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This three-day course teaches the basics of antenna and antenna array theory. Fundamental concepts such as beam patterns, radiation resistance, polarization, gain/directivity, aperture size, reciprocity, and matching techniques are presented. Different types of antennas such as dipole, loop, patch, horn, dish, and helical antennas are discussed and compared and contrasted from a performance - applications standpoint. The locations of the reactive near-field, radiating near-field (Fresnel region), and far-field (Fraunhofer region) are described and the Friis transmission formula is presented with worked examples. Propagation effects are presented. Antenna arrays are discussed, and array factors for different types of distributions (e.g., uniform, binomial, and Tschebyscheff arrays) are analyzed giving insight to sidelobe levels, null locations, and beam broadening (as the array scans from broadside.) The end-fire condition is discussed. Beam steering is described using phase shifters and true-time delay devices. Problems such as grating lobes, beam squint, quantization errors, and scan blindness are presented. Antenna systems (transmit/receive) with active amplifiers are introduced. Finally, measurement techniques commonly used in anechoic chambers are outlined. The textbook, Antenna Theory, Analysis & Design, is included as well as a comprehensive set of course notes.
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What you will learn from this course
• Basic antenna concepts and definitions
• The appropriate antenna for yourapplication
Copyright 2012 © by Steven Weiss – all rights reserved
application
• Factors that affect antenna array designsand antenna systems
• Measurement techniques commonly usedin anechoic chambers
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3
Example of a “Real World” Radar Antenna Array
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4
The MU (Middle and Upper atmosphere) radar constructed by the Radio Atmospheric Science Center of Kyoto University at Shigaraki,Shiga prefecture, Japan
• Investigates atmospheric and plasma dynamics in the wide region from the troposphere to the ionosphere.• The radar is a powerful monostatic pulse Doppler radar operating at 46.5MHz• It uses active phased array antenna, which consists of 475 crossed Yagi antennas and identical number of solid-state transmit/receive modules.• The antenna beam direction can be switched to any direction within the steering range of 30deg from zenith from pulse to pulse.• The antenna aperture is 8,330m^2 (103m in diameter), and the peak and average output power is 1MW and 50kW, respectively.• The antenna beam has a conical shape with the round-trip (two-way) half-power beamwidth of 2.6deg.
Examples of Antennas
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5
CSIRO Parkes radio telescope is the largest and oldestof the eight antennas comprising the 'AustralianTelescope National Facility'. The Compact Array of six22-metre dishes near Narrabri and another nearCoonabarabran link up with the 64 meter Parkes tosynthesize a telescope some 300 kilometers across.
The VLA is an array of telescopes that can be linkedtogether to synthesize the resolving power of a telescopeupto 36 km (22 miles) across, or grouped together tosynthesize one only a km (0.6 mile) across: the varyingresolutions are the equivalent of an astronomical zoomlens. This array is located near Socorro, NM
Copyright 2012 © by Steven Weiss – all rights reserved
6
Radio TelescopeArecibo, Puerto Rico
305m in Diameter
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7
Missile DefenseWorking inside a 10-story Pave Phased Array Warning System, or
Pave PAWS, the men and women of the 7th Space WarningSquadron continuously scan the horizon for missiles, satellites and
other man-made objects in space.
Eglin FPS-85 radar located near Ft. WaltonBeach, FL. This phased array radar is a dedicated
sensor to the U.S. satellite catalog.
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8
European Remote Sensing satellite (ERS)Provides information about the
Earth’s land, oceans and polar caps
InmarsatUsed for Global Communications
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9
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10
Types of Antennas
• Electrically small antennas
• Resonant antennas
• Broadband antennas
• Aperture antennas
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11
• Aperture antennas
Electrically Small Antennas
The extent of the antenna structure is much less than the wavelength• Very low directivity• Low input resistance• High input reactance• Low radiation efficiency
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12
Short Dipole
Small Loop
Resonant Antennas
The antenna operates well at a single or selected narrow frequency band• Low to moderate gain• Real input impedance• Narrow bandwidth
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13
2~
Half-wave Dipole
2~
Microstrip Patch
2~
Yagi
Broadband AntennasThe pattern, gain, and impedance remain acceptable and are nearly constantover a wide frequency range. They are characterized by an active region witha circumference of one wavelength or an extent of a half-wavelength whichrelocates on the antenna as the frequency changes
• Low to moderate gain• Constant gain• Real input impedance
Copyright 2012 © by Steven Weiss – all rights reserved
14
• Real input impedance• Wide Bandwidth
SpiralLog-periodic dipole array
Aperture AntennasHave a physical aperture through which the waves flow.
