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Introduction to Antennas
Dr Costas Constantinou
School of Electronic, Electrical & Computer Engineering
University of Birmingham
W: www.eee.bham.ac.uk/ConstantinouCC/
E: [email protected]
Recommended textbook
• Constantine A. Balanis, Antenna Theory:
Analysis and Design, 3rd Edition, WileyInterscience, 2005; ISBN:0-471-66782-X
– Chapters 1 & 2
2
Antennas
• An antenna can be
thought of as a
transition / transducer
device
• Two ways of describing
antenna operation
– Field point of view
– Circuit point of view
3
Antenna examples
• Wire antennas
– Monopoles
– Dipoles
– Arrays
4
Antenna examples
• Aperture Antennas
–
–
–
–
–
Reflectors
Lenses
Horns
Patches
Planar inverted F
5
Antennas
• Most antennas are
resonant structures
– Narrowband
– Size is inversely
proportional to frequency
of operation
• Travelling wave antennas
also important
1000 ft diameter; 50 MHz to 10 GHz
– Wideband
– Size dictates lowest
frequency of operation
chip size = 2 x 1 mm2; 60 GHz antenna
6
How does it work? – radiation
7
How does it work? – radiation
8
How does it work? – radiation
9
How does it work? – radiation
10
How does it work? – radiation
B
A
Sphere grows with time
(i.e. delay increases
with distance)
11
How does it work? – radiation
12
How does it work? – radiation
Source: MIT Open Courseware
13
How does it work? – radiation
Source: MIT Open Courseware
14
Antennas – TV aerial
• Radiation of power in space can be controlled by
carefully arranging the patterns of electron motion
• This is the same as their sensitivity to received signals
from different directions in space
15
Fundamental antenna parameters
• Radiation pattern; radiation power density;
radiation intensity
• Beamwidth; directivity; sidelobe levels
• Efficiency; gain
• Polarisation
• Impedance
• Bandwidth
• Vector effective length and equivalent area
• Antenna temperature
16
Radiation pattern
• A mathematical and/or
graphical representation
of the properties of an
antenna, usually the
radiation intensity vs.
spatial direction
coordinates sufficiently
far from the antenna
• Is polarisation specific
• Spherical polar
coordinates are always
used
Source: C.A. Balanis©
17
Radiation pattern
Linear pattern
Polar pattern
Source: C.A. Balanis©
18
Radiation pattern
Linear pattern
E plane is plane of electric field
H plane is plane of magnetic field
If field direction not known, do not use E or H plane
Source: C.A. Balanis©
19
Omnidirectional antenna radiation
pattern
H-plane
E-plane
λ/2 dipole antenna radiation pattern
Source: C.A. Balanis©
20
Radiation pattern definitions
• Isotropic antenna
– Radiates equally in all directions in space; physically
unrealisable
• Omnidirectional antenna
– Radiates equally in all directions in one plane only;
e.g. dipoles, monopoles, loops, etc.
• Directional antenna
– Radiates strongly in a given direction; has a principal
or main lobe, the maximum of which point in the
direction of the antenna’s boreside
– Can you guess what is meant by front-to-back ratio?
21
Field regions
•
Reactive near-field
– Phases of electric and magnetic fields are
often close to quadrature
– High reactive wave impedance
– High content of non-propagating stored
energy near the antenna
•
Radiative near-field (Fresnel)
– Fields are predominantly in-phase
– Wavefronts are not yet spherical; pattern
varies with distance
•
Radiative far-field (Fraunhofer)
– Electric and magnetic fields are in-phase
– Wavefront is spherical; field range
dependence is e-jkr/r
– Wave impedance is real (Eθ/Hφ = 120π =
377 Ω)
– Power flow is real; no stored energy
•
Field regions have no sharp boundaries
Source: C.A. Balanis©
22
Reminder on angular units
Radians
Steradians
For the whole sphere,
2
2
0 0
0
0
sin d d d sin d
2 cos 0 2 1 1
4 Sr
Source: C.A. Balanis©
23
Radiation power intensity and density
• Poynting vector S E H Wm2
1
• Time-averaged Poyting vector S Re E H* Wm 2
2
• Radiation power density W , S Wm 2
• Radiation intensity U , r 2W W/Sr
• Total radiated power Prad Pavg
2
Prad
S.dA
2
ˆ
S
.
