N.I. Voytovich - D.Sc. (Eng.), Head of Radio Equipment Design and Production Department, South Ural State University (National Research University). E-mail: voytovichni@mail.ru
A.B. Khashimov - Ph.D. (Phys.-Math.), Associate Professor of Radio Equipment Design and Production Department, South Ural State University (National Research University). E-mail: xab@kipr.susu.ac.ru

This paper proposes a method for calculation the radiation field of antennas for navigation systems. It is considered the case of location the dipoles of vertical polarization near a number of parallel extended cylindrical objects whose axes are parallel to the axes of antennas. The Lorentz lemma and auxiliary Green-s function are used for a rigorous electrodynamics formulation of the problem. It is shown that the radiation field is determined by the scattered field of a plane wave by the cylindrical objects and antennas radiation field for free space. The proposed mathematical model is corresponded to the principle of reciprocity applies to the case of arbitrary cross-sectional shape contours of cylinders and arbitrary values of the permittivity and the magnetic permeability of the medium, which filling the objects. Invariance of the location and polarization of the auxiliary dipole provides to single two separate fields out from the general solution, which determines the antennas far-field pattern in set coordinate planes. The pattern asymptotic representation is based on analysis of the integral stationary values over a large radius surface and gives formulas to calculate the antennas radiation field. This formulas have to do clear physical meaning. It is shown that numerical solution of the 3-D vector problem can be reduced to more simple scalar 2-D problem. Rightful of this assumption is confirmed by the results of numerical solution of the corresponding integral equations.

 

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