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Solved Problems-6

A transmission line of 0.4λ length has a characteristic impedance of 100 Ω and is terminated in a load impedance of (200 + j180)Ω. Find
  1. Reflection coefficient
  2. Standing wave ratio
  3. Input impedance of the line
Use a Smith chart. Compare the results with the theoretical results.
Here, Description: Description: 101639.png
Normalised impedance is Description: Description: 101632.png
Description: Description: 6-28.tif
Smith chart for reflection coefficient, SWR and input impedance
(a) To find Reflection Coefficient
1. We locate the point P in the Smith chart which is the intersection of the circles r = 2 and
x = 1.8.
2. We draw a circle with radius equal to OP and centre at O. This OP is the magnitude of the reflection coefficient which is measured to be 0.591.
Description: Description: 101559.png
3. To find the phase angle of the reflection coefficient, we extend the line OP so that it cuts the r = 0 circle at the point Q. This point is measured to be 0.207 in wavelength towards the generator. This point gives the phase angle of the reflection coefficient as,
Description: Description: 101567.png
Description: Description: 101574.png
(b) To find SWR
The circle cuts the centre line of the chart at the point A; OA gives the standing wave ratio. It is measured to be 4.
s = 4
(c) To find Input Impedance
In order to find the input impedance, the following steps are involved.
1. We start from the point corresponding to (2 + j1.8) (i.e., the point P) and move 0.4 wavelengths clockwise (towards generator) on the s-circle (i.e., the point B). This line OB cuts the circle at the point C. This OC gives the input impedance as,
Description: Description: 101590.png
2. So, the actual input impedance is given as,
Description: Description: 101598.png
 Description: Description: 101606.png

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