Lecture I, 24. Sep. 2001 Antennas & Propagation Antennas & Propagation Mischa Dohler Mischa Dohler King’s College London King’s College London Centre for Telecommunications Centre for Telecommunications Research Research
Lecture I, 24. Sep. 2001
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Ant
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Antennas
&
Propagation
Mischa DohlerMischa Dohler
King’s College LondonKing’s College London
Centre for Telecommunications ResearchCentre for Telecommunications Research
Lecture I, 24. Sep. 2001
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Overview (entire lecture)
- Introduction to Communication SystemsIntroduction to Communication Systems
- Mathematical & Physical FundamentalsMathematical & Physical Fundamentals
- Fundamentals of AntennasFundamentals of Antennas
- Practical AntennasPractical Antennas
- Propagation Propagation MechanismsMechanisms & & ModellingModelling
- Wireless Communication LinksWireless Communication Links
- Cellular Concept Cellular Concept
Lecture I, 24. Sep. 2001
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Ant
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Introduction
Lecture I, 24. Sep. 2001
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Communication Systems
1. GENERAL
SOURCE
SOURCECODING
CHANNELCODING
TRANSMITTERTx
SINK
SOURCEDE-COD
CHANNELDE-COD
NOISE &INTERF.
CHANNEL RECEIVERRx
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Communication Systems
2. DETAIL
SOURCE SOURCECODING
CHANNELCODING
Tx CHANNEL Rx CHANNELDE-COD
SOURCEDE-COD
SINK
- Human Speech- HiFi / TV- Data
Quality Delay
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Communication Systems
2. DETAIL
SOURCE SOURCECODING
CHANNELCODING
Tx CHANNEL Rx CHANNELDE-COD
SOURCEDE-COD
SINK
“ The process of efficiently converting the output of either
analogue or digital source into a sequence of binary digits is
called: “
SOURCE CODING1. Electromagnetic representation
(current)
2. Quantization/Digitalization
3. Compression (minimize redundancy)
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Communication Systems
2. DETAIL
SOURCE SOURCECODING
CHANNELCODING
Tx CHANNEL Rx CHANNELDE-COD
SOURCEDE-COD
SINK
“ The introduction of controlled redundancy into a signal to com-pensate for any sources of noise
and interference is called: “
CHANNEL CODING
- repetition (no intelligence)
- other coding (intelligence)
Input k bits Output n bits: k/n code rate
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Communication Systems
2. DETAIL
SOURCE SOURCECODING
CHANNELCODING
Tx CHANNEL Rx CHANNELDE-COD
SOURCEDE-COD
SINK
The interface which modulates the digital bit stream onto an
appropriate waveform, capable of propagating through the
communication channel, is called:
MODULATOR or TRANSMITTER
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Communication Systems
2. DETAIL
SOURCE SOURCECODING
CHANNELCODING
Tx CHANNEL Rx CHANNELDE-COD
SOURCEDE-COD
SINK
The medium between Tx and Rx is called:
CHANNEL
- Wireless- Telephone- Fiber cable
Each of the channels has unique features with respect to signal distortion and noise. Thus each is treated separately and the modulation schemes differ!
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Communication Systems
2. DETAIL
SOURCE SOURCECODING
CHANNELCODING
Tx NOISE Rx CHANNELDE-COD
SOURCEDE-COD
SINK
All processes which degrade the signal in an additive manner (and which autocorrelation function is a Dirac
delta) are called:
NOISE
- Thermal noise (Tx, cable, Rx)
- Natural and man-made noise- Interferences (usually from other man
operated systems)
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Communication Systems
2. DETAIL
SOURCE SOURCECODING
CHANNELCODING
Tx CHANNEL Rx CHANNELDE-COD
SOURCEDE-COD
SINK
- Performs optimum combining and processing of the received distorted wave form.
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Communication Systems
2. DETAIL
SOURCE SOURCECODING
CHANNELCODING
Tx CHANNEL Rx CHANNELDE-COD
SOURCEDE-COD
SINK
- Using the introduced redundancy it retrieves the desired information.
