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Integro-Differential Equation’s Linear, Biconical and Curvilinear Dipole Antennas


A.V. Sochilin, I.S. Eminov, S.I. Eminov

Electrodynamic analysis of biconical and curvilinear dipole antenna’s is based on the solution integro-differential equation’s. That equation’s are two-dimension. The work is developing the general method of transformation of two-dimension equation’s to one-dimension. The base of this method is separation of logarithmic features in a kernel in manifest form. In result, starting equation’s are transform to hyper-singular integro-differential equation’s. Solution of hyper-singular equation is seeked in form expansion in series with a correspondence to second type Chebyshev polynomials with some coefficient. The coefficient provide for realization Meixner condition’s on a edge. In the work a problem of calculation of matrix element is solved. Difficult converging double integrals determine analytically or transform to one-dimension integrals. The computer-based program is worked up and the numerical calculation is realized. The results of the calculation practical completely coincide with results, which sooner received by another method. Results in either case correspond to solution with using 40 basic functions. So, the numerical calculations are confirming the accuracy of theoretical positions, which considered in the article.
May 29, 2020

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