Antennas

1
AntennasPropagation

• Mischa Dohler
• Kings College London
• Centre for Telecommunications Research

2
Overview (entire lecture)

• Introduction to Communication Systems
• Mathematical Physical Fundamentals
• Fundamentals of Antennas
• Practical Antennas
• Propagation Mechanisms Modelling
• Wireless Communication Links
• Cellular Concept

3
Introduction
4
Communication Systems

• 1. GENERAL

5
Communication Systems

• 2. DETAIL

SOURCE
SOURCE CODING
CHANNEL CODING
Tx
CHANNEL
Rx
CHANNEL DE-COD
SOURCE DE-COD
SINK
6
Communication Systems

• 2. DETAIL

SOURCE
SOURCE CODING
CHANNEL CODING
Tx
CHANNEL
Rx
CHANNEL DE-COD
SOURCE DE-COD
SINK
7
Communication Systems

• 2. DETAIL

SOURCE
SOURCE CODING
CHANNEL CODING
Tx
CHANNEL
Rx
CHANNEL DE-COD
SOURCE DE-COD
SINK
8
Communication Systems

• 2. DETAIL

SOURCE
SOURCE CODING
CHANNEL CODING
Tx
CHANNEL
Rx
CHANNEL DE-COD
SOURCE DE-COD
SINK
9
Communication Systems

• 2. DETAIL

SOURCE
SOURCE CODING
CHANNEL CODING
Tx
CHANNEL
Rx
CHANNEL DE-COD
SOURCE DE-COD
SINK
10
Communication Systems

• 2. DETAIL

SOURCE
SOURCE CODING
CHANNEL CODING
Tx
NOISE
Rx
CHANNEL DE-COD
SOURCE DE-COD
SINK
11
Communication Systems

• 2. DETAIL

SOURCE
SOURCE CODING
CHANNEL CODING
Tx
CHANNEL
Rx
CHANNEL DE-COD
SOURCE DE-COD
SINK
12
Communication Systems

• 2. DETAIL

SOURCE
SOURCE CODING
CHANNEL CODING
Tx
CHANNEL
Rx
CHANNEL DE-COD
SOURCE DE-COD
SINK
13
Communication Systems

• 2. DETAIL

SOURCE
SOURCE CODING
CHANNEL CODING
Tx
CHANNEL
Rx
CHANNEL DE-COD
SOURCE DE-COD
SINK
14
Communication Systems

• 3. KINGS

SOURCE
SOURCE CODING
CHANNEL CODING
Tx
CHANNEL
Rx
CHANNEL DE-COD
SOURCE DE-COD
SINK
Dr. Marvasti Information Theory
Prof. Aghvami Digital Communication
15
Communication Systems

• 4. MATHS PHYSICS

SOURCE
SOURCE CODING
CHANNEL CODING
Tx
CHANNEL
Rx
CHANNEL DE-COD
SOURCE DE-COD
SINK
16
Communication Systems

• 4. MATHS PHYSICS

SOURCE
SOURCE CODING
CHANNEL CODING
Tx
CHANNEL
Rx
CHANNEL DE-COD
SOURCE DE-COD
SINK
17
Communication Systems

• 4. MATHS PHYSICS

SOURCE
SOURCE CODING
CHANNEL CODING
Tx
CHANNEL
Rx
CHANNEL DE-COD
SOURCE DE-COD
SINK
18
Communication Systems

• 4. MATHS PHYSICS

SOURCE
SOURCE CODING
CHANNEL CODING
Tx
CHANNEL
Rx
CHANNEL DE-COD
SOURCE DE-COD
SINK
19
Communication Systems

• 4. MATHS PHYSICS

SOURCE
SOURCE CODING
CHANNEL CODING
Tx
NOISE
Rx
CHANNEL DE-COD
SOURCE DE-COD
SINK
20
Mathematical Physical Foundations
21
Overview

• Fourier Transform
• Maxwells Equations
• Wave Equation
• Probability Theory

22
Fourier Transform

• Given a varying signal s(t) in the time-domain,
  the spectral components S(f) are obtained as
  follows

And vice versa
23
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)
(2) Functional Transformation (local)
(3) Integral Transformation (global)
24
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).
25
Fourier Transform

• Properties of the Integral Transformation

• 0 f(x) has
• components
• as g(x,w)

0 f(x) has no components as
g(x,w)
(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).
Example g(x)cos (wx ) and f(x)cos( w x )
f(x)cos( 2w x )
26
Fourier Transform

• Properties of the Integral Transformation

(3) Orthogonal If g(x,w) is orthogonal for
different w in the sense
then there does exist a UNIQUE inverse
transformation F-1. (Example)
If not, then not unique, yet still useful
(Wavelets)
27
Fourier Transform

• How did Physicists and Engineers use it?

