The 3D Smith Chart and Its Practical Applications

摘要

The mathematical theory of the 3D Smith chart1 unifies active and passive microwave circuit design on the surface of a Riemann sphere. The reflection coefficient plane is mapped stereographically through the South Pole on the surface of a unit sphere. As a result, the classical 2D Smith chart including the passive loads2 is mapped stereographically into the North hemisphere, while the circuits with negative resistance (that are outside the classical planar Smith chart) are mapped into the South one. The East hemisphere is the place of inductive circuits, whereas the West hemisphere hosts the capacitive circuits.