A.D.Patel institute of technology SUB: EM Wave Propagation Prepared by:- Chokshi Abhi (130010111001) Guided by :- Prof. Shailesh khant

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

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.

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.

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

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.

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

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

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

Maxwell’s equation in Point form 10

Maxwell’s Equation in Lossless medium 11

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

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

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

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

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

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

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

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

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

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

Thank You!