Propagation Of Electromagnetic Waves

Electromagnetic waves are waves of electric and magnetic fields that propagate through space, carrying energy from one place to another. These waves do not require a medium to travel; they can move through the vacuum of space at the speed of light, approximately 299,792 kilometres per second. The study of electromagnetic wave propagation is crucial for understanding how various forms of electromagnetic radiation, such as radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays, travel and interact with different materials and environments.

One of the most ubiquitous real-world applications of electromagnetic wave propagation is in communication technology. For instance, radio waves are used in broadcasting audio signals to radios in cars and homes. These waves travel long distances and can penetrate buildings, allowing people to receive radio broadcasts even in remote locations. Similarly, microwaves are employed in satellite communication.

Propagation of Electromagnetic Waves

Electromagnetic Waves are basically defined as superimposed oscillations of an Electric and Magnetic Field in space with their direction of propagation perpendicular to both of them. Electromagnetic waves are oscillations produced due to the crossing over of an electric and a magnetic field. The direction of the propagation of such waves is perpendicular to the direction of the force of either of these fields as shown in the diagram below.

In communication using radio waves, an antenna at the transmitter radiates Electromagnetic waves (em waves), which travel through space and reach the receiving antenna at the other end. As the em wave travels away from the transmitter, the strength of the wave keeps on decreasing. There are several factors which can influence the propagation of em waves and the path they follow.

Ground Wave

These waves are used for a low-frequency range transmission, mostly less than 1 MHz. This type of propagation employs the use of large antenna order which is equivalent to the wavelength of the waves and uses the ground or Troposphere for its propagation. Signals over large distances are not sent using this method. It causes severe attenuation which increases with the increased frequency of the waves.

Sky Wave

Used for the propagation of EM waves with a frequency range of 3 – 30 MHz. They are present in the ionosphere region of charged ions about 60 to 300 km from the earth's surface. These ions provide a reflecting medium to the radio or communication waves within a particular frequency range. We use this property of the ionosphere for long-distance transmission of the waves without much attenuation and loss of signal strength.

Another thing to consider is the angle of the emission of these waves from the ground. The transmitter emits the EM Waves at a critical angle to ensure total reflection to the ground just like the total internal reflection of optic waves otherwise the waves may escape into space. Skip Distance is the distance between the 2 points between which the wave transmission happens.

Space Wave

It is used for a line of Sight communication also known as LoS. Space satellite communication and very high-frequency waves use this method of propagation. It involves sending a signal in a straight line from the transmitter to the receiver. One must ensure that for very large distances, the height of the tower used for transmission is high enough to prevent waves from touching the earth's curvature thus preventing attenuation and loss of signal strength. The important relationship for determining the height of the antennas and their corresponding distance of transmission is given by:

$\begin{array}{rl}& d_M=\sqrt{2R{h}_T}+\sqrt{2R{h}_R}\\ & \text{where}\\ & {\mathrm{d}}_{\mathrm{m}}=\text{distance between}2\text{antennas}\\ & \mathrm{R}=\text{Radius of earth}=6400\mathrm{km}\\ & {\mathrm{h}}_{\mathrm{T}}=\text{Height of transmission antenna}\\ & {\mathrm{h}}_{\mathrm{R}}=\text{Height of receiver antenna}\end{array}$

Another important relation for determining the range of transmission(Dt) for a given antenna of height ${\mathrm{H}}_{\mathrm{t}}$ is
$d_T=\sqrt{2R{h}_T}$

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Solved Example Based On Propagation Of Electromagnetic Waves

Example 1: The following diagram shows the effect on radio wave communication due to varying incidence

T is the source of radio waves on earth and $S_1,S_2,S_3,S_4$ are four points where radio wave is received

Which among the following may be the skip distance for the above radio communication?

1) $T{S}_1$
2) $T{S}_2$
3) $T{S}_3$
4) $T{S}_4$

Solution:

The smallest distance from a transmitter along the earth’s surface at which a SKY wave of a fixed frequency but more than f_c is sent back to earth.

Skip distance is the smallest distance from the transmitter along the surface of the earth at which a sky wave is received on the earth

Here, the smallest distance at which the reflected sky wave is received is $T{S}_2$

Hence, the correct option is (1).

