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Antennas for Wireless Communications
– Basic Principles and System Applications
Warren Stutzman and Bill DavisVirginia Tech Antenna Group
June 9, 2006antenna.ece.vt.edu
OUTLINE1. Introduction Stutzman
2. Antenna Fundamentals Davis
3. Antenna Elements Davis
4. Array Antennas Stutzman
break
5. System Considerations Davis
6. Wireless Applications Both
7. Photo presentation Stutzman
1. INTRODUCTION
• The Speakers• Self Introductions of Class• Wireless versus Wireline• History of Communications• The Spectrum• Antenna Performance Parameters
Warren Stutzman
• Professor at VT for 37 years• Fellow of the IEEE• Past President of IEEE Ant
& Prop. Society• Distinguished alumnus of U
of Illinois• Founder of Virginia Tech
Antenna Group• Served as ECE Dept Head
twice
Bill Davis
• Professor at VT for 28 years
• Director of Virginia Tech Antenna Group
• Past Commission Chair –USNC/URSI Commission A
• URSI Meetings Coordinator• Vice Chair 2005 IEEE
APS/URSI Symposium
Wireless versus Wireline
• Fields of Application– Communications– Sensing and Imaging
• Active – Radar• Passive – Radiometry
– Industrial• Control Ex.: garage door opener• Medical• Heating, cooking, drying, ...
• Communications– Antennas must be used for:
• Mobile communications• Very long distances
– Space– Remote terrestrial locations
– Antennas are preferred for • Broadcast and point-to-multipoint comm.• Long distance communications• Thin routes• Portable and personal communications
– The physics of wireless vs. wireline• Loss in wireline is (e-αr)2• Loss in wireless is 1/r2
ReferencesW. Stutzman and G. Thiele, “Antenna Theory and Design,” 2e, Wiley, 1998.T. Rappaport, “Wireless Communications: Principles and Practice,”
Prentice-Hall, 1996.K. Siwiak, “Radiowave Propagation and Antennas for Personal
Communications,” Sec. Ed., Artech House, 1998.
The History of CommunicationsPre-modern civilization
Optical communications: Smoke signals, flags, ....Acoustical communications: Drums
[note – all are forms of digital communications]1844
Telegraph (Morse)1864
Maxwell’s equations – principles of radio waves1876
Telephone (Bell)1887
First antenna (Hertz)1897
First radio systems (Marconi, Popov)
1901
First transatlantic radio (Marconi)
World War II
Development of radar
1960
Fiber optics
1980s
Wireless reinvented
Wireless RadioWireless
⎥ ⎥⎥ ⎥1900 2000
The Spectrum
• Wavelength λ (m) = 300 / f(MHz) λ (cm) = 30 / f(GHz)
• Frequency bands
1 mm1 cm 30 GHz3 GHzSHF
10 cm1 m3 GHz300 MHzUHF
1 m10 m300 MHz30 MHzVHF
10 m100 m30 MHz3 MHzHF
100 m1 km3 MHz300 kHzMF
1 km10 km300 kHz30 kHzLF
10 km100 km30 kHz3 KHzVLF
Wavelengths
FrequenciesBand
Antenna Performance Parameters
• Radiation pattern F(θ,φ)The angular variation of radiation around an antenna
Pattern types:Directive (narrow main beam)OmnidirectionalShaped beamLow side lobe
• Directivity DRatio of power density in the direction of pattern maximum to the Average power density at the same distance from the antenna;i.e. how much more focused the power is than if isotropicallydistributed.
• Gain GDirectivity reduced by losses on the antenna
• PolarizationThe figure traced out with time by the instantaneous electricfield vector.
Types:Linear, circular, elliptical, dual (for diversity and reuse)
• ImpedanceInput impedance at the antenna terminals
• BandwidthRange of operating frequencies for which performance parameters are acceptable.
• ScanningMovement of the radiation pattern in angular spaceTypes: electronic, mechanical, hybrid
• MechanicalSize, weight, RCS, aerodynamics
• Cost
2. ANTENNA FUNDAMENTALS
• What is an antenna?• Connecting to the antenna• Basic properties
– Impedance– Gain– Pattern– Polarization
• Fundamental Limits
What is an antenna?
