Based on the complex analysis of the Lossy Transmission Line Theory, which involves the result of a Generalized Smith Chart, a new version of the last one arises when trying to characterize the wave impedance along the Transmission Line by means of analytical complex functions. Among these functions, the complex logarithm of the reflection coefficient leads to the logarithmic-reflexion coefficient-plane and its parameterized version, the Logarithmic Generalized Smith Chart. This plane is specially useful for characterizing the Transmission Line along its extension. To validate these results, some examples will be presented providing physical interpretations to the behaviour of a lossy TL and pointing out some practical applications.
Vidal Garcia, P., Gago-Ribas, E. (2017). A Logarithmic Version of the Complex Generalized Smith Chart. PROGRESS IN ELECTROMAGNETICS RESEARCH. LETTERS, 68, 53-58 [10.2528/PIERL17022009].