Association (1) f(x) ?? s(t) with inf lt t lt
inf (2) g(x,w) ?? sin(wt) , cos(wt)
28
Fourier Transform

• Main messages of the Fourier Transformation

(1) For a fixed frequency f the integral tells us
how much of that harmonic is present in the
signal s(t).
29
Fourier Transform

• (2) Smoothness

30
Fourier Transform

• (2) Smoothness

31
Fourier Transform

• (2) Smoothness

32
Fourier Transform

• (2) Smoothness

33
Fourier Transform

• Filter What makes spectrum infinite?

sinc(f)
T20ms
50Hz
34
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.

35
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.

36
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!
37
Fourier Transform
Blackboard!
? 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!
38
Maxwells Equations

• Mathematical Basics
• Physical Basics
• Physical Experiences
• Derivations ? Maxwells Equations
• Discussion

39
Maxwells Equations
(1) Mathematical Basics
- Scalar Quantity with magnitude only.
- Vector Quantity with magnitude and direction.
- dot-product AB ABcosf projection
active ? passive AxBx AyBy AzBz
(scalar)
40
Maxwells 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
The change has a magnitude and a direction,
thus is a vector!
? The gradient of a scalar field defines a vector
field.
41
Maxwells Equations
(1) Mathematical Basics
In general If we have a scalar field f, then it
defines a unique gradient field E and vice
versa!
Rule Working with vector fields, it is ALWAYS
easier to find and operate with the
appropriate scalar- field (potential) and then
to differentiate!
42
Maxwells Equations
(2) Physical Basics
a) Coulombs Law
F
F
Q1
Q2
43
Maxwells Equations
(2) Physical Basics
b) Electric Field (Intensity) E
Force ? ? Field
Q1
Q2
44
Maxwells Equations
(2) Physical Basics
c) 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.
45
Maxwells Equations
(2) Physical Basics
d) Charge Density ?
46
Maxwells Equations
(2) Physical Basics
e) Current I
47
Maxwells Equations
(2) Physical Basics
f) Current Density J
A
I
48
Maxwells Equations
(2) Physical Basics
g) Magnetic Flux (Density) B
I
Field (B)
N
S
F
As done with the electrical field we define the
magnetic field through its force on magnetic
objects.
49
Maxwells Equations
(2) Physical Basics
g) Magnetic Flux (Density) B
50
Maxwells Equations
(2) Physical Basics
h) Magnetic Field H
Again, we look for a physical value which is
independent of the materials involved
51
Maxwells Equations
(3) Mathematical Basics
a) Divergence div
We would like to be able to read and understand
that formula!
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.
52
Maxwells Equations
(3) Mathematical Basics
a) Divergence div
What do we know?
Impact ? Strength (of the source)
(i) Variable What does a water source
cause? a) water pressure (no direction, good
for grad) b) speed v of water (magnitude
direction)
53
Maxwells Equations
(3) Mathematical Basics
a) Divergence div
(ii) Measure In dependency of the distance from
the source, we want to evaluate the impact of
the source.
54
Maxwells Equations
(3) Mathematical Basics
a) Divergence div
Does a wave coming along the y-axis make me move
along x or z? NO!
A wave from x y z makes me move
simultaneously along x,y z!
55
Maxwells Equations
(3) Mathematical Basics
a) Divergence div
56
Maxwells Equations
(3) Mathematical Basics
a) Divergence div
Impact ? Strength (of the source)
57
Maxwells Equations
(3) Mathematical Basics
a) Divergence div
Strength (of the source) ?
58
Maxwells Equations
(3) Mathematical Basics
a) 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.
59
Maxwells Equations
(3) Mathematical Basics
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.
60
Maxwells Equations
(3) Mathematical Basics
b) Rotation rot (curl)
61
Maxwells Equations
(3) Mathematical Basics
c) Comparison div rot (curl)
z
y
x
Divergence field
Rotational field
62
Maxwells Equations
(3) Mathematical Basics
d) Nabla Notation
Nabla Vector
63
Maxwells Equations
64
Maxwells Equations
THE KEY TO ANY OPERATING ANTENNA
Suppose
1. There does exist an electric medium, which
provides a current I and thus a current density J.
2. This causes location varying magnetic field H
3. This causes location varying magnetic flux B,
but no time varying magnetic flux. Thus no rot E,
thus no time varying electric flux. Thus no wave!
65
Maxwells Equations
Suppose
1. There is a time varying current density J.
2. This causes location and time varying magnetic
field H
3. This causes location and time varying magnetic
flux B.
4. This causes location and time varying electric
field E.
5. This causes location and time varying electric
flux D.
6. This causes location and time varying magnetic
field H, even if without current density J.
66
Philosophy of Antennas
67
The Transmitting Antenna
Thus, we only need a medium, which is capable of
carrying a time-variant current. We will call
this medium Antenna.
Outside the Antenna the electromagnetic field can
propagate on its own without the source J, since
both fields are coupled through the formulas!
68
The Receiving Antenna
Thus, we only need a medium, which has free
electrons to generate a current out of a
time-varying electromagnetic field.
69
Antenna Philosophy
Blackboard!
Accelerated Charges
Efficiency?
70
Antenna Philosophy
An Antenna is an efficient way of converting a
guided wave into a radiating wave or vice versa.
71
Antenna Philosophy
Transmission Line
(Half-wave) Dipole
Radiation
72
Overview over Antennas
73
Categories

