REU
June 2013
Antennas
Tim Pratt, Instructor
tipratt@vt.edu
Summer 2013
© Tim Pratt 2013
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Topics
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Antenna types
Antenna gain and beamwidth
Antenna patterns
Yagi, horns and helix
Reflector antennas
Phased array principles
Fixed beam phased array antennas
Electronically steered phased arrays
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Antennas
• All antennas serve several purposes
• Generate controlled beam
• Provide gain
• Interface from waveguide or feed line to medium (air)
• Antennas are often the limiting factor in a radio
communication system
• Definition of antenna gain:
• Increase in power radiated in one direction relative to an
antenna that radiates equally in all directions
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Fig 10.1 Antenna Gain
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Isotropic or
omni-directional antenna
G = 1 or 0 dB
Directional antenna
Axis or boresight
G >> 1
Dish
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Fig 10.2 Low Gain, Wide Beam Antennas
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Dipole
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Helix
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Open ended waveguide
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Small horn
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Patch
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/2
Monopole
/4
Ground plane
Gain 0 to 3 dB
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Cellular Handset Antennas
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Antenna must be nearly omni-directional
Simplest antenna is a monopole
Length is one quarter wavelength
At 2000 MHz,  = 0.15 m = 15 cm = 6 inches
Quarter wavelength = /4 = 3.75 cm or about 1.5 ins
Older cell phones had antenna on top
Newer phones bury antenna inside case
Ground plane is user’s hand
Wider bandwidth requires a more sophisticated antenna
GPS signals are at 1575 MHz – a folded F may be used
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Transmission Lines
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Antennas must be fed by transmission lines
Open wire pair - rarely used now, low frequencies only
Coaxial line - available as rigid or flexible
Impedance is set by d1, d2, dielectric constant 
Impedances typically 50 ohms or 75 ohms
Waveguide – hollow rectangular or circular tube

• Electric field in waveguide controls radiation
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Fig 10.3 Rectangular Waveguide
• TE 10 is the dominant mode in rectangular waveguide
• Waveguide has dimensions a = 0.6  to 0.9 
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b < 0.5 
• E-filed is zero parallel to a conducting surface
TE 10
E-field
distribution
b
a
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Fig 10.4 Circular Waveguide
• TE 11 is the dominant mode in circular waveguide
• Waveguide has dimensions D ~ 1 
• E field must terminate normal to a conducting surface
TE 11
E-field
distribution
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Fig 10.5 Planar Transmission Lines
• Stripline and microstrip
w
Dielectric, 
t
Substrate
Microstrip
Impedance is set by w, t, 
Thickness of dielectric must be controlled carefully at
high microwave frequencies
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Medium Gain Antennas
• Higher gain can be obtained with horns and traveling
wave antennas
• Horns are aperture antennas
• Flare out waveguide to make aperture
• Field in aperture is same as in waveguide
• Must be a plane wave for maximum gain
• Traveling wave antennas are long – helix and Yagi
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Fig 10.6 Waveguide Horn
Waveguide horn with large aperture
Maximum gain ~ 25 dB
E field
In waveguide
Phase center
Phase front in horn aperture
is curved
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Traveling Wave Antennas
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Yagi
Helix
These antennas have small aperture, medium gain
Gain of Yagi antenna is approximately equal to the
number of elements (not in dB)
E.g. 20 elements, G ~ 13 dB
Elements are spaced about  / 4
Reminder: dB value = 10 log (P2 / P1)
Never 20 log [ ]
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Fig 10.7 Yagi (-Uda) Antenna
Reflector
Directors (passive)
Dipole
Feed line
End fire array
Gain is roughly equal to the number of directors (not in dB)
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High Gain Antennas
• In order of popularity:
• Reflector with feed
• Phased array
• Lens with feed (rare)
• Phased arrays are generally much more expensive than
reflector antennas for a given gain
• Phased arrays allow electronic steering of beam – used
mainly in radars
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Fig 10.8 Front Fed Reflector Antenna
Feed pattern
Waveguide horn
feed
Reflector
(Dish)
Parallel rays
Edge illumination
- 10 to –13 dB
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Unit 2 Analysis of Antennas
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Gain and beamwidth
Antenna patterns
Examples
Beam squint
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Antenna Gain
• Accurate formula for Gain (not in dB)
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G = A 4  A / 2 = 4  Ae / 2
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A = physical area of aperture
• Ae = effective area of aperture
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 = wavelength
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A = aperture efficiency