e
r
r d
1
*
2
ˆ
Re
E
H
.
e
r
0 0 2
r sin d d
24
Directivity
U , 4 U ,
D ,
U avg
Prad
Dmax
U max 4 U max
U0
Prad
D dB 10log10 Dmax dimensionless
25
Directivity
• Isotropic antenna Umax Uavg D 1 or D 0dB
• Current element L << λ U , Umax sin2
Prad
2
0 0
0
3
2
U
sin
d
d
2
U
sin
sin d
max
max
8
2 U max 1 u du
U max
3
1
1
2
Dmax
4U max 4U max
3
Dmax or D 1.76dB
8
Prad
2
U max
3
26
Directivity
cos 2 cos
• Half wave dipole L = λ/2 U , U max
sin
2
cos 2 cos
Prad U max
sin d d
sin
0 0
cos2 2 cos
2U max
d
sin
0
2
2
2U max 1.22
Dmax
4U max
4U max
Dmax 1.64 or D 2.15dB
Prad
1.22 2U max
27
Beamwidth
• Current element L << λ U , Umax sin2
• The half-power angles in E-plane are given by,
1
U 3dB , U max U max sin 2 3dB
2
1
3
sin 3dB
3dB,1 , 3dB,2
4
4
2
HPBW 3dB,2 3dB,1 90
• Halfwave dipole – a similar numerical calculation for the two
roots of
cos 2 cos3dB
1
HPBW 78
sin 3dB
2
28
Beamwidth vs. directivity
• The narrower the beamwidth of an
antenna, the bigger its directivity
• For a single main beam antenna
Dmax 4 A where ΩA is the main
lobe half power beam solid angle
• Kraus approximation for nonsymmetrical main lobes
4
41, 253
Dmax
1r2 r
1d 2 d
• Tai & Pereira approximation for non
symmetrical main lobes
32ln 2
72,815
Dmax 2
2
2
1r 2 r 1d 22d
Source: C.A. Balanis©
29
Antenna efficiency, ηant
• In an antenna, we
experience reduction in
radiated power due to
– Reflection at the input
terminals (impedance
mismatch)
– Ohmic conductor losses (c) in
the antenna conductors
– Dielectric losses (d) in the
antenna dielectrics
ant 1 in cd
2
Typical antenna efficiency values
Dipole ηant ~ 98%
Patch antenna ηant ~ 90%
Mobile phone PIFA ηant ~ 50%
– The latter two are grouped
Prad
under the term antenna rad cd
Pin
radiation efficiency
Source: C.A. Balanis©
30
Antenna Gain
4 U ,
G ,
a D ,
Pin
Gmax a Dmax
G dB 10log10 Gmax dimensionless
Antenna Absolute Gain
G , 1 D ,
2
abs
in
a
31
Bandwidth
• Many properties vary with frequency and
deteriorate in value from their optimum values:
– Pattern bandwidth
•
•
•
•
•
Directivity/gain
Sidelobe level
Beamwidth
Polarisation
Beam direction
– Impedance bandwidth
• Input impedance
• Radiation efficiency
32
Polarisation
• Antenna polarisation refers to the orientation of the
far-field radiated electric field vector from the
antenna
– A vertical dipole radiates a vertical electric field
– A horizontal dipole radiates a horizontal electric field
– A general (e.g. horn) antenna with a vertical aperture
electric field radiates a vertical electric field in the E-plane
and H-plane only; everywhere else the electric field vector
is inclined to the vertical and changes with angular
direction
33
Polarisation
• The polarisation of an electromagnetic wave can be
– Linear (as in all previously discussed examples)
– Circular (e.g. using a helical antenna to transmit)
– Elliptical (e.g. circular after reflection from a lossy
interface)
• Circular and elliptical
polarisations have a
sense of rotation
– Positive helicity (or right hand, clockwise)
– Negative helicity
Source: C.A. Balanis©
34
Polarisation
OA
Axial ratio, AR
OB
1 AR
Source: C.A. Balanis©
35
Polarisation
• Linearly polarised uniform plane wave (E0x and E0y real)
E x, y, z, t Re E0 x eˆ x E0 y eˆ y e jt e jk0 z
• Circularly polarised uniform plane wave (+/- corresponding to
positive/negative helicity)
E x, y, z, t Re E0 eˆ x jeˆ y e jt e jk0 z
• Elliptically polarised uniform plane wave (+/- corresponding to
