Antennas and Wave Propagation

B.TECH (III YEAR – I SEM)
Prepared by:
Mr. P.Venkata Ratnam.,M.Tech., (Ph.D)
Associate Professor
Department of Electronics and Communication Engineering
RAJAMAHENDRI INSTITUTE OF ENGINEERING & TECHNOLOGY
(Affiliated to JNTUK, Kakinada, Approved by AICTE - Accredited by NAAC )
Bhoopalapatnam, Rajamahendravaram, E.G.Dt, Andhra Pradesh

 Introduction
 Radiation Mechanism(Single wire, 2 wire, Dipoles )
 Current Distribution on a thin wire antenna.
 Antenna Parameters
 Radiation Patterns
 Patterns in Principal Planes
 Main Lobe and Side Lobes
 Beam widths
 Polarization

 Beam Area
 Radiation Intensity
 Beam Efficiency
 Directivity
 Gain and Resolution
 Antenna Apertures
 Aperture Efficiency
 Effective Height
 illustrated Problems

 An antenna is defined by Webster‘s Dictionary as ―
a usually metallic device (as a rod or wire) for
radiating or receiving radio waves.
 The IEEE Standard Definitions of Terms for
Antennas defines the antenna or aerial as ―a means
for radiating or receiving radio waves.
 In other words the antenna is the transitional
structure between free-space and a guiding device.
 The guiding device or transmission line may take the
form of a coaxial line or a hollow pipe (waveguide).

 An antenna may be a piece of conducting material
in the form of a wire, rod or any other shape with
excitation
 An antenna is a source or radiator of EM waves
 An antenna is a sensor of EM waves
 An antenna is a transducer
 An antenna is an impedance matching device
 An antenna is a coupler between a generator and
space or vice-versa

Types of Antennas :
1.Wire antennas:
 Dipole, Monopole, Loop antenna, Helix antennas
 Usually these are used in Personal applications,
Automobiles, Buildings, Ships, Aircrafts and
Spacecrafts.

2. Aperture antennas:
 Horn antennas, Waveguide opening
 Usually used in aircrafts and space crafts,
because these antennas can be flush-mounted.

3. Reflector antennas:
 Parabolic reflectors, Corner reflectors .
 These are high gain antennas usually used in
radio astronomy, microwave communication
and satellite tracking.

4.Lens antennas:
 Convex-plane, co vex-convex , convex-concave
and concave-plane lenses
 These antennas are usually used for very high
frequency applications.

5.Microstrip antennas :
 Rectangular, Circular etc. shaped metallic
patch above a ground plane
 Used in Aircraft, Spacecraft, Satellites, Missiles,
Cars, Mobile phones etc.

6. Array antennas :
 Yagi-Uda antenna, Microstrip Patch array,
Aperture array, Slotted waveguide array
 Used for very high gain applications with added
advantage, such as controllable radiation
pattern.

 When electric charges undergo acceleration or
deceleration, electromagnetic radiation will be
produced.
 Hence it is the motion of charges, that current is the
source of radiation.
 Here it may be highlighted that, not all current
distributions will produce a strong enough radiation
for communication.
 Antennas radiate or couples or directs electromagnetic
energy in the desired or assigned direction.
 An antenna may be isotropic or non directional
(Omni-directional) and unisotropic or Directional.

 To give a mathematical flavor to it, as we know :
 As shown in these equations, to create radiation (electric
field), there must be a time-varying current dI/dt or an
acceleration (or deceleration) a of a charge q.
 If the charge is not moving, a current is not created and
there is no radiation.

 If a charge is moving with an uniform velocity
 There is no radiation if the wire is straight, and
infinite in extent
 There is radiation if the wire is curved, bent,
discontinuous, terminated, or truncated
 If the charge is oscillating in a time-motion, it radiates
even if the wire is straight.
 These situations are shown in Fig. below

 So, it is the current distribution on the antennas
that produce the radiation.
 Usually these current distributions are excited
by transmission lines and waveguides

Radiation from a Single Wire :
 Conducting wires are characterized by the
motion of electric charges and the creation of
current flow.
 Assume that an electric volume charge density,
qv (coulombs/m3), is distributed uniformly in
a circular wire of cross-sectional area A and
volume V.

