Waves and Transmission Lines

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Wavesand Transmission Lines

• TechForce Spring 2002
• Externship
• Wang C. Ng

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Traveling Waves
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Standing Waves
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Standing Waves
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Envelop of a Standing Wave
Load
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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

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Reflection coefficient

• The ratio of the amplitude of the incident wave
  (v- ) and the amplitude the reflective wave (v)
  is called the reflection coefficient

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Reflection coefficient

• The reflection coefficient can be determine from
  the load impedance and the characteristic
  impedance of the line

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Short-circuited Load

• ZL 0
• ? -1
• v - - v at the load
• As a result, vL v v - 0

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Load
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Load
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Load
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Load
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Load
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Load
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Load
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Load
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Load
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(No Transcript)
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Standing Waves
Load
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Standing Waves
Load
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Load
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Open-circuited Load

• ZL ?
• ? 1
• v - v at the load
• As a result, vL v v - 2 v

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Load
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Load
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Load
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Load
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Load
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Load
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Load
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Load
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Load
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(No Transcript)
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Standing Waves
Load
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Standing Waves
Load
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Load
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Resistive Load

• ZL Z0
• ? 0
• v - 0 at the load
• As a result, vL v

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Traveling Waves
Load
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Load
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Resistive Load

• ZL 0.5 Z0
• ? - 1/3
• v - -0.333 v at the load
• As a result, vL v v - 0.667 v

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Load
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Load
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Load
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Load
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Load
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Load
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Load
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Load
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Load
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(No Transcript)
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Composite Waves
Load
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Composite Waves
Load
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Resistive Load

• ZL 2 Z0
• ? 1/3
• v - 0.333 v at the load
• As a result, vL v v - 1.333 v

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Load
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Load
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Load
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Load
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Load
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Load
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Load
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Load
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Load
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(No Transcript)
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Composite Waves
Load
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Composite Waves
Load
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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?

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Load
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Load
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Load
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Load
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Load
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Load
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Load
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Load
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Load
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(No Transcript)
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Composite Waves
Load
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Composite Waves
Load
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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?

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Load
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Load
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Load
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Load
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Load
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Load
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Load
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Load
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Load
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(No Transcript)
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Composite Waves
Load
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Composite Waves
Load
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Smith Chart

• Transmission Line
• Calculator

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j1
j0.5
j2
j4
0 0.5 1
2 4
j0
-j4
ZL / Z0 zL 1 j 2
-j2
-j0.5
-j1
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imaginary
?
?
real
0 0.5 1
? ? 0.7? 45? 0.5 j 0.5
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zL 1 j 2
? ? 0.7? 45?
?
?
j1
re
j0.5
j2
im
j4
?
?
0 0.5 1
2 4 ?
j 0
-j 4
-j2
-j0.5
-j1
96
zL 1 j 2
90?
135?
45?
j1
j2
j0.5
j4
0 0.5 1
2 4
0?
180?
j0
-j4
-j0.5
-j2
225?
-j1
315?
270?
? ? 0.7? 45?
97
90?
135?
45?
j1
j2
j0.5
j4
0 0.5 1
2 4
0?
180?
j0
-j4
-j0.5
-j2
225?
-j1
315?
? ? 0.45? -120?
270?
zL 0.5- j 0.5
98
90?
F
135?
45?
j1
j2
j0.5
j4
0 0.5 1
2 4
0?
180?
A
E
D C B
j0
? 0 0.5 1
-j4
-j0.5
-j2
225?
-j1
315?
G
270?