• Collection of metal/material objects– Wire– Plates (reflector, dish)– EM Bandgap Materials …
• Absence of metal– Slots– Waveguide apertures
Transformation from Electronics to Space
Determining the Radiation
• Start with the current (assume)– Wire: Approximate sinusoid/traveling wave
– Plate: Physical Optics approximation or image current
• Giving for example (dipole):
)()()cos(ˆ),( yxzIzrJ δδβω =rr
To the Fields
Current
Vector Potential
∫ •−
=V
rrjrj
dverJr
erA ')'(
4)( 'ˆ
rrrrr ββ
πμ
HErr
,
The Fields (far field)
• Electric Field
• Magnetic Field
)ˆ(1
ArjHrr
×−= βμ
)ˆ(ˆ rArAjHrE −−=×−=rrr
ωη
Far-Field Conditions
• Wavelength
• Distance
• Size
λ>>r
Drr =>> )'max(
16
2 2 λλ
<⇒> phaseD
r
Far Field
Projection ~ replace distance
Antenna
Observation
Distance
Diameter D
Example – Short Dipole
• Current
• Vector Potential
• Magnetic Field
• Electric Field
• Poynting Vector
)(ˆ~ rIzJ z
rrδΔ
z
rj
Izr
eA Δ=
−
ˆ4π
μβr
φθπ
ββ
ˆsin4 z
rj
Ir
ejH Δ=
−r
θθηπ
ββ
ˆsin4 z
rj
Ir
ejE Δ=
−r
πηβ
θπ
ηβ
12
sin16
ˆ2
1
2
1
22
2
222
22
2*
z
z
IP
r
IrHES
Δ=
Δ=×=
rrr
Radiation Resistance – Short Dipole
• EQUATE– Input Power &
Radiation Power
22
2
240
321 λ
πλ
ηπ zzradrad
I
PR
Δ≈
Δ⇒=
Radiation Pattern
• Variation of Fields with Elevation (θ) and Azimuth (φ)
• Variations:– Spherical– E-plane & H-plane (or Elevation & Azimuth)– Conical
dipoleshort for ,sinmax
),(),(
,
θϕθ
ϕθϕθ
==E
EF
Patterns
0.5
1
30
210
60
240
90
270
120
300
150
330
180 0
y = 0 or φ = 0° Cut
θ
0.5
1
30
210
60
240
90
270
120
300
150
330
180 0
x = 0 or φ = 90° Cut
θ
Linear, Principal-Plane Cuts
0.5
1
30
210
60
240
90
270
120
300
150
330
180 0
z = 0 or θ = 90° Cut
φ
Half-Power Beamwidth
Efficiency
• Loss
– Radiation Resistance
• Mismatch
• Total
lossrad
rad
RR
Re
+==
InputPower
RadiatedPower
dsRJI
R surface
S
Sloss
2
2
1∫=r
Real ,4
12
2
o
oAnt
Anto ZZZ
RZq
+=Γ−=
qeEfficiency =
Directivity & Directive Gain
∫ Ω==
φθ
φθπφθ
,
2
2
2
2
),(
4
)(),(
dF
F
FAverage
FD
)],(max[ φθDD =
A
DΩ
=π4
Angle Solid Beam,
2 =Ω=Ω ∫φθ
dFA
Directivity
θ
dΩ = sin θ dθ dφ
sin θ dφ
dθ
(a) Actual pattern (b)
UmUm
ΩA
Figure 1-17
Element of solid angle dΩ.
Figure 1-18
Antenna beam solid angle ΩA.
Open Circuit Voltage& Effective Length
• Open Circuit Voltage
• Effective Length
EhVOCrr
•−= *
Irej
E
dverJI
rrh
rjrad
Ant
rrj
)4/(
')'(1
ˆˆ),( 'ˆ
πωμ
φθ
β
β
−
•
−=
××−= ∫r
rrr r
Polarization
• Linear, Circular, Elliptical
• Polarization Factor
)cos(ˆcosˆ 21 δωω ++= tEytExE
222/ EhEhp
rrrr•=
-180° -135° -90° -45° 0° +45° +90° +135° +180°
Right-handed Left-handed
Counter-clockwise
Clockwise
0
1
2
1
2
∞
E
E2
1
jwt j( t + )ˆ ˆ ˆ ˆ = E + E = E e + E e ω δx y 1 2E x y x y
Figure 2-37 Polarization ellipses as a function of the ratio E2/E1 and phase angle δwith wave approaching. Clockwise rotation of the resultant E corresponds toleft-handed polarization (IEEE definition) while counterclockwise correspondsto right-handed polarization.
