Quasi-static analysis of multiconductor transmission lines in multilayered dielectric media above a ground plane perforated with holes of arbitrary shape

This dissertation consists of two parts. In the first part, a method of computing the capacitance and inductance matrices of a multiconducting transmission line above a ground plane perforated with small holes is presented. The number of conductors and dielectric layers is arbitrary. The conductors may be of finite cross section or infinitesimally thin. The method of solution consists of finding an equivalent problem in free space. We first short the holes and place unknown dipoles $P\sp{1}$ right above the surfaces of the holes and $P\sp{b}$ right below the surfaces of the holes to restore the boundary conditions of the original problem. Second, we use the equivalence principle to replace the signal lines and the dielectric interfaces by their equivalent unknown total charges in free space. Last, we use image theory to find an equivalent problem for the region above the ground plane. An equivalent problem for the region below the ground plane is also obtained. The formulation is obtained by using the free-space Green\u27s function in conjunction with the boundary conditions of the original problem. The unknown total charges and dipoles are found using the method of moments with pulse expansion and point matching. The average potential and normal field due to an array of an infinite number of dipoles over one period in the direction of periodicity is computed. The self terms on the ground plane are extracted from the Bethe theory of small holes. In the second part, the holes are replaced by their equivalent solenoidal magnetic currents, which in turn are equivalent to double layers of electric charges. Replacing the holes by their equivalent magnetic currents allows the treatment of relatively larger and arbitrarily shaped holes and smaller thickness of dielectric slab separating the ground plane from the signal lines. Entire domain expansion functions are used on the transmission lines and dielectric interfaces representing the equivalent total charges. On the ground plane, the holes are triangulated and pyramidal scalar expansion functions are used to represent the double layers of electric charges. A thorough analytical work is presented and simple and convenient formulas are developed. Numerical results are presented in the last chapter. The results are in very good agreement with the available data in the literature. Some of our numerical data are very valuable because they are the first to appear in the literature and hence they serve as future references