Efficient Impedance Computation for Multi- Conductor Transmission Lines of Rectangu- Lar Cross Section

Abstract—An efficient numerical solution is presented for computing per-unit-length impedance of metallic rectangular transmission lines backed by semi-infinite lossy substrate. We formulate the problem into the set of integral equations, the kernel of which is analytically expressed in terms of special functions in the quasi-static regime. The method of moments is applied to find the current density distributions in the metal regions, where the discretization of cross sections is performed by using non-uniform grid arranged according to the skin effect. The practical numerical computations concern the influence of the substrate loss on the per-unit-length impedance for some types of parallel lines. We thereby show that the substrate loss cannot be neglected at high frequencies. The effectiveness of the proposed method is confirmed by showing that the computed values of resistance satisfy the law of energy conservation with acceptable accuracy.