• High Gain• Gain increases with frequency• Moderate bandwidth
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15
Aperture Aperture
Basic Concepts
• Directivity
• Gain
• Antenna Patterns
• Beamwidth
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16
• Beamwidth
• Polarization
• Bandwidth
• Radiation Resistance/Input impedance
• Reciprocity
• Effective Aperture
What is the directivity of antenna?
Ratio of radiation intensity in a given directionto the radiation intensity that would be
obtained if the total power radiated by theantenna were to be radiated isotropically
Copyright 2012 © by Steven Weiss – all rights reserved
17
What is the gain of antenna?
Ratio of radiation intensity in a given direction tothe radiation intensity that would be obtained ifthe total power accepted by the antenna were to
be radiated isotropically
Simple Illustration (light bulb)Radiating with equal intensity in all
directions (isotropic radiation) Power meter reading radiatedpower (isotropic)
P (isotropic)
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18
Radiation is focused in a particulardirection due to the reflector
Power meter reading of radiatedpower (in a given direction)
P (direction)
Note that polarization must be considered with RF antennas
Directivity and Gain• The directivity can be thought of as the ratio of the maximum radiation
intensity emanating from an antenna to the total power leaving the antennaradiated isotropically per solid angle of a sphere.
• The radiation intensity of an isotropic source is: (Prad ) / (solid angle of asphere).
• The gain of an antenna can be thought of as the ratio of the maximumradiation intensity emanating from an antenna to the total power introduced
/ 4isotropic radiatedU P
Copyright 2012 © by Steven Weiss – all rights reserved
19
• The gain of an antenna can be thought of as the ratio of the maximumradiation intensity emanating from an antenna to the total power introducedinto the antenna: (Pin ) / (solid angle of a sphere).
• Losses prevent the power input into the antenna from equaling the radiatedpower.
rad inP P
• The gain of an antenna is always less than thedirectivity of a antenna.
,
4
,
4
,,
D
P
U
P
UG
radin
Formulas for Directivity and Gain
4
,
4
,, max
rado
rad P
UD
P
UD
Copyright 2012 © by Steven Weiss – all rights reserved
)(10)(10)(10dBiG
:formloginexpressedusuallyisGain
4
,
4
,
44
maxmax
LogDLogDLog
DP
U
P
UG
oo
oradin
o
20
A Directed Beam is Described by itsAntenna Pattern
Main lobe
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21
Side lobes
Back lobes
More Details about RadiationPatterns
Beamwidth (between 3 dB points)
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22
Patterns
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23
Omni-directional pattern
Equal power in one plane.
Hemispherical pattern
Equal power everywhere
in upper half-plane.
Isotropic pattern
Equal power everywhere.
Polarization
• Electric fields must be aligned for maximumpower transfer between two antennas.
• The alignment is described by a polarization lossfactor (PLF).
Copyright 2012 © by Steven Weiss – all rights reserved
24
factor (PLF).
• Analytically, the polarization loss factor is theelectric field of the incoming wave dotted withthe electric field that would be transmitted bythe receiving antenna.
An Introduction to Polarization
• When speaking of “polarization,” we are describingthe behavior of electric field of the antenna.
• The field may remain oriented in one direction as theelectric field propagates (linear polarization)
• The field may spin as the electric field propagates(circular or elliptical polarization)
Copyright 2012 © by Steven Weiss – all rights reserved
(circular or elliptical polarization)
• Polarization will be considered in detail later in thiscourse, but you already have enough material tounderstand how our math can describe such electricfields!
25
An Introduction to Polarization
Here is an interesting antenna that has two input ports. We willdesignate these as port 1 and port 2
Copyright 2012 © by Steven Weiss – all rights reserved
Port 1
Port 2
26
An Introduction to Polarization
Port 1
Port 2
Y
Addsome
geometry!
