On numerical convergence of moment solutions of moderately thick wire antennas using sinusoidal basis functions

Wire antennas are solved using a moments solution where the method of subsectional basis is applied with both the expansion and testing functions being sinusoidal distributions. This allows not only a simplification of near-field terms but also the far-field expression of the radiated field from each segment, regardless of the length . Using sinusoidal basis functions, the terms of the impedance matrix obtained become equivalent to the mutual impedances between the subsectional dipoles. These impedances are the familiar impedances found using the induced EMF method. In the induced EMF method an equivalent radius is usually used in the evaluation of the self-impedance term to reduce computation time. However, it is shown that only for very thin segments that the correct equivalent radius is independent of length. When the radius to length ratio ( ) is not small, an expansion for the equivalent radius in terms of is given for the self-impedance term. The use of incorrect self-term, obtained by using a constant equivalent radius term, is shown to be responsible for divergence of numerical solutions as the number of sections is increased. This occurrence is related to the ratio of of the subsections and hence becomes a problem for moderately thick wire antennas even for a reasonably small number of segments per wavelength. Examples are given showing the convergence with the correct self-terms and the divergence when only a length independent equivalent radius is used. The converged solutions are also compared to King\´s second- and third-order solutions for moderately thick dipoles.