1. Waves and Transmission Lines TechForce + Spring 2002 Externship Wang C. Ng

2. Traveling Waves

3. Standing Waves

5. Load Envelop of a Standing Wave

6. 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

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

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

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

10. Load

20. Standing Waves Load

21. Standing Waves

22. Load

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

24. Load

34. Standing Waves Load

35. Standing Waves

36. Load

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

38. Traveling Waves Load

40. 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 +

41. Load

51. Composite Waves Load

52. Composite Waves Load

53. 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 +

54. Load

64. Composite Waves Load

65. Composite Waves Load

66. 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 

67. Load

77. Composite Waves Load

78. Composite Waves Load

79. 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 

80. Load

90. Composite Waves Load

91. Composite Waves Load

92. Smith Chart Transmission Line Calculator

93. -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

94. 0 0.5 1   0.7  45  = 0.5 + j 0.5 real imaginary |||| 

95. -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

96. -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 

97. -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 

98. |  | 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