The advantages and disadvantages of more extended approximated analytical methods of the integral equations solution for the current in thin perfectly conducting and impedance vibrators have been investigated in details in this paper. The solutions of the problem about the electromagnetic waves scattering by the thin vibrators with the distributed surface impedance, obtained with the help of the method of expansion of the searched function for the current in a series on small parameter. The method of consistent iterations and asymptotic averaging method are given. The comparison of the calculated results with the experimental data in the case of excitation of the vi-brator in the centre by the point source of voltage is represented.
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