V.V. Akhiyarov – Ph.D. (Eng.), Senior Research Scientist,

Kotel’nikov IRE of RAS (Moscow);

Leading Engineer, JSC «SPC «SRI of Long-Distance Radio Communications» (Moscow) E-mail: vakhiyarov@gmail.com

The paper considers the problem of calculating the attenuation factor on the earth's surface using the integral equation method. As a rule, the use of this method is limited either to the case of long waves for a source located on the earth's surface (the Hufford equation) or to the VHF range (the Fredholm equation of the first or second kind). In the first case, the solution takes into account the electrical properties of the earth's surface, and in the second it is believed that the Dirichlet boundary condition is satisfied at the interface. The source of the field in both cases is assumed to be a point source.

It is traditionally believed that the calculation of the attenuation factor by the Hufford integral equation method is possible if the surface impedance module is much less than unity. This excludes the horizontal polarization from consideration and limits the maximum frequency for vertical polarization to 1−3 MHz.

This paper presents the results of calculations of the attenuation factor by the Hufford integral equation and explores the reasons that restrict the numerical solution of this equation. A new integral equation is given for calculating the attenuation factor on the earth's surface. This equation was obtained from the original Kirchhoff integral formula for the line-source excitation.

The distance dependences of the attenuation factor are obtained by the Hufford integral equation. It is shown that the restrictions on the frequency and polarization of radiation are associated not with the Hufford equation, but with the formulation of the problem. When the source is raised to a final height above the surface, and the integration path corresponds to the terrain profile, all restrictions associated with the accuracy of calculations are removed. A comparison of the attenuation factors obtained using the new integral equation and the Hufford equation shows that both equations provide approximately the same accuracy. However, the new integral equation is more preferable, since it was obtained without any approximations.

It is shown that the integral equation method taking into account the impedance properties of the earth is suitable for both vertical and horizontal polarization. The practical possibilities of the method are limited only by the computing capabilities.

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