Ultra-wideband (Uwb) antenna far-field radiation is typically characterized by the numerical computation of radiation integrals. This computation involves the free-space dyadic Green's functions. It is usually carried out in the frequency domain with the electromagnetic (EM) field's spatial distribution. At Delft University of Technology, however, Diego Caratelli and Alexander Yarovoy have proposed a methodology for the accurate time- and frequency-domain analysis and modeling of wave radiation processes in UWB antennas. This methodology is based on the singularity expansion method.
In this approach, the transient EM-field distribution in the Fraunhofer region is presented in analytical closed form as the superposition of outgoing, propagating, non-uniform spherical waves. The time dependence of the wave amplitudes is determined by the resonant phenomena occurring in the structure. Thus, any time-domain integral-equation or finite-difference technique can be adopted to carry out the full-wave analysis within a volume surrounding the antenna. Such a technique also can be used to determine a spherical harmonic expansion of the equivalent electric and magnetic currents that were excited on a suitable Huygens surface enclosing the radiating structure.
The EM-field distribution in the Fraunhofer region can be evaluated by applying a modified singularity expansion method (SEM) and properly using the theory of advanced special functions for mathematical physics. See "Unified Time- and Frequency-Domain Approach for Accurate Modeling of Electromagnetic Radiation Processes in Ultrawideband Antennas," IEEE Transactions On Antennas And Propagation, October 2010, p. 3239.