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Antenna and Propagation
“Antenna” Dr. Cahit Karakuş, 2018
2
Computational Electromagnetics
• Computational Electromagnetics has been successfully applied to several engineering areas, including:
– Antennas
– Microwave devices and circuits
– Surveillance and intelligence gathering
– Communications
– Homeland Security
– Energy generation and conservation
– Biological electromagnetic (EM) effects
– Medical diagnosis and treatment
– Electronic packaging and high speed circuits
– Superconductivity
– Law enforcement
– Environmental issues
– Avionics
– Signal Integrity
3
Overview of Computational Electromagnetics
• Engineering Electromagnetics
– The study of electrical and magnetic fields and their interaction
– Governed by Maxwell’s Equations
(Faraday’s Law, Ampère’s Circuital Law, and Gauss’ Laws)
• Maxwell’s Equations relate the following Vector and Scalar Fields
E: the Electric Field Intensity Vector (V/M)
H: the Magnetic Field Intensity Vector (A/m)
D: the Displacement Flux Density Vector (C/m2)
B: the Magnetic Flux Density Vector (T)
J: the Current Density Vector (A/m2)
r: the Volume Charge Density (C/m3)
m: is the Permeability of the medium (H/m)
e: the Permittivity of the medium (F/m)
r D
DJHt
0 B
BEt
Faraday’s Law:
Ampère’s Circuital Law:
Gauss’ Laws:
HB m ED e
Constitutive Equations:
Maxwell’s Equations
History Of Antenna
• 1884, James Clerk Maxwell
– Calculated the speed electromagnetic waves travel is approximately the speed of light.
– Visible light forms only a small part of the spectrum of electromagnetic waves. • 1888, Heinrich Hertz
– Proved that electricity could be transformed into electromagnetic waves.
– These waves travel at the speed of light.
• 1896, Guglielmo Marconi
– Built a wireless telegraph, a spark gap transmitter & receiver
– On December 12, 1901, accomplished the “Atlantic Leap” from Poldhu, Cornwall, England to Signal Hill,
Newfoundland
What is an antenna?
• A metallic apparatus for sending and receiving electromagnetic waves.
• A usually metallic device (as a rod or wire) for radiating or receiving radio waves.
• Balanis; Antenna Theory: An antenna is a transitional structure between free-space and a
guiding structure.
• An antenna is an electrical conductor or system of conductors
– Transmission - radiates electromagnetic energy into space
– Reception - collects electromagnetic energy from space
• In two-way communication, the same antenna can be used for transmission and reception
What is an Antenna?
• An antenna is a way of converting the guided waves present in a waveguide,
feeder cable or transmission line into radiating waves travelling in free space, or
vice versa.
• An antenna is a passive structure that serves as transition between a
transmission line and air used to transmit and/or receive electromagnetic waves.
• Converts Electrons to Photons of EM energy
• It is a transducer which interfaces a circuit and freespace
• Solid angle, WA and Radiation intensity, U
• Radiation pattern, Pn, sidelobes, HPBW
• Far field zone, rff
• Directivity, D or Gain, G
• Antenna radiation impedance, Rrad
• Effective Area, Ae
All of these parameters are expressed in terms of a transmission antenna, but are identically applicable to a receiving antenna. We’ll also study:
Antenna parameters
8
Antenna functions
• Transmission line – Power transport medium - must avoid power reflections, otherwise use matching devices
• Radiator – Must radiate efficiently – must be of a size comparable with the half-wavelength
• Resonator – Unavoidable - for broadband applications resonances must be attenuated
9
The role of antennas Antennas serve four primary functions
• Spatial filter
directionally-dependent sensitivity
• Polarization filter
polarization-dependent sensitivity
• Impedance transformer
transition between free space and transmission line
• Propagation mode adapter
from free-space fields to guided waves
(e.g., transmission line, waveguide)
10
Spatial filter
Antennas have the property of being more sensitive in one direction than in another which provides the ability to spatially filter signals from its environment.
Directive antenna. Radiation pattern of directive antenna.
11
Impedance transformer Intrinsic impedance of free-space, E/H
Characteristic impedance of transmission line, V/I
A typical value for Z0 is 50 W.
Clearly there is an impedance mismatch that must be addressed by the antenna.
W
em
7.376
120
000
12
Receiving antenna equivalent circuit
Ante
nna
Rr
jXA
VA
jXL
RL Rl
Thevenin equivalent
The antenna with the transmission line is represented by an (Thevenin) equivalent generator
The receiver is represented by its input impedance as seen from the antenna terminals (i.e. transformed by the transmission line)
VA is the (induced by the incident wave) voltage at the antenna terminals determined when the antenna is open circuited
Note: The antenna impedance is the same when the antenna is used to radiate and when it is used to receive energy
Radio wave Receiver Transm.line
Antenna
Antenna Radiation
13
Antennas
Wires passing an alternating current emit, or radiate, electromagnetic
energy. The shape and size of the current carrying structure determines
how much energy is radiated as well as the direction of radiation.
Transmitting Antenna: Any structure designed to efficiently radiate
electromagnetic radiation in a preferred direction is called a transmitting
antenna.
We also know that an electromagnetic field will induce current in a wire. The shape
and size of the structure determines how efficiently the field is converted into current,
or put another way, determines how well the radiation is captured. The shape and
size also determines from which direction the radiation is preferentially captured.
Receiving Antenna: Any structure designed to efficiently receive
electromagnetic radiation is called a transmitting antenna
Radiation & Induction Fields
• There are two induction fields or areas where signals collapse and radiate from the antenna. They are known as the near
field and far field. The distance that antenna inductance has on the transmitted signal is directly proportional to antenna
height and the dimensions of the wave
R 2D2
Where: R = the distance from the antenna
D = dimension of the antenna
= wavelength of the transmitted signal
Antenna Field Zones
• The dividing line “Rule of Thumb” is R = 2L2/
• The near field or Fresnel zone is r < R
• The far field or Fraunhofer zone is r > R
18
Propagation mode adapter During both transmission and receive operations the antenna must provide the transition between these two propagation modes.
