# Solved Problems-6

Problem-6

A transmission line of 0.4Î» length has a characteristic impedance of 100 Î© and is terminated in a load impedance of (200 +

*j*180)Î©. Find- Reflection coefficient
- Standing wave ratio
- Input impedance of the line

Use a Smith chart. Compare the results with the theoretical results.

Solution

Here,
Normalised impedance is

1. We locate the point

2. We draw a circle with radius equal to
3. To find the phase angle of the reflection coefficient, we extend the line

The circle cuts the centre line of the chart at the point
In order to find the input impedance, the following steps are involved.
1. We start from the point corresponding to (2 +
2. So, the actual input impedance is given as,

**Smith chart for reflection coefficient, SWR and input impedance**

**(a) To find Reflection Coefficient***P*in the Smith chart which is the intersection of the circles*r*= 2 and*x*= 1.8.*OP*and centre at*O*. This*OP*is the magnitude of the reflection coefficient which is measured to be 0.591.*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,**(b) To find SWR***A*;*OA*gives the standing wave ratio. It is measured to be 4.s = 4

**(c) To find Input Impedance***j*1.8) (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,