Gain & Realized Gain
• Gain
• Realized Gain
• Partial Realized Gain
eDG =qeDGR =
pqeDpGg RR ==
A Communication Link
• Friis’ Trans. Formula2
2
)4( R
GGPP RTXmitRcv π
λ=
Effective Area
),(4
),(2
φθπλφθ RR GA =
24 R
AGPP RTXmitRcv π
=
To Give
Transient Link
t
ti
c
Rth
Rthv trOC ∂
∂∗⎟⎠⎞
⎜⎝⎛ −⎟
⎠⎞
⎜⎝⎛•=
∗ )(
4)(
rr
πμ
Connections
• Connectors (coax, twin-lead)• Balanced vs Unbalanced
– Balun
• Feed Network (Arrays)– Phased– True Time-Delay
• Filtering & Impedance Transformation– Circuit & loading– Tapering
Properties
• Impedance– Treat as a circuit
element– By Reciprocity:
– Induced EMF Z
XmitRcv ZZ =
∫ Ω•=Ant
dJEJI
Z )(1
2
rrr
Properties
• Patterns
XmitRcv FF =
Pattern Reciprocity
Fundamental Limits• A bit of Controversy
– Chu (1948) – McLean
)1(
122233
22
++
=aa
aQ
βββ
aaQ
ββ11
33+=
0 0.5 1 1.5 2 2.510
-1
100
101
102
ka
Rad
iatio
n Q
Antenna Fundamental Limit
Dipole
Goubau
Inverted F
Dual Inverted F
Planar Inverted F
Patch
Foursquare
Wideband, Compact, Planar Inverted F
McLeanGrimesChu
2. ANTENNA ELEMENTS
• The Four Antenna Types– Electrically Small Antennas– Resonant Antennas– Broadband Antennas
• Frequency Independent• Ultra Wideband
– Aperture Antennas
The Four Antenna Types• Electrically Small Antennas
Examples
Short dipole Small loop
PropertiesLow directivityLow input resistanceLow efficiency and gain
• Resonant Antennas
Examples
Dipole Microstrip antenna Yagi
PropertiesLow to moderate gainReal input impedanceLow efficiency and gain
Monopoles and Images
• Broadband AntennasExamples (Frequency Independent)
Spiral Log Periodic Dipole Array
PropertiesLow to moderate gainReal input impedanceLow efficiency and gain
There are two types of broadband antennas, ones that havefrequency independent performance and ones that preserve signal properties in the time domain (UWB)
• Aperture Antennas
Examples
Horn antenna Parabolic reflector antenna
PropertiesLow to moderate gainReal input impedanceLow efficiency and gain
3. ANTENNA ARRAYS
A. Array Basics
B. Arrays of Isotropic Elements
C. Inclusion of Element Effects
D. Mutual Coupling
E. Phased Arrays
Def.: Array Antenna. An antenna comprised of a number of identical radiating elements in a regular arrangement and excited to obtain a prescribed radiation pattern.
Advantages of arrays:
• Many small antenna elements instead of one large mechanical structure
• Scanning at electronic speeds is possible
• Multiple user (target) tracking is possible
• Many geometries, including conformal, are possible
Problems:
• A feed network is required with its losses and bandwidth limitations
• Mutual coupling between elements affects performance and complicates design
• Computer control may be necessary
Receiver
Phase shifter
AttenuatorFeednetwork
⎧⎪⎪⎨⎪⎪⎩
Figure 3-1 A typical linear array. The symbols and indicate variable phase shifters and attenuators. The output currents are summed before entering the receiver
General array configuration with feed network
A. Array Basics
B. Linear Arrays of Isotropic Elements
• General array configuration of isotropic elements
Figure 3-2 Equivalent configurationof the array in Fig. 3-1 for determiningthe array factor. The elements of thearray are replaced by isotropic pointsources.
Wavefronts
Rays
Referencewavefront
Array factor
Phase = 0ξ 1ξnξ
θ
nξ = phases at element n due to incoming wave
= complex current representing the feed network amplitude and phase at element n
nI
0 1 2j j jI I I ...ξ ξ ξ= + + +0 1 2AF e e e
je 1ξ1je 0ξ1 nje ξ1
nIPh ( )
nI
jI e 0ξ0
jI e 1ξn njI e ξ
n
(3-3)
δ
0° 45° 90° 135° 180°
d λ=1
8
d λ=1
4
d λ=3
8
d λ=1
2
d λ=5
8
d λ= 1
φ
dI1 I δ∠1
Elements
From [Kraus]
• Two element arrays of isotropic elements of various spacingsand phasings
Figure 3-7 Equally spaced linear array of isotropic point sources.
θ
θz
r
d d
0 1 2
d cos θ
Nj d j d j nd
n
I I e I e I eβ θ β θ β θ−
= + + + = ∑1
cos 2 cos cos0 1 2 n
=0
AF L
where the n + 1th element leads the nth element in phase by a. Then (3-14) becomes
Define
Then
jnan nI A e=
Now consider the array to be transmitting. If the current has a linear phase progression(i.e., relative phase between adjacent elements is the same), we can separate the phase explicitly as
(3-14)
(3-15)
( )N
jn d an
n
A e β θ−
+
=∑
1cos
0
AF = (3-16)
Njn
nn
A e ψ−
=∑
1
0
AF =
d aψ β θ= cos + (3-17)
(3-18)
• General uniformly excited, equally spaced linear array (UE,ESLA)
Universal array factor
Properties of the universal array factor
• The array factor is periodic in 2π
• Visible region extent:
• Exactly one period of the array factor appears in the visible region when the element space is λ/2.