Copyright 2012 © by Steven Weiss – all rights reserved
X
!
27
An Introduction to Polarization
Port 1
Y
Exciting port 1 causes an electric field to exist between the two horizontal finsand the field at the “aperture” of the antenna is oriented in the x-direction
ˆ x oE a E
Copyright 2012 © by Steven Weiss – all rights reserved
X
28
An Introduction to Polarization
Port 2
Y
Exciting port 2 causes an electric field to exist between the two vertical finsand the field at the “aperture” of the antenna is oriented in the y-direction
ˆ y oE a E
Copyright 2012 © by Steven Weiss – all rights reserved
X
29
An Introduction to Polarization
We already know that we can represent time-varying fields as phasors.
If we excited both ports at once (with equal strength) , we expect the
phasor representation of the electric field at the aperture to be of the
form:
ˆ ˆ
The time-dependent behavoir at the aperture becomes:
x o y oE a E a E
Copyright 2012 © by Steven Weiss – all rights reserved
The time-dependent behavoir at the aperture becomes:
ˆ ˆ ˆ ˆ( ) Re[ ( ) ] ( ) ( )
It is illustrative to plot this
j tx o y o x o y ot a E a E e a E a E Cos t
electric field using certain "snapshots" of time.
Holding " " as a constant, there is an instant when the product equals
zero. Similarly, there are different instances when equals /2 and
and 3
t
t
/2 and so forth. Letting 1 / , we can make a table and
parametrically plot the time-dependent electric field at the aperture.
oE V m
30
An Introduction to Polarization
ˆ ˆ( ) ( )
ˆ ˆ0 ( )
/ 2 0
ˆ ˆ( )
3 / 2 0
x y
x y
x y
t a a Cos t
a a
a a
X
0t
/ 2t
t
Copyright 2012 © by Steven Weiss – all rights reserved
Y
The y-axis is pointed downward so that the z-axis would be into the page.
We observe the behavior of the electric field at 0 (at the aperture.)
The electric field is linearly polarized oriented at a
z
45 Degree angle with the
y-axis (the tilt angle " .") It is also at a 45 Degree angle with the x-axis,
but we define the tilt angle with respect to the y-axis.
31
An Introduction to Polarization
Now we make one "small" change to our phasor representation of
ˆthe electric field at the aperture placing a " " in front of the term:
So,
ˆ ˆ
This t
y
x o y o
j a
E a E j a E
erm has a significant impact on the time-dependent behavoir of
the elctric field:
Copyright 2012 © by Steven Weiss – all rights reserved
the elctric field:
ˆ ˆ( ) Re[ ( ) ]
ˆ ˆRe[ ( ) ( ( ) ( )) ]
ˆ ˆ( ) ( )
Again, we hol
j tx o y o
x o y o
x o y o
t a E j a E e
a E j a E Cos t j Sin t
a E Cos t a E Sin t
d " " as a constant and parametrically plot the time-
dependent electric field at the aperture. Again, let 1 / .oE V m
32
An Introduction to Polarization
ˆ ˆ( ) ( )
ˆ0
ˆ/ 2
ˆ
ˆ3 / 2
x y
x
y
x
y
t a Cos t a Sin t
a
a
a
a
/ 2t
Copyright 2012 © by Steven Weiss – all rights reserved
X
Y
0t t
3 / 2t
The electric field is spinning in a counter-clockwise direction!33
An Introduction to Polarization
Is it right-hand or left-hand polarization?
1) Place your thumb towards the direction of propagation. This would be
into the page.
2) If your fingers align with the "spin" you have answered the question!
Try it with each hand and you will find that this example is left-hand
circularly polarized (LHCP.) / 2t
Copyright 2012 © by Steven Weiss – all rights reserved
X
Y
0t t
3 / 2t 34
An Introduction to Polarization
So, is left-hand polarization counterclockwise and right-hand clockwise?
Answer: Not enough information!
You must state whether the field is "leaving" or "arriving."
A thumb pointed away from you indicates a leaving wave.
A thumb pointed toward you indicates an arriving wave.
