Question

Really appreciate any help. Thank you in advance!

1. Use the Smith chart to find the reflection coefficient corresponding to the load impedance ZL =30−j80Ω.

2. Use the Smith chart to find the impedance corresponding to a reflection coefficient of Γ = ◦ 0.5̸ −45. 3. A transmission line is terminated with a load ZL = 80 + j120 Ω. Use the Smith chart to find (a) the load reflection coefficient, (b) the standing wave ratio, (c) the input impedance at 0.2 λ from the load, and (d) the shortest line length for which the input impedance is purely resistive.

4. A transmission line and phase velocity 2 × 108 m/s is terminated with an open circuit. Use the Smith chart to find the shortest length of line in mm for which the input impedance is equivalent to a 1 pF capacitor at 1 GHz.

5. A transmission line with length 0.2 λ is terminated with a 100 Ω load. Find the input impedance.

6. A transmission line with length 0.4 λ is terminated with an unknown impedance. If the input impedance is j10 Ω, use the Smith chart to find ZL.

7. A transmission line is terminated with a 100 Ω load. (a) Find the shortest distance along the transmission line for which the normalized input admittance has the form 1 + jb. (b) Why is this useful? What can we attach to the transmission line at this distance to accomplish a useful design goal?

the characteristic impedance is 50

Answer 1

1) We know that on Smith chart we have to work with normalized values. Now convert the given load impedance ZL=30-j80 ohms to normalized impedance value. given characteristic impedance of 50 ohms.(i.e. divide load impedance by 50). Therefore the normalized load impedance become 0.6-j1.6 ohms. Represent this point on smith chart. Now measure the distance from center to this point and by using Reflection coefficient scale down under the smith chart we can able to find the Reflection coefficient of approximately 0.72L-59 (Represented on Smith chart).