 Current density in a volume with volume charge
density qV (C/m3 )
Jz = qV. Vz (A/m2)
 Surface current density in a section with a surface
charge density qS (C/m2 )
Js = qS .Vz (A/m)
 Current in a thin wire with a linear charge density qI
(C/m):
Iz = ql .Vz A
 To accelerate/decelerate charges, one needs sources of
electromotive force and/or discontinuities of the
medium in which the charges move.
 Such discontinuities can be bends or open ends of
wires, change in the electrical properties of the region,
etc.

In summary:
 It is a fundamental single wire antenna. From the principle
of radiation there must be some time varying current.
For a single wire antenna:
1.If a charge is not moving, current is not created and there is
no radiation.
2. If charge is moving with a uniform velocity:
a. There is no radiation if the wire is straight, and infinite
in extent.
b. There is radiation if the wire is Curved, Discontinuous,
Terminated, Bent or Truncated.
3. If charge is oscillating in a time-motion, it radiates even if
the wire is straight.

Radiation from a Two Wire :
 Let us consider a voltage source connected to a
two-conductor transmission line which is
connected to an antenna.
 This is shown in Figure, Applying a voltage
across the two conductor transmission line
creates an electric field between the conductors.

Radiation from a Dipole :
 The radiation of energy when done through
such a bent wire, the end of such transmission
line is termed as dipole or dipole antenna.
 Now let us attempt to explain the mechanism
by which the electric lines of force are detached
from the antenna to form the free-space waves.

Current distribution on a thin wire antenna :
 Let us consider a lossless two wire transmission
line in which the movement of charges creates a
current having value I with each wire.
 This current at the end of the transmission line is
reflected back, when the transmission line has
parallel end points resulting in formation of
standing waves in combination with incident
wave.

 When the transmission line is flared out at 900
forming geometry of dipole antenna.
 The current distribution remains unaltered and
the radiated fields not getting cancelled resulting
in net radiation from the dipole.
 If the length of the dipole l< λ/2, the phase of
current of the standing wave in each transmission
line remains same.

 If diameter of each line is small d<< λ/2,
 The current distribution along the lines will be
sinusoidal with null at end but overall
distribution depends on the length of the dipole
 The current distribution for dipole of length
l << λ

 When l > λ, the current goes phase reversal
between adjoining half-cycles.
 Hence, current is not having same phase along
all parts of transmission line.
 This will result into interference and cancelling
effects in the total radiation pattern.

 The current distributions we have seen represent
the maximum current excitation for any time.
 The current varies as a function of time as well.

Antenna Parameters :
 To describe the performance of an antenna,
definitions of various parameters are necessary.
 Some of the parameters are interrelated and not
all of them need be specified for complete
description of the antenna performance.
 Radiation Patterns. Patterns in Principal Planes,
Main Lobe and Side Lobes, Beam widths,
Polarization, Beam Area, Radiation Intensity, Beam
Efficiency, Directivity, Gain, Resolution, Antenna
Apertures, Aperture Efficiency, Effective Height

 An antenna radiation pattern or antenna pattern is
defined as ―a mathematical function or a graphical
representation of the radiation properties of the
antenna as a function of space coordinates.
 Radiation properties include power flux density,
radiation intensity, field strength, directivity, phase or
polarization.
 The radiation property of most concern is the two-
or three dimensional spatial distribution of
radiated energy as a function of the observer‘s
position along a path or surface of constant radius.

 A trace of the received electric (magnetic) field at
a constant radius is called field pattern.
 On the other hand, a graph of the spatial
variation of the power density along a constant
radius is called power pattern.
 Often the field and power patterns are
normalized with respect to their maximum value,
yielding normalized field and power patterns.

