Radio Frequency Integrated Circuit Design - Webs

Impedance Matching
Example 4.7 Matching Using a Two-Stage Ell Network
Match 200� to 50� at 1 GHz using an ell matching network. Do it first in
one step, then do it in two steps matching it first to 100�. Compare the
bandwidth of the two matching networks.
Solution
Figure 4.26 illustrates matching done in ‘‘one step’’ (with movement from a
to b to c) versus matching done in ‘‘two steps’’ (with movement from a to d
to c). One-step matching was previously shown in Example 4.3 and Figure 4.11.
Two-step matching calculations are also straightforward, with an ell network
converting from 200� to 100�, and then another ell network converting from
100� to 50�. The resulting network is shown in Figure 4.27.
A comparison of frequency response shown in Figure 4.28 clearly shows
the bandwidth broadening effect of matching in two steps. To quantify the
effect, the magnitude of the input impedance is shown in Figure 4.29.
Figure 4.26 Smith chart illustration of one-step versus two-step matching.
Figure 4.27 Circuit for two-step matching.
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