Introduction to Antennas

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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: c.constantinou@bham.ac.uk

Recommended textbook




Constantine A.
Balanis
,
Antenna Theory:
Analysis and Design
, 3
rd

Edition, Wiley
-
Interscience
, 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


Wideband


Size dictates lowest
frequency of operation

6

1000 ft diameter; 50 MHz to 10 GHz

chip size = 2 x 1 mm
2
; 60 GHz antenna

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

Source: MIT Open Courseware

How does it work?


radiation

13

Source: MIT Open Courseware

How does it work?


radiation

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

17


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
©

Radiation pattern

18

Polar pattern

Linear pattern

Source:
C.A.
Balanis
©

Radiation pattern

19

Linear pattern

Source:
C.A.
Balanis
©

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

Omnidirectional

antenna radiation
pattern

20

H
-
plane

E
-
plane

λ
/2 dipole antenna radiation pattern

Source:
C.A.
Balanis
©

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 (
E
θ
/
H
φ

= 120
π

=
377
Ω
)


Power flow is real; no stored energy


Field regions have no sharp boundaries

22

Source:
C.A.
Balanis
©

Reminder on angular units

23

Radians

Steradians

For the whole sphere,







2 2
0 0 0 0
0
sin sin
2 cos 2 1 1
4 Sr
d d d d
  

  
  

 
       

   
Source:
C.A.
Balanis
©

Radiation power intensity and density


Poynting

vector



Time
-
averaged
Poyting

vector



Radiation power density



Radiation intensity



Total radiated power

24

2
Wm

 
S E H
* 2
1
Re Wm
2

 
 
 
S E H




2
m
,
W
W



S


2
rad avg
2
2
*
rad
0 0
1
ˆ
Re.
2
ˆ
..
sin
r
r
P P d r d
P r d d


 
 

 
 
  
 


 
 
E e
S e
H
A S




2
,W/Sr
U r W


Directivity

25













avg rad
max max
max
0 rad
10 max
,4,
,
4
dB 10log dimensionless
U U
D
U P
U U
D
U P
D D
  


 
 

Directivity


Isotropic antenna



Current element
L <<
λ

26

max
1or 0dB
avg
U U D D
   


2
max
,sin
U U
 



2
3 2
rad max max
0 0 0
1
2
max max
1
sin 2 sin sin
8
2 1
3
P U d d U d
U u du U
 
   



 
  
  

max ma
ma
x
max
rad
x
max
3
1.76dB
2
4 4
8
3
U U
D
D
U
D
P
or
 

 
  
Directivity


Half wave dipole
L =
λ
/2

27





2
2
max
cos cos
,
sin
U U




 

 
 




2
2
2
rad max
0 0
2
2
max
0
max
cos cos
sin
sin
cos cos
2
sin
2 1.22
P U d d
U d
U








 


 

 
 

 
 

max max
max
rad max
max
4 4
1.22
1.6
2
4 2.15dB
U U
D
P U
D or D
 

  

 
Beamwidth

28


Current element
L <<
λ


The half
-
power angles in E
-
plane are given by,







Halfwave

dipole


a similar numerical calculation for the two
roots of



2
max
,sin
U U
 





2
3dB max max 3dB
3dB 3dB,1 3dB,2
3dB,2 3dB,1
1
,sin
2
1 3
sin,
9
4
2
0
4
U U U
HPBW
  
 
 




 
   
 
 


2
3dB
3dB
cos cos
1
sin
2
78
HPBW




 
Beamwidth

vs. directivity


The narrower the
beamwidth

of an
antenna, the bigger its directivity


For a
single main beam antenna


where
Ω
A

is the main
lobe half power beam solid angle


Kraus approximation for non
-
symmetrical main lobes




Tai & Pereira approximation for non
symmetrical main lobes


29

max
4
A
D

 
max
1 2 1 2
4 41,253
r r d d
D

 
 
max
2 2 2 2
1 2 1 2
32ln2 72,815
r r d d
D
   
 
 