Copyright 2012 © by Steven Weiss – all rights reserved
le f t-h a n d is
c lo c k w ise
a rr iv in g
rig h t-h a n d is
c lo c k w ise
le a v in g
le f t-h a n d is
c o u n te rc lo c k w ise
le a v in g
rig h t-h a n d is
c o u n te rc lo c k w ise
a rr iv in g 35
An Introduction to Polarization
Port 1Port 2
X
Y
Copyright 2012 © by Steven Weiss – all rights reserved
X
This antenna is capable of exciting orthogonal electric fields (i.e., in the x- and y-directions.)If the fields are excited in phase, the field leaving the antenna will be linearly polarized
leaving the antenna at a 45 Degree angle – if the signal strength is the same at both feeds.
o oFor example: Port 1 = V ( ) and Port 2 = V ( )Cos t Cos t 36
An Introduction to Polarization
Port 1Port 2
X
Y
Copyright 2012 © by Steven Weiss – all rights reserved
X
Again, the antenna is capable of exciting orthogonal electric fields (i.e., in the x- and y-directions.) If the fields are excited in phase quadrature, the field leaving the antenna will
be circularly polarized – if the signal strength is the same at both feeds.
o oFor example: Port 1 = V ( ) and Port 2 = V ( )Cos t Sin t 37
An Introduction to Polarization
We could achieve circular polarization with and RF source, a power splitter, and a 90 Degreephase shifter.
90
Power Splitter
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RF Source
38
Polarization (elliptical)
xy ,
yx EE ,
Assume any value
Not necessarily equal
OB
OARatioAxial AR
Copyright 2012 © by Steven Weiss – all rights reserved
39
OB
cos
2tan
2
1
2 22
1
yx
yx
EE
EE
yx
AR1
Tilt angle
+ for RH polarization- for LH polarization
CP Measurements
Axial Ratio
Copyright 2012 © by Steven Weiss – all rights reserved
Polarization Loss Factor2
2 2
ˆ ˆ
Inc Trans
Inc Trans
Inc Trans
E EPLF
E E
E E
Copyright 2012 © by Steven Weiss – all rights reserved
41
2
ˆ ˆ
ˆ ˆ
Inc Transw a
Inc trans
w a
E E
E E
PLF
The electric fields are in phasor form andmay be complex quantities
PolarizationPolarization is a critical issue when considering antennas
Antenna “A” transmits avertically polarized signal
Proper alignment – Maximum power transferred from antenna A to antenna B.
A B
Antenna “B” is oriented
to receive a vertically
polarized signal
Improper alignment – Minimum power transferred from antenna A to antenna B.
Copyright 2012 © by Steven Weiss – all rights reserved
42
Antenna “A” transmits acircularly polarized signal
Circular to linear – 1 / 2 the power transferred from antenna A to antenna B.
Antenna “B” is oriented to receivelinear polarization in any direction
BA
Antenna “A” transmits avertically polarized signal
Antenna “B” is oriented
to receive a horizontally
polarized signal
A B
Bandwidth
• There are 3 equivalent ways do describe thebandwidth of an antenna
– Return loss (-10 dB convention)
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43
– Return loss (-10 dB convention)
– VSWR (2:1 convention)
– Polar Plot (Smith chart) 0.316228
Definition of the Reflection Coefficient
V
oZ
Characteristic impedance of the transmission line
Transmitted Voltage
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44
V
V
V
Reflected Voltage
Reflection Coefficient – a complex ratio of thereflected voltage divided by the transmitted voltagemeasured at a defined reference place (e.g., the inputport of the antenna.
Reflected Power
2 * 2 2
r i r i r ij j
Copyright 2012 © by Steven Weiss – all rights reserved
45
2Percentage of power reflected from the antenna
21 Percentage of power entering the antenna
2
Note that the power entering the antenna is not equal to the power radiatedby the antenna. Some power is consumed in conductor and other losses
21
- 10
- 5
0
Bandwidth – A Logarithmic Plot
LfHf
A return loss of -10 dB is conventionally defines as the bandwidth of the antenna
H LBandwidth f f
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46
2 4 6 8 10Frequency
- 25
- 20
- 15
- 10
Bd
of
Bandwidth – VSWR Plot
The impedance mismatch between theAntenna’s input impedance and thecharacteristic impedance of thetransmission line causes a standingwave to exist along the length of thetransmission line.
