# Electromagnetics

#### 1. Course Information :

a) Catalog Description:
This course provides a foundation for the electromagnetic theory, with applications in electrical and electronic engineering. Topics include: electrostatics, Gauss’s laws, Faraday’s law for electromagnetic induction, Ampere’s law, electric and magnetic fields in materials, dielectrics, capacitance and inductance in circuit models, differential and integral forms of Maxwell’s equations, boundary field conditions; electromagnetic waves, propagation of plane waves, scattering of plane waves from media boundaries, radiation, antenna gain and directivity.
b) Course Objectives:

This course introduces students to handling electromagnetic theory using vector calculus. introduce students to the concepts of static and dynamic electromagnetic fields, to expose students to the physical meaning of Maxwell’s equations, to provide students with the necessary basics in wave and antenna theories.

c) Course Learning Outcomes (CLO):

After the course the student shall from a description of a situation that leads to an electromagnetic field problem be able to use their conceptual understanding of the electromagnetic laws in order to qualitatively describe the behavior of the solution to the problem, use their ability to manage the electromagnetic laws to, in simple situations, set up a computational model and perform the necessary calculations: select appropriate methods; make appropriate approximations; plausibility assesses the results.

2. Course details:Electromagnetic wave:

Electromagnetic waves or EM waves are waves that are created as a result of vibrations between an electric field and a magnetic field. In other words, EM waves are composed of oscillating magnetic and electric fields.

EM waves travel with a constant velocity of 3.00 x 108 ms-1 in vacuum. They are deflected neither by the electric field, nor by the magnetic field. However, they are capable of showing interference or diffraction. An electromagnetic wave can travel through anything – be it air, a solid material or vacuum. It does not need a medium to propagate or travel from one place to another. Mechanical waves (like sound waves or water waves), on the other hand, need a medium to travel. EM waves are ‘transverse’ waves. This means that they are measured by their amplitude (height) and wavelength (distance between the highest/lowest points of two consecutive waves).

The above diagram shows an electromagnetic wave propagating in the x direction, if the electric field is in the y direction and the magnetic in the z direction.

Characteristics of Electromagnetic Waves

• Electromagnetic waves are transverse in nature as they propagate by varying the electric and magnetic fields such that the two fields are perpendicular to each other.
• Accelerated charges are responsible to produce electromagnetic waves.
• Electromagnetic waves have constant velocity in vacuum and it is nearly equal to which is denoted by
• Electromagnetic wave propagation it does not require any material medium to travel.
• In an electromagnetic wave the oscillating electric and magnetic fields are in same phase and their magnitudes have a constant ratio. The ratio of the amplitudes of electric and magnetic fields is equal to the velocity of the electromagnetic wave,
• The inherent characteristic of electromagnetic wave is its frequency. Their frequencies remain unchanged but its wavelength changes when the wave travels from one medium to another.

The Electromagnetic Spectrum

The electromagnetic spectrum is the range of frequencies (the spectrum) of electromagnetic radiation and their respective wavelengths and photon energies.

Maxwell’s Equations

Maxwell’s Equations are a set of 4 complicated equations that describe the world of electromagnetics. These equations describe how electric and magnetic fields propagate, interact, and how they are influenced by objects.

The first is Faraday’s law of induction, the second is Ampere’s law as amended by Maxwell to include the displacement current ∂D/∂t, the third and fourth are Gauss’ laws for the electric and magnetic fields. For more information see reference [1], [2].

boundary condition

An equation that specifies the behavior of the solution to a system of differential equations at the boundary of its domain. Maxwell’s equations in differential form require known boundary values for a complete and unique solution.

In above image, the boundary condition will be when the incident wave travel from region 1 to region 2, and this boundary will be at x=0.

Introduction to Antennas

An antenna is used to radiate electromagnetic energy efficiently and in desired directions. Antennas act as matching systems between sources of electromagnetic energy and space. The goal in using antennas is to optimize this matching.

Antennas properties:

1-Field intensity for various directions (antenna pattern).
2-Total power radiated when the antenna is excited by a current or voltage of known intensity.
3-Radiation efficiency which is the ratio of power radiated to the total power.
4-The input impedance of the antenna for maximum power transfer (matching).
5-The bandwidth of the antenna or range of frequencies over which the above properties are nearly constant.

The radiation pattern of an antenna gives us information about its receiving and transmitting properties in different directions.

The given figure is a three-dimensional radiation pattern for an Omni directional pattern. This clearly indicates the three co-ordinates (x, y, z).

wo-dimensional pattern can be obtained from three-dimensional pattern by dividing it into horizontal and vertical planes. These resultant patterns are known as Horizontal pattern and Vertical pattern respectively.

Antennal Directivity and Gain:

A radio antenna radiates a given amount of power. This is the power dissipated in the radiation resistance of the Radio antenna. An isotropic radiator will distribute this equally in all directions. For an antenna with a directional pattern, less power will be radiated in some directions and more in others. The fact that more power is radiated in given directions implies that it can be considered to have a gain.

The gain can be defined as a ratio of the signal transmitted in the “maximum” direction to that of a standard or reference antenna. This may sometimes be called the “forward gain”.

Some types of Antenna:

• Dipole Antennas: The dipole is one of the most common antennas. It consists of a straight conductor excited by a voltage from a transmission line or a waveguide. Dipoles are easy to make.

• Loop Antennas: A loop of wire, with many turns, is used to radiate or receive electromagnetic energy

• Aperture Antennas : A horn as shown in the figure below is an example of an aperture antenna. These types of antennas are used in aircraft and spacecraft.

• Reflector Antennas: The parabolic reflector is a good example of reflectors at microwave frequencies. In the past, parabolic reflectors were used mainly in space applications but today they are very popular and are used by almost everyone who wishes to receive the large number of television channels transmitted all over the globe.

• Array Antennas: A grouping of similar or different antennas form an array antenna. The control of phase shift from element to element is used to scan electronically the direction of radiation.

3. Summary:

In this course, the student has a basic concept for electromagnetic theory, and study differential and integral forms of Maxwell’s equations, boundary field conditions. The student is given a short review about antenna and it is the concept of radiation pattern and how to the meaning of gain antenna.

4. References:

[1] Daniel fleisch, A Student’s Guide to Maxwell’s Equations, Cambridge University,2008.

[2] David Pozar, Microwave Engineering 4ed, Wiley_2012.