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Definition of the Smith Chart

The Smith Chart provides a graphical method for the visualisationof conditions on a

transmission linę and for the solution of transmission linę problems. The method rests on

the fact that the voltage reflection factor Mefines the conditions on the linę, and that

as we move along a lossless linę from the load to the source, the voltage reflection factor

Tytransforms in a simple way, viz. l"v(S) = rv(L)e-2jpi (3.2)

This equation tells us that, as we move along the linę in the direction of the generator

by a length I, the voltage reflection factor maintains constant magnitude and changes in

phase by an aount of 201. This transformation has a simple construction in the complex

piane illustrated in the Argand diagram of Figurę 3.2.

We now provide the basie 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 Tvin the complex piane, with some extra information added.

A skeletal form of a Smith chart is illustrated in Figurę 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 figurę.