```Antenna Terminology
• Antenna is a connecting link between Tx
and free space or free space and Rx
• Operational Characteristics of system are
designed around directional properties of
the antenna.
• Can be used in
Omnidirectional Applications
Directional Applications
Point to Point communication
which radiates uniformly in all the
directions. It is also called
• It is a hypothetical lossless radiator with
• It is used as a reference antenna.
• A Point source of sound is an example
• Radiated Energy from an antenna is not
uniform in all the directions.It can be more
in one direction and less or zero in other.
• Energy radiated in a particular direction is
measured in terms of field strength at a
particular point which is at a particular
distance from antenna.
• R P of a short diploe is shown
PATTERN
• Radiation Pattern is a graph which shows the
variation in actual field strength of
electromagnetic field at all points which are at
equal distance from the antenna.
• The graph of radiation pattern will be three
dimensional and can’t be represented on a plain
paper.
• Alternatively, The graphical representation of
radiation of an antenna as a function of
direction is given the name Radiation Pattern
of an antenna.
• Field Strength Pattern : If the radiation from an
antenna is expressed in terms of field strength E
(Volt/Meter) the R.P is called “Field Strength
Pattern”.
• Power Pattern : If the radiation from an antenna
is expressed in terms of Power per unit solid
angle the R.P is called “Power Pattern”.
• FIGURES 6.2, 6.3 SHOWING TWO & THREE
DIMENSIONAL R.Ps OF A SHORT DIPOLE
PRINCIPAL PATTERNS
E-PLANE PATTERN: The plane containing
the electric field vector and the direction of
H-PLANE PATTERN :The plane containing
the magnetic field vector and the direction
• Different parts of radiation pattern are
called as LOBES.
• A RADIATION LOBE is a portion of the
radiation pattern bounded by regions of
CLASSIFICATION OF LOBES
• Major Lobe :It is also called as main beam. It is
defined as “The radiation lobe containing the
• Minor Lobe :Any Lobe except a major lobe is a
minor lobe.
• Side Lobe :Radiation lobe in any direction other
than the intended lobe.
• Back Lobe :Radiation Lobe in a direction
opposite to the major lobe.
POLAR AND RECTANGULAR
PLOT OF LOBES
• Minor Lobes represent radiation in
undesired directions and they should be
minimised.Side Lobes are usually the
largest of minor lobes.
A radian is defined with the aid of
Figure a). It is the angle subtended
by an arc along the perimeter of the
circle with length equal to the radius.
A steradian may be defined using
Figure (b). Here, one steradian (sr)
is subtended by an area r2 at the
surface of a sphere of radius r.
• Radiation Intensity is defined as “Power
per unit solid angle”.
• Unit of Radiation intensity is
•
=
Differential Power(dWr)
Differential Element of Solid Angle
dWr  .d
Wr   dWr   .d
Wr   .d
• Also for an isotropic radiator,total solid angle
Wr   .4  4  
 4. av
 av
Wr

4
• Where φav is radiation intensity produced by
power Wr
GAIN
• The ability of an antenna to concentrate
the radiated power in a given direction or
conversely to absorb effectively the
incident power from that direction is
specified by various antenna terms like
Gain, Directive Gain, Directivity, Power
Gain etc.
DEFINITION OF ANTENNA GAIN
• Gain (G) of an antenna is defined as:
Max Radiation intensity from subject or test antenna
Max Radiation Intensity from reference antenna with
same power input.
When the reference antenna is isotropic,it will be lossless.
• Gain (G0) of an antenna is defined as:
Max Radiation intensity from subject or test antenna
Radiation Intensity from Isotropic antenna with
same power input.
