Electromagnetic Wave Theory
Lecture 7
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Electromagnetic Radiation
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Fundamentals of electromagnetic waves
Effects of environment
Propagation of waves
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Surface waves
Ionospheric Propagation
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Ionospheric Propagation
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Ionospheric structure
Critical frequency
Maximum useable frequency
Optimum working frequency
Lowest useable frequency
Line of sight propagation
Electromagnetic Radiation
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Electricity and electromagnetic waves are
related.
The electrical energy generated in a
circuit is converted into electromagnetic
energy.
An electromagnetic field is made up of an
electric and magnetic field. These fields
exist within all electric circuits.
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The energy within these fields is normally
confined within the circuit.
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In certain circumstances the energy is
radiated or set free from the circuit.
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In cases where such a radiation is
undesired it is called radio frequency
interference.
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For a radio transmitter the circuit is
specially designed to radiate maximum
energy.
The electric and magnetic fields are
perpendicular to each other and both
are also perpendicular to the direction
of propagation, as such they are said
to be transverse.
Wavefront
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If an electromagnetic wave were
radiated equally in all directions from a
point source, a spherical wavefront
would result. Such a source is said to
be isotropic.
A wavefront is a plane, which joins all
points of equal phase.
Note
In this instance the wavefront is spherical, but at large
distances from the source the wavefront will become nearly
flat.
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The power density (in watts per square
meter) at a wavefront is inversely
proportional to the square of the
distance from the source, with respect
to the power originally transmitted. In
mathematical terms.
Pt

2
4r
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where Pt is the power generated at the
source.
This is called the inverse square law
and it applies to all forms of radiation in
free space.
Electric and Magnetic field intensity
These are the direct counterparts of voltage and current in circuits.
Electric field intensity (E) is measured in volts per meter V/m
Magnetic field intensity (H) is measured in amperes per meter A/m.
It follows that
E  zH
where z is the characteristic impedance of the medium which is
defined as

z

For free space   4
permeability of medium
10  1.257 10
7
  1 36 10  8.854 10
9
12
6
H/m,
F/m,
electric permittivity
Making the above substitutions
1.257  10 6
z
 120  377 
12
8.854  10
The field strength can therefore be calculated at a distance r
from the point source.
Just like in electrical circuits, the power for electromagnetic
waves can be found by using
 E / z
2
E   z
2
Internal Noise
making the substitution for  and z we obtain
Pt
30 Pt
E 
 120  2
2
4r
r
2
30 Pt
E
r
Attenuation and Absorption
From the inverse square law it can be established that the power
density diminishes rapidly with distance from the source of the
electromagnetic waves.
The waves are then said to be attenuated as they move away from
the source and it is proportional to the square of the distance
travelled.
The attenuation is measured in decibels is numerically the same
for both field intensity and power density.
r2
  20 log
r1
In free space, absorption of radio waves does not occur, because
there is nothing there to absorb them.
In the atmosphere some of the energy in the electromagnetic wave
is transferred to atoms and molecules in the atmosphere.
At frequencies below 10 GHz this absorption is not significant.
Effects of environment
When waves are propagated near the earth several factors
have to be considered.
The waves are subject to reflection by the ground,
mountains and buildings.
The will also be refracted as they pass through different
layers of atmosphere.
They can also be diffracted by tall objects.
Reflection of waves
Similar to light waves electromagnetic waves are also reflected by
a conducting medium.
The angle of incidence will be equal to the angle of reflection.
The reflection coefficient, is defined as the ratio of the electric
intensity of the reflected wave to that of the incident wave. For a
perfect reflector it is unity.
It is important that the electric vector be perpendicular to the
conducting surface. If it is fully parallel to the surface, the electric
field is shorted out and all of the energy is dissipated in the form
of surface currents.
Refraction
This again is similar to the situation in light waves. The angle of
incidence equals the angle of refraction, Snell’s law.
n1 sin 1  n2 sin  2
where
n2
1
2
n1
is the refractive index of the incident medium,
is the refractive index of the refractive medium,
is the angle of incidence,
is the angle of refraction
Diffraction
This is the phenomenon whereby waves travelling in straight
paths bend around an obstacle.
It is known as Huygens’ principle. This states that each point
on a spherical wavefront maybe considered as a source of a
secondary spherical wavefront.
This concept explains why it is possible to obtain reception
behind a mountain or tall building.
Propagation of Waves
The basic modes by which radio waves are transmitted to a
receiving antenna are:
Ground (Surface) Waves
Space Waves
Sky Waves
Satellite Communication
Ground Waves
These travel along the surface of the earth (more or less
following the contour of the earth) and must be vertically
polarized to prevent short-circuiting.
They can travel considerable distances, well over the visual
horizon.
As the wave propagates over the earth, it tilts over more and
more. (A current is induced in the earth’s surface by the
electromagnetic wave, the result is the wavefront near the
surface slows down).
This causes the wave to short circuit completely at some
distance (in wavelengths) from its source.
This shows that the maximum range of such a transmitter depends
on its frequency as well as its power.
Increasing the frequency of transmission increases the loss. They
are therefore not effective above 2 MHz.
It is much better over water than dry ground. They are a reliable
communication link. Reception is not affected by daily or
seasonal changes.
Used effectively to communicate with submarines at extremely
low frequencies 30 – 300 Hz.
Field strength at a distance
Radiation from an antenna by means of ground wave taking into
consideration the gain of the transmitting antenna at a distance may
be found using
120ht I
E
d
If we place a receiving antenna at this point then the signal received
in volts will be
120ht hr I
V
d
where 120 is the characteristic impedance
ht
effective height of the transmitting antenna
hr
effective height of the receiving antenna
I
antenna current
d
distance from the transmitting antenna
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wavelength
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when propagation is over a good conductor
such as seawater, at low frequencies, surface
absorption is small, the attenuation is equally
small.
The angle of tilt is thus the main factor in the
long distance propagation of such a wave.
The degree of tilt depends on the distance
from the antenna in wavelengths. Low
frequency signals have large wavelengths
f 
c
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Example Problems
At 20 km in free space from a point source, the power
density is 200 W / m2 . What is the power density at 25
km away from this source?
Calculate the power density at
a) 500 m from a 500 W source and
b) 36 000 km from a 3 kW source.
Assume the source to be isotropic
A deep space high gain antenna and receiver system have a noise
figure such that a minimum received power of
3.7 1018 W is
required for satisfactory communication. What must be the
transmitting power from a Jupiter probe, situated 800 million km
from earth? Assume that the transmitting antenna is isotropic and
the equivalent area of the receiving antenna has an area of 8400
m2.
A 150 m antenna transmitting at 1.2 MHz (ground wave), has
an antenna current of 8 A. What voltage is received by the
receiving antenna 40 km away with a height of 2 m?