Efficient analysis of microstrip structures with multiple discontinuities

We describe an implicit mode matching scheme to solve the junction problem. The finite difference method is used to approximate the spatial derivatives along the transverse direction. The wave is propagated analytically along the z direction. This is done by expressing the fields in terms of matrix functions. A generalization of the spectral Lanczos decomposition method (SLDM) is used to solve for the asymmetric matrix functions in an efficient way. By enforcing boundary conditions on the electric and the magnetic fields at the waveguide junction, it is possible to solve for the reflected and the transmitted fields at the interface.