Go = Φ’m
Φo
• When antenna efficiency is 100 %
Gain = Directivity
In terms of signal power received by a rx-er at a distant point in the
Gain (G) of an antenna is defined as:
Max Power Received from subject or test antenna(P1)
Max Power Received from reference antenna(P2)
For the same input power in both the cases of test & reference antenna
In terms of field strength produced at a given distance
Gain (G) of an antenna is defined as:
Field Strength at a given distance from the practical
antenna in most favoured direction(E1)
Field Strength at the same distance from the isotropic
antenna(E2)
db gain= 10 Log10 G
DIRECTIVE GAIN
• The extent to which a practical antenna
concentrates its radiated energy relative to
that of some standard antenna is termed
as directive gain (Gd). It is expressed as
Radiation Intensity in a particular direction
Directive Gain
(Gd)=Radiation intensity in a particular direction
Gd (θ,φ)= Φ(θ,φ) = Φ(θ,φ) = 4πΦ(θ,φ)
Φav
Wr
Wr
4π
Gd (θ,φ)= 4πΦ(θ,φ)
∫ΦdΩ
Φ(θ,φ) = Radiation intensity in a particular direction
Φav = Average radiation intensity in that direction Wr
4π
Directive gain is expressed in decibels then :
dbGd (θ,φ) = 10 log10{ 4πΦ(θ,φ) }
∫ΦdΩ
2) Directive gain of an is defined, in a
particular direction as :
Gd = Power density radiated in a particular
direction by subject antenna
Power density radiated in a particular
direction by an isotropic antenna
Assuming both are radiating the same total power
Power Gain
The antenna power gain is defined as :
Gp = Power density radiated in a particular direction
by the subject antenna
Power density radiated in that direction by
isotropic antenna.
Assuming the same input power to both
Directive gain & Power gain is related as:
Gp = η Gd
η = Efficiency factor lies between 1 & 0
If η = 1,then
Gp = Gd
Power Gain(Contd..)
2) Gp = Radiation intensity in a given direction
Average total input power
Gp = Φ(θ,φ)
WT
4π
where WT = Wr+Wl = total input power
Wl = Ohmic Loss
Gp = 4π Φ(θ,φ)
WT
3) Gp = Power input supplied to the subject antenna in the
Power antenna supplied to reference antenna
Directivity(D)
• The maximum directive gain is called directivity of an
antenna and is denoted by D. where D is constant.
1) Directivity(D) = Maximum radiation intensity of
test antenna
test antenna
Or
D = Φ(θ,φ)max both of test antenna
Φav
Directivity(D)(Contd..)
2) Directivity(D) = Maximum radiation intensity of subject test
antenna
Radiation intensity of an isotropic antenna
Or
D = Φ(θ,φ)max.(test antenna)
Φ0(isotropic antenna)
3) Directivity of an antenna is in term of the radiated power is given as:
Directivity(D) = Power radiated from a test antenna
Power radiated from an isotropic antenna
D = W’
Wn
(from test antenna)
(from isotropic antenna)
Directivity(D)(Contd..)
Since the average radiation intensity()is obtained
given as:
D = Φ(θ,φ)max.
W
4π
D = 4π Φ(θ,φ)max.
W
Directivity(D)…..
Relation b/w Gain & Directivity
• G = KD
Where,
G=Gain
k=efficiency factor=1 for 100% efficiency
D=Directivity
In many antennas losses are extremely small and
hence the value of gain is almost equal to
directivity. That is why gain and directivity are
interchangeably used.
Antenna Efficiency ()
• Antenna Efficiency=
Total Input Power
• Antenna Efficiency represents the fraction of total energy
supplied to the antenna which is converted into
electromagnetic waves.
If WT => Total Input Power
Wl =>Ohmic Losses then
WT = Wr + Wl
Wr
Wr


WT
Wr  Wl
W r 4 ( ,  )


WT 4 ( ,  )
4 ( ,  )
Wr
1
Gp


 Gp.

WT
4 ( ,  )
Gd Gd
Wr
Wr
Gp



WT
Wr  Wl
Gd
• If current flowing in an
antenna is I then
I 2 Rr
 2
I ( Rr  Rl )
Where,
Rr
 (%) 
100
( Rr  Rl )
Rl =Ohmic Loss Resistance of
antenna conductor
Rr + Rl =Total Effective Resistance
Effective Area or Effective Aperture
or Capture Area
• A Tx-ing antenna transmits electromagnetic waves and a
• An antenna is considered to have an effective area or
aperture over which it extracts electromagnetic energy
from em waves.
