The modeling of antenna arrays by branched continual fractions
DOI:
https://doi.org/10.1109/ICATT.2005.1496935Keywords:
modulated antenna arrays, impedance and dielectric structures, photonic crystal, recurrence formula, branched continual fractionsAbstract
The results of generalization of mathematical models for wide class of one-dimensional modulated antenna arrays, photonic crystals, impedance and dielectric structures in the form of the branched continual fractions, which are built by recurrence formula, are represented in the article. These fractions describe the electrodynamics characteristics of structures as a function of construction's parameters. As an example the estimated directional diagram of periodic modulated impedance structure is shown.References
OLINER, A.A.; HESSEL, A. Guided waves on sinusoidally-modulatted reactance surfaces. IRE Trans. Antennas Propag., Dec. 1959, v.7, n.5, p.201-218, doi: http://dx.doi.org/10.1109/TAP.1959.1144771.
TALANOV, V.N. To the question of surface wave antenna's radiation with periodic impedance. Proc. of the High Educational Institutions of USSR. Radio Physics, 1960, n.5, p.802-807.
YEVSTROPOV, G.A. The surface waves above the ribbed surface with periodic impedance. The Questions of Radio Electronics, Ser. 12, 1960, v.3, p.13-23.
CHAPLIN, A.F. The excitation of heterogeneous periodic impedance structures. Proc. of VIII Symp. Waves and Diffraction, 1981, v.3, p.73-76.
HOBLYK, V.V. The analysis of field above the impedance plane with periodic discrete heterogeneity by Chaplin's method/Theoretical and experimental methods for antennas and SHF devices investigations. Proc. of Lvov Polytechnic Institute, 1984, n.1874.
HOBLYK, V.V.; CHAPLIN, A.F. About one summarizing of modulated impedance structures problems solution. Proc. of Lvov Polytechnic Institute, 1986, n.813.
HOBLYK, V.V. Thesis for Candidate Degree of Physics and Mathematics Sciences. Kharkiv: State University, 1986, 210 p.
HOBLYK, V.V. The excitation of modulated dielectric plate/The theory and design of semiconductors and radio electronic devices. Proc. of Lvov Polytechnic Institute, 1990, n.245, p.20-23.
HOBLYK, V.V. About the theory of equidistant arrays with periodic parameters/The theory and design of semiconductors and radio electronic devices. Proc. of Lviv Polytechnic State University, 1998, n.343, p.49-53.
HOBLYK, V.V.; HOBLYK, N.N. Branched continual fractions in the problems of wave diffraction. Radioelectronics and Telecommunications, 1998, n.352, p.150-153.
SKOROBOGAT'KO, V.Y., DRONIUK, N.S.; BOBYK, O.I.; PTASHNYK, B.J. The branched continual fractions. State Academy of Science. Ser. A, 1967, n.2, p.131-133.
SCOROBOGAT'KO, V.Y. The Theory of Branched Continual Fractions and Its Application in the Calculus Mathematics. Moscow: Science, 1983, 312 p. [in Russian].
HOBLYK, V.V.; HOBLYK, N.M. About one solution for periodic-heterogeneous impedance plain excitation problem/ The theory and design of semiconductors and radio electronic devices. Proc. of Lviv Polytechnic State University, 1998, n.343, p.53-57.
HOBLYK, V.V.; HOBLYK, N.N. About solution of the Fredholm integrated equation in a branched continual fraction type. Proc. of Int. School-Seminar on Continued Fraction, their Generalization and Application, Uzhhorod National University, 2002, p.16-18.
MARKOV, G.T.; CHAPLIN, A.F. Electromagnetic Field Excitation. Moscow, 1983, 179 p. [in Russian].