New kinds of immittance integral equations with integrable kernels

The integral equation method is widely used for the solution of electrodynamic boundary problems. There are two different kinds of these equations: the volumetric integral equations versus the volume conductivity or polarization currents, and the surface integral equations (SIE) versus the surface electrical or magnetic fields (magnetic or electrical currents). The immittance (impedance and admittance) SIE are usually derived using the spectral domain method operated with Treftz´s basis for the Maxwell equations and applying the mode-matching technique for fields at the boundaries of the partial areas. There are some problems in the application of the two dimensional SIE to structures with complicated forms as the kernels have nonintegrable singularity. If the singularity is strong then it is impossible to use the piece-constant two-dimensional basic functions for solution of such SIE. The goal of this paper is to introduce a new method for reducing such singularities, and to derive the new kinds of SIE. This method is based upon three points. The first is the representation of surface current through some new surface potentials. The second is the application of the vector integral theorems and transferring the differential operators from kernels to the introduced potentials. The third is the application of the inverse operator-function. The results are of interest in the study of microstrip lines.