# Methods of calculating linear arbitrarily curved antennas with complex and reactive loads

 Ovsyanikov, VV, Svinarenko, DM, Beznosova, ER, Tsypko, LZ Organization:  Oles Honchar Dnipro National University 72, Gagarin Avenue, Dnipro (Dnipropetrovsk), 49010, Ukraine E-mail: ovsyan37@i.ua https://doi.org/10.15407/rej2019.03.067 Language: russian Abstract:    The subject and purpose of the work. The methods and results of calculations of the electrical characteristics of the wire randomly bent antennas of the microwave range have been investigated with the purpose of significantly expanding their capabilities and increasing the accuracy of the electrical parameters computations. Methods and methodology of work. The methods and methodology of studies of arbitrarily curved wire whip and loop antennas are considered with concentrated arbitrary loads and excitation nodes included at arbitrary points. An approximate calculation of such antennas is performed by the method of an equivalent long line, and rigorous calculation by the integral equation method with respect to the distribution of the complex current on the antenna. Results of the work. The algorithm of step-by-step development of randomly bent wire whip and loop antennas with arbitrary concentrated loads and excitation nodes included at arbitrary points is proposed. A comparative analysis of the possibilities and errors in calculating approximate and rigorous methods for calculating similar antennas is performed. Аn approximate methods are quite useful for preliminary estimation of input parameters of antennas, and also as an initial approximation for the parametric synthesis of a developed antenna or antenna system. If the accuracy of calculating the antenna parameters by an approximate method is insufficient, it is recommended to apply a rigorous method – the integral equation. The singularities of solving integral equations with respect to the distribution of complex current on linear arbitrarily curved thin pin and loop antennas composed of rectilinear segments of conductors with an arbitrary number of concentrated complex loads and excitation nodes are studied. It is shown that the application of Fredholm integral equations of the first kind to the analysis of such antennas with allowance for the Pocklington integral equation makes it possible to expand the variety of variants of their configuration. However, such integral equations, as is well known, do not satisfy the condition for the correctness of the solution. This negative property leads to instability of the solution of the problem for the current by the integral equation method and to a decrease in the accuracy of calculation of the antenna parameters. To eliminate such a defect and to obtain a stable solution of the integral equation, a method is proposed for diagonalizing the matrix of the coefficients of the system of equations. To solve the problem of calculating such antennas, DISTRIBUTION software was proposed, with the help of which a number of calculations of various pin and loop bent antennas with loads were performed. Examples of calculation with the help of this computer program of the direct and inverse matrices of the system of algebraic equations are given and then the determination of the complex distribution of the current and the input resistance of the investigated antennas is given. The conclusion. The type of antennas under investigation is expanded and the accuracy of calculations of their parameters is increased. It was noted that for the first time in the world practice the method of the integral equation for the calculation of such antennas was proposed and published, which outstripped the development time, the methods and computer programs proposed subsequently. The results of the calculations are consistent with the literature data and experimental results. Based on the studies of antennas by the integral equation method, new designs were developed, some of which were introduced into production and operation when installed on space vehicles and other objects Keywords: antenna from rectilinear segments of conductor, arbitrarily curved linear antenna, concentrated load and excitation node, equivalent long-line method, integral equation method for current on antenna, segment of antenna splitting

Manuscript submitted 11.10.2018
PACS 84.40. Ba​

Full text  (PDF)

References:
1. Varyvdin, V.S., Kolomoytsev, F.I., Ovsyanikov, V.V., 1972. On the current distribution and the input resistance of curved vibrators of finite thickness. Izv. Vyssh. Uchebn. Zaved. Radiofiz., 15(9), pp. 1398–1406 (in Russian). DOI: https://doi.org/10.1007/BF01031827
2. Ovsyanikov, V.V., 2016. State of development of vibrator, dielectric and plasma antennas in the context of the historical development of antenna technology. Radiofiz. Elektron., 7(21)(3), pp. 58–73 (in Russian). DOI: https://doi.org/10.15407/rej2016.03.058.
3. Mittra, R. ed., 1973. Computed Techniques for Electromagnetics. University of Illinois, Urbana, Illinoi`s. Pergamon Press. Intern. Series of Monog. In Electr. Engin. Vol. 7. 485 p.
4. Pocklington, H.C., 1897. Electrical oscillations in wires. Camb. Phil. Soc. Proc., 9, pp. 324–332.
5. Tang, C.H., 1964. Input Impedance of Arc Antennas and Short Helical Radiators. IEEE Trans. Antennas Propag., 12(16), pp. 2–9. DOI: https://doi.org/10.1109/TAP.1964.1138164
6. Mei, K.K., 1965. On the Integral Equations of Thin Wire Antennas. IEEE Trans. Antennas Propag., 13(5), pp. 374–378.
7. Govorun, N.N., 1960. About first-order integral equation solution uniqueness of antenna theory. Dok. Akad. Nauk SSSR, 132(1), pp. 91–94 (in Russian).
8. Lavrentyev, M.M., 1962. About Some Incorrect Problems of Mathematic Physics. Novosibirsk: Sib. From the Academy of Sciences of the USSR Publ. (in Russian).
9. Markov, G.T., Vasiliev E.N., 1970. Mathematical methods of applied electrodynamics. Moscow: Sovetskoe radio Publ. (in Russian).
10. Buharov, S.V., Filins'kyy, L.A., 2015. Modelling of printed antennas for telecommunications systems. Proc. of X Annivers. Int. Conf. on Anten. Theory and Techn. (ICATT'15). Kharkiv, Ukraine, 21–24 April 2015, pp. 273–275. DOI: https://doi.org/10.1109/ICATT.2015.7136854
11. Buharov, S.V., Filins'kyy, L.A., 2017. Using of Printed Antennas to Evaluate the Permittivity of Materials. Proc. of XI Int. Conf. on Anten. Theory and Techn. (ICATT'17). Kyiv, Ukraine, 24–27 May 2017, pp. 239–242. DOI: https://doi.org/10.1109/ICATT.2017.7972631
12. Buharov, S.V., Ryabchiy, V.D., 2017. Modeling of Ultra-Wideband Antennas for broadband Systems for Various Purposes. Proc. of XI Int. Conf. on Anten. Theory and Techn. (ICATT'17). Kyiv, Ukraine, 24–27 May 2017, pp. 213–216. https://doi.org/10.1109/ICATT.2017.7972625
13. Khmyrov, B.E., Kavelin, S.S., Popel, A.M., Varivdin, V.S., Rodin, K.V., Ovsyanikov, V.V., 1982. The AUREOL-3 satellite. Ann. Géophys., 38(5), pp. 547–556.
14. Ovsyanikov, V.V. 2007. To the electrodynamic characteristics calculation of wire telecommunications antennas with impedance elements. Radioelectronics and Communications Systems, 50(7), pp. 51–59 (in Russian). DOI: https://doi.org/10.3103/S0735272707070060.
15. Fourie, A., Nitch, D., 2000. Super NEC: Antenna and Indoor-Propagation Simulation. IEEE Antennas Propag. Mag., 42(3), pp. 31–48. DOI: https://doi.org/10.1109/74.848946