19
Propagation mode adapter In free space the waves spherically expand following Huygens principle:
each point of an advancing
wave front is in fact the
center of a fresh disturbance
and the source of a new train of waves.
Within the sensor, the waves are guided within a transmission line or waveguide
that restricts propagation to one axis.
20
Power vs. field strength
2
0
0
2 2
0
0 377 ohms
for plane wave
in free space
r r
EP E P Z
Z
E E E
EH
Z
Z
21
Isotropic antenna
• Isotropic antenna or isotropic radiator is a hypothetical (not physically realizable) concept, used as a useful reference to describe real antennas.
• Isotropic antenna radiates equally in all directions.
– Its radiation pattern is represented by a sphere whose center coincides with the location of the isotropic radiator.
22
Anisotropic Sources: Gain
• Every real antenna radiates more energy in some directions than in others (i.e. has directional properties)
• Idealized example of directional antenna: the radiated energy is concentrated in the yellow region (cone).
• Directive antenna gain: the power flux density is increased by (roughly) the inverse ratio of the yellow area and the total surface of the isotropic sphere
– Gain in the field intensity may also be considered - it is equal to the square root of the power gain.
23
Directional Antenna
• Directional antenna is an antenna, which radiates (or receives) much more power in (or from) some
directions than in (or from) others.
– Note: Usually, this term is applied to antennas whose directivity is much higher than that of a half-
wavelength dipole.
24
Omnidirectional Antenna
• An antenna, which has a
non-directional pattern in a
plane
– It is usually directional in other
planes
Radiation Mechanism
Antennas – Radiation Power
Let us consider a transmitting antenna (transmitter) is located at the origin of a spherical coordinate system.
In the far-field, the radiated waves resemble plane waves propagating in the radiation direction and time-
harmonic fields can be related by the chapter 5 equations.
r
r
1
s o s
s s
o
and
E a H
H a E
*1, , Re
2s s
r P E H
The time-averaged power density vector of the wave is found by the Poynting Theorem
, , , ,r P r r
P a
2, , , , sin
radP r d P r r d d P S
The total power radiated by the antenna is found by integrating over a closed spherical surface,
Electric and Magnetic
Fields:
Power Density:
Radiated Power:
27
Antennas
– You would change a dipole antenna to make it resonant on a higher frequency by making it shorter.
– The electric field of vertical antennas is perpendicular to the Earth.
Vertical and Horizontal Polarization H & V Polarized Antennas
POLARIZATION
Polarization
• The polarization of an antenna defines the orientation of the E and H waves transmitted
or received by the antenna
– Linear polarization includes vertical, horizontal or slant (any angle)
– Typical non-linear includes right- and left-hand circular (also elliptical)
• The polarization of an antenna in a specific direction is defined to be the polarization of the
wave produced by the antenna at a great distance at this direction
Vertical
Horizontal
)/sin( txAEy
Plane-polarized light
)/sin( txAEz
Right circular
Left circular
Circularly polarized light
)90/sin( txAEy )/sin( txAEz
)90/sin( txAEy )/sin( txAEz
32
Elliptical Polarization
Ex = cos (wt)
Ey = cos (wt)
Ex = cos (wt)
Ey = cos (wt+pi/4) Ex = cos (wt)
Ey = -sin (wt)
Ex = cos (wt)
Ey = cos (wt+3pi/4)
Ex = cos (wt)
Ey = -cos (wt+pi/4)
Ex = cos (wt)
Ey = sin (wt)
LHC
RHC
33
Polarization ellipse
• The superposition of two plane-wave components results in an elliptically polarized wave
• The polarization ellipse is defined by its axial ratio N/M (ellipticity), tilt angle and sense of rotation
Ey
Ex
M
N
34
Polarization Efficiency
• The power received by an antenna
from a particular direction is maximal if the polarization of the
incident wave and the polarization of the antenna in the wave
arrival direction have:
– the same axial ratio
– the same sense of polarization
– the same spatial orientation
.
35
Polarization filter
Dipole antenna
Incident
E-field
vector
z
xy
0EzE V = h E0
+_
EhV
hzh
Incident
E-field
vector
0EyE
z
xy
V = 0+_
Dipole antenna
EhV
hzh
Antennas have the property of being more sensitive to one polarization than another which provides the ability to filter signals based on its polarization.
In this example, h is the antenna’s effective
height whose units are expressed in meters.
ANTENNA PERFORMANCE PARAMETERS
Performance parameters
• Common antenna performance parameters include:
– Gain and Directivity
– Frequency coverage
– Bandwidth
– Beamwidth
– Polarization
– Efficiency
– Field Patterns
– Impedance
– Front to Back Ratio
Frequency Coverage and Bandwidth (B) • The frequency coverage of an antenna is the range of frequencies over which an antenna maintains its
parametric performance
– Antennas are generally rated based upon their stated centre frequency
– Example:
9.85-10.15 GHz, fc = 10.0 GHz
• The bandwidth (B) of an antenna is the frequency range in units of frequency over which the antenna
operates
– Often stated in percentage bandwidth
– Previous example:
B = 300 MHz or 3%
Beamwidth (θB, ΦB)
• The “n”-db beamwidth (θB, ΦB) of an antenna is the angle
defined by the points either side of boresight at which the
power is reduced by n-dB, for a given plane.
– For example if θB, represents the beamwidth in the horizontal
plane, ΦB represents the beamwidth in the orthogonal (vertical)
plane.
– The 3-dB beamwidth defines the half-power beam.