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Communication Systems
2. DETAIL
SOURCE SOURCECODING
CHANNELCODING
Tx CHANNEL Rx CHANNELDE-COD
SOURCEDE-COD
SINK
- Reproduces the original signal from the source to be delivered to the sink.
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Communication Systems
3. KINGS
SOURCE SOURCECODING
CHANNELCODING
Tx CHANNEL Rx CHANNELDE-COD
SOURCEDE-COD
SINK
Dr. Marvasti: “Information Theory”
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Communication Systems
3. KINGS
SOURCE SOURCECODING
CHANNELCODING
Tx CHANNEL Rx CHANNELDE-COD
SOURCEDE-COD
SINK
Dr. Marvasti: “Information Theory”
Prof. Aghvami: “Digital Communication”
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Communication Systems
3. KINGS
SOURCE SOURCECODING
CHANNELCODING
Tx CHANNEL Rx CHANNELDE-COD
SOURCEDE-COD
SINK
Dr. Marvasti: “Information Theory”
Prof. Aghvami: “Digital Communication”
Mischa: “Antennas & Propagation”
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Communication Systems
SOURCE SOURCECODING
CHANNELCODING
Tx CHANNEL Rx CHANNELDE-COD
SOURCEDE-COD
SINK
4. MATHS & PHYSICS
PHYSICS: - transformation of non-electrical signals into electromagnetic signals
MATHEMATICS: - Nyquist sampling theorem- optimum digitalization laws- Shannon’s capacity formula
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Communication Systems
SOURCE SOURCECODING
CHANNELCODING
Tx CHANNEL Rx CHANNELDE-COD
SOURCEDE-COD
SINK
4. MATHS & PHYSICS
PHYSICS: - none
MATHEMATICS: - complete coding theory
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Communication Systems
SOURCE SOURCECODING
CHANNELCODING
Tx CHANNEL Rx CHANNELDE-COD
SOURCEDE-COD
SINK
4. MATHS & PHYSICS
PHYSICS: - Maxwell’s equations (current, decoupling waves, etc)
MATHEMATICS: - Vector analysis- Differential equations- Fourier transformation
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Communication Systems
SOURCE SOURCECODING
CHANNELCODING
Tx CHANNEL Rx CHANNELDE-COD
SOURCEDE-COD
SINK
4. MATHS & PHYSICS
PHYSICS: - Maxwell’s equations (free space, reflection, etc)
MATHEMATICS: - Probability theory (CLT, distributions, etc)
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Communication Systems
SOURCE SOURCECODING
CHANNELCODING
Tx NOISE Rx CHANNELDE-COD
SOURCEDE-COD
SINK
4. MATHS & PHYSICS
PHYSICS: - Quantum theory
MATHEMATICS: - Operator theory- Theory of stochastic processes
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Mathematical
&
Physical Foundations
Lecture I, 24. Sep. 2001
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Overview
- Fourier TransformFourier Transform
- Maxwell’s EquationsMaxwell’s Equations
- Wave EquationWave Equation
- Probability TheoryProbability Theory
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Fourier Transform
Given a varying signal s(t) in the time-domain, the
spectral components S(f) are obtained as follows:
dtetsfS ftj 2)()(
And vice versa:
dfefSts ftj 2)()(
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Fourier Transform
Mathematicians used to transform a function f(x) to
(a) make certain operations easier
(b) make certain features and properties
visible.There are 3 basic types of transformations of f(x):
(1) Differential Transformation (local):x
xfxD
)(
)(
(2) Functional Transformation (local): )()( 2 xfxF
(3) Integral Transformation (global): D
dxxfI )(
D
dxxgxfI ),()( D
dxxxfI )cos()(
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Fourier Transform
Properties of the Integral Transformation
(1) Global: It is global, because it accumulates (integration)
the weighted properties of the function f(x) over
the ENTIRE region of definition of f(x).
D
dxxgxfI ),()(
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Fourier Transform
Properties of the Integral Transformation
(2) Resonance: Function g(x,w) is a resonant function, because
the integration with f(x) makes those
components in f(x) visible, which equal or
resemble g(x,w).
