lec3.ppt: Excell sheet representing the various parameters of antenna and radiation

Antenna Basics. The important parameters of antenna. Radiation resistance, Gain etc.

1. Definition of Antenna
•That part of a transmitting or receiving system that is designed to radiate or to
receive electromagnetic waves.
•A transducer between a guided wave propagation along a transmission
line/waveguide and an electromagnetic wave propagation in an unbounded medium
(usually free space), or vice versa.

2. Isotropic and Omni-directional radiator
•Isotropic:- A hypothetical, lossless antenna having equal radiation intensity in all direction.
•Omni-directional:- An antenna having an essentially non-directional pattern in a given
plane of the antenna and a directional pattern in any orthogonal plane.
2
4
t
P
r
r
P


For an isotropic radiator, the power density is
given by dividing the total radiated power
equally over the surface of the sphere
A typical example is the
wire dipole (short dipole) –
non directional in XY plane

3. Figure shows how
a wave is
launched by a
hornlike antenna,
with the horn
acting as a
transition
between the
waveguide and
free space.

4. Radiation
•Any conducting structure can launch waves – or radiate – but when the “structure”
is designed to radiate efficiently with directional and polarisation properties
suitable for the intended application – that “structure” is called an antenna.
•Regardless of antenna type – all involve the same basic principle that radiation is
produced by accelerated (or decelerated) charge.

5. What makes a short dipole?
Length L is very short compared to wavelength (L<<).
Carries uniform current I along the entire length L. To allow such
uniform current, we attach plates at the ends of the dipole as
capacitive load. However, we assume the plates are small that their
radiation is negligible.
The dipole may be energized by balanced transmission line.
However, it is assumed that the transmission line does not radiate.
The diameter “d” of the dipole is small compared to its length
(d<<L).
+q
-q
I
L
Thus a short dipole consist simple of a thin
conductor of length L with a uniform current I and
point charges q at the ends.
dq
I
dt


6. Retarded current

m
R
I I cos t-
c

  

  
  
What is retardation effect?
The electromagnetic waves have finite propagation times. Thus, if a current is flowing
along the short dipole, the effect of the current is not felt instantaneously at the field
point P, but only after an interval equal to the time required for the disturbance to
propagate over the distance R.
The effect observed at a distant point P from a given source at any instant t is due to a
current flowing at an earlier time which is,
Instead of 
m
I cost
Retarded
current
Retardation
time

7. Types of radiating structures

8. Field regions
Radiating near
field (Fresnel)
region
Reactive near
field region, or
Far field (Fraunhofer) region
antenna
No abrupt changes in
the field
configurations are
noted as the
boundaries are
crossed – but there
are distinct
differences between
the fields
Intermediate /transition region

9. Antenna Pattern and Antenna Parameter
•Our primary interest is in far-field which is also known as radiation field.
•The graph that describes the relative far-zone field strength versus direction at a fixed
distance from antenna is called the radiation pattern of an antenna, or antenna
pattern.

10. •In general, antenna pattern is 3-D, varying with ө and Φ in spherical coordinate system. Since
3-D pattern is very difficult to plot, therefore for simplicity we separate the 3-D pattern into
two parts.
•E-Plane Pattern: represents the magnitude of normalized field strength (with respect to the
peak value) versus ө for constant Φ. e.g. At a given R, E-field of Hertzian dipole is
independent of Φ and the normalized magnitude of E-field is
•This is the E-plane pattern function of Hertzian dipole. For any given Φ, the above equation
represents a pair of circles as shown below:
sinNormalized E


0
( ) sin
4
j R
Id e
E j
R


  





12. Typical H-patterns (in polar coordinate, rectangular coordinate, Decibel scale)

13. Characteristic Parameters of Antenna Pattern
•Width of main beam (beamwidth) :
The radiation lobe containing the direction
of maximum radiation. It is generally
taken to be the angular width of a pattern
between half-power, or -3(dB).
•In electric-intensity plots it is the angular
width between points that are or
0.707 times the maximum intensity.
•In the radiation pattern the beamwidth is
equal to:
•First null beamwidth is the angular width
beam between -10 (dB) or between first
nulls on either side of the main beam.
This
 determines the antenna's ability to
reject signals/interference from unwanted
directions.
1
2
2 1
3 dB Beamwidth= 

14. •Sidelobe levels: Sidelobe of a directive (non-isotropic) pattern represent regions of unwanted
radiation. They should have levels as low as possible.
•The level of the side lobes nearer to the main beam is larger than other lobes.
•Back lobe: It is a radiation lobe whose axis makes an angle of approximately 180
0
w.r.t the
main lobe of antenna. Usually it refers to a minor lobe that occupies the hemisphere in a
direction opposite to that of main lobe.
• A commonly used parameter to measure the over all ability of an antenna to direct the
radiated power in a given direction is called directive gain.
•Directive gain is defined in terms of radiation intensity.
•Radiation intensity is the time-average power per unit solid angle. or radiated power per
solid angle (radiated power normalized to a unit sphere).
•Radiation intensity , U, equals R
2
times the time-average poynting vector, P
av
•The total time-average radiated power is:
•Where dΩ is the differential solid angle,
2
(W/sr)
av
U R P
rad
P ds (w)
av
s s
P Ud     
sind d d  
*1
Re{ }
2
av
P E H 
 

