Synthetic Conformal Mappings for Analysis of Complex 2-D and 3-D Conductor Arrangements

The closed-form conformal mappings for auxiliary canonical domains have been adapted to obtain the equivalent circuit parameters of two- (2-D) and three-dimensional (3-D) conductor arrangements of complex shapes. Combined with the distributed circuit analysis, the developed synthetic models enable for the solution of both a direct problem of analysis and an inverse problem of retrieving physical dimensions from the specified electrical parameters. Enhanced algorithms for evaluating elliptic functions and elliptic integrals (EI) of the 1st kind were devised to overcome the crowding effect and provide rapidly convergent solutions for a broad range of the structure dimensions. Applications of the developed approach will be illustrated by the examples of rectangular coaxial lines, coupled bars, step discontinuities, chip capacitors, resonators, etc