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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 |Tv| < 1. To do this, let z = r + jxbe the normalized impedance at any point, thenwhich, 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 Tv, 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 Tvso that we can

employ familiar results of Cartesian co-ordinate geometry. The results of doing this are

illustrated in Figurę 3.4.