3.6 The Smith Chart
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The curves leading up to the values at the periphery of the chart are used to represent the reactance
of our normalised impedance,
(Figure 3.6-4). Note how, in Figure 3.6-4, we have actually shown
the imaginary part of the impedance, which features the imaginary constant , not just
. This was
done to increase clarity however usually on a Smith chart, the imaginary constant is not displayed
and the values of the reactance alone are shown.
Let us illustrate the usefulness of the Smith chart with an example. Suppose that we have
measured a reflection coefficient with a magnitude of 0.45 and an angle of 63.5ι across an unknown
load. Also assume that our measurement system uses transmission lines with a characteristic
impedance of 50Ω. Figure 3.6-5 shows this reflection coefficient on a polar plot. We now overlap our
impedance "mask" to transform our polar plot into a Smith chart (Figure 3.6-6).
Figure 3.6-5 Polar plot of reflection coefficient, 0.45∠63.5ι
Now the point which represents our reflection coefficient is located at the intersection of a circle,
which meets the real axis at point 1, and a curve which leads up to a value on the perimeter of the
chart which is equal to 1. This means that the normalised impedance corresponding to our reflection
coefficient is characterised by a normalised resistance
and a normalised susceptance
. So
the actual impedance observed at the measurement port turns out to be
( )
We
will be talking about the Smith Chart in a lot more detail in section 4.4 and we will see just how
excellent a tool it has been for design engineers.
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Conquer Radio Frequency
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