• Dipole, Loop, Helix
• Slot, Horn, Frequ. Indep.

• Arrays (linear, planar, Yagi)
• Reflectors (corner, parab.)

74
Basic Structures
Blackboard!
a) Dipole
r (radial) distance

• Coordinate system

? Elevation
z
f Azimuth
Load
Tr. Line
y
x

• Electric and Magnetic Field Vector

H
E
r
The longer the vectors E H at point r, the
more energy is available at that point.
BUT! We are also interested in the changes from
location to location.
75
Basic Structures
Blackboard!
a) Dipole

• Radiation Pattern

Radiation Pattern is defined as the
variation of the magnitude of the electric or
magnetic field as a function of direction (at a
distance far from the antenna).
76
Basic Structures
Blackboard!
77
Wire Structures
Blackboard!
a) Dipole
b) Cross Dipole (any polarisation)
c) Loop Antenna
d) Helix Antenna (circular polarisation)
e) Frequency Independent Antenna (high bandwidth)
f) Uda-Yagi Antenna (parasitic elements)
g) Linear Antenna Array (fan beam)
h) Planar Antenna Array (pencil beam)
78
Aperture Structures
Blackboard!
a) Slot Antenna
b) Horn Antenna (efficient at microwaves)
c) Reflector Antennas
d) Micro Strip Antenna (patch on substrate)
79
Analytical Tools
80
Vector Relationships
Blackboard!
81
Vector Relationships
Blackboard!
82
Wave Equation
Blackboard!
(1)
(2)
(5)
(3)
(4)
83
Wave Equation
Blackboard!
The magnetic vector potential A is defined such
that
The electric scalar potential F is defined such
that
They are normalised through the Lorentz condition
84
Wave Equation
Blackboard!
Time-dependent inhomogeneous wave equation
85
Wave Equation
Blackboard!
Harmonic excitation
86
Wave Equation
Advantageous procedure to solve radiation
problems.
1. Represent signal to be transmitted through
current density J.
2. Resolve J into its harmonics.
3. Find the harmonic magnetic vector potential A.
6. To find the overall field of the signal, apply
inverse FT.
87
Solution of Wave Equation
Blackboard!
Time-dependent inhomogeneous wave equation
Point Charge Q(t) at (0,0,0)
88
Solution of Wave Equation
Blackboard!
Outside the source charge.
Substitution RrF
Solution wave
89
Solution of Wave Equation
Blackboard!
Neglecting the time derivative!
Poissons equation for the electrostatic
potential.
90
Solution of Wave Equation
The Solution for Poissons equation is the
Coulomb potential
91
Solution of Wave Equation
Volume Charge Q(r,t) in V
92
Retarded Potentials
93
Wave Equation
Advantageous procedure to solve radiation
problems.
1. Represent signal to be transmitted through
current density J.
2. Resolve J into its harmonics.
solved
3. Find the harmonic magnetic vector potential A.
6. To find the overall field of the signal, apply
inverse FT.
94
Hertzian Dipole
95
Hertzian Dipole
Blackboard!
Impact of current along infinitesimal small wire.
Current along z of a wire length ?L
?L

• current constant?
• coordinate system?
• distance r r?

