Novel Smith chart approaches to solve problems in periodic structures

In this paper, two Smith chart approaches are introduced to solve problems in periodic structures. One approach is based on the traditional matching theory that can be used in lossy periodic structures. The other is based on the nonreciprocal transmission line theory and a nonlinear mapping that can only be used in lossless cases. It is believed that the two approaches would offer flexibility and convenience in the analysis of periodic structures. Considering the limitation of the conventional Smith chart, only periodic structures with passive Bloch impedance in the passband are considered in this paper.