0.2 0.4 0.6 0.8 1
0.25
0.5
0.75
1
1.25
1.5
1.75
2
1
Distance back from the reference plane
Copyright 2012 © by Steven Weiss – all rights reserved
47
H LBandwidth f f
0.2 0.4 0.6 0.8 1
Frequency
1
2 4 6 8 10Frequency
1
2
3
4
5
6
RW
SV
Distance back from the reference plane
Lf Hf
of
1
1VSWR
Bandwidth – Polar Plot
H LBandwidth f f 1
I
LfDiscrete Data pointsmeasured on aNetwork Analyzer
Copyright 2012 © by Steven Weiss – all rights reserved
48
R
0.316228
Hf of
Bandwidth – Polar Plot/Smith Chart
L o
R I
L o
Z Zj
Z Z
IFrom transmission line theory
LfWhen the real andimaginary parts of the loadimpedance aredetermined as a function
Copyright 2012 © by Steven Weiss – all rights reserved
49
Hf
0.316228
R
Hf
determined as a functionof the real and imaginaryparts of the reflectioncoefficient, the resultingcircles and arcs define theSmith Chart.
Realized (or actual) Gain
oorealized DGG )1()1(22
Copyright 2012 © by Steven Weiss – all rights reserved
50
oorealized DGG )1()1(
Bandwidth – Equivalent Quantities
Return Loss
-10 dB
VSWR
1.9245
0.316228 0.9
21
Copyright 2012 © by Steven Weiss – all rights reserved
51
-20 dB
-30 dB
1.2222
1.0653
0.100000
0.031622
0.99
0.999
Antenna Impedance(Transmit)
The input impedance is theimpedance presented by an
antenna at its terminals
agenerator
gZ
radiated waves
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52
b
gZ
AAA jXRZ
A R LR R R
radiation resistance
Input Impedance of Antennas (Transmit)
( ) ( )
g g
g
A g R L g A g
V VI
Z Z R R R j X X
2
2
2 2
1
2 2 ( ) ( )
g rr g R
R L g A g
V RP I R
R R R X X
2
2
2 2
1
2 2 ( ) ( )
g LL g L
V RP I R
R R R X X
Power delivered to theantenna for radiation
Power dissipated asheat on the antenna
From circuit theory
Copyright 2012 © by Steven Weiss – all rights reserved
53
2 22 2 ( ) ( )L g L
R L g A g
P I RR R R X X
2
2
2 2
1
2 2 ( ) ( )
g g
g g g
R L g A g
V RP I R
R R R X X
*gA ZZ
R L gR R R
gA XX
heat on the antenna
Power dissipated as heaton the internal resistanceof the generator
Conjugate matched conditions deliverthe the maximum power to the antenna.
Input Impedance of Antennas (transmit)2
28 ( )
g rr
R L
V RP
R R
2
28 ( )
g LL
R L
V RP
R R
2 2
28 ( ) 8
g gg
g
V VRP
R R R
Radiated power assuming conjugate matching
Dissipated power in the antenna assuming conjugate matching
Dissipated power in the generator’s internal impedance
Copyright 2012 © by Steven Weiss – all rights reserved
54
28 ( ) 8g
R L g
PR R R
g R LP P P
2
*1 1
2 4
g
g g g
R L
VP V I
R R
The total power is:
Power supplied by thegenerator :
Therefore, under conjugate match conditions, half the power that issupplied by the generator is dissipated as heat in its internal resistanceand the other half is delivered to the antenna.
Antenna Impedance(receive)
Again, the input impedance isthe impedance presented byan antenna at its terminals
Copyright 2012 © by Steven Weiss – all rights reserved
55
Input Impedance of Antennas (receive)
2
8T
T
T
VP
R Power delivered to the antenna’s terminating impedance
Assuming conjugate matched conditions delivering the maximum power to the antenna.
