Elementary properties of the Smith Chart We will now develop a number of important properties of the Smith Chart, the first of
which is that for lines with passive terminations, the chart is confined to the interior (and
the edge) of the unit circle.
For any impedance with positive real part, we will show that |Γv| ≤ 1. To do this, let
z = r + jx be the normalized impedance at any point, then which, for passive impedances which must have positive values of r, is negative. Thus,
the Smith Chart for passive terminations lies within the unit circle.
Now we ask what other information might usefully be put on a Smith Chart? Since
there is a one-to-one correspondence between z and Γv, we can put values of z = r + jx
on the chart in the form of a curvilinear grid. To find out what these curves look like, we
will, for the moment, insert after all a Cartesian co-ordinate system for Γv so that we can
employ familiar results of Cartesian co-ordinate geometry. The results of doing this are
illustrated in Figure 3.4.
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