Proof: Width of the visible region = 2βdAF period = 2πFor one period visible:
2π = 2βd = 2(2π/λ)dd = λ/2
For d > λ/2, grating lobes may appear in the visible region depending on α.
For d ≥ λ, grating lobes will appear in the visible region
Proof: ( ) ( )
( )
jn 2n
jn jn2 jnn n
AF 2 A e
A e e A e
AF
ψ π
ψ π ψ
ψ π
ψ
++ =
= =
=
∑∑ ∑
180° θ 0
1 < cos θ < 1
βd < βd cos θ < βd
α βd < < α βd+ψ
≥ ≥ °−−−
The general array factor expression for a UE,ESLA
( ) ( )( )
Njn
n
j N
A A A
A e
NA e
ψ
ψ ψψ
−
=
−
= = =
=
∑
0 1 2
1
00
1 /20
AF =
sin /2
sin /2
L
( ) ( )A A Nψ = =0 0AF = 0 1+1 + +1L
( ) ( )( )
N
f UE, ESLAN
ψψ
ψsin /2
sin /2
The expression is maximum for ψ = 0
This is the normalized array factor for an N element UE, ESLA that is centered aboutthe coordinate origin.
(3-33)
Figure 3-11 Array factor of an equally spaced, uniformly excited linear array for a few array numbers. (a) Three elements. (b) Five elements. (c) Ten elements.
(b)
1.0
00
ψ
( )f ψ
N = 5
0.4π 0.8π 1.2π 1.6π 2π
(c)
1.0
00
ψ
( )f ψ
N = 10
2π1.6π 1.8π1.4π1.2π0.2π 0.4π 0.6π 0.8π π
(a)
1.0
00
ψ
( )f ψ
N = 3
2ππ23
π43
Universal array factors for N = 3, 5, 10
1z
ψ
z
( )je π /21 je π1 ( )j 3e π /21d
1.0( )f
ψψ ψ=
sin 2
4 sin2
π-π 2ππ
−2
π2
π3
2
θo = 120°
βd = ππ
α =2
θ
(a)
(b)
(c)
Figure 3-12 Array factor for afour-element, uniformly excited,equally spaced phased array(Examples 3-5). (a) The arrayexcitations. (b) Universal patternfor N = 4. (c) Polar plot for d = λ/2 and α = π/2.
Example 3-5 Four-element array steered to 120°
• Scanning the pattern of a linear array in space
The main beam maximum occurs for ψ = 0. Let θo be the value of θ in the directionof the beam maximum. Then o
o
ψ = 0 = βd cos θ +α
α = βd cos θ
This element-to-element phase shift will scan the main beam peak to θ = θ0.
Often, we express ψ asoψ = βd (cos θ - cosθ )
(3-36)
(3-38)
• Beamwidth of the main beam
( )
o
For Nd >> (Nd L length of the array)
HP 0.886( /Nd) csc near broadside
HP 2 0.886 /Nd at endfire
≅
⎡ ⎤≅ ⎣ ⎦1/2
λ = =
λ θ
λ
( ) ( )( )
[ ] ( )o
1/2
o
Example N 20 d /2
0.886 /Nd 0.886 / 20 /2 0.0886 radians
90 HP 0.0886 r 0.0886 180/ 5.1°
0 HP 2 0.0886 0.595 180/ 34.1°
π
π
⎡ ⎤= =⎣ ⎦= ° =
= ° =
= = λ
λ λ λ
θ = =
θ = =
(3-45)
(3-46)
• Directivity of Uniformly Excited, Equally Spaced Linear Arrays
( )( )
/2
/2N
m
N
ND
N mm d m
N N m d
δδπ
α−
=
= =Ω + ∑
14
21
sin
sin41 2 -
sin β cos β
λ= 0
2If , d n
D NThen
α=
=
L Nd
D broadside≈ =2 2λ λ
(3-78)
Figure 3-20 Directivity as a function of element spacing for a broadside array of isotropic elements for several element numbers N.