D
dxxgxfI ),()(
0 : f(x) has components as g(x,w)
= 0 : f(x) has no components as g(x,w)
Example: g(x)=cos (wx ) and f(x)=cos( w x ) | f(x)=cos( 2w x )
D
dxxxI 0)cos()cos(
D
dxxxI 0)cos()2cos(
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Fourier Transform
Properties of the Integral Transformation
(3) Orthogonal: If g(x,w) is orthogonal for different w in the
sense:
D
dxxgxfI ),()(
D
dxxgxg 0),(),( 21
then there does exist a UNIQUEinverse
transformation F-1. (Example)
If not, then not unique, yet still useful (Wavelets)
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Fourier Transform
How did Physicists and Engineers use it?
Association: (1) f(x) s(t) with –inf < t < +inf
(2) g(x,w) { sin(w*t) , cos(w*t) }
D
dxxgxfI ),()(
dtfttsfS )2sin()()(1 Thus we get:
dtfttsfS )2cos()()(2
dtetsfS ftj 2)()(
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Fourier Transform
Main messages of the Fourier Transformation:
dtetsfS ftj 2)()(
(1) For a fixed frequency f the integral tells us how
much of that harmonic is present in the signal s(t).
Spectrogram
fA
f
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Fourier Transform
(2) Smoothness:
s(t)
t
Very
smooth
|S(f)|
f
FT
|S(f)|
f
FT
50Hz
s(t)
t
smooth50Hz
|S(f)|
f
FT
100Hz
s(t)
t
steeper
100Hz
(more changes per time!)
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Fourier Transform
(2) Smoothness:
s(t)
t
smooth
|S(f)|
f
FT50Hz
50Hz
s(t)
t
steeper
|S(f)|
f
FT100Hz
100Hz
+
s(t)
t
even
steeper
|S(f)|
f
FT
100Hz
50Hz + 100Hz
50Hz
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Fourier Transform
(2) Smoothness:
s(t)
t
|S(f)|
f
FT
50Hz
smooth
s(t)
t
|S(f)|
f
FT
100Hz
‘rocky’
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Fourier Transform
(2) Smoothness:
s(t)
t
|S(f)|
f
FT
50Hz
T=20mssinc(f)
s(t)
t
|S(f)|
f
FT
100Hz
T=10ms
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Fourier Transform
Filter: What makes spectrum infinite?
s(t)
t
|S(f)|
f
FT
50Hz
T=20mssinc(f)
|S(f)|
f50Hz
s(t)
t
IFTT=20ms
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Fourier Transform
Filter: In Telecommunications each user is
confined to a certain spectrum band. Thus,
filters have to be applied to confine the infinite
bandwidth of the rectangular pulse.
s(t)
t
T=20ms
|S(f)|
f50Hz
s(t)
t
IFTT=20ms
|S(f)|
f
FT
50Hz
filter
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Fourier Transform
“The steeper the signal in time and the
more amplitude changes per time a
signal has, the higher are the high
frequency components of the
spectrum.”
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Fourier Transform
CAUTION!!!
Do NOT FORGET that the transformation is global!
We summed upon the entire time-domain. Thus, what
happens at certain instances or during a short period of
time is AVERAGED OUT!
T=20ms
s(t)
t
|S(f)|
f
FT
50Hz
sinc(f)‘0’ ‘0’‘1’
s(t)
t
T=10ms‘00’ ‘00’‘11’
|S(f)|
f100Hz
FT
theoretically
prac
tical
ly
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Fourier Transform
Thus the traditional FT has drawbacks:
It does tell us which frequencies are used,
but not when!
Example: Chirp (what makes spectrum appear infinite?)
Moral: Just use the FT if you are interested, which
(approximate) spectrum the signal
occupies during the entire time of
appearance!
Blackboard!
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Maxwell’s Equations
1. Mathematical Basics
2. Physical Basics
3. Physical Experiences
4. Derivations Maxwell’s Equations
5. Discussion
D div 0 div B
t
B
Erot t
DJHrot
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Maxwell’s Equations
(1) Mathematical Basics:
- Scalar: Quantity with magnitude only.
- Vector: Quantity with magnitude and direction.