For an antenna, the
 a). Field pattern(in linear scale) typically
represents a plot of the magnitude of the
electric or magnetic field as a function of the
angular space.
 b). Power pattern (in linear scale) typically
represents a plot of the square of the
magnitude of the electric or magnetic field as a
function of the angular space.
 c). Power pattern (in dB) represents the
magnitude of the electric or magnetic field, in
decibels, as a function of the angular space.

Coordinate system for antenna analysis

 Dividing a field component by its maximum value,
we obtain a normalized or relative field pattern which is
a dimensionless number with maximum value of unity
 Eθ (θ,ɸ) →The θ-component of the electric field as a
function of angles θ and ɸ (v/m)
 Eɸ(θ,ɸ) → The ɸ-component of electric field as a
function of angle θ and ɸ(v/m)
 δθ(θ,ɸ) or δɸ(θ,ɸ) → The phase angles of both the
field components (deg. Or rad.)

 Below Figures are principal plane field and
power patterns in polar coordinates.

 The angular beamwidth at the half-power level
or half-power beamwidth (HPBW) (or −3-dB
beamwidth) and the beamwidth between first
nulls (FNBW)
 An isotropic radiator is defined as ―a
hypothetical lossless antenna having equal
radiation in all directions.
 A directional antenna is one ―having the
property of radiating or receiving
electromagnetic waves more effectively in
some directions than in others.

 For a linearly polarized antenna, performance is
often described in terms of its principal E- and
H-plane patterns
 The E-plane is defined as ―the plane containing
the electric field vector and the direction of
maximum radiation
 The H-plane as ―the plane containing the
magnetic-field vector and the direction of
maximum radiation.

 For this example, the x-z plane (elevation plane;
θ) is the principal E-plane
 The x-y plane (azimuthal plane; ɸ) is the
principal H-plane.

Radian and Steradian:
 The measure of a plane angle is a radian. One
radian is defined as the plane angle with its
vertex at the center of a circle of radius r that is
subtended by an arc whose length is r.
 The measure of a solid angle is a steradian One
steradian is defined as the solid angle with its
vertex at the center of a sphere of radius r that is
subtended by a spherical surface area equal to
that of a square with each side of length r.

 Since the area of a sphere of radius r is A = 4πr2,
there are 4π sr (4πr2/r2) in a closed sphere.

Main Lobe and Side Lobes :
 Various parts of a radiation pattern are referred
to as lobes, which may be sub classified into major
or main, minor, side, and back lobes.
 A radiation lobe is a portion of the radiation pattern
bounded by regions of relatively weak
radiation intensity.

 A major lobe (also called main beam) is defined as the
radiation lobe containing the direction of maximum
radiation.
 A minor lobe is any lobe except a major lobe. all the
lobes with the exception of the major can be
classified as minor lobes.
 A side lobe is a radiation lobe in any
 direction other than the intended lobe.
 A back lobe is a radiation lobe whose axis
makes an angle of approximately 180◦
with respect to the beam of an antenna.

Beam Width :
 In the radiation pattern of an antenna, the main
lobe is the main beam of the antenna where
maximum and constant energy radiated by the
antenna.
 Beam width is the aperture angle from where
most of the power is radiated.
 The two main considerations of this beam width
are
Half Power Beam Width (HPBW)
First Null Beam Width (FNBW).

Half-Power Beam Width :
 According to the standard definition, “The angular
separation, in which the magnitude of the radiation
pattern decreases by 50% (or -3dB) from the peak of
the main beam, is the Half Power Beam Width.”
 In other words, Beam width is the area where most
of the power is radiated, which is the peak power.
 Half power beam width is the angle in which
relative power is more than 50% of the peak power,
in the effective radiated field of the antenna.

