Fundamentals of Antenna Parameters

RADIATION & PROPOGATION
-Fundamental Parameters of Antennas
AJAL.A.J

Assistant Professor –Dept of ECE,
UNIVERSAL ENGINEERING COLLEGE
Mob: 8907305642 MAIL: ec2reach@gmail.com
AJAL.A.J- AP ECE

UNIVERSAL ENGG COLLEGE

An antenna is a way of converting the guided waves
present in a waveguide, feeder cable or transmission line
into radiating waves travelling in free space, or vice
versa.

AJAL.A.J- AP ECE


Radiation Pattern Lobes

Main lobe

Full Null Beamwidth
Between
1st NULLS
Side lobes
Back lobes

Only accelerating charges produce radiation.
Idealized
Point Radiator

Isotropic
AJAL.A.J- AP ECE

Vertical Dipole

Omnidirectional

Radar Dish

Directional


Two fields regions:
oNear field or Fresnel region: The region within the
radius of the smallest sphere which completely encloses
the antenna is called Fresnel region.
In sitting an antenna ,it’s crucial to keep objects out of
the near field region to avoid coupling the currents in the
antenna with objects.
oFar

Field or Fraunhofer region: The region beyond
Fresnel region is called Fraunhofer region

AJAL.A.J- AP ECE


Antenna parameters are:
1.Radiation Pattern
2.Directivity
3.Radiation Resistance and Efficiency
4.Power Gain
5.Bandwidth
6.Reciprocity
7.Effective Aperture
8.Beamwidth and Directivity
9.The Friis Formula: Antennas in Free Space
10.Polarisation Matching

AJAL.A.J- AP ECE


The radiation pattern of an antenna is a plot of the farfield radiation from the antenna. More specifically, it is a
plot of the power radiated from an antenna per unit solid
angle, or its radiation intensity U [watts per unit solid
angle]. This is arrived at by simply multiplying the power
density at a given distance by the square of the distance r,
where the power density S [watts per square metre] is
given by the magnitude of the time-averaged Poynting
vector:
U=r^²S
AJAL.A.J- AP ECE


Radiation Intensity

Aside on Solid Angles
surface area = r 2

ρ

θ = 1.0 rad

arc length = ρ

total circumfrance = 2π radians

r
Ω = 1.0 sr

total surface area = S o = 4π r 2 = Ω r 2
So
Ω = 2 sr
r
infinitesimal area
ds = r 2 sin(θ ) dθ dφ
of surface of sphere
ds
dΩ = 2 = sin(θ ) dθ dφ
r

The directivity D of an antenna, a function of direction
is defined by the ratio of radiation intensity of antenna in
direction to the mean radiation intensity in all
directions.

AJAL.A.J- AP ECE


The resistive part of the antenna impedance is split into two parts, a
radiation resistance Rr and a loss resistance Rl. The power dissipated in
the radiation resistance is the power actually radiated by the antenna, and
the loss resistance is power lost within the antenna itself. This may be due
to losses in either the conducting or the dielectric parts of the antenna.
Radiation efficiency e of the antenna as e is the ratio of power radiated
to the power accepted by antenna
antenna with high radiation efficiency therefore has high associated
radiation resistance compared with the losses. The antenna is said to be
resonant if its input reactance Xa =0.

AJAL.A.J- AP ECE


The power gain G, or simply the gain, of an antenna is
the ratio of its radiation intensity to that
of an isotropic antenna radiating the same total power
as accepted by the real antenna. When
antenna manufacturers specify simply the gain of an
antenna they are usually referring to the
maximum value of G.

AJAL.A.J- AP ECE


Antenna Gain

U (θ , ϕ )
G (θ , ϕ ) = 4π
Pinput
DIRECTIVITY

POWER DENSITY IN A CERTAIN DIRECTION
DIVIDED BY THE TOTAL POWER RADIATED

GAIN

POWER DENSITY IN A CERTAIN DIRECTION
DIVIDED BY THE TOTAL INPUT POWER
TO THE ANTENNA TERMINALS (FEED POINTS)

IF ANTENNA HAS OHMIC LOSS…
THEN, GAIN < DIRECTIVITY

The bandwidth of an antenna expresses its ability to
operate over a wide frequency range. It is often defined
as the range over which the power gain is maintained to
within 3dB of its maximum value, or the range over
which the VSWR is no greater than 2:1, whichever is
smaller. The bandwidth is usually given as a percentage of
the nominal operating frequency. The radiation
pattern of an antenna may change dramatically outside
its specified operating bandwidth.

AJAL.A.J- AP ECE


Reciprocity theorem:
If a voltage is applied to the terminals of an antenna A and
the current measured at the terminals of another antenna B
then an equal current will be obtained at the terminals of
antenna A if the same voltage is applied to the terminals of
antenna B.

AJAL.A.J- AP ECE


Effective Aperture
If an antenna is used to receive a wave with a power density S [W m2], it will produce a
power in its terminating impedance (usually a receiver input impedance) of Pr watts. The
constant of proportionality between Pr and S is Ae, the effective aperture of the antenna in
square metres:
Pr = AeS
For some antennas, such as horn or dish antennas, the aperture has an obvious physical
interpretation, being almost the same as the physical area of the antenna, but the concept is
just as valid for all antennas. The effective aperture may often be very much larger than the
physical area, especially in the case of wire antennas. Note, however, that the effective
aperture will reduce as the efficiency of an antenna decreases.
The antenna gain G is related to the effective aperture as follows
G=4pi/ (lamda)2Ae

AJAL.A.J- AP ECE


Effective Aperture

Aphysical

Pload

Question:

plane wave
incident

?

