De fi nition of the Smith Chart The Smith Chart provides a graphical method for the visualisation of conditions on a
transmission line and for the solution of transmission line problems. The method rests on
the fact that the voltage reflection factor Γv defines the conditions on the line, and that
as we move along a lossless line from the load to the source, the voltage reflection factor
Γv transforms in a simple way, viz.
Γv(S) = Γv(L)e−2jβl (3.2)
This equation tells us that, as we move along the line in the direction of the generator
by a length l, the voltage reflection factor maintains constant magnitude and changes in
phase by an aount of 2βl. This transformation has a simple construction in the complex
plane illustrated in the Argand diagram of Figure 3.2.
We now provide the basic definition of the Smith Chart. Close attention should be
paid to this definition, which should be committed to memory. This point is given some
emphasis, because by the time the Smith Chart has been fully developed, many students
have lost sight of its origin, and are thus handicapped in their understanding of it.
The Smith Chart is a plot of Γv in the complex plane,
with some extra information added.
A skeletal form of a Smith chart is illustrated in Figure 3.3. Although we will do so
later, for the purpose of developing theory, it is not usual to put in any Cartesian axes
because we think of the voltage reflection factor simply in terms of the magnitude in phase
terms illustrated in that figure.
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