- dot-product: A·B = |A|·|B|·cosφ projection: active
passive
= AxBx+ AyBy+ AzBz (scalar)
- vector-prod.: AB = |A|·|B|·sinφ area: active
active
= (vector) Zyx
zyx
BBB
AAA
zyx
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Maxwell’s Equations
(1) Mathematical Basics:
- Vector-Field: Region where in each point a vector is
defined.- Scalar-Field: Region where in each point a scalar is
defined.Lets look at the change within a scalar field (Temperature):
(0,0,0)m T(0,0,0) = 10°
(1,1,1)m T(1,1,1) = 20°m
Km
TT
3
10
)0,0,0()1,1,1(
)0,0,0()1,1,1(
The ‘change’ has a magnitude and a direction, thus is a
vector!
The gradient of a scalar field defines a vector field.
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Maxwell’s Equations
(1) Mathematical Basics:
In general: If we have a scalar field φ, then it defines a
unique gradient field E and vice versa!
grad
,,,,,,
,,,,,,
zyx
zyxE
z
zyx
y
zyx
x
zyx
z
zyx
y
zyx
x
zyx
Rule: Working with vector fields, it is ALWAYS
easier to find and operate with the
appropriate scalar- field (potential) and
then to differentiate!
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Maxwell’s Equations
(2) Physical Basics:
a) Coulomb’s Lawa) Coulomb’s Law
FF
Q1 Q2
r
rF
221
0
221
4
1
r
QQr
QQk
ε … permittivity (weakening)
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Maxwell’s Equations
(2) Physical Basics:
b) Electric Field (Intensity) Eb) Electric Field (Intensity) E
Q1
Q2
Test charge Q2
Force Field
rF
Ε21
02 4
1
r
Q
Q
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Maxwell’s Equations
(2) Physical Basics:
c) Electric Flux (Density) Dc) Electric Flux (Density) D
Roughly speaking, we look for a quantity, which
describes the electric field independent of the
materials but exclusively dependent on the sources.
rΕ21
04
1
r
Q
rD
21
4 r
Q
ED 0
Q1
Area
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Maxwell’s Equations
(2) Physical Basics:
d) Charge Density d) Charge Density ρρ
V
Q
dV
dQ
V
QV
0
lim
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Maxwell’s Equations
(2) Physical Basics:
e) Current Ie) Current I
dt
dQ
t
QI
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Maxwell’s Equations
(2) Physical Basics:
f) Current Density Jf) Current Density J
dA
dI
A
IJ
I
A
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Maxwell’s Equations
(2) Physical Basics:
g) Magnetic Flux (Density) Bg) Magnetic Flux (Density) B
N SField (B)
I
F
BLF I
L
FB
I
As done with the
electrical field we define
the magnetic field
through its force on
magnetic objects.
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In 1820 Biot and Savart found out:
20
2 4 r
LI
r
LIk
B
μ … permeability (strength.)I
ΔL
Maxwell’s Equations
(2) Physical Basics:
g) Magnetic Flux (Density) Bg) Magnetic Flux (Density) B
20 sin
4 r
LI
20
4 r
I dlrdB
)(0 If
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Maxwell’s Equations
(2) Physical Basics:
h) Magnetic Field Hh) Magnetic Field H
Again, we look for a physical value which is independent of the
materials involved:
)(0 If B
0
BH
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Maxwell’s Equations
(3) Mathematical Basics:
a) Divergence diva) Divergence div
We would like to be able to read and understand that formula!
D div
Imagine we have a source, e.g. a spring of water.
We want to find a physical variable and a measure, which
somehow characterises the impact of that source onto its
surroundings.
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Maxwell’s Equations
(3) Mathematical Basics:
a) Divergence diva) Divergence div
What do we know?
(i) Variable What does a water source cause?
a) water pressure (no direction, good for grad)
b) speed v of water (magnitude & direction)
Impact Strength (of the source)
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Maxwell’s Equations
(3) Mathematical Basics:
a) Divergence diva) Divergence div
(ii) Measure In dependency of the distance from the source,
we want to evaluate the impact of the
source.First Choice
Impact absolute value of the water speed. Reasonable?