Pload = AphysicalWinc

Answer: Usually NOT

Pload = Aeff Winc ⇒ Aeff =

Pload
Winc

The directivity of an antenna increases as its beamwidth is
made smaller, as the energy
radiated is concentrated into a smaller solid angle

AJAL.A.J- AP ECE


2

Pr  λ 
 Dto Dro
=
 4π R 
Pt 


AJAL.A.J- AP ECE


Directivity and Maximum Effective Aperture
(no losses)
Antenna #1
transmit

Atm, Dt

Antenna #2
Direction of wave propagation

R

λ2
Aem =
Do
4π

receiver

Arm, Dr

Directivity and Maximum Effective Aperture
(include losses)
Antenna #1

Antenna #2
Direction of wave propagation

transmit

Atm, Dt

receiver

Arm, Dr

R

λ2
* 2
ˆ ˆ
Aem = ecd (1 − Γ )
Do ρ w ⋅ ρ a
4π
2

conductor and
dielectric losses

reflection losses
(impedance mismatch)

polarization mismatch

Friis Transmission Equation (no loss)
Antenna #1
tran
s

Antenna #2

mit

Atm ,

(θr,φr)

Dt

(θt,φt)

receive

R

Arm , D

r

The transmitted power density supplied by Antenna #1
at a distance R and direction (θr,φr) is given by:

Wt =

Pt Dgt (θ t , ϕ t )
4π R 2

The power collected (received) by Antenna #2 is given by:

Pr = Wt Ar =

Pt Dgt (θ t , ϕ t )
4π R
2

2

Ar =

Pt Dgt (θ t , ϕ t ) Dgr (θ r , ϕ r )λ2
4π R 2

Pr  λ 
=
 4π R  Dgt (θ t , ϕ t ) Dgr (θ r , ϕ r )

Pt 


4π

r

Friis Transmission Equation (no loss)
Antenna #1
tran
s

Antenna #2

mit

Atm ,

(θr,φr)

Dt

(θt,φt)

R

receive

Arm , D

r

2

Pr  λ 
=
 4π R  Dgt (θ t , ϕ t ) Dgr (θ r , ϕ r )

Pt 

If both antennas are pointing in the direction of their maximum radiation pattern:
2

Pr  λ 
=
 4π R  Dto Dro

Pt 


r

The polarisation mismatch loss is the ratio between
the power received by the antenna and the power
which would be received by an antenna perfectly
matched to the incident wave

AJAL.A.J- AP ECE


Friis Transmission Equation: Example #1
A typical analog cell phone antenna has a directivity of 3 dBi at its operating frequency of
800.0 MHz. The cell tower is 1 mile away and has an antenna with a directivity of 6 dBi.
Assuming that the power at the input terminals of the transmitting antenna is 0.6 W, and
the antennas are aligned for maximum radiation between them and the polarizations are
matched, find the power delivered to the receiver. Assume the two antennas are well
matched with a negligible amount of loss.
2

Pr
2
2  λ 
* 2
max
max
ˆ ˆ
= ecdt ecdr (1 − Γr )(1 − Γt )
 4π R  Dt Dr ρ w ⋅ ρ a

Pt


=1

λ=

=1

c
3e8
=
= 0.375m
f 800e6

Dtmax = 103 /10 = 2.0
Drmax = 10 6 /10 = 4.0

=0

=0

=1

2

0.375


Pr = 0.6 watts ⋅ 
 ⋅ 2 ⋅ 4 = 1.65 nW
 4π ⋅1 609.344 

A half wavelength dipole antenna (max gain = 2.14 dBi) is used to communicate from an
old satellite phone to a low orbiting Iridium communication satellite in the L band (~ 1.6
GHz). Assume the communication satellite has antenna that has a maximum directivity of
24 dBi and is orbiting at a distance of 781 km above the earth. Assuming that the power at
the input terminals of the transmitting antenna is 1.0 W, and the antennas are aligned for
maximum radiation between them and the polarizations are matched, find the power
delivered to the receiver. Assume the two antennas are well matched with a negligible
amount of loss.
2

Pr
2
2  λ 
* 2
max
max
ˆ ˆ
= ecdt ecdr (1 − Γr )(1 − Γt )

Pt


=1

λ=

=1

c
3e8
=
= 0.1875m
f 800e6

Dtmax = 10 2.14 /10 = 1.64
Drmax = 10 24 /10 = 251.0

=0

=0

=1
2

 0.1875 
Pr = 1.0 watts ⋅ 
 ⋅1.64 ⋅ 251 = 0.15 pW
 4π ⋅ 781,000 

A roof-top dish antenna (max gain = 40.0 dBi) is used to communicate from an old satellite
phone to a low orbiting Iridium communication satellite in the Ku band (~ 12 GHz).
Assume the communication satellite has antenna that has a maximum directivity of 30 dBi
and is orbiting at a distance of 36,000 km above the earth. How much transmitter power is
required to receive 100 pW of power at your home. Assume the antennas are aligned for
maximum radiation between them and the polarizations are matched, find the power
delivered to the receiver. Assume the two antennas are well matched with a negligible
amount of loss.
2

Pr
2
2  λ 
* 2
max
max
ˆ ˆ
= ecdt ecdr (1 − Γr )(1 − Γt )

Pt


=1

=1

c
3e8
λ= =
= 0.025m
f 800e6
Drmax = 10 40 /10 = 10,000
Dtmax = 1030 /10 = 1000.0

=0

=0

Pt =

=1

100 ⋅10 −12 watts
2

0.025



 ⋅10,000 ⋅1000
 4π ⋅ 36,000,000 

= 82 W

Fundamentals of Antenna Parameters

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