First Null Beam Width :
 According to the standard definition, “The
angular span between the first pattern nulls
adjacent to the main lobe, is called as the First
Null Beam Width.”
 Simply, FNBW is the angular
separation, quoted away
from the main beam, which
is drawn between the null
points of radiation pattern,
on its major lobe

Antenna Polarization :
 Polarization of an antenna in a given direction is
defined as vector orientation of Electric field
component of the Wave radiated by the antenna.
 In practice, polarization of the radiated energy
varies with the direction from the center of the
antenna, so that different parts of the pattern may
have different polarizations.
 Polarization then is the curve traced by the end
point of the arrow (vector) representing the
instantaneous electric field.
 The field must be observed along the direction of
propagation.

 Polarization may be classified as
Linear Polarization
Circular Polarization
Elliptical Polarization
 The linear polarization of the antenna helps in
maintaining the wave in a particular direction,
avoiding all the other directions.(both Vertical
and Horizontal polarizations)
 Though this linear polarization is used, the
electric field vector stays in the same plane.
Hence, we use this linear polarization to
improve the directivity of the antenna.

 When a wave is circularly polarized, the electric
field vector appears to be rotated with all its
components loosing orientation.
 The mode of rotation may also be different at times.
However, by using circular polarization, the effect of
multi-path gets reduced and hence it is used in
satellite communications such as GPS.
 Another form of polarization is known as Elliptical
polarization. It occurs when there is a mix of linear
and circular polarization.
 This can be visualized as before by the tip of the
electric field vector tracing out an elliptically shaped
corkscrew.

Beam Area :
 Beam area is the solid angle through which all
the power radiated by the antenna P (θ, Ø)
maintained its maximum value over ΩA and
was zero elsewhere.
 The radiated beam of the antenna comes out
from an angle at the antenna, known as solid
angle, where the power radiation intensity is
maximum.
 This solid beam angle is termed as the beam
area. It is represented by ΩA.

 The radiation intensity P (θ, Ø) should be
maintained constant and maximum throughout
the solid beam angle ΩA, its value being zero
elsewhere.

Radiation Intensity :
 The power radiated from an antenna per unit
solid angle is called the radiation intensity U
 Radiation emitted from an antenna which is
more intense in a particular direction, indicates
the maximum intensity of that antenna.
 The emission of radiation to a maximum
possible extent is nothing but the radiation
intensity.

 The radiation intensity is a far-field parameter,
and it can be obtained by simply multiplying the
radiation density by the square of the distance.
 In mathematical form it is expressed as
U (θ, ɸ ) = r2 Prad (θ, ɸ )
Where
U (θ, ɸ ) = radiation intensity (W/unit solid angle)
Prad (θ, ɸ ) = radiation density (W/m2)

 Thus the total power radiated is given by

 Thus the radiation intensity U (θ, ɸ ) is
expressed in watts per steradian and it is
defined as time average power per unit solid
angle.
 The average value of radiation intensity of an
isotropic source is given by

Beam Efficiency :
 The beam efficiency states the ratio of the
beam area of the main beam to the total beam
area radiated
 The beam area ΩA consists of the main beam
area ΩM plus the minor-lobe area Ω m .
 Thus,
ΩA = ΩM + Ω m

 The ratio of the main beam area to the (total)
beam area is called the (main) beam efficiency
εM Thus,

Directivity :
 Directivity of an antenna or array is a measure
of the antenna’s ability to focus the energy in
one or more specific directions.
 You can determine an antenna’s directivity by
looking at its radiation pattern.
 In an array propagating a given amount of
energy, more radiation takes place in certain
directions than in others
 It is defined as the ratio of maximum radiation
intensity of test antenna to the radiation
intensity of an isotropic antenna.

 Directivity is defined as the ratio of maximum
radiation intensity to the average radiation
intensity.
 Directivity (D) in terms of total power radiated
is

 The directivity of an antenna is equal to the ratio
of the maximum power density P( θ,ɸ)max
(watts/m2) to its average value over a sphere
as observed in the far field of an antenna.
 Thus,

 Therefore, the directivity
 Thus, the directivity is the ratio of the area of a
sphere (4π sr) to the beam area ΩA of the antenna.
 The smaller the beam area, the larger the
directivity D.

