The logarithmic generalized smith chart: Theoretical analysis

A logarithmic version of the Generalized Smith Chart is presented emphasizing its usefulnesses when analyzing the behavior of the wave parameters along the transmission line. Due to the facilities the Logarithmic Generalized Smith Chart provides to this kind of analysis, the spiral which describes the wave impedance is analytically identifyed with an hyperbolic cotangent spiral. The transformations between the main wave parameters involved - the reflection coefficient, the wave impedance and the logarithm of the reflection coefficient which underlies the Logarithmic Generlized Smith Chart-are also characterized and graphically studied. Finally, the possibilities of the new chart are pointed out by means of its application to some examples.