A spherical representation of the Smith chart

In this article a limitation of the conventional 2D Smith chart has been highlighted and discussed. An extension to the Smith chart has been proposed in an attempt to overcome these limitations. The extension involved transforming the 2D impedance plane into three dimensions and mapping it onto the surface of a sphere. This is believed to be the first time that this formulation of the Smith chart has been presented. A number of representations of the spherical Smith chart were then considered. These included the use of constant resistance, reactance, impedance, and reflection coefficient lines. Finally some of the issues associated with the graphical displaying of the 3D Smith chart were discussed.