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Chapter 3: Antennas for Wireless Systems 1
Terrestrial and Satellite-based Radio Systems 3-FS-antennas.doc
3. Antennas for wireless systemsVarious antennas are used depending on
the frequency range, e.g. 1) dipole antennas f < 2 GHz2) aperture antennas f > 1 GHz
the properties being required 3) omni-directional antenna diagram,e.g. line circuit stations in satellite mobile radio
4) very directional antenna diagram,e.g. receiving antenna for satellite-TV
5) polarization (linear or circular)
6) compactness7) cost8) steerable / scanning (mechanically or electronically)
Within the scope of this lecture we will focus on three types of antennas most often used inwireless communication systems (more types and the fundamental principles are given in theantenna lecture):1. aperture antennas ( high-gain antennas ) f > 1 GHz, G > 15 dB2. dipole antennas (crossed-dipole) f < 2 GHz, G < 15 dB3. antenna arrays
to scan the antenna diagram (tracking)to increase the directivity and resolutionfor multi-beams to increase the capacityfor interference suppression by space filtering
The antennas on board of a satellite serve for up-link signal receiving and for radiation of
down-link signals. The various types of antennas ranges from dipole antennas with omni-directional characteristics to antennas with a narrow beamwidth for high gain used for wide-distance links.
3.1 Aperture antennasUsually beam shaping of high-gain antennas is accomplished by reflectors, mostly parabolicreflectors. The antenna gain of a parabolic antenna in comparison to an isotropic radiator andthe 3-dB-beamwidth ( Half Power BeamWidth , HPBW ) respectively is given by
2
20 0 2 2
4 4
ap
e
rad t rad phy ap ap
A
DG D A a
with ap 0.3 0.8
64.65
4 180 57.3... 62.5 ap ap
c k HPBW
D D
in [deg],
where indicates the wavelength, D the reflector diameter and ap the aperture efficiency of the antenna. The latter consists of the aperture taper efficiency t and the radiation efficiency
rad of the antenna and usually the losses for horn- and reflector antennas can be neglected( rad 1):
t = 1 for constant distribution along the aperture t 0.8 for cos-distribution along the aperture t 0.6 for cos 2-distribution along the aperture
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Chapter 3: Antennas for Wireless Systems 2
Terrestrial and Satellite-based Radio Systems 3-FS-antennas.doc
Example: Parabolic reflector with ap = 0.6 for 12 GHz.
D in m 0.4 0.6 0.8 1 2 5 10 20 30 D/ 16 25 32 40 80 200 400 800 1200G in dB 31.8 35.3 37.8 39.8 45.8 53.7 59.8 65.8 69.3
HPBW
in deg4.38 2.9 2.2 1.75 0.88 0.36 0,18 0.091 0.063
The relation D/ is the decisive parameter (value?) in above equations, because the gainfactor is proportional to ( D/ )2 and the beamwidth is inversely proportional to D/ .
Examples of area coverage:
The area coverage can be determined by the following approximation, where the satelliteantenna with diameter D1 produces a footprint (area coverage) with diameter of about a1 onEarth for small HPBW .
21
11
D
G ap and 111
57.3 ap
HPBW D
d a HPBW 11tan 1
11
57.3180
ap
a d D
for small HPBW 1
A n
t e n n a g a i n
[ d B ]
1.5 GHz
4 GHz
50 GHz30 GHz
12 GHz
100 GHz
Aperture diameter [m]1.5 2 2.5 3 3.50.5 10
0
70
20
10
30
60
50
40
0.6ap
2
10 lg ap D
G
H a l
f - P o w e r B
e a m
W i d t h [ d e g
]
0 0.5 1.0 1.5 2.0 2.5 3.0
Aperture diameter [m]
1.5 GHz
4 GHz
12 GHz
30 GHz
50
40
30
20
10
0
157.3
ap
HPBW D
6.0ap
H a l
f - P o w e r B
e a m
W i d t h [ d e g
]
0 0.5 1.0 1.5 2.0 2.5 3.0
Aperture diameter [m]
1.5 GHz
4 GHz
12 GHz
30 GHz
50
40
30
20
10
0
157.3
ap
HPBW D
6.0ap
Fig. 3-1: Gain and half-power beamwidth of aperture antennas.
D1
D2
Ellipticalreflector
Feed horn
HPBW 1 HPBW 2
3 dB gaincontour
Service area=Required flux density (dBW/m 2)
at given frequency and polarization1 21 2
57.3 57.3; ap ap
HPBW HPBW D D
22
1 1 21 2
57.3 apG D D HPBW HPBW Earth
Satellite
Fig. 3-2: Elliptically shaped area coverage on Earth by anelliptically shaped reflector antenna.