• It is defined as the ratio of power received at the antenna
load terminal to the poynting vector(or power density)in
Watts/meter2 of the incident wave.Thus
Effective Area=
Poynting Vector of incident wave
Ae = W/P
Let a rx-ing antenna is placed in the field of
plane polarised travelling waves having an
effective area A and the rxing antenna is
terminated at a load impedance ZL=RL+XL
I
Direction
Of propagation of
Plane polarised wave
ZL
Fig 1
• If I be the terminal current then Rx-ed Power is
W=Irms2RL
ZL
Irms =>Terminal rms current
V
ZA
Therefore A =
W =
P
Irms2RL
P
Fig 2
The entire system can be replaced by an equivalent thevenin
circuit as shown in Fig 2
V=>Equivalent Thevenin Voltage
ZA =>Equivalent Thevenin Impedance
•
Irms=
Equivalent Voltage
Equivalent Impedance
Irms = V
Z L + ZA
Where ZA= RA + jXA =>Complex Antenna Impedance
RA= Rr + Rl = Rr if Rl is assumed to be 0
Rl =Loss Resistance
Putting the values of ZA and ZL in Eq 1 we get
I rms
V

( RL  jX L )  ( RA  jX A )
Eq 1
| I rms |
| I rms |
|V |
( RL  RA ) 2  ( X L  X A ) 2
|V |
( RL  Rr  Rl ) 2  ( X L  X A ) 2
Where,
XA=Antenna Reactance
W=Irms2RL
V 2 RL
W
( RL  RA ) 2  ( X L  X A ) 2
Eq 2
V 2 RL
Ae 
[(RL  RA ) 2  ( X L  X A ) 2 ]P
V 2 RL
Ae 
[(RL  Rr  Rl ) 2  ( X L  X A ) 2 ]P
According to maximum power transfer theorem, maximum power will be
transferred from antenna to the antenna terminating load if
XL  X A
RL  R A  Rl  R r
RL  Rr
Eq-3
If Rl=0
Obtained by putting eq 3 in eq 2
Wmax
V 2 RL
V2
V2



2
4 RL
4 RL
4 Rr
Wmax
V2

4 Rr
• Maximum Effective Aperture
V2
( Ae ) max 
4PRr
Eq 4
The ratio of effective area and max effective area is known as effectiveness
Ratio and is denoted by α

Ae
( Ae ) max
The value of α lies between o and 1
Scattering, Loss Aperture (AS, Al)
• Scattering and Loss Aperture corresponds
resistance and antenna loss resistance
respectively
Mathematically, A  I R
I
R
2
rms
s
P
2
r
Al 
rms
P
V 2 Rr
As 
[(RL  RA ) 2  ( X L  X A ) 2 ]P
V 2 Rl
Al 
[(RL  RA ) 2  ( X L  X A ) 2 ]P
l
• Putting the conditions of maximum transfer of energy from eq 3
V 2 Rr
V 2 Rr V 2
( AS )max 
 2 
2
( RL  Rr ) P 4Rr P 4Rr P
Eq 5
From Eq 4 and Eq 5 it is clear that under the condition of maximum transfer
of energy maximum scattering aperture and maximum effective aperture are same
( AS ) max  ( Ae ) max
Further the ratio of scattering aperture to effective aperture is called as
Scattering ratio and is denoted by β.Thus
As

Ae
Collecting Aperture
•
Out of the power collected by antenna there are losses as heat in load
resistance (RL), radiation resistance (Rr) and antenna loss resistance (Rl)
and correspondingly these apertures are Effective, Scattering and Loss. By
virtue of conservation of energy these three apertures are collectively known
as Collecting Aperture (AC). Mathematically it is given as,
AC=Ae+As+Al
AC  I rms RL  I rms Rr  I rms Rl
2
2
2
V 2 RL
V 2 Rr
AC 

2
2
[(RL  R A )  ( X L  X A ) ]P [(RL  R A ) 2  ( X L  X A ) 2 ]P
V 2 Rl

[(RL  R A ) 2  ( X L  X A ) 2 ]P
V 2 ( RL  Rr  Rl )
AC 
[(RL  RA ) 2  ( X L  X A ) 2 ]P
PHYSICAL APERTURE : This is related to actual physical size of antenna
and is denoted by Ap.In larger cross antennas like horn, parabolic reflector
the physical aperture is greater than effective aperture.
