"Jerry" wrote in
:

....
As you may already know, the Smith Chart is simply a plot that shows
*all*
impedances with a real resistance. Smith displays the impedances so
the user can quickly see how any given impedance can be adjusted by
adding any series or parallel resistances and/or reactances. Series
inductance moves the impedance "upward" along the circles of constant
Resistance. Shunt inductance will move an impedance along the circles
of constant conductance.

There are a range of formats for plotting "*all* impedances with a real
resistance", and Philip Smith found some of them in his quest for what is
now known as the Smith chart. It is not simply a plot of R and X, but in
fact a plot of the complex voltage reflection coefficient and it can have
R and X scales overlaid (along with a bunch of TL related radial scales),
and because of the behaviour of transmission lines, G and B scales. The
R, X, G, B scales are a consequence of the plot of the voltage reflection
coefficient, an overlay, and not the fundamental quantity plotted.

The magic that underlies the Smith chart is the Telegrapher's Equation
(or a lossless form for most applications).

Owen