Unified Time- and Frequency-Domain Approach for Accurate Modelling of Electromagnetic Radiation Processes in Ultra-Wideband Antennas

In this paper, a singularity-expansion-method-based approach is proposed for the accurate time- and frequency-domain modelling of electromagnetic field radiation processes in ultra-wideband antennas. By the use of a dedicated two-step vector fitting procedure, a minimal pole/residue spherical harmonic expansion of time-domain equivalent electric and magnetic currents excited on a suitable spherical Huygens surface enclosing the considered radiating structure has been derived. The transient electromagnetic field distribution in Fraunhofer region is presented in closed form as the superposition of outgoing propagating non-uniform spherical waves attenuating along with the radial distance and time according to the real part of the poles accounting for complex resonant processes occurring in the structure. The proposed approach has been validated by application to an ultra-wideband resistively-loaded bow-tie antenna for ground-penetrating radar applications.