Sat 1Area
coverage
HPBW 1a 1
Earth
d
d a
HPBW 11 )tan(
d a
HPBW 1
1 for small HPBW 1
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Chapter 3: Antennas for Wireless Systems 4
Terrestrial and Satellite-based Radio Systems 3-FS-antennas.doc
Fig. 3-4: Parabolic reflector antennas.
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Chapter 3: Antennas for Wireless Systems 5
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Fig. 3-5: Cassegrain antenna.
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Chapter 3: Antennas for Wireless Systems 6
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Fig. 3-6: Earth station antenna (Cassegrain).
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Chapter 3: Antennas for Wireless Systems 7
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Fig. 3-7: Antenna requirements.
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Chapter 3: Antennas for Wireless Systems 8
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3.2 Dipole antennas
Ideal dipole with uniform current distributionLet us first consider an ideal dipole or infinitesimal current element according to the figure
below, to be z-directed and placed in the origin of a co-ordinate system. It is ideal in the sense
that it has a very short length (incremental length) compared to the wavelength z Q
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Chapter 3: Antennas for Wireless Systems 9
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The average power density and average power of an ideal dipole are given by
,av r S (r, , )2 2
0 20 sin
4Q
r
z u I
r
and P rad =2
20 03
Q z I
.
Hence, the radiation resistance for an ideal dipole with uniform current distribution( /50), i.e. an input current I A = I 0 = const. along the length z Q is given by:
2 2
2, 02
2 280
3Q Qrad
rad u
A
z z P R
I
for /50 and a uniform current
distribution0.32 for /50Q z .
The Fig. 3-9 shows the far field of an ideal dipole, e.g. the angular variation of E and H over a sphere with constant radius r . An electric field probe antenna moved over the spheresurface and oriented parallel to E will have an output proportional to the normalized patternc( ) = sin . Any plane containing the z-axis has the same radiation pattern of sin since
there is no -variation in the fields due to the symmetry of the source. A pattern taken in oneof these planes is called a E-plane pattern because it contains the electric field vector E . A pattern taken in a plane perpendicular to the E-plane (the x,y-plane in this case) is an H-plane pattern because it contains the magnetic field H [Stutz]. The complete three-dimensional pattern for the ideal dipole is shown in Fig.3-9(d) . It is an omni-directional pattern inazimuth since it is uniform in the x,y-plane.Omni-directional antennas in azimuth arevery popular particularly in ground-basedmobile communications because of the time-and space-dependent angular (primarily -)variations of the incident wave of the mobilestation due to shadowing and multi-patheffects. The maximum directivity of theideal dipole is given by:
2
0, 00, 0 0 2
(( , ) 4
| ( , ) |u u
c D D
c d
=
0
22
0
sinsin
4
d d
=
0
3sin2
4
d
=
0
2
cos32
3cossin
2=
23
1.76 dB
This means, that in the direction of maximum radiation 0, the radiation intensity is 50%more than that which would occur from an isotropic source radiating the same total power.
Fig. 3-9: Normalized far-field pattern of the ideal dipole[Bal]: (a) Field components; (b) E -plane radiation pattern;(c) H -plane radiation pattern; (d) 3D-radiation pattern.
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Chapter 3: Antennas for Wireless Systems 10
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Crossed-Dipole Antenna (Ohmori page 101)
A dipole antenna with a half-wavelength ( /2) is the most widely used, e.g. in mobile satellitecommunications. A half-wavelength dipole is a linear antenna, whose current amplitudevaries one-half of a sine wave with a maximum at the center.
Far-field of an
2
-dipole: 0
02
( )
cos cos
2 sin
P jkr
P
c
I e E j
r
; 0/ H E
As a dipole antenna radiates linearly polarized waves, two crossed-dipole antennas have beenused in order to generate circular-polarized waves. The two dipoles are geometricallyorthogonal ( x and y axes in the Fig. 3-10 ), and equal amplitude signals are fed to them with
/2 in-phase difference.
Characteristic of a crossed-dipole antenna 1 2, , ,c c c dipole#1: along the x-axis rotational symmetrical around
= angle between length axis and P r only dependent from
1
2cos cos( )sin
c
dipole#2: along the y-axis rotational symmetrical around = angle between length axis and P r only dependent from = 90 -
2
2 2cos cos cos sin( )sin cos
c
Overall pattern of the crossed-dipole with equal amplitudes but with2
in-phase difference:
2 2cos cos cos sin
,sin cos
c j
The patterns 1c and 2c are indicated in by the thick and thin lines respectively,within a coordination system. The radiation pattern of a crossed-dipole antenna is alsoindicated by the thick line in Fig. 3-10 , which is nearly omni-directional in the horizontal
plane. A dipole antenna needs a balun to be excited by coaxial cables, which is an unbalancedfeed line. Further, a 3-dB hybrid (power divider) is generally used to feed a cross-dipole inorder to be able to feed the same power a phase difference of /2 for each dipole element.A crossed-dipole antenna has a maximum gain in the boresight direction ( z axis direction in
Fig. 3-10 ). In mobile satellite communications, especially in land-mobile communications,elevation angles to the satellite are not 90 except immediately under the satellite. In order tooptimize the radiation pattern, a set of dipole antennas are bent toward the ground as shown in
y
x
I (zQ)2
r PQ
r P
z Q P
HPBW78
Z Q Angle between length axis of the dipoleand far-field point P.