In an ideal size when there are no thermal losses, the physical aperture
and effective aperture are equal and under these conditions maximum
directivity is achieved i.e
Ap=Ae when there are no losses
Further the ratio of maximum effective aperture to the physical aperture is
given the name absorption ratio and is denoted by γ
( Ae ) max

Ap
Relation between max aperture
and gain or directivity
• It is found in practice that directivity of rx-ing antenna is directly
proportional to the maximum effective apertures.
Let there be two antennas A and B whose directivities and maximum
effective apertures are denoted by Da,Db and (Aea)max,(Aeb)max
respectively.
Therefore,
D  (A )
a
ea max
Db  ( Aeb ) max
Eq 1
Da ( Aea ) max

Db ( Aeb ) max
Relation between gain and directivity is given by G=KD, k can be replaced by
Effectiveness ratio α. i.e G= αD
Let us assume Goa, αa,Da being the gain, effectiveness ratio and directivity of
Antenna A and Gob, αb,Db corresponding quantities for antenna B.
Goa   a Da
Gob   b Db
Goa  a Da  a ( Aea ) max


Gob  b Db  b ( Aeb ) max
But from definition
a 
Aea
( Aea ) max
Aea   a ( Aea ) max
Aeb   b ( Aeb ) max
Eq 2
Eq 3
Putting the values from eq 3 into eq 2
Goa ( Aea )

Gob ( Aeb )
In eq 1 assume that antenna A is an isotropic antenna then its directivity Da=1
Putting this condition in eq 1
Da
1 ( Aea ) max


Db Db ( Aeb ) max
( Aeb ) max
( Aea ) max 
Db
This eq indicates that if maximum effective aperture and directivity of an antenna
B is known then the ratio of two will give maximum effective aperture of an
Isotropic antenna.Further if max effective aperture of an isotropic antenna is
Calculated then directivity of any antenna can be calculated by following formula,
( Aeb ) max
Db 
( Aea ) max
The above expression shows that directivity of any antenna is the ratio of its
maximum effective aperture and the maximum effective aperture of an isotropic
Antenna.
For e.g take the case of a short dipole whose max. effective aperture and directivity
If calculated will be given by (3/8π)λ2 and 3/2 respectively
Therefore
( Aea ) max 
( Aeb ) max
Db
32 / 8 2
( Aea ) max 

3/ 2
4
2
( Aea ) max 
4
( Aeb ) max
 Db  2
 / 4
4
Db  2 ( Aeb ) max

In general the relation between directivity and maximum effective aperture of
An antenna is given as below
D 
4

2
( Ae ) max
Effective Length
The term effective length represents the effectiveness of an
antenna as radiator or collector of electromagnetic wave
energy. It indicates how far an antenna is effective in
transmitting or receiving the electromagnetic wave
energy.
Effective Length is the ratio of induced voltage at the
terminal of the receiving antenna under open circuited
condition to the incident electric field intensity (or
strength) E. Thus,
Effective Length = Open Circuited Voltage
Incident Field Strength
le =V/E meter or wavelength
V 2 RL
Ae 
[(RL  RA ) 2  ( X L  X A ) 2 ]P
2
2
A
[(
R

R
)

(
X

X
)
2
e
L
A
L
A ]P
V 
RL
E2
P 
Z
V
Ae [( RL  R A ) 2  ( X L  X A ) 2 ] E 2
ZR L
Under conditions for maximum effective aperture when
X A  XL
R A  Rr  Rl  RL
R A  Rr  RL ifRl  0
le 
( Ae ) m ( 2 Rr ) 2
le  2
ZRr
( Ae ) m Rr
Z
2
( Ae ) m
l Z
 e
4 Rr
This is the relation between maximum effective aperture and effective length
For transmitting antenna the effective length is that length of an
equivalent linear antenna that has the same current I(c) (as at
terminals of the actual antenna) at all the points along its length and
that radiates the same field intensity E as the actual antenna.
If I(c)=>Current at the terminals of actual antenna
I(z)=>Current at any point Z of antenna
le=>Effective Length
l / 2
l=>Actual Length
I (c)le 
 I ( z)dz
l / 2
l / 2
1
le 
I ( z )dz

I (c )  l / 2
l/2
2
le 
I ( z )dz

I (c ) 0
RECIPROCITY THEOREM
STATEMENT: If an emf is applied to the terminals of an antenna no. 1 and
the current measured at the terminals of another antenna no.2 ,then an
equal current both in amplitude and phase will be obtained at the
terminals of antenna no.1 if the same emf is applied to the terminals of
antenna no.2
OR
If a current I1 at the terminals of antenna no. 1 induces emf E21 at the open
terminals of antenna no. 2 and a current I2 at the terminals of antenna
no. 2 induces emf E12 at the open terminals of antenna no. 1 then
E21=E12 PROVIDED I1=I2.