Efficiency (η)
• Total antenna efficiency (η) provides a measure of how much input
signal power is output (radiated) by an antenna
– The two major components are radiation efficiency (ηrad) and effective
aperture (ηap)
– Losses include spillover, ohmic heating, phase nonconformity, surface
roughness and cross-polarization
• η = ηrad ηap
Antennas – Efficiency
Power is fed to an antenna through a T-Line and the antenna appears
as a complex impedance
Efficiency
.ant ant ant
Z R jX
ant rad disR R R
where the antenna resistance consists of radiation resistance and
and a dissipative resistance.
21
2rad o rad
P I R21
2diss o diss
P I R
The power dissipated by ohmic losses is The power radiated by the antenna is
An antenna efficiency e can be defined as the ratio of the radiated power to the total power fed to the
antenna.
rad rad
rad diss rad diss
P Re
P P R R
For the antenna is driven by phasor current j
o sI I e
Example
D8.3: Suppose an antenna has D = 4, Rrad = 40 W and Rdiss = 10 W. Find antenna efficiency and maximum
power gain. (Ans: e = 0.80, Gmax = 3.2).
40
10 400.8 (or) 80%rad
rad diss
Re
R R
Antenna efficiency
Maximum power gain
max max 4 0.8 3.2G eD
max max10 1010log 10log 3.2 5.05G GdB
Maximum power gain in dB
Antennas – Efficiency
Radiation Efficiency
• The radiation efficiency (ηrad) is a measure of the total power
radiated by the antenna (transmitted or received) as
compared to the power fed into the antenna
– For many antennas this value is close to 1
Aperture efficiency
• The aperture efficiency (ηap ) is a ratio of the effective aperture area (Ae) and the physical aperture area (Ap). It is a function of the electric field distribution over the aperture.
– For many antennas this value is close to 0.5
ηap = Ae/ Ap
45
Antenna sitting
• Radio horizon
• Effects of obstacles & structures nearby
• Safety
– operating procedures
– Grounding
• lightning strikes
• static charges
– Surge protection
• lightning searches for a second path to ground
Antenna Theory
46
47
Theory • Antennas include wire and aperture types.
• Wire types include dipoles, monopoles, loops, rods, stubs, helicies, Yagi-Udas, spirals.
• Aperture types include horns, reflectors, parabolic, lenses.
• In wire-type antennas the radiation characteristics are determined by the current distribution which produces the local magnetic field.
• In aperture-type antennas the radiation characteristics are determined by the field distribution across the aperture.
48
Theory – wire antenna example
Some simplifying approximations can be made to take advantage the far-field conditions.
49
Theory – wire antenna example Once E and E are known, the radiation characteristics can be determined.
Defining the directional function f (, ) from
50
Theory – aperture antenna example
Where Sr is the radial component of the power density, S0 is
the maximum value of Sr, and Fn is the normalized version of
the radiation pattern F(, )
The far-field radiation pattern can be found from the Fourier transform of the near-field
pattern.
zyzx
D4
77.00
51
Theory
Reciprocity If an emf is applied to the terminals of antenna A and the current measured at the terminals
of another antenna B, then an equal current (both in amplitude and phase) will be obtained at
the terminals of antenna A if the same emf is applied to the terminals of antenna B.
emf: electromotive force, i.e., voltage
Result – the radiation pattern of an antenna is the same regardless of whether it is used to
transmit or receive a signal.
Radiation Pattern
52
53
Three-dimensional representation of the radiation pattern
of a dipole antenna
Radiation pattern Radiation pattern – variation of the field intensity of an antenna as an angular function with respect
to the axis
54
Radiation pattern Spherical coordinate system
55
Radiation pattern
57
Characteristics
Radiation pattern
58
Characteristics
Radiation pattern
59
Radiation pattern
60
Radiation pattern
61
Radiation Pattern
• The radiation pattern of antenna is a representation (pictorial or mathematical) of
the distribution of the power out-flowing (radiated) from the antenna (in the case
of transmitting antenna), or inflowing (received) to the antenna (in the case of
receiving antenna) as a function of direction angles from the antenna • Antenna radiation pattern (antenna pattern):
– is defined for large distances from the antenna, where the spatial (angular) distribution of the radiated power
does not depend on the distance from the radiation source
– is independent on the power flow direction: it is the same when the antenna is used to transmit and when it
is used to receive radio waves
– is usually different for different frequencies and different polarizations of radio wave radiated/ received
62
Power pattern vs. Field pattern
• The power pattern is the measured (calculated) and plotted received power: |P(θ, ϕ)| at a constant (large) distance from the antenna
• The amplitude field pattern is the measured (calculated) and plotted electric (magnetic) field intensity, |E(θ, ϕ)| or |H(θ, ϕ)| at a constant (large) distance from the antenna
Power or field-strength meter
Antenna under test
Turntable
Generator
Auxiliary antenna
Large distance
• The power pattern and the field patterns are inter-related: P(θ, ϕ) = (1/)*|E(θ, ϕ)|2 = *|H(θ, ϕ)|2
P = power
E = electrical field component vector
H = magnetic field component vector
= 377 ohm (free-space, plane wave impedance)
Antennas – Radiation Patterns
Radiation patterns usually indicate either electric field intensity or power intensity. Magnetic field
intensity has the same radiation pattern as the electric field intensity, related by o
max
, ,,n
P rP
P
It is customary to divide the field or power component by its maximum value and to
plot a normalized function
Normalized radiation intensity:
Isotropic antenna: The antenna radiates electromagnetic waves equally in
all directions.
, 1n iso
P
Antennas – Radiation Patterns
A directional antenna radiates and receives preferentially in some direction.
A polar plot
A rectangular plot
It is customary, then, to take slices of the pattern and generate
two-dimensional plots.
