Single Shunt Stub Matching Network

Given

A load Z_L=R_L+jX_L or a load having a Reflection Coefficent G_L=re^jq to be matched to a transmission line of charactersitic impedance of Z_c. The matching will be done using a single stub shunt element.

The matching network will look like this:

Since a shunt elemnt will be added to the network, Admittance rather than Impedance will be usefull.

• Locate
  • The normalized Z_L or
  • The Reflection Coeficient re^jq
  on the Smith Chart as shown in the figure.
• Locate the corresponding Load Admittance Y_L. [180^o with the same r_L].
  • From now on the chart becomes an ADMITTANCE CHART
• Draw a circle with radius r_L.
• Move on this constant circle TOWARD THE GENERATOR until G=1 circle is intersected.
• At this point, you have reached 1+jB₁
  • Actually there are two points that may be intersected on the G=1 circle. These are either 1+jB₁ or 1-jB₂.
  • The length of the transmission line to reach 1+jB₁ is d₁. This can be read from the periphery of the Smith Chart.
• If we now add a shunt element (either open-circuited or short-circuited) equal to -jB₁ or +jB₂, we will reach the center of the Smith Chart.

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Figure Below shows how to find the length d₂ of an open-circiuted line so that it will give an admittance -jB₁ to be added as a shunt element to the Transmiion line

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