ASSUMPTIONS:1)emfs are of same frequency
2)Medium between two antennas are linear passive and isotropic
3)Generator producing emf and ammeter for producing current have zero
impedance or if not both the generator and ammeter impedances are
equal
Transfer Impedance=Z12=E12/I2
Z21 =E21 /I1
From Reciprocity it follows
E12 E21
Z m  Z12  Z 21 

I2
I1
Proof: To prove the reciprocity theorem the space between antenna 1 and antenna
2 is replaced by a network of linear ,passive and bilateral impedances.
Z11,Z22=>Self Impedance of antenna 1 and 2 respectively
Zm=>Mutual Impedance between two antennas
I1
1
E12
1
Z11
1
Z22
Zm
2
2
I2
2
I1
1
Z11
I1
1
Z22
Zm
2
2
E21
2
1
Applying kirchoff’s mesh law to loop 2
( Z 22  Z m ) I 2  Z m I1  0
I 2  I1
Zm
Z 22  Z m
Eq1
Applying kirchoff’s mesh law to loop 1
( Z11  Z m ) I1  Z m I 2  E12
2
Zm
( Z11  Z m ) I1 
I1  E12
( Z 22  Z m )
( Z  Z m )(Z 22  Z m )  Z m
I1 11
 E12
( Z 22  Z m )
2
Z Z  Z11Z m  Z 22 Z m  Z m  Z m
I1 11 22
 E12
( Z 22  Z m )
2
2
Z11 Z 22  Z11 Z m  Z 22 Z m  Z m  Z m
I1
 E12
( Z 22  Z m )
2
2
E12 ( Z 22  Z m )
I1 
Z11 Z 22  Z11 Z m  Z 22 Z m
I1 
E12 ( Z 22  Z m )
Z11 Z 22  Z m ( Z11  Z 22 )
Eq2
Putting value of I1 from eq 2 in eq 1
E12 ( Z 22  Z m ).Z m
I2 
[ Z11 Z 22  Z m ( Z11  Z 22 )](Z 22  Z m )
I2 
E12 Z m
[ Z11 Z 22  Z m ( Z11  Z 22 )]
Eq 3
Similarly the current I1 can be obtained by symmetry Suffix 2 may be replaced by 1
And vice versa
E21Z m
I1 
Eq 4
[ Z11Z 22  Z m ( Z11  Z 22 )]
From Eq 3 and Eq 4 it is clear that if E21 and E12 are same then I1=I2
• The antenna is a radiating device in which power is
radiated into space in the form of electromagnetic waves
.Hence there must be power dissipation which may be
expressed in usual manner as
W=I2R
• If it is assumed that all this power appears as
electromagnetic radio waves then this power can be
divided by square of current i.e
Rr=W/I2
at a point where it is fed to antenna and obtain a fictitious
• It is normally denoted by Rr or Ra or Ro
• Thus Radiation Resistance can be defined as that fictitious
resistance which when substituted in series with the antenna will
consume the same power as is actually radiated.
• Total Power loss in an antenna is sum of the two losses
Total Power Loss = Ohmic Loss + Radiation Loss
W  W '  W ''
 I 2 Rr  I 2 Rl
 I 2 ( Rr  Rl )
 I 2R
If R=Rr+Rl
The value of Radiation Resistance depends on
 Configuration of Antenna
 The Point where radiation resistance is considered
 Location of antenna with respect to ground and other
objects
 Ratio of length of diameter of conductor used
 Corona Discharge-a luminous discharge round the
surface of antenna due to ionization of air etc.
Self Impedance
• Self Impedance is the impedance at a point where the
transmission line carrying RF power from the transmitter
is connected.
• Since at this point input to the antenna is supplied so it is
also called as antenna input impedance
• Also at this point RF power from the transmitter is fed so
this is also called as Feed Point impedance
• Also at this point the transmission line operates
so it is also called as driving point impedance or
terminal impedance
Antenna Input impedance is very important because it is
generally desired to supply maximum available power
from the transmitter to the antenna or to extract
maximum amount of received energy from the antenna.
