Editing Smith chart (section)

==3D Smith chart==
[[File:3D Smith Chart representation.jpg|thumb|100px|alt=3D Smith chart representation.|3D Smith chart representation.]]
A generalization of the Smith chart to a three dimensional sphere, based on the extended complex plane ([[Riemann sphere]]) and [[inversive geometry]], was proposed by Muller, ''et al'' in 2011.<ref name="Muller-Soto-Dascalu-Neculoiu-Boria_2011"/>

The chart unifies the passive and active circuit design on little and big circles on the surface of a unit sphere, using a stereographic [[conformal map]] of the reflection coefficient's generalized plane. Considering the point at infinity, the space of the new chart includes all possible loads: The north pole is the perfectly matched point, while the south pole is the completely mismatched point.<ref name="Muller-Soto-Dascalu-Neculoiu-Boria_2011"/>

The 3D Smith chart has been further extended outside of the spherical surface, for plotting various scalar parameters, such as group delay, quality factors, or frequency orientation. The visual frequency orientation (clockwise vs. counter-clockwise) enables one to differentiate between a negative / capacitance and positive / inductive whose reflection coefficients are the same when plotted on a 2D Smith chart, but whose orientations diverge as frequency increases.<ref name="Muller-Asavei-Moldoveanu-Sanabria-Codesal-Khadar-Popescu-Dascalu-Ionescu_2020"/>