Contents I. Introduction
In RF/microwave engineering, a Smith chart is a graphical measuring tool used to design, analyze, and develop RF/microwave circuits and components. Smith [1] created the rectangular Smith chart in 1931 [2], which is the predecessor of the circular Smith chart, i.e., the 2-D conventional Smith chart [3]. The rectangular chart was initially created to aid in the resolution of transmission line problems that arose during the development of directional shortwave antennas for Bell System applications [2], but its wider applicability was not anticipated. The 2-D conventional Smith chart is essentially the Mobius transformation of the impedance plane [3], [4], [5], [6]. This 2-D conventional Smith chart has a few drawbacks, including the inability to plot negative resistance parameters and whole reactance curves within a finite space [7], [8], [9]. Even if the point with negative resistance can be mapped back into the unit circle using the approach described in [10], [11], [12], [13], and [14], the fact that it shares the same space as the impedances with positive resistance parts, is not esthetically appealing [8], [9], [15].