96
Hertzian Dipole
Blackboard!
97
Hertzian Dipole
Blackboard!
98
Hertzian Dipole
Intrinsic impedance (120p ? 377ohm for free space)
99
Hertzian Dipole
Near Field Approximation
Far Field Approximation
Fresnel Region
Fraunhofer Region
E H are in quadrature phase, thus merely energy
storage
E H are in phase, thus they carry energy!
100
Antenna Parameters Definitions
101
Plane Wave of the far field

• E?

H?
z
r gtgt ?
?90
y
x
102
Polarisation

• E?

H?
z
Linear Linear (tilted) Circular Elliptical
E?
- x
103
Power Density S (Pointing Vector)
Instantaneous Power Density
in W/m2
Pointing Vector S
Averaged Power Density
Hertzian Dipole
104
Total Power P
Average power through area d?
Total average power P radiated is
Hertzian Dipole
105
Radiation Resistance Rr
Radiation Resistance Rr is defined as the
value of a hypothetical resistor which dissipates
a power equal to the power radiated by the
antenna when fed by the same current I.
Hertzian Dipole
106
Antenna Impedance ZA
The Antenna Impedance ZA is defined as the
ratio of the voltage at the feeding point V(0) of
the antenna to the resulting current flowing in
the antenna I.
If IAntenna Imax then ZA impedance referred to
the loop current
If IAntenna I(0) then ZA impedance referred to
the base current
Resistance
Reactance
107
Equivalent Circuit
Zg
Loss within Antenna
Rg
Xg
RLoss
RA
V
ZA
XA
Reactance Tells us how much power is reflected.
Or how much I and V are out of phase.
Resistance Tells us how much power is radiated.
108
Antenna conjugate Matching
Power Pr delivered to antenna for radiation is
given by
Maximum Power Pmax is delivered for conjugate
matching
109
Effective Length le
The Effective Length le characterises the
antennas ability to transform the impinging
electric field E into a voltage at the feeding
point V0, and vice versa. (Receiving Antenna!)
The more voltage is induced with less electric
field strength, the bigger the effective length
of the antenna.
110
Effective Area Ae
The Effective Area Ae characterises the
antennas ability to absorb the incident power
density w and to deliver it to the load.
(Receiving Antenna!)
The higher the delivered power with respect to
the incident power density, the higher the
effective area.
111
Radiation Intensity U
Radiation Intensity U is defined as power P
per solid angle ?. It is independent of distance!
?
Hertzian Dipole
112
Radiation Intensity U
Since the Radiation Intensity U is independent of
the distance of observations but only depends
upon antenna inherent parameters, it can be taken
to describe the Radiation Pattern of an Antenna
113
Radiation Pattern Lobes
Rolled out generic Radiation Pattern
Intensity
Main Lobe
HPBW
Side Lobe
Back Lobe
FNBW
Angle
?
?
?/2
?/2
HPBW Half Power Beamwidth
FNBW First Null Beamwidth
114
Half Power Beamwidth
Dipole HPBW90
115
Bandwidth B
The Bandwidth B is defined as the range of
frequencies within the performance of the
antenna, with respect to some characteristics,
conforms to a specified standard.
Pattern Bandwidth beamwidth, gain,
etc. Impedance Bandwidth input impedance,
radiation efficiency
Broadband Antennas Bbroad fupper flower
(B101) Narrowband Antennas Bnarrow
(fupper flower) / fcentre (B5)
Frequency Independent Antennas Bfr.ind. gt 40 1
116
Hypothetical Isotropic Radiator i
An Isotropic Radiator i is defined as a
radiator which radiates the same amount of power
in all directions. It is a purely hypothetical
radiator!!!!
Radiation Intensity U0
117
Directive Gain g
The Directive Gain g is defined as the ratio
of the radiation intensity U of the antenna to
that of an isotropic radiator U0 radiating the
same amount of power. It is a function of
direction!!!
Hertzian Dipole
118
Directivity D
The Directivity D is defined as the ratio of
the maximum radiation intensity Umax of the
antenna to that of an isotropic radiator U0
radiating the same amount of power. It is not a
function of direction!!!
Hertzian Dipole
119
Radiation Efficiency e
The Radiation Efficiency e is defined as the
ratio of the radiated power P to the total power
Pinput accepted by the antenna. Pinput P PLoss
Hertzian Dipole Including Skin Effect
120
Power Gain G
The Power Gain G is defined as the ratio of
the radiation intensity U of the antenna to that
of an isotropic radiator U0 radiating an amount
of power equal to the power accepted by the
antenna.
121
Summary
The following definitions are applicable to all
antennas
1. Power Density w ReS 2.Total Radiated Power
P
3. Radiation Resistance Rr 4. Antenna Impedance
ZA 5. Equivalent Circuit 6. Load matching
7. Effective Length le 8. Effective Area Ae
12. Directivity D 13. Radiation Efficiency e 14.
(Power) Gain G
9. Radiation Intensity U 10. HPBW / Bandwidth
B 11. Directive Gain g
122
Finite Length Dipole with Gap
123
Effective Length
z
P
zo
r'
?
r
dz
?
L
y
yo
x
Far field condition
Transmitting Antenna Characteristic
Still has to be determined!
124
Current Distribution
First choice Analogy with Transmission Line
Theory
Second choice Halléns Integral Equation
125
Halléns Integral
a radius of the antenna L length of the
antenna
Criterion for sinusoidal current distribution
L/a gt 60 Hallén's Integral ? Transmission Line
126
Pattern Factor P
127
Pattern Factor P
The pattern factor P describes how the radiation
in the far zone varies with direction.
Patterns for typical dipoles
128
Radiation Power P
129
Radiation Resistance Rr
130
Directivity D
131
Finite Gap Width
The linearity of the electromagnetic field and
thus of Maxwells Equations allows one to assume
-