The polar plot can also be in terms of decibels.
max
, ,,
n
E rE
E
, 20log ,n n
E dB E
, 10log ,n n
P dB P
It is interesting to note that a normalized electric field pattern in dB will
be identical to the power pattern in dB.
Radiation Pattern:
Antennas – Radiation Patterns
A polar plot
A rectangular plot
It is clear in Figure that in some very specific directions there
are zeros, or nulls, in the pattern indicating no radiation.
The protuberances between the nulls are referred to as lobes,
and the main, or major, lobe is in the direction of maximum
radiation.
There are also side lobes and back lobes. These other lobes
divert power away from the main beam and are desired as
small as possible.
One measure of a beam’s directional nature is the beamwidth, also
called the half-power beamwidth or 3-dB beamwidth.
Radiation Pattern:
Beam Width:
Antennas – S
A radian is defined with the aid of Figure a). It is the angle subtended by an
arc along the perimeter of the circle with length equal to the radius.
A steradian may be defined using Figure (b). Here, one steradian (sr) is
subtended by an area r2 at the surface of a sphere of radius r.
sin .d d d W
A differential solid angle, dW, in sr, is defined as
2
0 0
sin 4 ( ).d d sr
W
For a sphere, the solid angle is found by integrating
An antenna’s pattern solid angle,
,p n
P d W W
Antenna Pattern Solid Angle:
All of the radiation emitted by the antenna is concentrated in a cone of solid angle Wp over which the radiation
is constant and equal to the antenna’s maximum radiation value.
67
3-D pattern
• Antenna radiation pattern is
3-dimensional
• The 3-D plot of antenna pattern
assumes both angles θ and ϕ
varying, which is difficult to produce
and to interpret
3-D pattern
68
2-D pattern
Two 2-D patterns
• Usually the antenna pattern is presented as a 2-D plot, with only one of the direction angles, θ or ϕ varies
• It is an intersection of the 3-D one with a given plane – usually it is a θ = const plane or a ϕ= const
plane that contains the pattern’s maximum
69
Principal patterns
• Principal patterns are the 2-D patterns of linearly
polarized antennas, measured in 2 planes
1. the E-plane: a plane parallel to the E vector and containing
the direction of maximum radiation, and
2. the H-plane: a plane parallel to the H vector, orthogonal to
the E-plane, and containing the direction of maximum
radiation
Source: NK Nikolova
Antenna Radiation Pattern
(Polar Representation)
3dB
3dB Down
Side Lobes
3dB = 70 ( / D)
Antenna Pattern 3D
Antenna Radiation Pattern
(Cartesian Representation)
Isotropic Level
Gain
3dB Main Beam
First side lobe F/B
Back Lobe
0 +180 -180
HPBW
Antenna beam definitions
74
Antenna beam definitions
Directivity
75
Antennas – Directivity
,,
,
n
n avg
P
PD
The directive gain,, of an antenna is the ratio of the normalized power in a
particular direction to the average normalized power, or
max
max max
,
,,
n
n avg
PD D
P
The directivity, Dmax, is the maximum directive gain,
max
4
p
D
W
Directivity:
,
,4
n p
n avg
P dP
d
W W
W
Where the normalized power’s average value taken over the entire
spherical solid angle is
max
1,nP Using
*
2
2
2
*
*
1 1, , Re Re
2 2
1 1Re Re
2 2
1Re sin
2
sin sin
sin sin sin sin
s s
o
o
o s s
j j j j
o o o o o o
r
I
r
I I
r r
I e I e I e I e
r r r r
P E H a a
a a a a
a a 2
2
r2
1sin
2
oo
I
r
a
In free space, suppose a wave propagating radially away from an antenna at the origin has
Example
sin s
s
I
r
H a
where the driving current phasor j
s oI I e Find (1) Es
r r rsin sin sin
s s o s
s o s o o
I I I
r r r
a a aE a H a a
Find (2) P(r,,)
2
2
2, ,
1sin
2
oor
IP
r Magnitude:
Antennas – Directivity
2
2
22
2
223
2
0 0
223
2
0 0
2
2
, , , , sin
sin
1sin
2
1 sin
2
1 sin
2
1 4 2
2 3rad
rad
rad
rad
rad
oo
oo
oo
ooP
P r d P r r d d
P r d d
P d d
P d
I
r
I
r
Id
r
I
r
P S
24
3o oI
Find (3) Prad
Find (4) Pn(r,,) Normalized Power Pattern
max
, ,,n
P rP
P
2
2
2, ,
1sin
2
oor
IP
r
2
max 2
1
2
oo
IP
r
2, sinnP
We make use of the formula
33
cos
sin cos3
d
33
0 0
3 3
cos
sin cos3
cos cos 0cos cos0
3 3
1 1 2 41 1 2
3 3 3 3
d
Antennas – Directivity
Find (5) Beam Width
2, sinnP
21sin
2HP
1sin
2HP
1sin
2HP
,1 45HP ,2 135HP and
135 45 90Beamwidth BW
,1 45HP
,2 135HP
90BW
0.5nP
0.5nP
z
(6) Pattern Solid Angle Ωp (Integrate over the entire sphere!)
2 2
2 3 3
0 0 0 0
4 8
sin sin sin sin 23 3
P d d dd d d
W
,p n
P d W W
(7) directivity Dmax
max
4 4 21.5
8 3
3P
D
W
Antennas – Directivity
(8) Half-power Pattern Solid Angle Ωp,HP (Integrate over the beamwidth!)
2 135 135 2
2 3 3
,
0 045 45
5 5 2
sin sin sin sin 233 2
P HP d d dd d d
W
,,
p HP nP d W W
135 3 3135 3
3
45 45
cos 135 cos 45cos
sin cos cos 135 cos 453 3 3
1 1 1 1 2 2 10 5
2 6 2 2 6 2 2 6 2 6 2 3 2
d
Power radiated through the beam width
,
5 25 23 0.88 (or) 88%
8 8
3
P HP
BW
P
P
W
W
BW
z
= 88%BWP
Antennas – Directivity
81
Beamwidth and beam solid angle
WW4
np d,F
The beam or pattern solid angle, Wp [steradians or sr] is defined as
where dW is the elemental solid angle given by W ddsind
82
Directivity, gain, effective area Directivity – the ratio of the radiation intensity in a given direction from the antenna to the radiation intensity
averaged over all directions.
