Communication Principles
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Transmission Lines
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Transmission Lines
Communication Principles
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College of Electronics Engineering
Transmission Line Theory
In an electronic system, the delivery of power requires the
connection of two wires between the source and the load.
Transmission Lines
Communication Principles
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Analysis of differences between Low and High Frequency
At low frequencies, the circuit elements are lumped since voltage and
current waves affect the entire circuit at the same time.
At microwave frequencies, such treatment of circuit elements is not possible
since voltage and current waves do not affect the entire circuit at the same
time.
The circuit must be broken down into unit sections within which the circuit
elements are considered to be lumped.
This is because the dimensions of the circuit are long comparable to the
wavelength of the waves according to the formula:
c/f
where,
c = velocity of light
f = frequency
Transmission Lines
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Presence of Electric and Magnetic Fields
Both Electric and Magnetic fields are present in the transmission lines
These fields are perpendicular to each other and to the direction of wave
propagation for Transverse Electro- Magnetic (TEM) mode waves, which is the
simplest mode.
Electric field is established by a potential difference between two
conductors.
Implies equivalent circuit model must contain capacitor.
Magnetic field induced by current flowing on the line
Implies equivalent circuit model must contain inductor.
Transmission Lines
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Transmission Lines
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Transmission Lines
z .
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Transmission Lines
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Transmission Lines
-
)
(
- z
(
)
+
+
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Now dividing by
z
:
Transmission Lines
Omitting the argument ( z , t ):
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Substituting in equations (1) & (2) yields :
Transmission Lines
=Z I
=Y V
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Transmission Lines
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Hence
Characteristic Impedance Z
0
(cont.)
From this we have:
Using
We have
Transmission Lines
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Transmission Lines
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Transmission Lines
Communication Principles
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Transmission Lines
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Lossless Transmission Line
Transmission Lines
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Transmission Lines
Communication Principles
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Transmission Lines
d.
d
d
d
d
d
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Transmission Lines
Communication Principles
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Reflection Coefficient at Load
=
Transmission Lines
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Special Cases to Remember
1
Zo
Zo
0
Zo
Zo
Zo
Zo
1
0
0
Zo
Zo
Vs
Zs
Zo
Zo
A: Terminated in Zo
Vs
Zs
Zo
B: Short Circuit
Vs
Zs
Zo
C: Open Circuit
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Lossless Case
so
0
LC
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Communication Principles
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Lossy Transmission Line
Transmission Lines
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At the load ( = 0):
Recall
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Transmission Lines
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Standing Waves
Transmission Lines
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Transmission Lines
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Note
To find the locations of the
maxima and minima :
min
max
Transmission Lines
d
d
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Transmission Lines
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Z
L
z = 0
Z
0
z
+
-
V(z)
I(z)
Given:
Find:
Example:
Transmission Lines
d
d
d
d
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Transmission Lines
d
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Reverse problem:
Given:
What is the unknown load impedance?
Transmission Lines
+
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or
The calculation yields
Transmission Lines
Communication Principles
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Communication Principles
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Thank you
Transmission Lines