, Penza State University (40 Krasnaya street, Penza, Russia), boikov@pnzgu.ru
Aykashev Pavel Vladimirovich, Postgraduate student, Penza State University (40 Krasnaya street, Penza, Russia), math@pnzgu.ru

Index UDK

520.272.2

DOI

10.21685/2072-3059-2018-1-8

Abstract

Background. At present, antenna theory and technology is one of the most rapidly developing areas of radio engineering. This is due to the need for miniaturization of antennas used in mobile devices. Modern achievements in antenna theory and technology are based on the latest achievements in physics and mathematics. In recent decades, there has been an increasing interest in the mood and research of fractal and genetic antennas. In this connection, there is a need to develop analytical, numerical and program analysis and synthesis methods for fractal and genetic antennas.
The article is devoted to the investigation of fractal antennas built on the topology of the "perfect" set of Cantor and Sierpinski's "carpet".
Materials and methods. The work uses methods of computational mathematics, mathematical modeling, computational physics.
Results. Electrodynamic characteristics of fractal antennas based on the prefractals of the perfect set of Cantor and the prefractals of Sierpinsky's "carpet" are obtained (on third and second iterations of corresponding fractals). The analysis of the influence of the topology of fractal antennas on electrodynamic characteristics is carried out.
Conclusions. The influence of the geometrical structure of the antenna on its electrodynamic characteristics is demonstrated. The possibility of synthesizing fractal antennas is shown on the basis of the method of local residuals. The results of the work can be used in the study and design of fractal antennas with different topologies.

Key words

Fractal antennas, directivity diagram, standing wave coefficient

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References

1. Mal'debrot B. Fraktal'naya geometriya prirody. per. s angliyskogo [fractal geometry of nature: translated from English]. Moscow; Izhevsk: Intstitut komp'yuternykh issledovaniy, 2002, 656 p.
2. Bozhokin S. V., Parshin D. A. Fraktaly i mul'tifraktaly [Fractals and multifractal]. Izhevsk: Regulyarnaya i khaoticheskaya dinamika, 2001, 128 p.
3. Morozov A. D. Vvedenie v teoriyu fraktalov [Introduction into the theory of fractals]. Moscow; Izhevsk: Institut komp'yuternykh issledovaniy, 2002, 160 p.
4. Potapov A. A. Fraktaly v radiofizike i radiolokatsii: Topologiya vyborki [Fractals in radiophysics and radiolocation. Sample topology]. Moscow: Universitetskaya kniga, 2005, 848 p.
5. Kim I., Dzhaggard D. L. Trudy Instituta inzhenerov po elektrotekhnike i radioelektronike [Proceedings of Engineering Institute of electrical engineering and radio electronics]. 1986, vol. 74, no. 9, pp. 124–126.
6. Efremova A. O., Belousov O. A., Kalashnikov S. N., Kazaryan O. A. Voprosy sovremennoy nauki i praktiki. Universitet im. V. I. Vernadskogo [Issues of modern science and practice. University named by V. I. Vernadsky]. 2014, no. 3 (53), pp. 56–61.
7. Slyusar' V. I. Novye tekhnologii. Sovremennye telekommunikatsii [New technologies. Modern telecommunications]. 2002, no. 9, pp. 54–56.
8. Liang X., Zhensen W., Wenbung W. Electron. Lett. 1996, vol. 32, no. 21, pp. 1940–1941.
9. Slyusar' V. Elektronika: Nauka. Tekhnologiya. Biznes [Electronics: Science. Technology. Business]. 2007, no. 6, pp. 82–89.
10. Belov K. I., Lebedev B. B. Materialy nauchno-prakticheskoy konferentsii s mezhdunarodnom uchastiem. 2–7 dekabrya 2013 ch. Ch. 1. [Materials of the scientific and practical conference with international participation. 2-7th of December 2013. Part 1].
Saint-Petersburg: Gos. politekhn. universitet, 2014, pp. 3–5.
11. Tsaliev T. A. Naukovi pratsi ONAZ im. O. S. Popova. Ser.: Radiotekhnika, telekomunikatsiya ta elektronika [Radio engineering, telecommunications and electronics]. 2015, no. 1, pp. 5–11.
12. Boykov I. V., Aykashev P. V. Izvestiya vysshikh uchebnykh zavedeniy. Povolzhskiy region. Fiziko-matematicheskie nauki [University proceedings. Volga region. Physical and mathematical sciences]. 2017, no. 1 (41), pp. 51–67.
13. Jaggard D. C. Symmetry in Electrodynamics. Taylor, Francis, London, 1995.
14. Khurgin Ya. I., Yakovlev V. P. Metody teorii tselykh funktsiy v radiofizike, teorii svyazi i optike [Methods of the theory of entire functions in radiophysics, communication theory and optics]. Moscow: GIFML, 1962, 222 p.
15. Natanson I. P. Konstruktivnaya teoriya funktsiy [Constructive theory of functions]. Moscow; Leningrad: GITTL, 1949, 684 p.
16. Boykov I. V. Izvestiya vysshikh uchebnykh zavedeniy. Povolzhskiy region. Fizikomatematicheskie nauki [University proceedings. Volga region. Physical and mathematical sciences]. 2018, no. 1 (45), pp. 5–25.
17. Gorelik G. S. Kolebaniya i volny [Oscillations and waves]. Moscow: GITTL, 1950, 552 p.

 

Дата создания: 13.06.2018 14:04
Дата обновления: 03.07.2018 16:19