Complex Analysis of the Transmission Line Theory: Analytical Characterization and Examples of Use

In this paper the main contributions to the Complex Transmission Line Theory regarding the characterization of the lossy Transmision Lines (TLs) will be summarized. They are introduced together with their physical interpretations and emphasized through some examples. To achieve the present results two different but complementary direct and inverse characterizations in lossy Transmission Line Theory are developed. The first one (direct characterization) is concerned with the parameterization of the TL parameters in terms of losses, while the second one ( inverse characterization) is particulary useful to know which losses lead to a particular specification of the TL. Due to the importance of the graphical analysis in the Complex Transmission Line Theory, every characterization is related to a representation in a complex plane underlying a very important normalization procedure which will be also summarized in this paper. Thus, each graph describes a "universalized" behavior of a set of TLs parameterized by the same losses in the direct characterization, or by the same TL specification in the inverse characterization. All the analysis presented in this paper and the TL problems solved to exemplify its use become very important to study and design real waveguide systems, as well as pasive circuits and components based on losses.