• Aperture efficiency is typically 65% in well designed
antenna
• For an antenna with a circular aperture diameter D
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G = A ( D / ) 2
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Approximation for Antenna Gain
• Approximate formula for G [empirical]
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G = 33,000 / (a  b) [not dB]
• where a and b are antenna beamwidths in degrees in
two orthogonal planes
• E.g. Azimuth and Elevation
• Equal beamwidths:
G = 33,000 / 2
• This formula is empirical and not particularly accurate
• It is useful for finding gain when beamwidths are known
• Example: Satellite transmit antenna creates 3o x 4o beam
• Gain is approximately 33,000 / 12 = 2750 or 34.4 dB
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Fig 10.9 Creation of Antenna Pattern
with an Aperture
Main
beam
Plane
wave
aperture
sidelobes
Aperture is derived from concept in optics
Same effect when a plane wave is created by an antenna
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Antenna Pattern
• Antenna pattern shows the distribution of transmitted
power with angle for axis of beam (where gain is
maximum) - see Fig 10.10
• Usually plotted in Cartesian coordinates with relative
gain on vertical axis and maximum gain set to 0 dB
• Beamwidth is defined between half power (-3 dB) angles
• Pattern has main beam and sidelobes
• Gain is highest and sidelobes largest with uniform
illumination – constant field across aperture
• Tapered illumination has lower field at aperture edge
• Gain is lower, beam is broader and sidelobes are lower
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Fig 10.10 Antenna Patterns
Relative Gain dB
0 dB
-3 dB
Uniform
illumination
Tapered
illumination
Main beam
First sidelobe
-13.2 dB
axis
3 dB beamwidth
0o
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angle
First null
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Reciprocity in Antennas
• Gain and Pattern of any antenna is always same for
transmit and receive
• We usually think of antenna pattern of transmitting
antenna
• Same pattern applies to antenna when receiving
• Principle is called reciprocity
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Rayleigh Range
• Antenna requires uniform phase across aperture
• Field radiates from antenna, diffracts in far field (long
distance from antenna)
• Forms far field pattern at R > D2 / 
• Pattern is constant beyond Rayleigh Range R = 2 D2 / 
• Beamwidth in far field is set by aperture dimension D and
illumination
• Typical 3 dB beamwidth for reflector antenna is 75  / D
• Example: Antenna with 5 m aperture diameter at 12 GHz
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 = 0.025 m, 3 dB B/W = 75 x 0.025 / 5 = 0.375o
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Antenna Beamwidths and Sidelobes
• Beamwidth depends on aperture dimension D and
illumination of aperture
• Examples:
• Uniform illumination  = 51 D /  degrees
• Tapered illumination  > 57 D /  degrees
• Depends on taper - heavier taper, wider beam
• First sidelobe peak:
• Uniform illumination - 13.2 dB linear, -17.6 dB circular
• Tapered illumination << -13.2 dB
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Antenna Example
• Large antenna at 6 GHz with 30 m aperture, 65 %
aperture efficiency
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G = 10 log ( 0.65 x ( D / )2 )
• At 6 GHz,  = 0.05 m
• G = 10 log ( 0.65 x ( x 30 / 0.05)2 )
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= 10 log ( 0.65 x (1885)2 )
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= 63.6 dB
• This is the upper limit for gain with a reflector antenna
• Holding surface accuracy of paraboloidal dish for
diameters > 30 m is difficult
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Antenna Example
• 3 dB Beamwidth
• Typical value is 75  / D degrees
• For D = 30 m,  = 0.05 m
• 3 dB Beamwidth = 0.125 degrees
• Antenna will have to be steered to follow any signal
source that moves more than 0.03 degrees, such as a
GEO satellite
• Typical cost: $ 5 M
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Antenna Imperfections
• Blockage of aperture causes null filling, higher sidelobes
• Phase errors caused by surface errors also cause null
filling
• Asymmetric phase errors cause coma distortion
• Sidelobes on one side of beam are higher than on other
• Seen when feed is displaced transverse from focus of a
reflector antenna
• Displacing feed gives beam squint
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Fig 10.11 Beam Squint with Off-axis Feed
Reflector
Off-axis
feed
Center
ray
Focus
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Distorted
wavefront
phase
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Gain, dB
Nulls
filled
0
High
sidelobes
Coma
distortion
Low
sidelobes
0
angle
Fig 10.12 Antenna Pattern with Off-axis Feed
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Reflector Antenna Configurations
• Front feed: Feed blocks aperture
• Offset front feed: Feed below aperture, avoids blockage
• Cassegrain : Dual reflector - sub reflector inside focus
of main reflector
• Gregorian: Dual reflector - sub reflector outside focus of
main reflector
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Fig 10.13 Front Fed Reflector Antenna
Feed pattern
Waveguide horn
feed
Reflector
(Dish)
Parallel rays
Edge illumination
- 10 to –13 dB
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Fig 10.14 Offset Front Fed Reflector
Offset
Reflector
Feed pattern
Parallel rays
Feed
This configuration is used by Directv and Dish network
for direct to home satellite TV reception. The feed and LNB
are below the antenna beam, avoiding blocking.
