Analysis of the omnipotent Smith chart with imaginary characteristic impedances

As the most extensive Smith chart in recent times, the omnipotent Smith chart (OSC) would take on a number of special features in different cases. This paper mainly discusses the features of the OSC with imaginary characteristic impedances, and it turns out that a close connection exists between the OSC and the conventional Smith chart in the graphical and numerical properties. It is believed that the conclusion will be conducive to the completeness of the OSC theory as well as the application of the transmission lines with imaginary characteristic impedances.