132
Extensions of the finite length Dipole
133
Folded Dipole
A folded dipole has a radiation pattern the same
as a dipole but with a four-fold increase in
radiation resistance.
double strength double amplitude four-fold
power four-fold resistance
L?/2 Rr 473? 292?
134
Monopole Antenna
A monopole antenna is straight conductor above a
conducting plane. It behaves like a dipole twice
its length but double directivity.
Tool of Analysis Image Theory.
half power half radiation resistance
L?/4 Rr 36.5? D 3.28
135
Reciprocity Theorem
136
Reciprocity Theorem (Carson)
If a voltage VA is applied to the terminal of
antenna A and the current IB measured at the
terminal of another antenna B, then an equal
current IA will be obtained at the terminal of
antenna A if the same voltage VB is applied to
the terminal of antenna B.
2 Antennas
1 Antenna
137
Consequences
Transmitting Receiving Antenna
All the concepts introduced for the transmitting
antenna hold for the receiving and vice
versa! impedance, effective length, effective
area, directional pattern, etc
Friis Transmission Formula
138
Mutual and Self Impedance
139
Definitions
Self Impedance
Mutual Impedance
140
Mutual Impedance
Mutual Impedance of 2 vertically aligned dipoles.
141
Mutual Impedance
Mutual Impedance of 2 vertically aligned dipoles.
Approximated current distribution
Electromagnetic Field in the Near Field
?
142
Retrospection
(1) Maxwells Equations

