Time-domain Green´s functions for the source of HMD in multilayered structures

Planar microwave circuits etched on a dielectric substrate are usually backed by a ground plane. Very often, there are slots on the ground plane for specific coupling purposes. Transient analyses of scattering and radiation from these slots are important problems in understanding the electromagnetic compatibility of the microwave circuits. In modeling the aperture-coupling problem, we replace the electric field across the slots by an equivalent magnetic current. For the transient analyses of the planar layered structures, the time-domain integral equation (TDIE) formulation involves a more efficient discretization compared with the method of finite-difference time-domain (FDTD), where volume discretization is required. Using the TDIE method to analyze the planar structures with slots on the conducting ground plane, the time-domain Green´s functions for the magnetic currents in the layered medium are required. Using a numerical method based on the combination of full wave discrete image theory (FWDI) and fast Fourier transform (FFT), Green´s functions for an impulsive electric dipole on the top of dielectric substrate with a conducting ground plane were obtained (see Yu, Y. et al., Proc. CJMW, 2000; Xu, Y. et al., Electronics Letters, vol.36, no.22, p.1855-7, 2000). We apply the same algorithm to obtain the time-domain Green´s functions for the magnetic source on the conducting ground plane. Numerical results are compared with those of rigorous solutions obtained by the Cagniard-de Hoop method. Good agreements are found between these two methods.