Source:
C.A.
Balanis
©

Antenna efficiency,
η
ant


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




The latter two are grouped
under the term antenna
radiation efficiency

30



2
ant in
1
c d
 
  
rad
rad
in
c d
P
P
 
 
Source:
C.A.
Balanis
©

Typical antenna efficiency values

Dipole
η
ant

~ 98%

Patch antenna
η
ant

~ 90%

Mobile phone PIFA
η
ant

~ 50%

Antenna Gain

31













in
max max
10 max
4,
,,
dB 10log dimensionless
a
a
U
G D
P
G D
G G
 
  

 


Antenna Absolute Gain







2
abs in
,1,
a
G D
  
  
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

34

Source:
C.A.
Balanis
©

Polarisation

35

Source:
C.A.
Balanis
©

1
OA
AR
OB
AR

  
Axial ratio,
Polarisation


Linearly polarised uniform plane wave (
E
0
x

and
E
0
y

real)




Circularly polarised uniform plane wave (+/
-

corresponding to
positive/negative
helicity
)




Elliptically polarised uniform plane wave (+/
-

corresponding to
positive/negative
helicity
;
E
0
x

and
E
0
y

real)

36







0
0 0
ˆ ˆ
,,,Re
jk z
j t
x x y y
x y z t E E e e


 
E e e






0
0
ˆ ˆ
,,,Re
jk z
j t
x y
x y z t E j e e


 
E e e






0
0 0
ˆ ˆ
,,,Re
jk z
j j t
x x y y
x y z t E E e e e
 

 
E e e


0 0 0 0
,,,2 1
2
x y x y
E E n E E n

  
      
or
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 3
rd

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

38

generator

(
Z
g

=
R
g

+
jX
g
)

receiver

(
Z
rx
)

Thevenin

equivalent
circuit (suitable for
electric radiators, e.g.
monopole, dipole, etc.)

Norton equivalent
circuit (suitable for
magnetic radiators, e.g.
loop, etc.)

R
L

X
A

R
r

R
g

X
g

V
g

a

b

I
g

R
L

X
A

R
r

R
rx

X
rx

a

b

I
a

V
a

I
g

G
g

B
g

G
r

G
L

B
A

a

b

G
rx

B
rx

G
r

G
L

B
A

a

b

I
a

Impedance


The antenna operation is characterised by an impedance
Z
A


An equivalent radiation resistance,
R
r


A loss (
ohmic

and dielectric) resistance,
R
L


A reactance,
X
A


When connected to a generator, usually via a transmission
line, the usual transmission line and circuit theories apply


Radiated power


Maximum power transferred from generator to antenna
(maximum power transfer theorem)



Half of generator power is consumed
intenally
, other half is
shared between antenna losses and antenna radiation

39

2
1
2
r g r
P I R

&
A r L g A g
R R R R X X
    
Impedance

40









2
2
2
2
2
2
8
8
;
1
8
4
g
r
r
r L
g
L
L
r L
r L g A g
g
r L g
r L
g
T g r L
r L
V
R
P
R R
V
R
P
R R
R R R X X
V
P P P
R R
V
P P P P
R R




   
  

   

Since
Total
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

41

rad
r
r L
R
R R



Antenna effective length


The voltage at the antenna
terminals is determined
from the incident field


The effective length is a
vector



When taking the maximum
value over
θ
,
φ

this becomes



For linear antennas

42



..,
i i
a OC e
C
V V

  

E dl E l
.
i
a e
V

E l
physical
e

l
Source:
C.A.
Balanis
©

Effective aperture area
A
e


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




P
T

is the power delivered to a matched load in
W


W
i

is the incident wave power density in
Wm

2


A
e

is the antenna effective aperture area in
m
2


For any passive antenna we can invoke the principle of
reciprocity to show that

43

T
e
i
P
A
W

2
4
Tx
Rx
e
G
A



Antenna aperture efficiency


For all aperture antennas



This allows us to introduce the concept of antenna aperture
efficiency




For aperture antennas


For wire antennas where the physical aperture is taken
to be the cross sectional area of the wire

44

physical
e
A A

physical
e
a
A
A


1
a


1
a

Friis

free
-
space transmission


From your propagation lectures, assuming matched antennas,




This expression is a statement of the principle of conservation
of energy coupled with the notions of antenna gain and
antenna effective aperture area

45

2
4
Rx
Tx Rx
Tx
P d
G G
P


 

 
 