# Waves and Transmission Lines Wang C. Ng. Traveling Waves.

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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

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

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

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 +

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 +

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 

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 

Smith Chart Transmission Line Calculator

-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

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

-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

-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 

-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 

|  | 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