Lecture I, 24. Sep. 2001 Antennas & Propagation Mischa Dohler King’s College London Centre for Telecommunications Research

Lecture I, 24. Sep. 2001

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Antennas

&

Propagation

Mischa DohlerMischa Dohler

King’s College LondonKing’s College London

Centre for Telecommunications ResearchCentre for Telecommunications Research


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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


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Ant

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Introduction


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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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2. DETAIL

SOURCE SOURCECODING

CHANNELCODING

Tx CHANNEL Rx CHANNELDE-COD

SOURCEDE-COD

SINK

- Human Speech- HiFi / TV- Data

Quality Delay


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2. DETAIL

SOURCE SOURCECODING

CHANNELCODING


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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2. DETAIL

SOURCE SOURCECODING

CHANNELCODING


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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2. DETAIL

SOURCE SOURCECODING

CHANNELCODING


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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2. DETAIL

SOURCE SOURCECODING

CHANNELCODING


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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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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2. DETAIL

SOURCE SOURCECODING

CHANNELCODING


SOURCEDE-COD

SINK

- Performs optimum combining and processing of the received distorted wave form.


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2. DETAIL

SOURCE SOURCECODING

CHANNELCODING


SOURCEDE-COD

SINK

- Using the introduced redundancy it retrieves the desired information.


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2. DETAIL

SOURCE SOURCECODING

CHANNELCODING


SOURCEDE-COD

SINK

- Reproduces the original signal from the source to be delivered to the sink.


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3. KINGS

SOURCE SOURCECODING

CHANNELCODING


SOURCEDE-COD

SINK

Dr. Marvasti: “Information Theory”


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3. KINGS

SOURCE SOURCECODING

CHANNELCODING


SOURCEDE-COD

SINK


Prof. Aghvami: “Digital Communication”


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3. KINGS

SOURCE SOURCECODING

CHANNELCODING


SOURCEDE-COD

SINK


Prof. Aghvami: “Digital Communication”

Mischa: “Antennas & Propagation”


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SOURCE SOURCECODING

CHANNELCODING


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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SOURCE SOURCECODING

CHANNELCODING


SOURCEDE-COD

SINK

4. MATHS & PHYSICS

PHYSICS: - none

MATHEMATICS: - complete coding theory


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SOURCE SOURCECODING

CHANNELCODING


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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SOURCE SOURCECODING

CHANNELCODING


SOURCEDE-COD

SINK

4. MATHS & PHYSICS

PHYSICS: - Maxwell’s equations (free space, reflection, etc)

MATHEMATICS: - Probability theory (CLT, distributions, etc)


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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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Ant

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Mathematical

&

Physical Foundations


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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


(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


(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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(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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- 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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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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(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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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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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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d) Charge Density d) Charge Density ρρ

V

Q

dV

dQ

V

QV

0

lim


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e) Current Ie) Current I

dt

dQ

t

QI


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f) Current Density Jf) Current Density J

dA

dI

A

IJ

I

A


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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



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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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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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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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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(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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(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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zyxzyx

vvv

Impact

zyxzyx

vvv

Impact

v divImpact


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Impact Strength (of the source) (Distance)

)(MessengerImpact

(Distance)

)(Messenger source) theof (Strength


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Strength (of the source) = ρ

Electric Field E

Electric Flux D = Messenger

D

DDD

div

zyxzyx


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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.


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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


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b) Rotation rot (curl)b) Rotation rot (curl)

JH rot J

H

How to read it?

zHH

yHH

xHH

J

yxxzzyxyzxyz


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c) Comparison div & rot (curl)c) Comparison div & rot (curl)

zHH

yHH

xHH

H

yxxzzyxyzxyzrot

zyxzyx

DDD

D div

z

y

x


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d) Nabla Notationd) Nabla Notation

zyxzyx

Nabla Vector

zyxzyx

zyxzyx

DDD

D

... H

gradDD div

HH rot


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D div 0 div B

t

B

Erot t

DJHrot

HB

ED

0

0

They seem coupled.


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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

Documents

Lecture I, 24. Sep. 2001 Antennas & Propagation Mischa Dohler King’s College London Centre for Telecommunications Research