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Analysis of some integral equations in the theory of wire antennas


M. V. Davidovich – ScD, Professor, Saratov State University. E-mail:
S. P. Skobelev – PhD, Leading Research Associate, JSC «Radiofizika», teacher of MIPT. E-mail:

In spite of the long history of the wire antenna theory, contemporary researches continue revealing their interest to developing it. In particular, the author of paper (Buzova M.A., A Fredholm integral equation of the second kind for a linear dipole on the basis of the boundary condition for magnetic field // Antennas. № 9. P. 18–22) has proposed an approximate Fredholm integral equation of the second kind based on the suggestion that the axial current determining the scattered field equals the surface current determined by the total (incident plus scattered) azimuth magnetic field according to the boundary condition for the latter on the perfectly conducting antenna surface. In the subsequent work (Buzova M. A., Yudin V. V., Design of wire antennas on the basis of integral equations: Textbook for the Institutes of higher education. Moscow: Radio & Svyaz Press. 2005), the approach indicated above has been generalized on the cases of curvilinear conductors as well as on wire antennas arranged in the vicinity of other passive conductors arbitrarily arranged in space, and there has been derived an appropriate integral equation. Later on, for instance in paper (Buzova M.A., Electrodynamical analysis of eclectic antenna systems // Radiotekhnika. 2011. № 11. P. 55–59), the indicated equation has been written in somewhat different form. In the present paper, analysis of appropriateness of the proposed equation to the problem to solve is carried out. It is shown that the former generalization contains a discrepancy of dimensions, as well as it is not reduced to the original equation corresponding to a rectilinear antenna. Along with the mistake in dimensions, the latter generalization also contains a mistake in the kernel. In conclusion, there is given a correct form the integral equation for a curvilinear wire antenna.

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