Example 2: A signal is to be transmitted through a wave of wavelength λ, using a linear antenna. The length of the antenna and effective power radiated P_eff will be given respectively as : (K is a constant of proportionality)

$\begin{array}{rl}& \text{1)}\lambda ,P_{eff}=K{\left(\frac{1}{\lambda }\right)}^2\\ & \text{2)}\frac{\lambda }{8},P_{eff}=K\left(\frac{1}{\lambda }\right)\\ & \text{3)}\frac{\lambda }{16},P_{eff}=K{\left(\frac{1}{\lambda }\right)}^3\\ & \frac{\lambda }{4{)}^5},P_{eff}=K{\left(\frac{1}{\lambda }\right)}^{\frac{1}{2}}\\ & \end{array}$

Solution:

Range of transmitting antenna

$d_T=\sqrt{2h_{T}R}$

wherein

$h_T=$ height of antenna
$R=$ Radius of earth

Length of antenna = Comparable to

Power radiated by a linear antenna inversely depends on the square wavelength and directly on the length of the antenna.

Hence.
$\begin{array}{rl}& \text{Hence, Power}=\mu {\left(\frac{1}{\lambda }\right)}^2\\ & \mu =k\end{array}$

Hence, the correct option is (1).

Example 3: To double the covering range of a TV transmission tower, its height should be multiplied by :

1) 4

2) 1.4

3) 0.7

4) 2

Solution:

Range of transmitting antenna

$d_T=\sqrt{2h_{T}R}$

wherein
$h_T=$ height of antenna
$R=$ Radius of earth
Range $=\sqrt{2h{R}_e}$
where $\mathrm{h}=$ height of transmission tower
$\begin{array}{rl}& R_1=\sqrt{2h_1{R}_e}\\ & R_2=\sqrt{2h_2{R}_e}\\ & R_2=2R_1\\ & h_2=4h_1\end{array}$

Hence, the correct option is (1).

Example 4: In a line-of-sight radio communication a distance of about 50km is kept between the transmitting and receiving antennas. If the height of the receiving antennas 70 m, then the minimum height (in meters) of the transmitting antenna should be:

(Radius of the Earth= )

1)32

2)51

3)20

4)40

Solution:

Range of transmitting antenna

Range of transmitting antenna
$d_T=\sqrt{2h_{T}R}$
where:
$h_T=\text{height of antenna}$
$R=$ Radius of earth
$R=6.4\times {10}^6$
$\mathrm{d}=$ Range $=50\mathrm{km}$
$\begin{array}{rl}& d=\sqrt{2R{h}_T}+\sqrt{2R{h}_R}\\ & \Rightarrow 50\times {10}^3=\sqrt{2\times 64\times {10}^5{h}_T}+\sqrt{2\times 64\times {10}^5{h}_R}\\ & \Rightarrow h_T=32\mathrm{m}\end{array}$

Hence, the correct option is (1).

Example 5: For VHF signal broadcasting, ____ ${\mathrm{km}}^2$ of the maximum service area will be covered by an antenna tower of a height of 30 m if the receiving antenna is placed at the ground. Let the radius of the earth be 6400 km . (Round off to the Nearest Integer) (Take $\pi$ as 3.14)

1) 1206

2) 13

3) 45

4) 56

Solution:

The range of transmission(d) for a given antenna of height h is:

$\begin{array}{rl}& \mathrm{d}=\sqrt{2\mathrm{Rh}}\\ & \mathrm{A}=\pi {\mathrm{d}}^2\\ & \mathrm{A}=\pi 2\mathrm{Rh}=3.14\times 2\times 6400\times \frac{30}{1000}\\ & \mathrm{A}=1205.76{\mathrm{km}}^2\\ & \mathrm{A}=1206{\mathrm{km}}^2\end{array}$

Hence, the correct option is (1).

Summary

Electromagnetic waves are oscillations of electric and magnetic fields that propagate through space without requiring a medium, travelling at the speed of light. These waves are fundamental in communication technologies, utilizing ground waves, sky waves, and space waves for transmitting signals over various distances. Key factors influencing wave propagation include frequency, antenna height, and environmental conditions, impacting signal strength and coverage. Practical applications are demonstrated through examples of skip distance, antenna height calculations, and effective power radiation.