 If the half-power beamwidths of an antenna are
known, its directivity

Gain :
 Gain of an antenna (in a given direction) is defined
as “the ratio of the intensity, in a given direction, to
the radiation intensity that would be obtained if the
power accepted by the antenna were radiated
isotropically.
 In equation form this can be expressed as
 When the direction is not stated, the power gain is
usually taken in the direction of maximum
radiation.

 The gain G of an antenna is an actual or
realized quantity which is less than the
directivity D due to ohmic losses in the antenna
 In transmitting, these losses involve power fed
to the antenna which is not radiated but heats
the antenna structure.
 The ratio of the gain to the directivity is the
antenna efficiency factor. Thus, η
G = η D
Where η is the antenna efficiency factor (0 < k < 1 )

Resolution :
 The resolution of an antenna is defined as half
of the beam width between first nulls
 But half the beam width between first nulls is
approximately equal to the HPBW of an
antenna.
 Practically , HPBW is slightly less than
FNBW/2

 The antenna beam area is given by the product
of two half power beam width in two principle
planes.
 If there are N no. of point sources of radiation
distributed uniformly, then antenna resolve
those and is given by

 But by the definition, the directivity of antenna
is defined as,
 Hence D = N →So, ideally no. of point sources
resolved by an antenna is equal to directivity of
an antenna.
 The resolution of antenna is also called
Rayleigh Resolution

Antenna Apertures :
 Aperture of an Antenna is the area through which the
power is radiated or receive. Concept of Apertures is
most simply introduced by considering a Receiving
Antenna.
 Let the Poynting vector, or power density, of the plane
wave be S watts per square meter and the area, or
physical aperture of the horn, be Ap square meters.

 If the horn extracts all the power from the wave
over its entire physical aperture, then the total
power P absorbed from the wave is
P= S.Ap =(E2/Z). Ap Watts
Where S is pointing impedance of medium
Z is intrinsic impedance of medium
E is rms value of electric field

 Effective aperture is defined as the ratio of
power received in the load to the average
power density produced at the point
 Power received by the antenna may be denoted
by PR.
 An antenna should have maximum useful area
to extract energy and thus the max. effective
aperture is obtained when power received is
maximum, denoted by Aem.

 Let us calculate effective aperture for the Herzian
dipole, when the Hertzian dipole is used as the
receiving antenna
 It extracts power from the incident waves and
delivers it to the load, producing voltage in it.
The voltage induced in the antenna is given by
Voc = |E| dL
Where
|E| is the magnitude of Electric Field
Intensity produced at the receiving point
dL is the length of the Hertzian dipole

 Then the current flowing the load is given by
I = Voc / Z + ZL
 For the maximum power transfer condition,
load is selected as the complex conjugate of the
antenna impedance (ZL = Z*)
 Substituting the values of impedance Z and ZL,
the current flowing can be written as

 Therefore
 The maximum effective aperture is given by

Aperture Efficiency :
 According to the standard definition, “Aperture
efficiency of an antenna, is the ratio of the effective
radiating area (or effective area) to the physical area
of the aperture.
 An antenna has an aperture through which the
power is radiated.
 This radiation should be effective with minimum
losses.
 The physical area of the aperture should also be
taken into consideration, as the effectiveness of the
radiation depends upon the area of the aperture,
physically on the antenna.

 The mathematical expression for aperture
efficiency is as follows

Effective Height :
 The Effective length is the ratio of the
magnitude of voltage at the open terminals of
the receiving antenna to the magnitude of the
field strength of the incident wave front, in the
same direction of antenna polarization.
 When an incident wave arrives at the antenna’s
input terminals, this wave has some field
strength, whose magnitude depends upon the
antenna’s polarization.
 This polarization should match with the
magnitude of the voltage at receiver terminals.

 The mathematical expression for effective
length is
Leff = Voc / E i
Where
Leff is the effective length.
Voc is open-circuit voltage.
Ei is the field strength of the incident wave.

Summary of Important Parameters and Associated Formulas

Antennas and Wave Propagation

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