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Fig 10.15 DBS-TV receive antennas
Offset front fed dish
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Fig 10.16 Cassegrain Antenna
Secondary Reflector
(sub-reflector)
Hyperboloid
Feed
Main
Reflector
Paraboloid
Main reflector
focus
Parallel rays
Cassegrain antennas are used mainly for large earth
stations that need high gain antennas
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Fig 10.17 Large Cassegrain antenna - fully steerable
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Fig 10.18 Echostar transmit / receive station
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Fig 10.19 Gregorian Antenna
Sub-reflector
Paraboloid
Feed
Main reflector
focus
Main
Reflector
Paraboloid
Gregorain antennas are used for mid size transportable
earth stations on satellite trucks
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Fig 10.20 Mobile earth station with Gregorian antenna
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Reflector Antennas
• Much of the development of antennas came from radar
requirements
• Surveillance radar needs high gain antenna
• Beam scans horizon to warn of approaching aircraft,
ships, missiles
• Scan rate is typically 6 to 10 rpm
• Tracking antenna: radar locks to target
• Needs smaller antenna with high slew rate, tracking
beams
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Phased Arrays
• Uses same aperture illumination principles as reflector
antenna
• Can be a fixed array or an electronically steered array
• Electronic steering is used mainly in radar antennas
• Beam is scanned electronically with variable phase
shifters
• Multiple beams are possible
• Random scan possible (defeat ECM)
• Nulling of jammers is possible
• Complex and expensive
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Radar Antennas
• The ideal radar antenna is a phased array
• Advantages:
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Great flexibility
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Multiple functions
• Disadvantages:
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Cost
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Complexity
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Fig 10.21 Planar Phased Array with
Square Aperture
a
d
Element
a
Aperture area = a2
Element spacing = d
N elements, with N = ( a/d ) 2
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Phased Array Antennas
• Phased array is made up of many active elements
• Element is a dipole, helix, open ended waveguide
– any small antenna with gain ~ 0 dB
• Element spacing is typically d = 0.6 wavelengths
• Look at number of elements needed:
• For gain of G = 36 dB = 4000 = A 4  A / 2
• Assume A = 0.6
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A / 2 = 531 and a =  531 2 = 23
• For d = 0.6  N = 38 elements per side
• Total number of elements in array is N 2 = 382 = 1444
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Phased Array Antennas
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If beamwidth = 1.4o
Length of side increases to 46 
Area increases to 4 x 531 2 = 2124 2
Gain increases to 36 + 6 = 42 dB
N = 76 elements per side
Total number of elements in the array is N2
76 x 76 = 5776
Making and driving 5776 microwave devices is
expensive
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Phased Array Antennas
• Phased array design and cost are dominated by
requirement for thousands of active elements
• Useful number of elements is in range 1000 to 10,000 for
array scanned in two planes
• Example: 5,000 elements at $1000 each gives phased
array cost of $ 5M
• A reflector antenna will cost much less
• Electronic scanning in one plane only reduces cost
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Phased Array Antennas
• High cost of an electronically steered phased array
antenna can be justified when:
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Antenna performs multiple functions
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Antenna must have good ECCM capability
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Random beam pointing is required
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Rapid beam steering is required
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Variable dwell time is needed
• Radar has been the primary user of phased arrays
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Fig 10.22 Pave Paws phased array antenna
Long range VHF radar for detection of ICBMs
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Fig 10.23 A/N SPY-1 phased array radar antenna
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Fig 10.24
A/N SPY-1
phased array
radar antenna
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Fig 10.25 Phased array using slotted elements
Flat panel is scanned mechanically
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One Dimensional Phased Array
• Simplest phased array is a linear (1-D) array
• Elements are in a straight line, spaced d wavelengths
apart
• Element spacing d must be in range 0.5 to 1.0
wavelengths
• Used to create omni directional antennas with a narrow
beam in the vertical plane
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Dipoles with uniform phase
Broadside beam
Fig 10.26 Omni directional dipole array
Transmitted RF wave is vertically polarized
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Phase
0o
10o
Dipoles with progressive phase shift
Beam is depressed to
improve coverage of ground
20o
30o
40o
Fig 10.27 Omni directional dipole array
Transmitted RF wave is vertically polarized
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Fig 10.28 Series Fed Linear Array
wavefront
Beam direction
T
wavelets
dipoles
T
T
T
T
load
Equal time delays
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Cellular Phone Base Station Antennas
• Cell phone base stations use linear array antennas like
the one shown in Fig 10.27.