The directivity of a broadside array of isotropic elements is approximated by
where L = Nd is the array length. This is a straight-line approximation to the curves
Dir
ecti
vity
(D
)
d
λ
α= 0δ = 0
for L
D N= =2 10λ
N = 109876
543
2.01.51.00.500
5
10
15
20
(3-80)
• Nonuniformly excited, ESLA N-1
jnn
n=0
AF A e βd cosψ ψ θ α= = +∑
1.0
1.0
1.0
1.0
1.0
0.5
0.5
0.5
0.5
00
0
0
0
00
0
λ
λ
λ
λ
λ
2λ
2λ
2λ
2λ
2λ
z
z
z
z
z
1/2λ
1/2λ
1/2λ
1/2λ
1/2λ
3/2λ
3/2λ
3/2λ
3/2λ
3/2λ
An
An
An
An
An
(a)
(b)
(c)
(d)
(e)
Uniform
1: 1 : 1 : 1 : 1
Triangular
1 : 2 : 3 : 2 : 1
Binomial
1 : 4 : 6 : 4 : 1
Dolph-Chebyshevfor a side lobe level of -20dB
1 : 1.61 : 1.94 : 1.61 : 1
Dolph-Chebyshevfor a side lobe level of -30dB
1 : 2.41 : 3.14 : 2.41 : 1
Figure 3-24 Current distributionscorresponding to the patterns ofFig. 3-23. The current phases arezero (α = 0). Currents are normal-ized to unity at the array center.(a) Uniform. (b) Triangular.(c) Binomial. (d) Dolph-Chebyshev (SLL = -20 dB).(e) Dolph-Chebyshev.
Figure 3-23 Patterns of several uniform phase (θo = 90°), equally spaced (d = λ/2) linear arrays with various amplitude distributions. The currents are plotted in Fig. 3-24.
180°
(a) Uniform currents, 1 : 1 : 1 : 1 : 1. (b) Triangular current amplitudedistribution, 1 : 2 : 3 : 2 : 1.
(c) Binomial current amplitudedistribution, 1 : 4 : 6 : 4 : 1.
D 5
HP 20.5
SLL 12 dB
== °
= −
180°180°0° 0° 0°
1.00 1.00 1.000.75 0.75 0.75
0.250.250.25 0.500.500.50
D 4.26
HP 26.0
SLL 19.1 dB
== °
= −
D 3.66
HP 30.3
SLL dB
== °
= −∞
180° 0°
1.000.75
0.250.50
(d) Dolph-Chebyshev
Current amplitude distribution, 1 : 1.61 : 1.94 : 1.61 : 1for a side lobe level of -20 dB.
(e) Dolph-Chebyshev
Current amplitude distribution,1 : 2.41 : 3.14 : 2.41 : 1, with a side
lobe level of -30 dB.
D 4.22
HP 26.4
SLL 30 dB
== °
= −
180° 0°
1.000.75
0.500.25
D 4.68
HP 23.6
SLL 20 dB-
== °
=
Fig. 3-23 (continued)
We can draw a general conclusion from the foregoing examples that applies to antennas in general:
As amplitude taper increases:
Beamwidth increases
Directivity decreases (as a consequence of beamwidth increasing)
Sidelobes decrease
Current envelope:
Pattern:
Directivity of nonuniformly excited, isotropic element arrays
General case of unequally spacings and nonuniform phasings
Equal spacings and broadside operation
(3-91)
(3-92)
Spacings a multiple of a half-wavelength and broadside
(3-93)
( ) ( )( )
m p
N
k
N Nm pj
m pm p m p
A
Dsin z z
A A ez z
k
α α β
β
−
− −−
⎛ ⎞⎜ ⎟⎝ ⎠=
⎡ ⎤−⎣ ⎦−
∑
∑∑
21
=0
1 1
=0 =0
( )( )
0,
N
kk
n nN N
m pm p
A
D z ndm p d
A Am p d
αβ
β
−
− −
⎛ ⎞⎜ ⎟⎝ ⎠= = =
⎡ ⎤−⎣ ⎦−
∑
∑∑
21
=0
1 1
=0 =0
sin
( ) , . . .
N
nn
N
nn
A
D d ,A
λλ
−
−
⎛ ⎞⎜ ⎟⎝ ⎠= =∑
∑
21
=01
2
=0
2
C. Inclusion of Element EffectsPrinciple of Pattern Multiplication: The pattern of an array (array pattern, F) consisting of similar elements is the product of the pattern of one of the elements (the element pattern, ga) and the pattern f the array of isotropic elements with the same locations, relative amplitudes and phases as the original array (the array factor, f).
Pattern F
Element pattern ga
Array factor f
F(θ,φ) = ga (θ,φ) f(θ,φ) (3-36)
Collinear elements
Example: Two collinear short dipoles
λ
2I Io = =11 1
| |z
θ
(a) The array.
Figure 3-17 Array of two half-wavelength spaced, equal amplitude, equal phase, collinear short dipoles (Example 3-8).
Figure 3-18 A linear array of parallel line sources.
Elementpattern
Arrayfactor
Totalpattern
(b) The pattern.
