Waves and Transmission Lines Wang C. Ng
Traveling Waves
Load Envelop of a Standing Wave
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
Reflection coefficient The ratio of the amplitude of the incident wave (v + ) and the amplitude the reflective wave (v - ) is called the reflection coefficient:
Reflection coefficient The reflection coefficient can be determine from the load impedance and the characteristic impedance of the line:
Short-circuited Load Z L = 0 = -1 v - = - v + at the load As a result, v L = v + + v - = 0
Load
Open-circuited Load Z L = = +1 v - = v + at the load As a result, v L = v + + v - = 2 v +
Load
Resistive Load Z L = Z 0 = 0 v - = 0 at the load As a result, v L = v +
Traveling Waves Load
Resistive Load Z L = 0.5 Z 0 = - 1/3 v - = v + at the load As a result, v L = v + + v - = v +
Composite Waves Load
Resistive Load Z L = 2 Z 0 = + 1/3 v - = v + at the load As a result, v L = v + + v - = v +
Composite Waves Load
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 + = v + 45
Composite Waves Load
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 + = v + -45
Composite Waves Load
Smith Chart Transmission Line Calculator
-j2 -j4 -j1 -j0.5 j0.5 j1 j4 j2 j Z L / Z 0 = z L = 1 + j 2
0.7 45 = j 0.5 real imaginary ||||
-j2 -j 4 -j1 -j0.5 j0.5 j1 j4 j2 j z L = 1 + j 2 0.7 45 |||| |||| re im
-j2 -j4 -j1 -j0.5 j0.5 j1 j4 j2 j z L = 1 + j 2 0.7 45 45 0 135 90 180 225 270 315
-j2 -j4 -j1 -j0.5 j0.5 j1 j4 j2 j z L = 0.5- j 0.5 0.45 -120 45 0 135 90 180 225 270 315
| | j2 -j4 -j1 -j0.5 j0.5 j1 j4 j2 j 0 135 90 180 225 270 315 D C B E A F G