[unitless]
Maximum directivity, Do, found in the direction (, ) where Fn= 1
Given Do, D can be found
and or
83
Directivity, gain, effective area
t
ol
P
P
olo DG
Gain – ratio of the power at the input of a loss-free isotropic antenna to the power supplied to the input of
the given antenna to produce, in a given direction, the same field strength at the same distance
Of the total power Pt supplied to the antenna, a part Po is radiated out into space and the remainder Pl is
dissipated as heat in the antenna structure. The radiation efficiency l is defined as the ratio of Po to Pt
Therefore gain, G, is related to directivity, D, as
And maximum gain, Go, is related to maximum directivity, Do, as
,, DG l
84
Directivity, gain, effective area
paeff AAD
220
44
yzxzp
effA
W
22
yyz l
Effective area – the functional equivalent area from which an antenna directed toward the source of the
received signal gathers or absorbs the energy of an incident electromagnetic wave
It can be shown that the maximum directivity Do of an antenna is related to an effective area (or effective
aperture) Aeff, by
where Ap is the physical aperture of the antenna and a = Aeff / Ap is the aperture efficiency (0 ≤ a ≤ 1)
Consequently
For a rectangular aperture with dimensions lx and ly in the x- and y-axes, and an aperture efficiency a = 1, we
get
xxz l
[m2]
[rad] [rad]
85
Directivity, gain, effective area Therefore the maximum gain and the effective area can be used interchangeably by assuming a value for the
radiation efficiency (e.g., l = 1)
zyzx
effAG
4420
effl AG
20
4
4
2
0GAeff
Example: For a 30-cm x 10-cm aperture, f = 10 GHz ( = 3 cm)
xz 0.1 radian or 5.7°, yz 0.3 radian or 17.2°
G0 419 or 26 dBi
(dBi: dB relative to an isotropic radiator)
Antenna Gain
Antennas – Gain
Gain
, ,G eD
The power gain, G, of an antenna is very much like its directive gain, but also takes into account
efficiency
The maximum power gain max maxG eD
The maximum power gain is often expressed in dB. max max1010logG GdB
• Unless otherwise specified, the gain refers to the direction of maximum radiation.
• Gain is a dimension-less factor related to power and usually expressed in decibels
• Gi “Isotropic Power Gain” – theoretical concept, the reference antenna is isotropic
• Gd - the reference antenna is a half-wave dipole
Directivity & Gain
• Directivity is the maximum radiation intensity in a given
direction relative to the average radiation intensity (isotropic)
A general gain equation
G ≈ η (4π/λ2) Ap
where
– η – efficiency of the antenna
– λ – wavelength in meters
– Ap – the physical area of the aperture in m2
Antenna Gain
• Relationship between antenna gain and effective area
• G = antenna gain
• Ae = effective area
• f = carrier frequency
• c = speed of light ( 3 108 m/s)
• = carrier wavelength
2
2
2
44
c
AfAG ee
93
Gain, Directivity, Radiation Efficiency
• The radiation intensity, directivity and gain are
measures of the ability of an antenna to concentrate
power in a particular direction.
• Directivity relates to the power radiated by antenna (P0
)
• Gain relates to the power delivered to antenna (PT) • : radiation efficiency (0.5 - 0.75)
0
),(),(
P
P
DG
T
94
Antenna gain measurement
Antenna Gain = (P/Po) S=S0
Actual
antenna
P = Power
delivered to the
actual antenna
S = Power
received
(the same in both steps)
Measuring
equipment
Step 2: substitution
Reference
antenna
Po = Power
delivered to the
reference antenna
S0 = Power
received (the
same in both
steps)
Measuring
equipment
Step 1: reference
Antenna gain measurement
96
Antenna gain and effective area
• Measure of the effective absorption area presented by an antenna
to an incident plane wave.
• Depends on the antenna gain and wavelength
22( , ) [m ]
4eA G
Aperture efficiency: a = Ae / A
A: physical area of antenna’s aperture, square meters
Dipole, Monopole, Ground Plane
97
98
Implementation
Dipole, monopole, and ground plane For a center-fed, half-wave dipole oriented parallel to the z axis
2
2
2
0
sin
cos2
cos15
r
ISr
Tuned half-wave dipole
antenna
(V/m) rkj0 e
sin
cos2
cos
r
I60jE
(W/m2)
dB15.264.1D0
78
2
2
nnsin
cos2
cos
F,F
99
Dipole antennas
Versions of broadband dipole antennas
100
Dipole antennas
101
Monopole antenna
Ground
plane
Mirroring principle creates image of monopole,
transforming it into a dipole
Radition pattern of vertical monopole above ground of (A) perfect
and (B) average conductivity
102
Ground plane A ground plane will produce an image of nearby currents. The image will have a phase shift of 180°
with respect to the original current. Therefore as the current element is placed close to the surface,
the induced image current will effectively cancel the radiating fields from the current.
The ground plane may be any conducting surface including a metal sheet, a water surface, or the
ground (soil, pavement, rock).
Horizontal current element
Current element image
Conducting surface
(ground plane)
Antenna Arrays
103
104
Antenna array composed of several similar radiating elements (e.g., dipoles or horns).
Element spacing and the relative amplitudes and phases of the element excitation determine the array’s radiative properties.
