A load with a reflection coefficent G_L=0.23e^-j120o is connected to the following network.

Find

1. Using the Smith Chart only, find the input impedance of the network.
2. What is the power delivered to the load?

1. Solution I:

   

   • Normalize the given component values to 50 W. Note that since jX₂ is in parallel with the load it is converted to a normalized susceptance.
   • Locate G_L on the Smith Chart.
   • Read z_L.
   • Find y_L
   • Add jb₂ to y_L (move on a constant g_L circle).
   • Read y₁.
   • Read z₁.
   • Move on constant G₁ circle toward the generator a length 0.14l.
   • Read z₂.
   • Add jx₁ to z₂ (move on a constant r₂ circle).
   • Read z_in.
   • Find Z_in (z_inx50W).

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2. Solution II:

   Since the network elements are lossless, the power delivered to the load can be calculated from

   

   Substituting the given values