• Exact Solution

(2) Dipole of infinitesimal length ?L ? dl

• Exact Solution
• Near Field
• Far Field

(3) Finite Dipole of length L

• Exact Solution ?
• Near Field ?
• Far Field

143
Near Field of (a real) Antenna
Derivation see blackboard!
144
Mutual Impedance Z21
145
Other Configurations
1. Mutual impedance of parallel antennas side by
side.
2. Mutual impedance of collinear antennas.
3. Mutual impedance of antennas in echelon.
146
Self Impedance Za
Good approximation for thin dipole of radius a
2 filamentary antennas with a?0 but a spacing
equal to a.
a
Thus all formulas with appropriate replacement
d?a apply.
147
Basics of Antenna Arrays
148
Current Sheet
z
P(r, ?, ?)
y
J
x
149
Current Sheet
Derivation see blackboard!
150
Current Sheet
2-dimensional Fourier Transform
Source Distribution
151
Far Field Components
Power Density, Power, Radiation Resistance, etc.
152
Aperture/Pattern Factor
Degenerated Aperture
E and H Plane Patterns
E Plane
H Plane
153
Linear Antenna Arrays
154
Nyquist Criterion
z
P(r, ?, ?)
y
x
J
Aperture ? Array
? gt 2d
155
Linear Antenna Array
Assumption equal antenna elements
Current variation along z
Complex nth terminal current
156
Principle of Pattern Multiplication
Principle of Pattern Multiplication
Individual Pattern
ARRAY FACTOR
157
Collinear Antenna Array
Principle of Pattern Multiplication
AF just on elevation dependent!
158
M ? N Planar Antenna Array
Principle of Pattern Multiplication
159
Uniformly Spaced Antenna Arrays
160
Fourier Transform
Array Factor
with
N5
161
Visible Region
-1 lt Visible Region lt 1
162
Visible Region
Equal Current Feeding
163
Visible Region
Unequal Current Feeding
164
Progressive Phaseshift Array
An array for which the following phase
relationship holds is called progressive
phaseshift array
Progressive Phaseshift Array Factor
Main Beam
165
Broadside Array
Main Beam orthogonal to the Array
x
166
Endfire Array
Main Beam along the Array
x
167
Uniform Array
168
Uniform Array
An array with equispaced elements which are fed
with current of equal magnitude and having a
progressive phase-shift along the array is called
UNIFORM ARRAY
with
Principle Maximum
Zeros
Secondary Maxima
169
Uniform Array
13.5dB
1. Sidelobe level 13.5dB ? independent of N!
2. Beamwidth ? dependent of N!
170
Broadside Array
Main beam is for u0. ?
Broadside Array
?
?
Main Beamwidth (MBW)BS
171
Ordinary Endfire Array
Main beam is for u0. ?
Ordinary Endfire Array
?
?
Main Beamwidth (MBW)OE
172
Endfire Array with increased Directivity
Endfire Array with increased Directivity
?
?
Main Beamwidth (MBW)EID
(71 of OE)
173
Pattern Analysis
174
Array Polynomial
Progressive Phase Shift
Deviation from progressive PS
175
Array Polynomial
u?/2
Visible Region
1
u0
Nulls on unity circle indicate no-radiation in
that particular direction!
176
N4 Broadside Array
u?/2
z1
z2
1
u0
z3
Nulls on unity circle indicate no-radiation in
that particular direction!
Broader Mainlobe?
Narrower Mainlobe?
177
Binomial Array for d?/2
Broadest Mainlobe
u?/2
z1
1
z2
u0
z3
Always just one lobe!
178
Dolph-Tschebyscheff Array
Optimum Design Coefficients to satisfy

• The narrowest main-lobe for a given side-lobe
  level.
• The lowest side-lobe level for a given main-lobe.

179
Pattern Synthesis
180
Odd Array
- Odd Array with N 2m 1
N 22 1 ? m2
x
Feeding Current
181
Fourier Coefficients
- Symmetric feeding
- Trigonometric Series with
182
Synthesis Procedure

• Specify the Array Factor f(?) either graphically
  or analytically
• Find the Fourier series expansion coefficients of
  f(?)
• Relate the coefficients to the feeding current
  amplitude and phase.

Example, see blackboard.
183
Uda-Yagi Antenna
184
3-element Uda-Yagi
z
d2
Endfire Regime
d1
y
Directivity 9dB
Reflector
reflector 5 longer
Driver
x
director 5 shorter
Director
dd1d2 0.15? - 0.25?
significant backlobe radiation
highly frequency sensitive
185
2 - element antenna
1 driven element ? 1 parasitic element
(reflector/director)
Pattern Multiplication Principle (although not
strictly applicable)
186
Reflector - Director
E-field in the Azimuth-plane
Maximum Radiation corresponding to
Reflector
Director
187
Reflector Director Length
Maximum Radiation corresponding to
Reflector
Director
? insensitive to d/? ? d1 d2 d
sensitive to L/? ? Reflector 5 longer ? Director
5 shorter
188
Reflector
Reflector
Driver
189
Director
Director
Driver
190
3 - Element Uda-Yagi
Director
Driver
Reflector
191
Application of Uda-Yagi
The Uda-Yagi is the most popular receiving
antenna in VHF-UHF due to

• Simple feeding system design
• Low cost
• Light weight
• Relatively high gain

192
Application of Uda-Yagi
Higher frequencies cause higher propagation
losses. Thus higher gains with more directors are
required.
FM-Radio (88MHz-108MHz)
3 element UY
TV (low) (54MHz-88MHz)
3 element UY
VHF
TV (high) (174MHz-216MHz)
5-6 element UY
TV (470MHz-890MHz)
10-12 element UY
UHF
193
Practical Design Criteria

• Closer spacing between elements results in higher
  front-to-back ratio with a broader main beam.
• Wider spacing yields the opposite.
• Wider spacing has a greater bandwidth.
• Uda-Yagi has broader bandwidth if reflector is
  longer than optimum and director shorter.
• Folded dipole as driven element to gain more
  radiation power and broader bandwidth.
• To broaden bandwidth reflector should be replaced
  by flat sheet (or wire grid).
• Tilted fan dipole for broader bandwidth.

