1. A.D.Patel institute of technology
SUB: EM Wave Propagation Prepared by:- Chokshi Abhi ( ) Guided by :- Prof. Shailesh khant

2. What is a wave?
a wave is a disturbance that travels through a medium from one location to another.
a wave is the motion of a disturbance

3. Wave frequency
We know that frequency measure how often something happens over a certain amount of time.
We can measure how many times a pulse passes a fixed point over a given amount of time, and this will give us the frequency.

4. Wave frequency
Suppose I just back and forth, and count that 6 waves pass a point in 2 seconds. What would the frequency be?
3 cycles / second
3 Hz
we use the term Hertz (Hz) to stand for cycles per second.

5. Wave Period
The period describes the same thing as it did with a pendulum.
It is the time it takes for one cycle to complete.
It also is the reciprocal of the frequency.
T = 1 / f
f = 1 / T

6. Wave Speed
We can use what we know to determine how fast a wave is moving.
What is the formula for velocity?
velocity = distance / time
What distance do we know about a wave
wavelength
period =  / T
T = 1 / f
so we can also write
v = f 
velocity = frequency * wavelength
This is known as the wave equation.

7. Electromagnetic Waves are characterized by:
Wavelength, l [m, cm, mm, mm etc]
Frequency, f [s-1, hertz (hz), megahertz (Mhz), gigahertz (Ghz)
where: c = l f

8. Modes of Wave Propagation
If Eym = 0, Electric field oscillates in the x direction
and wave is said to be “horizontally polarized”
Also called TE mode of Propagation
If Exm = 0, Electric field oscillates in the y direction
and wave is said to be “vertically polarized”
Also called TM mode of propagation
If Exm = Eym, and d = p/2 or - p/2, electric field vector rotates in a circle and wave is circularly polarized
Also called TEM mode of propagation

9. Terms used in Wave anatomy
Speed of light in a vacuum:
Speed of light in air:
Refractive index:
At sea level: n = 1.003
In space: n = 1.000
Radio refractivity:
At sea level: N = 3000
In space: N = 0

10. Maxwell’s equation in Point form10

11. Maxwell’s Equation in Lossless medium11

12. The wave equations are not independent.
Wave Equations for Electromagnetic Waves in a Simple, Source-Free, Lossless Medium
The wave equations are not independent.
Usually we solve the electric field wave equation and determine H from E using Faraday’s law. 12

13. Uniform Plane wave
A uniform plane wave is an electromagnetic wave in which the electric and magnetic fields and the direction of propagation are mutually orthogonal, and their amplitudes and phases are constant over planes perpendicular to the direction of propagation. 13

14. Velocity of Wave Propagation
The velocity of propagation is determined solely by the medium:
The functions p1 and p2 are determined by the source and the other boundary conditions. 14

15. Intrinsic Impedance
h is the intrinsic impedance of the medium given by
Like the velocity of propagation, the intrinsic impedance is independent of the source and is determined only by the properties of the medium.
Intrinsic impedence of Air is 377Ohm 15

16. Helmholtz equation The Helmholtz equations are not independent.
Usually we solve the electric field equation and determine H from E using Faraday’s law. 16

17. Plane Wave Propagation in Lossy Media
Assume a wave propagating in the +z-direction:
We consider two special cases:
Low-loss dielectric.
Good (but not perfect) conductor. 17

19. Plane Waves in a Good Conductor
In a perfect conductor, the electromagnetic field must vanish.
In a good conductor, the electromagnetic field experiences significant attenuation as it propagates.
The properties of a good conductor are determined primarily by its conductivity. 19

20. Plane Waves in a Good Conductor
For a good conductor,
Hence, 20

21. Plane Waves in a Good Conductor (Cont’d)21

22. Skin effect in good conductor
For a good conductor, we have 22

23. Thank You!