Transmission Line
Transmission Line
ZL
Antenna Terminals
Antenna
Terminals
If the antenna is lossless and isolated then the
antenna terminal impedance is same as the
self impedance of the antenna. Mathematically,
Z11  R11  jX11
For a linear half wave centre fed antenna the self impedance is calculated to be
Z11  R11  jX 11
 73  j 42.45
• Thus for a lossless antenna self impedance and terminal
impedance are equal which is a complex quantity the
real part of which is known as self resistance or radiation
resistance and imaginary part as self reactance
• But if antenna is in nearby of other objects then terminal
impedance gets modified because besides self
impedance mutual impedance comes into existence due
to current flowing in neighboring antennas
• This is why self impedance of an antenna is defined
as its input impedance when all other antennas are
completely removed i.e away from it.
Mutual Impedance
• Mutual Impedance is defined as negative ratio of
the voltage induced in one circuit (by a current
flowing in the second circuit) to the current in the
second circuit with all the circuits open circuited
except second circuit
I1
Ckt 1
P
Ckt 2
S
E21
By Definition
Z 21
E21

I1
Z12
E12

I2
E21=>Open Ckt Voltage across ckt no. 2 due to current I1 in ckt no 1
E12=>Open Ckt Voltage across ckt no. 1 due to current I2 in ckt no 2
Mutual Impedance depends upon
Magnitude of Induced Current
Phase Relationship between induced and original currents
Tuning Conditions of nearby antennas
Front to Back Ratio
It is defined as the ratio of power radiated in
desired direction to the power radiated in
opposite direction.
 Higher the front to back ratio better it is.
 FBR depends upon tuning conditions or
electrical length of parasitic elements
 Higher FBR can be achieved by diverting the
gain in opposite direction to the desired direction
by tuning the length of parasitic elements
to get maximum FBR rather than maximum gain.
Antenna Bandwidth
• Antenna Bandwidth is the range of
frequency over which the antenna
maintains certain required characteristics
like gain, front to back ratio or SWR
pattern (shape or direction), polarization
and impedance
• It is the bandwidth within which the
antenna maintains a certain set of given
specifications.
w  w2  w1  wr / Q  Bandwidth
f  f 2  f1  f r / Q
1
f 
Q
fr=Centre or Resonant Frequency
Q= 2π
Total Energy Stored by antenna
Energy Radiated or Dissipated per cycle
Lower the Q of antenna higher is the bandwidth and vice versa
• In frequency independent antennas like
log periodic antennas etc. which have
unlimited bandwidth where lower and
upper frequency limits are specified
independently ,the bandwidth is specified
as the ratio of highest to lowest operating
frequency
Antenna Beam width
• Antenna Beam width is an angular width in degrees
measured on the radiation pattern (major lobe) between
points where the radiated power has fallen to half its
maximum value. This is called as “beam width” between
half power points or half power beam width (HPBW)
because power at half power points is just half.
• Half Power Beam width is also known as 3 db beam
width because at half power points the power is 3 db
down of the maximum power value of major lobe.
• Further at half power points the field intensity (voltage)
equals 1/21/2 or 0.707 times its maximum value
• Sometimes radiation pattern is described in
terms of angular width between first nulls or first
side lobes known as beam width between first
nulls or first side lobes known as beam width
between first nulls (BWFN).
• Directivity is given as
4 4
D

A
B
B= HPBW in horizontal plane x HPBW in
= HPBW in E plane x HPBW in H plane
B   E   H ...........radians2
4
D
 E  H
4  (57.3) 2
D
..............squaredeg rees


 E  H
41,257
D 

 E  H
• For direction finding applications a narrow beam
is desirable and accuracy of direction finding is
inversely proportional to beam width
1
D 
B
Antenna Beam Efficiency
• The parameter is defined as the ratio of main beam area (ΩM) to
the total beam area (ΩA)
Total Beam area=Main Beam Area + Minor Lobe Area
M
M

A
 A  M  m
1
m
M

A
A
1  M  m
M 
m
M
A
= Stray Factor
m

= Beam Efficiency
A
```