194
VHF TV Receive Antenna
Man-made noise was found to be preferably
vertical polarised.
? TV broadcast is horizontally polarised!
Sheet Reflector
Folded Dipole Driver
Feeding Mast
5-6 Directors
195
Corner Reflector
196
Application of Corner Reflector
Tilted Dipole in the Corner Reflector produces an
elliptically polarised wave.

• Application
• Communication through ionosphere (Faraday
  Rotation)
• Minimises clutter echoes from raindrops

197
Turnstile Antenna
198
Turnstile Antenna
z
Small Cross-Dipole with quadrature current
feeding
P
r
B
A
dL
y
x
199
Polarisations
x-z plane (? 0)
? Linearly Polarised
x-y plane (? 90)
? ? 0 Linear Polarisation
? 0 lt ? lt 90 Elliptical
? ? 90 Circular
y-z plane (? 90)
? ? 0 Linear Polarisation
? 0 lt ? lt 90 Elliptical
? ? 90 Circular
200
Radiation Pattern
3-D Pattern of infinitesimal Turnstile Antenna
Radiation in all directions!
z
y
x
2-D x-z plane Field Pattern of Turnstile Antennas
z
z
Infinitesimal Turnstile
Finite Length Turnstile
x
x
201
Application

• Circular polarisation in Broadside direction
• ? Satellite Communication
• ? Radar Application
• Communication of unstabilised space-crafts due to
  radiation property in all directions.

• In x-z plane almost circular radiation pattern
• ? TV-broadcast transmit antenna

202
Loop Antenna
203
Loop Antennas (rectangular, loop)
Circular Loop
Loop coefficients B0, Bn see graph.
z
P
r
a
y
x
Radius of wire b
Small Circular Loop
The Loop pattern has exactly the same shape as
that of a Hertzian Dipole, where the electric and
magnetic fields are interchanged.
204
Parameters of the Loop
Radiation intensity U
Radiation Power P
Radiation Resistance Rr
Directive Gain g
Radiation Efficiency e
205
Application

• Bad transmitter, but spatially very compact
• ? Low Frequency AM receiver (HiFi)
• Connection to high impedance to give high
  induced voltage.
• Ferrite as kernel will give even better
  performance.
• Multiple loop turns to increase radiation
  resistance
• Directional Finder (combined with dipole)

z
y
Dipole
Resultant Pattern
-

x
y
x
Loop
206
Helical Antenna
207
Helical Antenna
Diameter D
The Helical Antenna was invented by John Kraus in
1946. (see his books)
Number of turns N
z
Turn spacing S
Pitch Angle ?
x
Circumference C
Ground Plane gt ?/2
Operational Modes
Normal Mode Radiation
Axial Mode Radiation
208
Normal Mode Radiation
Diameter D
z
y
x
Entire Helix Length L
Normal Mode Radiation (broadside) appears if
Current is sinusoidal along wire, thus radiation
from a loop
D ltlt ?
entire L ltlt ?
209
Axial Mode Radiation preferred mode
Axial Mode Radiation (endfire) appears if
3/4 lt C/? lt 4/3

• Narrow Mainbeam with minor sidelobes
• HPBW ? 1/(Number of turns)
• Circular Polarisation (orientation ? helix
  orientation)
• Wide Bandwidth
• No coupling between elements
• Supergain Endfire Array

z
y
x
Circumference C
210
Parameter of Axial Mode Radiation
HPBW
Gain
Input Impedance
Axial Ratio (Polarisation)
211
Application

• High gain, large bandwidth, simplicity, circular
  polarisation in AXIAL MODE
• ? Space Communication (200-300MHz)
• Arrays of Helixes with higher gain (they hardly
  couple!)

212
Quadrifilar Helix Antenna
213
Quadrifilar Helix Antenna
The Helical Antenna was invented by Kilgus in
1968. (see his papers)

• Used for communication between mobile user and
  non-geostationary satellite systems
• Gives Circular Polarisation in all directions,
  thus becomes independent of elevation angle of
  satellite.

