Exact closed-form expression of the electromagnetic field excited by pulse-shaped and triangular line currents

The exact closed-form expression for the electromagnetic field excited by pulse-shaped and triangular line currents is presented. The analytical formulation, based on the incomplete Hankel functions, shows that the field is composed of cylindrical waves excited near the current axis and spherical waves arising from the source critical points. Spherical waves related with pulse-shaped current basis functions are shown to have stronger field singularities than for triangular basis functions because of the impulsive charges present at the current truncations. For triangular line currents, it is further shown that an additional spherical wave arises from the critical point featuring a charge jump discontinuity. Near and high-frequency asymptotic field expressions show explicitly the nature of the field singularities. Using the analytical properties of the incomplete Hankel functions, the Galerkin's impedance matrix coefficients, useful to solve radiation and scattering problems in truncated cylindrical structures using the method of moments, are finally derived in a closed-form. Numerical examples show the accuracy of the proposed field representation.