1. Waves and Transmission Lines Wang C. Ng

2. Traveling Waves

3. Load Envelop of a Standing Wave

4. Waves in a transmission line Electrical energy is transmitted as waves in a transmission line. Waves travel from the generator to the load (incident wave). If the resistance of the load does not match the characteristic impedance of the transmission line, part of the energy will be reflected back toward the generator. This is called the reflected wave

5. Reflection coefficient The ratio of the amplitude of the incident wave (v + ) and the amplitude the reflective wave (v - ) is called the reflection coefficient:

6. Reflection coefficient The reflection coefficient can be determine from the load impedance and the characteristic impedance of the line:

7. Short-circuited Load Z L = 0  = -1 v - = - v + at the load As a result, v L = v + + v - = 0

8. Load

9. Open-circuited Load Z L =   = +1 v - = v + at the load As a result, v L = v + + v - = 2 v +

10. Load

11. Resistive Load Z L = Z 0  = 0 v - = 0 at the load As a result, v L = v +

12. Traveling Waves Load

13. Resistive Load Z L = 0.5 Z 0  = - 1/3 v - = -0.333 v + at the load As a result, v L = v + + v - = 0.667 v +

14. Composite Waves Load

15. Resistive Load Z L = 2 Z 0  = + 1/3 v - = 0.333 v + at the load As a result, v L = v + + v - = 1.333 v +

16. Composite Waves Load

17. Reactive Load (Inductive) Z L = j Z 0  = + j1 v - = v +  90  at the load As a result, v L = v + + v - = (1 + j1) v + = 1.414 v +  45 

18. Composite Waves Load

19. Reactive Load (Capacitive) Z L = -j Z 0  = - j1 v - = v +  -90  at the load As a result, v L = v + + v - = (1 - j1) v + = 1.414 v +  -45 

20. Composite Waves Load

21. Smith Chart Transmission Line Calculator

22. -j2 -j4 -j1 -j0.5 j0.5 j1 j4 j2 j0 0 0.5 1 2 4 Z L / Z 0 = z L = 1 + j 2

23. 0 0.5 1   0.7  45  = 0.5 + j 0.5 real imaginary |||| 

24. -j2 -j 4 -j1 -j0.5 j0.5 j1 j4 j2 j 0 0 0.5 1 2 4  z L = 1 + j 2   0.7  45  ||||  ||||  re im

25. -j2 -j4 -j1 -j0.5 j0.5 j1 j4 j2 j0 0 0.5 1 2 4 z L = 1 + j 2   0.7  45  45  0  135  90  180  225  270  315 

26. -j2 -j4 -j1 -j0.5 j0.5 j1 j4 j2 j0 0 0.5 1 2 4 z L = 0.5- j 0.5   0.45  -120  45  0  135  90  180  225  270  315 

27. |  | 0 0.5 1 -j2 -j4 -j1 -j0.5 j0.5 j1 j4 j2 j0 0 0.5 1 2 4 45  0  135  90  180  225  270  315  D C B E A F G