15. •Directive gain:, G(ө, Φ), of an antenna pattern is the ratio of the radiation intensity
in the direction (ө, Φ) to the average radiation intensity:
•The directive gain of isotropic or Omnidirectional antenna (an antenna that radiates
uniformly in all directions) is unity. But practically there exists no isotropic
antenna.
•The maximum directive gain of an antenna is called the directivity of an antenna.
•In general, Directivity is given by

( , ) 4 ( , )
,
/4
D
r
s
U U
G
P Ud
    
 

 

max max
4
(Dimentionless)
av r
U U
D
U P

 
2
2
2
0 0
4 ( , )
(dimentionless)
( , ) sin
f
D
f d d
 
  
    


av
U

16. •For example: Find the directive gain and the directivity of a Hertzian dipole.
•The time-average poynting vector is given by:
•Radiation Intensity become,
•The directive gain can be obtained as follow:
•The directivity is the maximum value of G
D
(ө, Φ):
•Which corresponds to 10Log(1.5) or 1.76 (dB)
* *1 1
Re E H
2 2
av
P E H
 
  
 
2
2 2
02
( )
sin
32
av
Id
U R P   

 

2
2
2
2
0 0
4 sin 3
( , ) sin
2
(sin )sin
D
G
d d
 
 
  
   
 
 
( , ) 1.5
2
D
D G

 
( ) sin
4
j R
Id e
H j
R


 




0
( ) sin
4
j R
Id e
E j
R


  




2
2
2
0 0
4 ( , )
( , ) sin
f
D
f d d
 
  
    

 
Far-zone field due to E-dipole
( , )
av
U
U
 
OR

17. •A measure of antenna efficiency is the power gain. The power gain or simply the gain,
G
p of an antenna referred to an isotropic source is the ratio of its maximum radiation
intensity to the radiation intensity of lossless isotropic source with same power input.
•Due to the lossy nature of antenna as well as the nearby lossy structure including
ground, the radiated power is less than the total input power. We have
• The power gain of an antenna is then:
•The ratio of the gain to the directivity of an antenna is the radiation efficiency, η
r
•A useful measure of the amount of power radiated by an antenna is radiation resistance.
Radiation Resistance of an antenna is the value of a hypothetical resistance that
dissipate an amount of power equal to the radiated power when the current in resistance
equal to the maximum current along antenna. Naturally, a high radiation resistance is a
desirable property for an antenna.
i r
P P P 

max
4
p
i
U
G
P


(Dimensionless)
p r
r
i
GP
D P
 
21
2
r r
P I R

18. •Example: Find the radiation resistance of
a Hertzian dipole.
•For no ohmic loss, the time-average power
radiated by Hertzian dipole for an input
time-harmonic current with an amplitude
“I” is given by
•Using the expressions in red color, we get
•Since
•We obtain the radiation resistance of short
Hertzian dipole
*
( ) sin
4
j R
Id e
H j
R


 




2
* 2
0 0
1
sin
2
r
P E H R d d
 
 
  
0
( ) sin
4
j R
Id e
E j
R


  




22
2 3
02
0 0
2
2 2
2 2
0
( )
sin
32
( )
80
12 2
r
Id
P d d
Id I d
 
    

  
 

 
 
    
   


 
0
120
2
 





2
2
r
r
I R
P
2
2
80
r
d
R

 

 
 

Compare

19. •Consider, If dl=0.01λ, Rr =0.08Ω, an
extremely small value. Hence a short
dipole antenna is a poor radiator of
electromagnetic power
•Example: Now we will find the radiation
efficiency of an isolated Hertzian dipole
made of a metal wire of radius a, length d,
and conductivity σ.
•Let I represent the magnitude of current in
the wire dipole, then the ohmic power loss
is
•The radiation power is given by
•Radiation efficiency
•Loss resistance of metal wire in term of
surface resistance Rs
•The radiation efficiency of an isolated
Hertzian dipole become
21

2
P I R
 
21
2
r r
P I R
1
1 /
r r
r
r r r
P R
P P R R R R
  
  
  
2
2
80
r
d
R

 

 
 

0
s
, R
s
fd
R R
 
 
 
 
 
 


3
1
1
160
r
s
R
a d

 


  

  
  

20. •Suppose that a=1.8(mm), dl=2 (m), operating frequency f=1.5 (MHz), and σ(for
copper)=5.80x10
7
(S/m), we find that
•And
•Which is low. For low value of and in
•Result in low radiation.
2
22
80 0.079
200
r
R
 
  
 
 
0.079
58%
0.079 0.057
r
 

a

 
 
 
d

 
 
 

3
1
1
160
r
s
R
a d

 


  

  
  

21. Bandwidth
•The range of frequencies within which the performance of the antenna, with respect
to some characteristic, conforms to a specified standard
•Normally expressed as a fraction of centre frequency
•Normally used standards - Impedance bandwidth; Gain bandwidth; Radiation
pattern bandwidth; side lobe level; beamwidth; polarization; beam direction

22. Polarization (of an antenna)
•In a given direction from the antenna, the polarization of the wave transmitted by
the antenna
•Polarization of a wave describes the shape and locus of the tip of the E vector at a
given point in space as a function of time.
•General locus is ellipse – elliptically polarized
•Under certain conditions – ellipse becomes a circle – circular polarization, or
straight line – linear polarization.

23. Polarization of a wave
•When E field is traced in clockwise direction – right-hand polarization, otherwise
left-hand polarization
•Note that polarization rotation is opposite the direction of rotation of E field as a
function of distance at a fixed point in time
•Common usage is with linear polarization, vertical and horizontal