Complex analysis and parameterization of the lossy Transmission Line Theory and its application to solve related physical problems

This paper provides the current state of the analysis of the Transmission Line Theory based on complex analyses. These analyses include important parameterizations which are determined by specific normalizations, leading to graphical representations of the behavior of any circuit based on transmission lines with arbitrary losses. These graphical representations facilitate not only the physical understanding of the effects of losses but also reduce the study of any problem in terms of geometrical transformations. Finally, some illustrative examples will be summarized in order to get some insight of the Complex Transmission Line Theory.