Parallel elements
θsinπ
θ⎛ ⎞⎜ ⎟⎝ ⎠
cos cos2
π
θ θ⎛ ⎞⎜ ⎟⎝ ⎠
sin cos cos2
x
z
γ
θ
y
Parallel half-wave dipoles
For a half-wave dipole along z-axis
z
For an array of parallel half-wave dipoles it is best to orient the elements along the x-axis. Then the element pattern is expressed as
x
z
(2-8)
(3-68)
(3-69)
( ) half wave dipole
π θθ
⎡ ⎤⎣ ⎦ −cos /2 cos
sin
( ) ( )
( )( )
a
a
g
cos
g ,
π γγ
γ
γ θ φ γ θ φ
π θ φθ φ
θ φ
⎡ ⎤⎣ ⎦=
=
⎡ ⎤⎣ ⎦=
2 2
2 2
cos /2 cos
sin
sin cos sin = 1- sin cos
cos /2 sin cos
1- sin cos
Prob. 3.3-2
From (2-7) ( )
π⎛ ⎞⎜ ⎟⎝ ⎠=a
cos cosθ2
g θsinθ
From (3-13)
So
(Fig. 2-5b) (Fig. 3-6c)
ga x f F
z z z
=
π2
1 1λ
( ) ( )f π=θ cos cosθ
( ) ( ) ( ) ( )
π
π θ
⎛ ⎞⎜ ⎟⎝ ⎠= =a
cos cosθ2
F θ g θ f θ cos cossinθ
• Method used in practice to produce a single endfire beam
Problem 3.7-7 uses array theory to find the patterns
x y
z
Ground plane
λ
4
Image theory solution The array factor is that of Example 3-2
-1 -11 1
x y
λd =
2λ
d =2
yz-plane (arrayfactor)
xz-plane (includingλ/2 dipole effect)
There is no general exact formula for the directivity of arrays includingthe element pattern. The following often- quoted approximate directivityformula must be used with caution
( ) ( )e iD D D≈ = =1.5 4 6
e
e
i
D D D
D directivity of a single element
D directivity of the array with isotropic elements
≈
=
=
i
Example: 4-element, broadside array of collinear short dipoles with spacing d = λ/2
(3-83) gives D = 5.6, an exact answer
• Directivity of arrays of real elements
d 0.72λ=
L2λ
= ( )
e i
From code
D 7.75 dBi d 0.72
5.6 dBd
Approximate directivity
D D D 1.64(5.4) 8.9, using Fig. 3-20
9.5 dB 7.3 dBd
= =
=
=
λ
≈ = =
=
• Base Station Collinear Arrays
The tower enhances the gain by making
pattern more directive
Base station with elements in opposing pairs and clocked90 degrees around the towerto produce nearly anomnidirectional pattern
Feed network
1 2 m N
D. Mutual Coupling
There are three mechanisms responsible for mutual coupling:Direct free space coupling between elements
Indirect coupling due to scattering by nearby objects
Coupling through the feed network
In many arrays the elements are impedance matched to the feed network and feed coupling can be ignored. Then the array can be modeled with independent generators, leading to the conventional circuit N port representation.
where the mutual impedance is
and reciprocity has been assumed through Zmn = Znm
Figure 3-26 (a) Mechanisms for coupling between elements of an array.
1 11 1 12 2 1N N
2 12 1 22 2 2N N
N 1N 1 1N 2 NN N
V Z I Z I Z I
V Z I Z I Z I V Z I Z I Z I
= + + +
= + + +••
= + + +
K
K
K
mmn
m
VZ
I iwith I 0 for all i except i = n= =
The input impedance of the mth element in an array with all elements activeand mutual coupling included is
m 1 2 Nm m1 m2 mN
m m m m
V I I 1Z Z Z Z
I I I 1⋅⋅⋅⋅⋅⋅⋅⋅= = + + + (3-103)
Note that active impedance depends on mutual impedances between elementsas well as the excitations of all elements. This dependence includes the
current phases and thus scan angle in phased arrays.
The effects of mutual coupling include:
• The impedance of an element in an array differs from its free space value and dependson that array scan angle (element phases) and the element location.
• The pattern of an element is changed from its isolated pattern and depends on arrayposition.
• Polarization characteristics deteriorate.
mV
mZmI
gmV
gmZ
This is often called active impedance or driving point impedance.
Current generatorVoltage generator (loaded)
0
-10dB
-20
φ = 180° φ = 0°
Figure 10-27 Linear array pattern with main beam steered to φo = 45° and ideal current generators (solid curve) compared to patterns from an array with voltage generators for 72-Ω loaded voltage generator excitations (dashed curve).
Also see: D. Kelley and W. Stutzman, “Array antenna pattern modeling methods that include mutual coupling effects,” IEEE Trans. On Ant. And Prop., Dec. 1993.