Antenna arrays
Linear array examples
Two-dimensional array of microstrip
patch antennas
105
Antenna arrays The far-field radiation characteristics Sr(, ) of an N-element array composed of identical radiating elements
can be expressed as a product of two functions:
Where Fa(, ) is the array factor, and Se(, ) is the power directional pattern of an individual element.
This relationship is known as the pattern multiplication principle.
The array factor, Fa(, ), is a range-dependent function and is therefore determined by the array’s geometry.
The elemental pattern, Se(, ), depends on the range-independent far-field radiation pattern of the individual
element. (Element-to-element coupling is ignored here.)
,S,F,S ear
2
1
0
N
i
rkj
iaieA,F
106
Antenna arrays In the array factor, Ai is the feeding coefficient representing the complex excitation of each
individual element in terms of the amplitude, ai, and the phase factor, i, as
and ri is the range to the distant observation point.
ij
ii eaA
107
Antenna arrays
For a linear array with equal spacing d between adjacent elements, which
approximates to
For this case, the array factor becomes
Note that the e-jkR term which is common to all of the summation terms can be
neglected as it evaluates to 1.
2
1N
0i
cosdkijj
iaa eeaF,F i
cosdiRri
108
Antenna arrays By adjusting the amplitude and phase of each elements excitation, the beam characteristics can be modified.
109
Implementation
Antenna arrays
110
Antenna arrays
111
Implementation
Example: 2-element array Isotropic radiators
112
Implementation
Example: 2-element array Isotropic radiators
113
Implementation
Example: 2-element array Half-wave dipole radiators
114
Implementation
Example: 2-element array Half-wave dipole radiators
115
Implementation
Example: 6-element array Half-wave dipole radiators
grating lobes
d ≥ produces two grating lobes
116
Antenna arrays
Beam steering effects
Inter-element separation affects linear array gain and grating lobes
• The broadside array gain is approximately
where d is the inter-element spacing and N is the number of elements in the
linear array
• To avoid grating lobes, the maximum inter-element spacing varies with beam
steering angle or look angle, , as
5~Nfor,GdN2
G elementarray
sin1dmax
117
Antenna arrays
Beamwidth and gain An 2-D planar array with uniform spacing, N x M elements in the two dimensions
with inter-element spacing of /2 provides a broadside array gain of
approximately
The beamwidth of a steered beam from a uniform
N-element array is approximately (for N > ~5)
where b is the window function broadening factor (b = 1 for uniform window
function) and d is the inter-element spacing
5M,Nfor,GMNG elementarray
1800forradians,dN
b
sin
866.0
Array Antennas
Antenna Types
119
120
Antenna types Antennas come in a wide variety of sizes and shapes
Horn antenna Parabolic reflector antenna Helical antenna
Types of Antennas
• Wire antennas
• Aperture antennas
• Array antennas
• Reflector antennas
• Lens antennas
• Patch antennas
124
Monopole (dipole over plane)
Low-Q
Broadband
High-Q
Narrowband
• If there is an inhomogeneity (obstacle) a reflected wave, standing wave, & higher field modes appear
• With pure standing wave the energy is stored and oscillates from entirely electric to entirely magnetic and back
• Model: a resonator with high Q = (energy stored) / (energy lost) per cycle, as in LC circuits • Kraus p.2
Smooth
transition region
Uniform wave
traveling
along the line
MICROSTRIP ANTENNA
Microstrip Antennas
• MICROSTRIP LINE:
• In a microstrip line most of the electric field lines are concentrated underneath the microstrip.
• Because all fields do not exist between microstrip and ground plane (air above) we have a different dielectric constant than that of the substrate. It could be less, depending on geometry.(effective )
• The electric field underneath the microstrip line is uniform across the line. It is possible to excite an undesired transverse resonant mode if the frequency or line width increases. This condition behaves like a resonator consuming power.
• A standing wave develops across its width as it acts as a resonator. The electric field is at a maximum at both edges and goes to zero in the center.
re
Microstrip Antennas
• Microstrip discontinuities can be used to advantage.
• Abrupt truncation of microstrip lines develop fringing fields storing energy and acting like a capacitor because changes
in electric field distribution are greater than that for magnetic field distribution.
• The line is electrically longer than its physical length due to capacitance.
• For a microstrip patch the width is much larger than that of the line where the fringing fields also radiate.
• An equivalent circuit for a microstrip patch illustrates a parallel combination of conductance and capacitance at each
edge.
• Radiation from the patch is linearly polarized with the E field lying in the same direction as path length.
tconsdielectricrelative
wavelengthspacefreeiswhere
re
o
re
o
tan
e
e
2/112
1115.0
/5.0
W
H
L
rreffr
reo
eee
e
W = 0.5 to 2 times the guide wavelength.
Where: L = patch length
Where: W = patch width
Microstrip Antennas
Horn Antenna
129
130
Implementation
Horn antennas
131
Implementation
Horn antennas
“Reflector Antenna”
133
Reflector antennas
• Reflectors are used to concentrate flux of EM energy radiated/ received, or to change its direction
• Usually, they are parabolic (paraboloidal).
– The first parabolic (cylinder) reflector antenna was used by Heinrich Hertz in 1888.
• Large reflectors have high gain and directivity
– Are not easy to fabricate
– Are not mechanically robust
– Typical applications: radio telescopes, satellite telecommunications.
134
Lens antennas
Lenses play a similar role to that of reflectors in reflector antennas: they collimate divergent energy Often preferred to reflectors at frequencies > 100 GHz.
Some Types of Reflector Antennas
Paraboloid Parabolic cylinder Shaped
Stacked beam Monopulse Cassegrain
Parabolic reflectors still serve as a basis for many radar They provide:
Maximum available gain
Minimum beamwidths
Simplest and smallest feeds.
