Accurate simulation of lossy transmission lines with skin effects has always been difficult or at least inefficient. Although modeling lossy transmission lines without skin effects can be carried out efficiently and accurately, including accurate skin effect model either affect accuracy or efficiency. Skin effect is accurately approximated using the simple form A+B√s at high frequencies, i.e. when s is large. However, this form is not passive. Passivity guarantees stability. Since a transmission line is a passive device, its model should also be passive such that the simulation depending on it is stable. If skin effect is approximated by A+B√s and directly incorporated into a model, the simulation based on that model may become unstable.
In this thesis, a method to generate a passive, accurate and compact model for a lossy transmission line with skin effect is introduced. The method is developed on a RLC lumped equivalent circuit of a transmission line. By applying a passive model order reduction algorithm and exploring the properties of the transmission line equivalent circuit, we found out a novel way to map the model reduction process into solving integrals. By matching moments implicitly, a passive and accurate model for a lossy transmission line with skin effect can be generated rapidly.