• The linear array makes a narrow beam in the horizontal
plane that is tilted down a little for best coverage over the
earth’s surface
• Directional elements can be used to make the beam
cover a sector
• Cell phone towers with a large number of antennas are
covering several frequency bands and providing sector
coverage to increase the number of users
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Fig 10.29
Cell phone tower with
sector and omni antennas.
Small dishes link tower to
cell phone HQ and other
towers.
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Fig 10.30 Cell phone tower with sector antennas
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Fig 10.31 Cell phone tower disguised as a tree
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Fig 10.32 Parallel Fed Linear Array
wavefront
Beam direction
T
wavelets
dipoles
T
T
T
T
Progressive
time
delays
Splitters
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Beam Steering
• Beam is steered by changing relative phase between
elements
• Fixed time (phase) delays give fixed beam
• Cell phone tower antenna has fixed beams
• Electronically controlled phase shifter gives movable
beam
• Used mainly in military radars because of high cost
• Elements must be excited with correct amplitude
distribution to control sidelobes
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Beam Steering
• Time delays are difficult to achieve
• Phase delay is used instead
• Relative phasing between elements determines beam
direction
• Analyze for transmit case … apply reciprocity for receive
• Consider case of two adjacent elements
• One element has phase shift 0o
• Adjacent element has phase shift 
• Beam direction is  to the array normal where
 = (2/) d sin 
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Fig 10.33 Setting Beam Angle 
Broadside
Beam angle

x

d

0o
d
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x = d sin
 = (2 / ) d sin 
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Beam Steering
• To form beam at angle  we need progressive phase
delay along array of 0o, , 2 , 3 , 4 , 5  …
• Eventually N  > 360o
• Reset phase to N  - 360o
• Beam is correctly pointed only in steady state
• Beam transient occurs as wavelets emerge from
elements
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Beam Steering
• Example #1: Steer beam to 30o from normal (broadside)
• Element spacing d = 0.6 
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 = (2  / ) d sin 
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= 2  x 0.6 x sin 30o
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= 1.2  x ½ = 0.6  = 108o
• We must insert 108o phase shift between elements
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Fig 10.34 Parallel fed linear array scanned 30o
Beam direction
30 degrees
108o
wavefronts
0
108
216
324
Phase
Shifts in
degrees
Splitters
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Beam Steering
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Example #2: Steer beam to 45o from normal
Element spacing d = 0.6 
 = (2  / ) d sin 
= 2  x 0.6 x sin 45o
= 1.2  x ½ = 0.848  = 153o
We must insert 153o phase shift between elements
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Fig 10.35 Linear array scanned 45o
Beam direction
45 degrees
153o
wavefronts
0
153
306
99
Phase
shifts in
degrees
Splitters
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Conclusion
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All radio transmitters and receivers need antennas
Simplest antenna is a monopole or dipole
Omni-directional radiation pattern, low gain
Used in mobile and portable radios – e.g. cell phone
Reflector and phased array antennas provide high gain
and narrow beam
• Used mainly for microwave links, satellite comms and
radars
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