Ga (dBi) = 10 log10 [ 4 Aa / 2 ]
and = 70 / D
Ga = Antenna Directive Gain
= Aperture Efficiency (50-55%)
Aa = Antenna Aperture Area
= Wavelength
= 3 dB HPBW
139
Implementation
Parabolic reflector antennas Circular aperture with uniform illumination. Aperture radius = a.
Ap = a 2
qa
qaJe
r
AEjqE rkjp
2
22 10
2
10
2
22
qa
qaJSqSr
where sinq
where 22
22
0
02
0r
AESS
p
r
J1( ) is the Bessel function of the first kind, zero order
20
4
pAD
a221
Parabolic reflectors still serve as a basis for many radar They provide:
Maximum available gain
Minimum beamwidths
Simplest and smallest feeds.
Ga (dBi) = 10 log10 [ 4 Aa / 2 ]
and = 70 / D
Ga = Antenna Directive Gain
= Aperture Efficiency (50-55%)
Aa = Antenna Aperture Area
= Wavelength
= 3 dB HPBW
Basic Geometry and operation
For a parabolic conducting reflector
surface of focal length f with a feed at
the focus F.
In rect. coordinates
z = (x2 + y2)/4f
In spherical coordinates
r = f sec2 /2
tan o/2 = D/4f
Aperture angle = 2o
A spherical wave emerging from
F and incident on the reflector is
transformed after reflection into a
plane wave traveling in the
positive z direction
Reflectors with the longer focal lengths, which are flattest and introduce the
least distortion of polarization and of off-axis beams, require the narrowest
primary beams and therefore the largest feeds.
For example, the size of a horn to feed a reflector of f/D = 1.0 is approximately 4
times that of a feed for a reflector of f/D = 0.25. Most reflectors are chosen to have a
focal length between 0.25 and 0.5 times the diameter.
As side lobe levels are reduced and feed blockage becomes intolerable, offset feeds
become necessary.
Offset results
unsymmetrical illumination.
The corners of most paraboloidal reflectors are rounded or mitered to minimize
the area and especially to minimize the torque required to turn the antenna.
The deleted areas have low illumination and therefore
least contribution to the gain.
Circular and elliptical outlines produce side lobes at all angles from the
principal planes. If low side lobes are specified away from the principal planes,
it may be necessary to maintain square corners, as
Parabolic-Cylinder Antenna
It is quite common that either the elevation or the azimuth beam must be steerable or
shaped while the other is not.
A parabolic cylindrical reflector fed by a line source can accomplish this at a modest
cost.
The line source feed may assume many different forms ranging from a parallel-plate
lens to a slotted waveguide to a phased
array using standard designs.
The parabolic cylinder has application even where both patterns are fixed in shape.
Elevation beam shaping incorporate a steep skirt at
the horizon
Allow operation at low
elevation angles without degradation from ground
reflection
A vertical array can produce much sharper skirts
than a shaped dish of equal height can, since a
shaped dish uses part of its height for high-angle
coverage.
Parabolic cylinders suffer from large blockage if they are
symmetrical, and they are therefore often built offset.
Properly designed, however, a cylinder fed by an offset
multiple-element line source can have excellent
performance.
Shaped Reflectors.
Fan beams with a specified shape are required for a variety of reasons. The most common
requirement is that the elevation beam provide coverage to a constant altitude.
The simplest way to shape the beam is to shape the reflector.
Each portion of the reflector is aimed in a
different direction and, to the extent that
geometric optics applies, the amplitude at that
angle is the integrated sum of the power density
from the feed across that portion.
Elimination of blockage.
A large fraction of the aperture is not used in forming the main beam. If the feed pattern
is symmetrical and half of the power is directed to wide angles, it follows that the main
beam will use half of the aperture and have double the beamwidth. This corresponds to
shaping an array pattern with phase only and may represent a severe problem if sharp
pattern skirts are required. It can be avoided with extended feeds.
Limitation
Multiple Beams and Extended Feeds
• A feed at the focal point of a parabola forms a beam
parallel to the focal axis.
• Additional feeds displaced from the focal point form additional beams at
angles from the axis.
This is a powerful capability of the reflector antenna to provide extended coverage with
a modest increase in hardware
Each additional beam can have nearly full gain, and adjacent beams can be compared
with each other to interpolate angle.
A parabola reflects a spherical wave into a plane wave only when the source is at the
focus. With the source off the focus, a phase distortion results that increases with the
angular displacement in beam widths and decreases with an increase
in the focal length. The following figures show the effect of this distortion on the pattern
of a typical dish as a feed is moved off axis. A flat dish with a long focal length minimizes
the distortions. Progressively illuminating a smaller fraction of the reflector as the feed is
displaced accomplishes the same purpose.
Patterns for off-axis feeds.
Monopulse is the most common form of multiple beam antenna, normally used in
tracking systems in which a movable antenna keeps the target near the null and
measures the mechanical angle, as opposed to a surveillance system having
overlapping beams with angles measured from RF difference data.
Monopulse Feeds
Two basic monopulse systems
Amplitude
comparison
Phase
comparison
Amplitude comparison is far more prevalent in radar antennas
The sum of the two feed outputs forms a high-gain (target detection)
Low-side lobe beam
The difference forms a precise deep null at boresight
(Angle determination)
Azimuth and elevation differences can be provided
If a reflector is illuminated with a group of four feed elements, a conflict arises between the
goals of high sum-beam efficiency and high difference-beam slopes. The former requires a
small overall horn size, while the latter requires large individual horns.
Some of the shortcomings of paraboloidal reflectors can be overcome by adding a
secondary reflector. The contour of the
added reflector determines how the power will be distributed across the primary reflector
and thereby gives control over amplitude in addition to phase in the aperture.
Multiple-Reflector Antennas
This can be used to produce very low spillover or to produce a specific low-sidelobe
distribution. The secondary reflector may also be used to relocate the feed close to the
source or receiver. By suitable choice of shape, the apparent focal length can be
enlarged so that the feed size is convenient, as is sometimes necessary for monopulse
operation.
