Electromagnetic Wave Theory

Lecture 7

Electromagnetic Radiation Fundamentals of electromagnetic

waves Effects of environment

Propagation of waves Surface waves Ionospheric Propagation

Ionospheric Propagation Ionospheric structure Critical frequency Maximum useable frequency Optimum working frequency Lowest useable frequency

Line of sight propagation

Electromagnetic Radiation 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.

The energy within these fields is

normally confined within the circuit.

In certain circumstances the energy is

radiated or set free from the circuit.

In cases where such a radiation is

undesired it is called radio frequency

interference.

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.

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.

Wavefront

NoteIn this instance the wavefront is spherical, but at large distances from the source the wavefront will become nearly flat.

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.

24 r

Pt

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.

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

where z is the characteristic impedance of the medium which is defined as

Electric and Magnetic field intensity

zHE

z

For free space H/m,

permeability of medium

F/m, electric permittivity

Making the above substitutions

67 10257.1104

129 10854.810361

37712010854.8

10257.112

6

z

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

zE /2

zE 2

making the substitution for and z we obtain

Internal Noise

22

2 30120

4 r

P

r

PE tt

r

PE t30

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.

1

2log20r

r

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.

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.

Effects of environment

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.

Reflection of waves

This again is similar to the situation in light waves. The angle of

incidence equals the angle of refraction, Snell’s law.

where 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

2211 sinsin nn

1n

2n1

2

Refraction

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.

Diffraction

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

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.

Ground Waves

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.

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

If we place a receiving antenna at this point then the signal received in volts will be

d

IhE t

120

d

IhhV rt

120

Field strength at a distance

where is the characteristic impedance

effective height of the transmitting antenna

effective height of the receiving antenna

I antenna current

d distance from the transmitting antenna

wavelength

rhth

120

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

cf

At 20 km in free space from a point source, the power

density is 200 . What is the power density at 25

km away from this source?

2/mW

Example Problems

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 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.

18107.3

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?