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Introduction to Parallel Matching

Module by: Bill Wilson. E-mail the author

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Summary: An introduction to using the Smith Chart to perform matching in parallel.

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Let's start with the load. With the same 25Ω 25 Ω resistor for the load, and plot its admittance Y L Y 0 =2 Y L Y 0 2 . If we start moving away from the load towards the generator, in about 0.10λ 0.10 λ we again run into the circle which represents ℜYs Y 0 =1 Y s Y 0 1 . This is such an important circle is has gained its own name, and it is frequently called the matching circle Figure 1.

Figure 1
Getting to the Matching Circle
Getting to the Matching Circle (818.png)
Note that to find out how far we had to move, we had to start at relative position 0.25λ 0.25 λ as our zero, or reference location. Point "B" seems to be at about 0.35λ 0.35 λ on the scale, and since we started at 0.25λ 0.25 λ , the distance is 0.35−0.25=0.10 0.35 0.25 0.10 . At "B", Y s Y 0 =-1.0+0.7ⅈ Y s Y 0 -1.00.7 . Thus, if we add a susceptance ⅈB B with a value of +ⅈ0.014Ω-1 0.014 Ω -1 we would again match the line. Positive susceptance comes from a capacitor as well, and so Figure 2 shows how we match.
Figure 2
Matching With a Shunt Capacitor
Matching With a Shunt Capacitor (819.png)
Note that we are not required to go to point "B". Any point on the matching circle that we can get to is fair game. Another such point is "C" in Figure 1. This is at a distance of about 0.40λ 0.40 λ from the load. At "C", Y s Y 0 =1.0+0.7ⅈ Y s Y 0 1.00.7 and so we would put in an inductor, with a susceptance 1ⅈωL=-ⅈ0.014Ω-1 1 ω L 0.014 Ω -1 Figure 3.
Figure 3
Matching With a Shunt Inductor
Matching With a Shunt Inductor (820.png)

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