Example: Mutual coupling effect on a 12-element, half-wave spaced linear array
y
z
x
x
180° 0°
θo= 90°90°
0.250.50
0.751.00
(a) θo= 90°
z
(b) θo= 90°
180° 0°
θo= 75°90°
0.250.50
0.751.00
(c) θo= 75°
180° 0°
θo= 30°90°
0.250.50
0.751.0
(d) θo = 30° (bifurcated pattern)
180° 0°
θo= 0°90°
0.250.50 0.75
1.0
(e) Endfire (θo = 0°)
z
(f) Endfire (θo = 90°)
Figure 3-32 Example of phase-scanned patterns for a five-element linear array alongthe z-axis with elements equally spaced at d = 0.4λ and with uniform current magnitudes for various main beam pointing angles θo.
E. Phased Arrays
Important point to remember:The array factor scans inside the envelope of the fixed element pattern
Example: Linear array of four broadside elements spaced 0.7λ apart. The elementpattern is g(θ) = (cos θ)2.
Broadside operation Scanned 30° off broadsideFmag(θ)
g(θ)
1
0.8
0.6
0.4
0.2
0-90-80-70 -60-50 -40-30-20 -10 0
1
0.8
0.6
0.4
0.2
0-90-80-70 -60-50 -40-30-20 -10 0 4010 20 30 50 60 70 80 90 4010 20 30 50 60 70 80 90
θ θ
• Basic Feed Types
(a) Parallel, or corporate, feed. (b) Series feed.
Primarytransmittingantenna
Pickupantenna
Secondarytransmittingantenna
(c) Space feed. (d) Parallel-series feed.
Figure 3-33 Types of array feed networks.
Mounted on top of aircraft such as E-3A, E-2C for aerial surveil-lance and detection of bombers and low flying fighters coming inover north pole
First operational radar antenna with very low sidelobes: -40 dBSlotted waveguide array with 4000 slotsScanned in vertical plane using ferrite phase shiftersRotated for azimuth coverageNext generation: phased array conforming to the aircraft
Phased array example: AWACS (Airborne Warning and Control System)
E-2C
• Beam switched scanning
1 x 4 Switch
1 x 4 Switch
RotmanLens or
Butler Matrix
ERP = PTGT = GePs
(a)
(b) (c)
43 2 1
Switched antenna system vs linear array configurations: (a) switched antennas;(b) multiple-beam array; (c) steered-beam array.
[Microwave Journal, January 1987]
oGe sP P=
sP
sPsP
oG
1 2 3 4
eP oG se
PP
4=
se
PP
4=
T T o o
10 Log N 6 dB for N 4
ERP P G NG NP
=
=
+=
= ⋅
s s4G P=
• Digital Beam Forming
ReceivingAntenna
Array
Beams
CalibrationTone
WeightsController
DigitalBeamformer
RX
RX
RX
ADC
ADC
ADC
Directions of Look
. .
1 1.5 2 2.5 30
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
90
41.8
25.4
14.5
6.4
0
Max
imum
Sca
n A
ngle
Nor
mal
ized
Ele
men
t Spa
cing
(d/λ)
Bandwidth (f/f )L
1
Sinuous
Foursquare
Spirals
• Scanning arrays of wideband elements[Stutzman and Buxton, Microwave Journal, Feb. 2000.]
• The future for phased arrays- Wideband, multifunctional arrays will be used- Intelligence will be integrated with arrays, creating “smart arrays” that can
adapt to changing conditions and faults- Radiating elements will be printed, giving low cost and uniform geometrical
construction (see figure)- Feed networks will make use of integrated fabrication techniques
such as MMIC.- Elements and feeds will be integrated together- Beam steering:
Low cost phase shifters: MEMS, Ferroelectric, . . .Photonic feedsDigital beam forming will be very popular as RF and DSP module
performance and cost improve
2x2 array of Foursquare elements
capable of 2:1 bandwidth and dual polarization
Fourpoint element
5. SYSTEM CONSIDERATIONS
• Friis Transmission Equation• Propagation in real links• Factors in selecting an operating
frequency
• Factors in operating frequency selection
– Propagation and link budget considerations• VHF and below for long distance, narrow bandwidth• UHF and above for wide bandwidth• Above 10 GHz, atmospheric losses are high
– Antenna considerations• Very long distance point-to-point communications
require high frequencies to enable large antenna gains
– Regulatory issues• Must use allocated bands• Licensed vs. unlicensed bands
6. WIRELESS APPLICATIONS
• Base Station Antennas for Land Mobile
• Antennas for Satellite Communications
• Vehicle Antennas
• Antennas for Personal Communications
• UWB– Some Concepts
• Radiation Safety
Base Station Antennas for Land Mobile Radio
• Cell Coverage Types
OmnidirectionalSectorized
Smart antenna thatforms beams on users