0
0
2 1 for 0 2
( )2
1 for 02
Q z Q
Q z Q
z u I z
I z z
u I z
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Chapter 3: Antennas for Wireless Systems 11
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Fig. 3-11 , which is called a drooping dipole antenna. The crossed drooping dipole is one of the most interesting candidates for land-mobile satellite communications, where the requiredangular coverage is narrow and almost constant in elevation. By adjusting the height betweenthe dipole elements and the ground plane and the bending angle of the dipoles, the gain andelevation pattern can be optimized for the coverage region of interest. Fig. 3-11 shows theradiation patterns for the antenna designed by Jet Propulsion Laboratory (JPL) which is to be
used over the entire continental Unites States (CONUS). It has a 4-dBi gain [8].
Fig. 3-10: Radiation patterns of a dipole, a cross-dipole, and thecoordination system.
Fig. 3-11: (a) Crossed drooping dipole antenna and (b) its radiation pattern.
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Chapter 3: Antennas for Wireless Systems 12
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3.3 Phased-Array Antennas
Fig. 3-12: Linear phased array with four dipoles.
Several antennas can be arrayed in space to make a directional pattern or one with a desiredradiation pattern. This type of antenna is called an array antenna, which consists of more thantwo elements. Each element of an array antenna is excites by equal amplitude an phase, andits radiation pattern is fixed. On the other hand, the radiation pattern can be scanned in space
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Chapter 3: Antennas for Wireless Systems 13
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by controlling the phase of the exciting current in each element of the array. This type of antenna is called a phased-array antenna [13], which has many advantages in terms of mobilesatellite communications such as compactness, light weight, high-speed tracking
performance, and potentially low cost.Arrays are found in many geometrical configurations. The most typical type in mobilesatellite communications is the planar array, in which elements are arrayed in a plane to scan
the beam at both azimuth and elevation angles to track the satellite. Fig. 3-12 shows the mostsimple linear phase array that is composed of four elements, which have the same electricalcharacteristics, and are arrayed at equal spaces of d along the x axis.In Fig. 3-12, if each element is excited equally in amplitude, but with different phases, the far field of the array antenna is given by
1 2 1 23 3
2 2 2 2sin sin sin sind d d d
jkr jk jk jk jk e E c e e e e
r
1 2 1 23 3
2 2 2 2sin sin sin sind d d d
jkr jk jk jk jk e E c e e e e
r
1 232 22 cos sin cos sin jkr
kd kd e cr
42 jkr e
c AF r
where the phase center is at the coordinate origin, and c( ) is the radiation pattern of theelement. The 1 and 2 including their signed are the values of phase shifters, as shown in Fig.4.15. the coefficient AF is called the array factor. The radiation pattern for the array antennais found by multiplying the radiation pattern of the element antenna and the array factor.
The array factors AF 2 and AF 4 of linear arrays with two and four elements, excites by equal phase ( 1 = 2 = 0), whose spacing between elements is half a wavelength ( d = /2), are asfollows:
4 32 2cos sin cos sin AF
Figure 3-12 below shows patterns of array factors for the four-element linear array. The space between element is half a wavelength. The maximum value was obtained in the boresightdirection ( y axis).The array factor will reach maximum in direction 0 when cos( ) = 1are satisfied. This can
physically be explained by the fact that the phases of wave fronts become equal, as shown inFig. 3-12.
0 1 0 23
2 2sin sin ( 0, 1, 2, )kd kd n n
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Chapter 3: Antennas for Wireless Systems 14
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Therefore, in case of n = 0
1 02 sinkd and 2 0
32 sinkd
It is found that maximum gain can be obtained in the desired direction, and the beam can bescanned into a desired angle off the boresight direction. The radiation pattern of phased arrayantennas with four elements can be calculated by the following equation:
4 0 032cos sin cos sin sin sc sin
where 0 denotes the angle of scanned direction. Each element is assumed to benondirectional, and element spacing is half a wavelength ( d = /2).
Fig. 3-12 shows radiation patterns of phased array antennas for four-element linear arrays.The beam is scanned at an angle of 30 degrees.