Copyright 2012 © by Steven Weiss – all rights reserved
56
2
28 ( )T L
L
R L
V RP
R R
2
28 ( )T R
r
R L
V RP
R R
Power across the radiation resistance of the antenna
Power dissipated as heat due to the losses in the antenna
Reciprocity for Antennas
1
1I
2 ( , )V
2
1( , )V
2I
Copyright 2012 © by Steven Weiss – all rights reserved
57
Important Point!!! The transmit and receive patterns of an antenna arethe same for a reciprocal antenna.
Transmitting pattern of antenna “1” Receiving pattern of antenna “2”
212
1
( , )( , )
VZ
I
2
21
1
( , )( , )
VZ
I
12 21( , ) ( , )Z Z
Aperture Size
• Antenna engineers frequently discuss antennas interms of Aperture Size.
• A common term is the “effective aperture” size.
• Another term is the “physical aperture” size.
• Aperture size is related to the beamwidth and
Copyright 2012 © by Steven Weiss – all rights reserved
58
• Aperture size is related to the beamwidth andaccordingly the directivity and gain.
LZ
Effective Aperture Size
• The effective aperture size is a relationship between theincident electromagnetic field and the power delivered to theterminating impedance on the antenna’s input port.
(w)impedancengterminatitheacrossdevelopedpowerThe
)(m2
T
incident
Teffective
P
W
PA
Copyright 2012 © by Steven Weiss – all rights reserved
59
)(w/mantennatheofapertureat the
fieldneticelectromagincidenttheofstrengthThe
(w)impedancengterminatitheacrossdevelopedpowerThe
2
incident
T
W
P
LZincidentWTP
Effective Aperture Size
• The effective aperture size is related to the directivity of the antenna
• Anything that diminishes the power across the terminating impedancedecreases the effective aperture size
• If no power develops across the terminating impedance, the effectiveaperture size is zero - even if there is an incident electromagnetic field.
)(mD4
2O
2
meA
Copyright 2012 © by Steven Weiss – all rights reserved
60
LZincidentWTP
)(mˆˆD4
)1(
4
22
O
22
awdc
inc
T
eW
PA
Physical Aperture Size andAperture Efficiency
Copyright 2012 © by Steven Weiss – all rights reserved
61
idthLength x WArea 2rArea
AreaPhysical
ApertureEffectiveMaximiumap
p
me
A
A
Friis Transmission Formula
Copyright 2012 © by Steven Weiss – all rights reserved
62
Friis Transmission Formula
r erP W A
tPW G
Time average power density transmitted by satellite
effective aperture ofreceiving antenna
total transmitted power
R
SatelliteAntenna
dishantenna
tt GP ,
rG
Copyright 2012 © by Steven Weiss – all rights reserved
63
24t
t
PW G
R
2
4r erG A
Friis transmission formula
so
gain of transmitting antenna
2
4er rA G
2
2(4 )r t t rP P G G
R
Communication Link
R
),( tttG ),( rrrG
LZ
Copyright 2012 © by Steven Weiss – all rights reserved
64
2 2 22 ˆ ˆ(1 ) (1 ) ( ) ( , ) ( , )4
rt r t t t r r r w a
t
PG G
P R
Communication Links in dBm
2
2(4 )r t t rP P G G
R
GdBG log10)(
10
Power Milliwatts( ) 10
1 MilliwattrP dBm Log
Friis transmission formula
Divide each side by 1 mw and take the log
Copyright 2012 © by Steven Weiss – all rights reserved
65
( ) ( ) ( ) ( )
20 log ( ) 20 log ( ) 32.44
r t t rP dBm P dBm G dB G dB
R km f MHz
Note:f
c
C = Speed of light
F = frequency
Divide each side by 1 mw and take the log
The Friis Transmission Formula
Our work with the Friis transmissionformula presumed a rather pristine
environment where one did not haveto worry about the attenuation through
the atmosphere. Of course, theseeffects cannot be ignored. Shown tothe left is a plot of attenuation effects
due to oxygen and water vapor.
Copyright 2012 © by Steven Weiss – all rights reserved
66
Accordingly, any link budget would needto be adjusted to take these (and other)propagation effects into account. At this
point we begin to leave the study ofantenna theory and enter the realm of
propagation theory.
R. E. Collin, Antennas and Radiowave Propagation, New York, McGraw Hill, 1985, pp 409.
Much more!!!
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67
Much more!!!
