The solution of pair integral equations for microstrip and slot lines

Gipsman and Samokhin (1982) have discussed an effective method for the calculation of the characteristics of striplines. The original system of integrodifferential equations is reduced to a system of integral equations with accessory conditions (diagonalization of the operator of impedances). The obtained integral equations are solved with the aid of a quadrature summation approach. In the present investigation, it is shown that the diagonalization is related to the characteristics of the boundary conditions for microstrip and slot lines. Pairs of integral equations are obtained and solved. The solution procedure is based on a utilization of a factorization process and the Galerkin method. The fields in microstrip and slot lines can be conveniently described with the aid of the y component of magnetic and electric Herz vectors, taking into account, in particular, cases involving multilayer substrates.