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Waves and Transmission Lines

Waves and Transmission Lines. Wang C. Ng. Traveling Waves. Envelop of a Standing Wave. Load. 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).

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Waves and Transmission Lines

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  1. Wavesand Transmission Lines Wang C. Ng

  2. Traveling Waves

  3. Envelop of a Standing Wave Load

  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 • ZL = 0 • = -1 • v - = - v + at the load • As a result, vL = v + + v - = 0

  8. Load

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

  10. Load

  11. Resistive Load • ZL = Z0 • = 0 • v - = 0 at the load • As a result, vL = v +

  12. Traveling Waves Load

  13. Resistive Load • ZL = 0.5 Z0 • = - 1/3 • v - = -0.333 v + at the load • As a result, vL = v + + v - = 0.667 v +

  14. Composite Waves Load

  15. Resistive Load • ZL = 2 Z0 • = + 1/3 • v - = 0.333 v + at the load • As a result, vL = v + + v - = 1.333 v +

  16. Composite Waves Load

  17. Reactive Load (Inductive) • ZL = j Z0 • = + j1 • v - = v +90 at the load • As a result, vL = v + + v - = (1 + j1) v + = 1.414 v +45

  18. Composite Waves Load

  19. Reactive Load (Capacitive) • ZL = -j Z0 • = - j1 • v - = v +-90 at the load • As a result, vL = v + + v - = (1 - j1) v + = 1.414 v +-45

  20. Composite Waves Load

  21. Smith Chart Transmission Line Calculator

  22. j1 j0.5 j2 j4 0 0.5 1 2 4 j0 -j4 ZL / Z0 = zL = 1 + j 2 -j2 -j0.5 -j1

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

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

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

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

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

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