# Ch.2 Transmission Line Theory (1/2)

```Microwave Engineering
Ch.2 Transmission Line Theory (1/2)
Prof. Jong-Won Yu
KAIST
http://rfss.kaist.ac.kr
Chap 2. Transmission Line Theory
z Plane Wave Propagation
Orientation of the Ε , H, and k = k0 n vectors for a general plane wave.
Plane wave reflection from a lossy medium; normal incidence
2
.
Chap 2. Transmission Line Theory
z Two-wire line
z Coaxial cable
3
Chap 2. Transmission Line Theory
z Microstrip line
4
Chap 2. Transmission Line Theory
z High frequency implies spatial voltage distribution
z Voltage has a time and space behavior.
z Space is neglected for low frequency applications.
z For RF there can be a large spatial variation.
z For low frequency (1MHz)
y Kirchhoff’s laws apply
z For high frequency (1GHz)
y Kirchhoff’s laws do not
apply anymore
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Chap 2. Transmission Line Theory
z Kirchhoff’s laws on a microscopic level
Conductor
Appropriate
Circuit model
Transmission Line
M d l takes
Model
k iinto account liline llosses and
d di
dielectric
l
i llosses
6
Chap 2. Transmission Line Theory
z The Lumped-Element Circuit Model for a Transmission Line
z T/L is a distributed network, Voltages and currents can vary in magnitude
and phase over its length
Voltage and Current Definitions
z
Lumped-element Equivalent CKT
Using K.V.L &amp; K.C.L
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Chap 2. Transmission Line Theory
z Wave Propagation on a Transmission Line
Time Harmonic Case
Wave Equations for V &amp; I
Coupled Eqs
Propagation constant
Wave propagation in the +z
direction
Solutions
Characteristic
Impedance
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Chap 2. Transmission Line Theory
z Characteristic Impedance, Wavelength &amp; Phase velocity
Z=V/I
z
Characteristic Impedance
p
is the ratio of voltage
g to current of either wave
independently.
z
Time domain waveform
Wavelength
Phase velocity
9
Chap 2. Transmission Line Theory
z Transmission-line parameters
z R,L,G,L are given per unit length and depend on geometry
10
Chap 2. Transmission Line Theory
z Coaxial Cable
z
Characteristic Impedance
z
Velocity Factor
y Whenever you apply a signal to a transmission line
line, the inductance and
capacitance of that line will cause signal to travel more slowly that it
would in free space
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Chap 2. Transmission Line Theory
z Microstrip Line
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Chap 2. Transmission Line Theory
z Lossless Transmission Line
Lumped-element
Lumped
element Equivalent CKT
13
Chap 2. Transmission Line Theory
z Terminated T/L : Reflection Coefficient
The total voltage and current on the line
Th ttotal
The
t l voltage
lt
and
d currentt att th
d
R fl i
Reflection
C
Coefficient
ffi i
Solving for
The total V &amp; I on the line in terms of the refection coefficient
A super position of an
incident and reflected wave
Standing waves
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Chap 2. Transmission Line Theory
z Terminated T/L : Input Impedance
Input impedance at
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Chap 2. Transmission Line Theory
z Terminated T/L : Return Loss, SWR
The total V &amp; I on the line in terms
of
the refection coefficient
Incident power
Th ti
The
time-average power flow
fl
along
l
the
th liline att th
the point
i tz
Purely imaginary
The return loss (RL)
The Standing Wave Ratio (SWR)
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Chap 2. Transmission Line Theory
z Lossless T/L : Short Termination
V l
Voltage
Current
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Chap 2. Transmission Line Theory
z Lossless T/L : Short Termination
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Chap 2. Transmission Line Theory
z Lossless T/L : Open Termination
Voltage
Current
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Chap 2. Transmission Line Theory
z Lossless T/L : Open Termination
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Chap 2. Transmission Line Theory
z
Lossless
l
T/L :
A half-wavelength line does not alter or transform the load impedance,
regardless of the characteristic impedance
z
Lossless T/L :
Impedance
Inverter
Open impedance
Short impedance
21
Chap 2. Transmission Line Theory
z Insertion Loss
Consider the reflection and transmission at the junction of two T/L with different Zo
Equating voltages at z=0
Insertion Loss (IL)
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Chap 2. Transmission Line Theory
z Homework #1
z
D.M.Pozar :Microwave Engineering 3rd Ed.
z
Problem
Problem
Problem
Problem
z
z
z
2.6
2.7
2.8
2.9
(Page87)
(Page87)
(Page87)
(Page88)
g
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