Question

(Use Smith Chart) A 50 Ω line is terminated by a 75 Ω resistor. The input terminals are connected to the output terminals of a 30 Ω line. Both lines are 0.12 λ long.

a. Find Zin and Γin at the input of the 30 Ω line

b. SWR values on both lines

Use Smith Chart

Answer 1

Answer:- For the 50 ohm line, the normalized load impedance is-

The point A is the point for above normalized load impedance. Making a circle (black) of radius OA (black line). The point (S1 same as A) is the SWR for this 50 ohm line.

Now moving clockwise from A for a length of 0.12*lambda, we reach at point B (at 0.25 + 0.12 = 0.37*lambda). The normalized load impedance value at B is 0.95 - j0.4. Thus the input impedance for 50 ohm is-

Now for 30 ohm line, the normalized load impedance is-

Let C be the point on the smith chart for the above normalized value. Making SWR circle assuming OC as radius (red line). Point S2 is the SWR value for 30 ohm line-

Moving clockwise from C (at 0.202*lambda) for a length of 0.12*lambda, we reach at point D (at 0.322*lambda). The normalized load impedance value at D is 1.28 - j0.72. Thus the input impedance for 30 ohm is-