214
Frequency Independent Antennas
215
Rumseys Principle
All antenna characteristics so far were always
scaled with respect to ?. Thus, changing ?
changes the characteristic.
The impedance and pattern properties of an
antenna will be frequency independent if the
antenna shape is specified only in terms of
angles and the antenna itself is infinite.
216
Rumseys Principle
Scaling through angles ? self-scaling Infinite
size ? problem of realisation
Current should decay fast
Finite Bowtie Antenna
217
Log-periodic toothed Antenna
Effectively infinite ? current decays
fast Current decays fast ? introduce
discontinuities Discontinuities ? destroy
self-scaling nature Self-scaling nature ?
log-periodic toothed antenna
Log-periodic sheet Log-periodic wire
Characteristic will be repeated at (discrete)
?nf1.
218
Log-periodic Dipole Array
219
Spiral Antenna
220
Fractal Antenna
221
Aperture Antennas
222
Huygens Principle
Any wavefront can be considered to be the source
of secondary waves that add to produce distant
wavefronts.
z
P
r
en
r
J, ?
y
x
223
Aperture Plane
Towards infinity
Aperture Plane

• E-field vanishes on the Hemisphere at infinity.
• Total field is derived from the knowledge of the
  field on the aperture plane.

Closing Hemisphere
224
Rectangular Aperture
y
P
r
x
b/2
r
?
z
Polarisation in the far field is the same as in
the aperture.
-a/2
a
225
Parameter Rectangular Aperture
y-z plane
x-z plane
226
Circular Aperture
y
P
r
x
r
?
z
a
Polarisation in the far field is the same as in
the aperture.
J1(x) is the first order Bessel Function of first
kind.
227
Parameter Circular Aperture
y-z plane
x-z plane
Large Apertures
228
Directivity
Rectangular Aperture
Definition
Real Physical Area
Circular Aperture
Thus, for the uniform rectangular and circular
aperture the physical area is equal to the
effective area.
Non-uniform apertures or fields
Aperture Antennas 30-90
Aperture Efficiency
Horn Antennas 50
229
Horn Antennas
230
Horn Antennas
TE10
E-Plane sectoral horn
H-Plane sectoral horn
Pyramidal horn
Excitation TE10 mode
Impedance Matching through flare
Gradual Transmission with minimised reflection
231
Specifications

• Directive Radiator
• Primary feed for parabolic reflectors
• High gain, wide bandwidth and simple
• Particularly used in microwave region (gt1GHz)
• Fan radiation patterns

232
Slot Antennas
233
Slot Antennas
z
-x
L
y
w
Bookers Principle
234
Slot on Waveguide Walls
TE10 mode
Radiation is maximum at maximal interrupted
current
Radiation
No Radiation
235
Applications

• Slot Antennas are used in fast-moving vehicles.
• The slot-length is usually ?/2
• Particularly used in microwave region (gt1GHz)

236
Microstrip (Patch) Antennas
237
Patch Structure
Patch
Feed
Substrate
L
t
- - - -

?r
d
- - - -

238
Patch Shapes
Rectangular
Dipole
Circular Ring
Elliptical

• Analysing Methods
• Transmission Line
• Cavity
• Maxwell Equations

Triangular
239
Application Performance

• It is applied where small antennas are required
• ? aircrafts, mobiles, etc
• 2. Due to shape variations they are versatile in
  polarisation, pattern, impedance, etc.
• 3. They have a low efficiency, spurious feed
  radiation and a narrow bandwidth
• 4. They usually operate in broadside regime
• 5. ?/3 lt L lt ?/2 and 2 lt ?r lt 12

240
Parabolic Reflector Antennas
241
Large Gains

• Uda-Yagi 15dB
• Helical Antenna 15dB
• Antenna Arrays high gains ? many elements
• Horn high gains ? large size

Complicated Feeding
Artificially increase size
Aperture increasing Reflector

• (re-) transmitted waves are in phase
• (re-) transmitted waves are as parallel as
  possible

242
Parabolic Reflector
Parallel and in-phase waves
Parabolic Dish
Feed
r

• Dish has to be 100 parabolic
• Feeder shouldnt block too much

Non-uniform fields due to aperture blocking etc
Aperture Efficiency 80
243
Applications

• Used where high gains are required
• ? Cosmic Radiation, etc.
• Navigation

• Beam is slightly steerable
• Deviation from perfect surface can be made lt1mm
• Diameters are usually 100m-300m

244
Practical Considerations
245
Practical Considerations
- The Quality Factor Q - Electrically Small
Antennas - Physically Small Antennas -
Imperfect Ground
246
Feeding
247
Exotic Antennas
- Fractal Antennas - Light Antennas - Gravity
Antennas
Everything what propagates can be transmitted.
Everything what can be transmitted can be
received. - EM waves, sound, smell, light,
gravity and maybe 6th sense -