The Cassegrain antenna, derived from telescope designs, is the most common
antenna using multiple reflectors. The feed illuminates the hyperboloidal
subreflector, which in turn illuminates the paraboloidal main reflector.
The feed is placed at one focus of the hyperboloid and the paraboloid focus at the
other. A similar antenna is the gregorian, which uses an ellipsoidal subreflector in
place of the hyperboloid.
blockage elimination
FEEDS
At lower frequencies (L band and lower) dipole feeds are
sometimes used, particularly in the form of a linear array of
dipoles to feed a parabolic-cylinder reflector.
Other feed types used in some cases include waveguide slots, troughs, and open-
ended waveguides, but the flared waveguide horns are most widely used
Front Feed Offset Feed
Cassegrain Feed
Gregorain Feed
Simple Pyramidal horn
Corrugated Conical Horn
Simple Conical
Other considerations include operating bandwidth and whether the antenna is a single-
beam, multibeam, or monopulse antenna.
The feeder in the receive mode
• Must be point-source radiators
In the transmit mode, it
• Must radiate spherical phase fronts if the desired directive antenna
pattern is to be achieved.
• Must also be capable of handling the required peak and average
power levels without breakdown under all operational
environments
• Must provide proper illumination of the reflector with a prescribed
amplitude distribution and minimum spillover and correct
polarization with minimum cross polarization.
Rectangular (pyramidal) waveguide horns propagating the dominant TE01 mode are
widely used because they meet the high power and other requirements, although in
some cases circular waveguide feeds with conical flares propagating
the TE11 mode have been used. These single-mode, simply flared horns suffice for
pencil-beam antennas with just one linear polarization.
In some applications it is desirable to have very low sidelobes from a pencil-beam reflector. In this instance,
considerable improvement can be obtained by the use of metal shielding around the reflector aperture.
The typical sidelobes are
at about 0 dBi, which for most reflectors represents a value of the order of -30 to -40 dB below the peak
gain. With a shielding technique, the far-out sidelobes can be reduced to -8OdB.
Shielded-Aperture Reflectors
The simplest approach to shielding the reflector is a cylindrical
"shroud," or tunnel, of metal around the edge of a circular
reflector. If the aperture is elliptical in cross section, an elliptical
cylinder can be used.
Radome:
Reducing wind loading & Protection against Ice, Snow and Dirt
Trade-off between different dish principles
The capability of rapidly and accurately switching beams permits:
• Multiple radar functions to be performed, interlaced in time or even simultaneously.
• An electronically steered array radar may track a great multiplicity of targets, illuminate a number of targets
with RF energy and guide missiles toward them, perform complete hemispherical search with automatic
target selection, and hand over to tracking
• It may even act as a communication system, directing high-gain
beams toward distant receivers and transmitters.
• Complete flexibility is possible; search and track rates may be adjusted to best meet particular situations, all
within the limitations set by the total use of time.
• The antenna beamwidth may be changed to search some areas more rapidly with less gain.
• Frequency agility is possible with the frequency of transmission changing at will from pulse to pulse or,
with coding, within a pulse. Very high powers may be generated from a multiplicity of amplifiers distributed
across the aperture. Electronically controlled array antennas can give radars the flexibility needed to perform
all the various functions in a way best suited for the specific task at hand. The functions may be
programmed adaptively to the limit of one's capability to exercise effective automatic management and
control.
165
Terminology
Antenna – structure or device used to collect or radiate electromagnetic waves
Array – assembly of antenna elements with dimensions, spacing, and illumination sequency such that the fields of the individual elements combine to produce a maximum intensity in a particular direction and minimum intensities in other directions
Beamwidth – the angle between the half-power (3-dB) points of the main lobe, when referenced to the peak effective radiated power of the main lobe
Directivity – the ratio of the radiation intensity in a given direction from the antenna to the radiation intensity averaged over all directions
Effective area – the functional equivalent area from which an antenna directed toward the source of the received signal gathers or absorbs the energy of an incident electromagnetic wave
Efficiency – ratio of the total radiated power to the total input power
Far field – region where wavefront is considered planar
Gain – ratio of the power at the input of a loss-free isotropic antenna to the power supplied to the input of the given antenna to produce, in a given direction, the same field strength at the same distance
Isotropic – radiates equally in all directions
Main lobe – the lobe containing the maximum power
Null – a zone in which the effective radiated power is at a minimum relative to the maximum effective radiation power of the main lobe
Radiation pattern – variation of the field intensity of an antenna as an angular function with respect to the axis
Radiation resistance – resistance that, if inserted in place of the antenna, would consume that same amount of power that is radiated by the antenna
Side lobe – a lobe in any direction other than the main lobe
Kaynaklar
• Antennas from Theory to Practice, Yi Huang, University of Liverpool UK, Kevin Boyle NXP Semiconductors
UK, Wiley, 2008.
• Antenna Theory Analysis And Desıgn, Third Edition, Constantine A. Balanis, Wiley, 2005
• Antennas and Wave Propagation, By: Harish, A.R.; Sachidananda, M. Oxford University Press, 2007.
• Navy Electricity and Electronics Training Series Module 10—Introduction to Wave Propagation,
Transmission Lines, and Antennas NAVEDTRA 14182, 1998 Edition Prepared by FCC(SW) R. Stephen
Howard and CWO3 Harvey D. Vaughan.
• Lecture notes from internet.
Usage Notes
• These slides were gathered from the presentations published on the internet. I would like to
thank who prepared slides and documents.
• Also, these slides are made publicly available on the web for anyone to use
• If you choose to use them, I ask that you alert me of any mistakes which were made and allow
me the option of incorporating such changes (with an acknowledgment) in my set of slides.
Sincerely,
Dr. Cahit Karakuş