Second Choice
Impact difference of the absolute value of the water speed.
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Maxwell’s Equations
(3) Mathematical Basics:
a) Divergence diva) Divergence div
(Distance)
)(MessengerImpact
x
v
Does a wave coming along the y-axis make me move along x or z? NO!
xx
v
Impact
A wave from x & y & z makes me move simultaneously along x,y & z!
zyxzyx
vvv
Impact
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Maxwell’s Equations
(3) Mathematical Basics:
a) Divergence diva) Divergence div
zyxzyx
vvv
Impact
zyxzyx
vvv
Impact
v divImpact
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Maxwell’s Equations
(3) Mathematical Basics:
a) Divergence diva) Divergence div
Impact Strength (of the source) (Distance)
)(MessengerImpact
(Distance)
)(Messenger source) theof (Strength
Lecture I, 24. Sep. 2001
Ant
enna
s &
Pro
paga
tion
Ant
enna
s &
Pro
paga
tion
Maxwell’s Equations
(3) Mathematical Basics:
a) Divergence diva) Divergence div
Strength (of the source) = ρ
Electric Field E
Electric Flux D = Messenger
D
DDD
div
zyxzyx
Lecture I, 24. Sep. 2001
Ant
enna
s &
Pro
paga
tion
Ant
enna
s &
Pro
paga
tion
Maxwell’s Equations
(3) Mathematical Basics:
a) Divergence diva) Divergence div
What does then mean: div B = 0
How to read that?
1. Lets turn it round: 0 = div B
2. There is nothing, what causes a magnetic field to
diverge. Thus, there do not exist magnetic charges.
Thus there does not exist a source and a
sink of the magnetic field. Thus the magnetic field
lines are ALWAYS closed.
Lecture I, 24. Sep. 2001
Ant
enna
s &
Pro
paga
tion
Ant
enna
s &
Pro
paga
tion
Maxwell’s Equations
(3) Mathematical Basics:
b) Rotation rot (curl)b) Rotation rot (curl)
We would like to be able to read and understand that formula, too!
Basically, the same principles as for the divergence apply. The only
differences are that
1. The impact is perpendicular to its cause, thus perpendicular to
the action of the source. (sailing)
2. Since it has a direction, it is a vector.
JH rot
Lecture I, 24. Sep. 2001
Ant
enna
s &
Pro
paga
tion
Ant
enna
s &
Pro
paga
tion
Maxwell’s Equations
(3) Mathematical Basics:
b) Rotation rot (curl)b) Rotation rot (curl)
JH rot J
H
How to read it?
zHH
yHH
xHH
J
yxxzzyxyzxyz
Lecture I, 24. Sep. 2001
Ant
enna
s &
Pro
paga
tion
Ant
enna
s &
Pro
paga
tion
Maxwell’s Equations
(3) Mathematical Basics:
c) Comparison div & rot (curl)c) Comparison div & rot (curl)
zHH
yHH
xHH
H
yxxzzyxyzxyzrot
zyxzyx
DDD
D div
z
y
x
Lecture I, 24. Sep. 2001
Ant
enna
s &
Pro
paga
tion
Ant
enna
s &
Pro
paga
tion
Maxwell’s Equations
(3) Mathematical Basics:
d) Nabla Notationd) Nabla Notation
zyxzyx
Nabla Vector
zyxzyx
zyxzyx
DDD
D
... H
gradDD div
HH rot
Lecture I, 24. Sep. 2001
Ant
enna
s &
Pro
paga
tion
Ant
enna
s &
Pro
paga
tion
Maxwell’s Equations
D div 0 div B
t
B
Erot t
DJHrot
HB
ED
0
0
They seem coupled.
Lecture I, 24. Sep. 2001
Ant
enna
s &
Pro
paga
tion
Ant
enna
s &
Pro
paga
tion
Maxwell’s Equations
t
B
Erot
THE KEY TO ANY OPERATING ANTENNA
1. You create a time variant current density J
2. This causes a varying magnetic field H
3. This causes a varying electric field E
4. This causes varying magnetic field H
t
D
JHrot