positive/negative helicity; E0x and E0y real)
E x, y, z, t Re E0 x eˆ x E0 y e j eˆ y e jt e jk0 z
E0 x E0 y , n , or
E0 x E0 y , 2n 1
2
36
Polarisation
•
The radiation pattern performance of
antennas is often specified in terms of
its co-polar and cross-polar
components
–
–
–
Detailed mathematical definition is
Ludwig’s 3rd definition of cross-polarisation
(A. Ludwig (1973), “The definition of cross
polarization,” IEEE Transactions on
Antennas and Propagation, 21(1))
Co-polar radiation pattern of an antenna is
measured with a suitably polarised probe
antenna which is sensitive to the “wanted”
polarisation
Cross-polarised pattern is measured for
linear polarisation by rotating the probe
antenna by π/2 around the line joining the
two antennas, or for circular/elliptical
polarisation by changing the probe
antenna helicity sign
37
Impedance
• Transmitting operation
• Receiving operation
generator
receiver
(Zg = Rg + jXg)
(Zrx)
a
Vg
RL
Ig
Rg
Rr
Xg
b
Gg
Bg
Gr
b
GL
BA
Norton equivalent
circuit (suitable for
magnetic radiators, e.g.
loop, etc.)
Va
Ia
Rrx
Rr
Xrx
b
XA
a
Ig
Thevenin equivalent
circuit (suitable for
electric radiators, e.g.
monopole, dipole, etc.)
RL
a
XA
a
Grx
Gr
Brx
GL
Ia
BA
b
38
Impedance
• The antenna operation is characterised by an impedance ZA
– An equivalent radiation resistance, Rr
– A loss (ohmic and dielectric) resistance, RL
– A reactance, XA
• When connected to a generator, usually via a transmission
line, the usual transmission line and circuit theories apply
2
1
• Radiated power Pr 2 I g Rr
• Maximum power transferred from generator to antenna
(maximum power transfer theorem)
RA Rr RL Rg & X A X g
• Half of generator power is consumed intenally, other half is
shared between antenna losses and antenna radiation
39
Impedance
Pr
PL
Vg
2
Rr
Rr RL
8
Vg
8
2
2
RL
Rr RL
2
Since Rr RL Rg ;
Vg
X A Xg
2
1
Pr PL
Pg
8 Rr RL
Total PT Pg Pr PL
Vg
2
4 Rr RL
40
Radiation efficiency
• We have come across radiation efficiency before, but now we
express it in circuit theory equivalent terms
• Describes how much power is radiated vs. dissipated in the
antenna
Rr
rad
Rr RL
41
Antenna effective length
• The voltage at the antenna
terminals is determined
from the incident field
• The effective length is a
vector
Va VOC Ei .dl Ei .l e ,
C
• When taking the maximum
value over θ,φ this becomes
Va Ei .le
• For linear antennas
le physical
Source: C.A. Balanis©
42
Effective aperture area Ae
• This is usually assumed to refer to the co-polar radiation
pattern on the boreside of an antenna
• The antenna effective aperture area is defined as a ratio
PT
Ae
Wi
– PT is the power delivered to a matched load in W
– Wi is the incident wave power density in Wm–2
– Ae is the antenna effective aperture area in m2
• For any passive antenna we can invoke the principle of
reciprocity to show that
GTx 4
2
Rx
Ae
43
Antenna aperture efficiency
• For all aperture antennas
Ae Aphysical
• This allows us to introduce the concept of antenna aperture
efficiency
Ae
a
Aphysical
• For aperture antennas a 1
• For wire antennas a 1 where the physical aperture is taken
to be the cross sectional area of the wire
44
Friis free-space transmission
• From your propagation lectures, assuming matched antennas,
PRx
4 d
GTxGRx
PTx
• This expression is a statement of the principle of conservation
of energy coupled with the notions of antenna gain and
antenna effective aperture area
2
45