• Omnidirectional pattern base station antennas
– Pattern is constant in azimuth and narrow in elevation
– Usually realized with collinear array of dipoles
Example: Cellular base station
Antel Cellular Base Station Antenna
870-970 MHzCollinear dipoles136 in long10 dBd gain1.25 deg downtilt
• Sector base station antennasTypical 120 deg sectors, VP
Polarization diversity120 deg sectors, dual slant 45 deg LP
• Sector (“panel”) antennas– Elements
• Dipoles in front of a ground plane• Log periodic dipole (LPDA) and LPDA vees• Patches• Fourpoint antenna (VT) covers both cellular and PCS
with dual polarization
– Considerations• Bandwidth (VSWR<2)• Power handling• Intermodulation products
DB Products LPDA vee antenna
• A new wideband base station antenna developed at
VTAG:– Minimum number of antennas on tower
– Dual-polarized for diversity
– Multi-functional capability (800 ~ 2200 MHz)
– Low profile and compact
– Printed antenna on a PCB
Front view Tuning plate on back
Fourpoint Antenna Data
AMPS, GSM, DCS, PCS, etc
Measured Radiation PatternsMeasured Radiation Patterns
900 MHz 1800 MHz• HPBW: 60° ~ 80 °• Low cross-pol, less than -30 dB
E-planeH-plane
• Satellite communications antennas
Satellite servicesFSS – Fixed Satellite Service
[gateways, VSATs]BSS – Broadcast Satellite Service (DBS, DTH)Mobile (Iridium, Orbcom, Inmarsat)
Gain of spacecraft antenna Global coverage 19 dBUS coverage 34 dB
Ground station antennasReflectors are used above a few GHz
Small offset reflectors for VSATLarge, dual reflectors for gateways
Direct Broadcast systemfrom DirecTV manual________________________12.2 -12.7 GHz downlink
to user17.3-17.8 GHz uplink from
gatewayDual circularly polarized
Vehicular Antennas • Broadcast reception
Traditional 31” (0.003 λ at AM) fender mount whip antennais vanishing.
New cars have mostly on-glass antennas
Example of a Ford rear windowglass antenna
• Two-way land mobile vehicle antennasVHF and below
Short monopoleQuarter-wave
monopole
Example quarter-wavemonopole
UHF Quarter-wave monopole5/8 over ¼ wavelength
Example 5/8 over¼ wavelength
• Aircraft antennas
Example: Commercial MD-80 airplane
• Antennas for fixed wireless– Access points and terminals
Omnidirectional antennasCollinears for access pointsStubby or planar antennas for terminals
High gain (20 dB or more) – reflectorsModerate gain
YagiStub loaded helix antenna
75% volume reductionCircularly polarized
Example; Stub loadedhelix antennawww.frc-corp.com
• Antennas for personal communicationsVHF
Short monopoleLoops, small and/or loadedNormal mode helix
UHFMonopoleNormal mode helixPatchInverted-L Planar inverted-LEmbedded
Perhaps the most popular antenna for cell phones is the stubby antenna with an extendable wire antenna
Nokia Patent5,612,704
• Inverted-L family of antennas
Inverted-LInverted-F Dual
Inverted-F
PlanarInverted-F
43WC PIFA
12Dipole
8PIFA
4DIFA
2IFA
1Patch
Bandwidth
(%)
AntennaWideband Compact PIFA
VT patent 6,795,028
UWB Antennas
TEM Horn Ridged Horn BiCone
Tapered Slot (Vivaldi) Impulse Radiating Antenna (IRA)
Half-Disk
PICA & VSWR
2 4 6 8 10 12 14 16 18 201
1.5
2
2.5
3
3.5
4
4.5
5S imulation Meas urement
Typical Responses – TEM Horn
0 2 4 6 8 10 12 14 16 18 20-40
-30
-20
-10
0Return Loss
Frequency (GHz)
Am
plitu
de (
dB)
0 2 4 6 8 10 12 14 16 18 20-400
-200
0
200Phase - Delay Phase
Frequency (GHz)
Pha
se (
degr
ees)
0 2 4 6 8 10 12 14 16 18 20-100
-50
0
Frequency Response s21
Frequency (GHz)
s 21 (
dB)
0 2 4 6 8 10 12 14 16 18 20-1
0
1
2x 10
9 Impulse Response s21
Time (nsec)
Am
plitu
de (
s-1)
Reflection Transmission Link
Phase Transient Transmission
Radiation Safety & Interference
• SAR – Specific Absorption Rate– Power per area absorption
• HAC – Hearing Aid Compatibility– Buzzing and related noise in Hearing Aid
• System Interference and Cross-Modulation
Facilities
INSTRUMENTATION
•ANTCOM 7+1 axis near field –far field scanner
•Agilent 8510, 8511, 8530 Network Analyzer
Measured Near Field Pattern
Calculated Far Field Pattern
For those interested in an in-depth antennas short course
ANTENNAS: Principles, Design, and Measurements
July 17-20Albuquerque, NM
antennacourse.com