Derivation of the Smith chart equations for use with MathCAD

A MathCAD document is described that provides the capability for plotting a set of normalized complex impedance data, which can be provided either from a data array or from an analytical expression. The generation of the Smith chart axis is done with analytical expressions, rather than with numerical techniques. An example of the use of this program is given, using a rectangular microstrip patch antenna model, generated by the HP Momentum electromagnetic simulator. The complete MathCAD document is provided as part of this paper.