3.6 The Smith Chart
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3.6 The Smith Chart
As mentioned in the previous section, there is a direct correspondence between reflection
coefficient and impedance (eq.(3.5-3)). One of the most useful tools for RF engineers is a chart that
allows them to make this conversion by just overlapping (Figure 3.6-2) a particular impedance
"mask" (Figure 3.6-1 (b)) on the polar plot of a reflection coefficient (Figure 3.6-1(a)). There is a little
stumbling block that must be overcome however. Unlike the reflection coefficient, the magnitude of
which only varies between zero and one
27
, the impedance varies over a much wider range and it
would be difficult to cram large numbers in the impedance chart. What we do therefore is normalise
all the values on the "mask" (Figure 3.6-1 (b)) to the characteristic impedance of the line which, in
most cases, is 50Ω. This makes the chart more legible although it also means that we will have to
divide our impedance values by the characteristic impedance before plotting them on the chart and
multiply them by the characteristic impedance after reading them off the chart.
Figure 3.6-1 Polar plot (a), Smith chart (b)
Figure 3.6-2 Overlap of Smith chart grid on polar plot
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This is always true for passive networks but not always true for active circuits!
0.2 0.5
1
2
5
+j0.2
-j0.2
+j0.5
-j0.5
+j1
-j1
+j2
-j2
+j5
-j5
0.0
(a) (b)
0.2 0.5
1
2
5
+j0.2
-j0.2
+j0.5
-j0.5
+j1
-j1
+j2
-j2
+j5
-j5
0.0
Conquer Radio Frequency
141 www.cadence.com/go/awr
