### Information and Coding Theory - School of Electronic, Electrical and

```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
• Beamwidth; directivity; sidelobe levels
• Efficiency; gain
• Polarisation
• Impedance
• Bandwidth
• Vector effective length and equivalent area
• Antenna temperature
16
• A mathematical and/or
graphical representation
of the properties of an
antenna, usually the
spatial direction
coordinates sufficiently
far from the antenna
• Is polarisation specific
• Spherical polar
coordinates are always
used
17
Linear pattern
Polar pattern
18
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
19
pattern
H-plane
E-plane
20
• 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
– High reactive wave impedance
– High content of non-propagating stored
energy near the antenna
•
– Fields are predominantly in-phase
– Wavefronts are not yet spherical; pattern
varies with distance
•
– 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
22
Reminder on angular units
For the whole sphere,

2 
2

0 0
0
0
  sin  d d   d  sin  d
 2    cos  0  2     1  1

 4 Sr
23
• Poynting vector S  E  H Wm2
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 
2 
 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
Dmax
U max 4 U max


U0
D  dB  10log10  Dmax  dimensionless  
25
Directivity
• Isotropic antenna Umax  Uavg  D  1 or D  0dB
• Current element L << λ U  ,   Umax sin2 
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
4U max 4U max
3


 Dmax  or D  1.76dB
8
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  
 2U max 
 d
sin 
0
2 

2
 2U max  1.22
Dmax
4U max
4U max


 Dmax  1.64 or D  2.15dB
1.22  2U 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 cos3dB 
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 

1r2 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
29
Antenna efficiency, ηant
• In an antenna, we
experience reduction in
– 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 cd
2
Typical antenna efficiency values
Dipole ηant ~ 98%
Patch antenna ηant ~ 90%
Mobile phone PIFA ηant ~ 50%
– The latter two are grouped
under the term antenna rad  cd 
Pin
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
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
34
Polarisation
OA
Axial ratio, AR 
OB
1  AR  
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 jt 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 jt 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 jt e  jk0 z
E0 x  E0 y ,    n , or

E0 x  E0 y ,     2n  1

2
36
Polarisation
•
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
(Zg = Rg + jXg)
(Zrx)
a
Vg
RL
Ig
Rg
Rr
Xg
b
Gg
Bg
Gr
b
GL
BA
Norton equivalent
circuit (suitable for
loop, etc.)
Va
Ia
Rrx
Rr
Xrx
b
XA
a
Ig
Thevenin equivalent
circuit (suitable for
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
• 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
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
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
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