waves and transmission lines techforce + spring 2002 externship wang c. ng
TRANSCRIPT
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Wavesand
Transmission Lines
TechForce + Spring 2002Externship
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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Load
Envelop of a Standing Wave
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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:
v
vΓ
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Reflection coefficient
• The reflection coefficient can be determine from the load impedance and the characteristic impedance of the line:
0
0
ZZ
ZZΓ
L
L
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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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Standing Waves
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Standing Waves
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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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Standing Waves
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Standing Waves
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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
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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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Composite Waves
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Composite Waves
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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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Composite Waves
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Composite Waves
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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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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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Smith Chart
Transmission Line
Calculator
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-j2
-j4
-j1
-j0.5
j0.5
j1
j4
j2
j0 0 0.5 1 2 4
ZL / Z0 = zL = 1 + j 2
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0 0.5 1
0.7 45
= 0.5 + j 0.5
real
imaginary
||
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-j2
-j 4
-j1
-j0.5
j0.5
j1
j4
j2
j 0 0 0.5 1 2 4
zL = 1 + j 2 0.7 45
||
||
re
im
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-j2
-j4
-j1
-j0.5
j0.5
j1
j4
j2
j0 0 0.5 1 2 4
zL = 1 + j 2
0.7 45
45
0
135
90
180
225
270
315
zL 1 j 2
zL 1
zL 1
0.5 0.5i
0.707
arg 45deg
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-j2
-j4
-j1
-j0.5
j0.5
j1
j4
j2
j0 0 0.5 1 2 4
zL = 0.5- j 0.5 0.45 -120
45
0
135
90
180
225
270
315
zL 0.5 j 0.5
zL 1
zL 1
0.2 0.4i
0.447
arg 116.565 deg
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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
Re Im Mag AngleA 0 1 0 OpenB 2 0 1/3 0 Resistive = 2Z 0
C 1 0 0 0 Matched loadD 0.5 0 1/3 180° Resistive = Z 0/2E 0 0 1 180 Short F 0 1 1 90 Inductive = jZ 0
G 0 -1 1 -90° Capacitive = -jZ 0
zL Load