# Amrutha Harichandran Assistant Professor ECE Dept., ASE

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Amrutha Harichandran Assistant Professor ECE Dept., ASE
EM THEORY Amrutha Harichandran Assistant Professor ECE Dept., ASE

EM Theory and related subject
Area of interest EM Theory and related subject Difficulties

WAVES: Transfer energy from one place to another
Mechanical Electromagnetic Require a medium Not Require a medium Eg: Water and sound waves Speed of electromagnetic waves = 300,000,000 m/s 8 minutes to move from the sun to earth {150 million miles}

When an electric field changes, so does the magnetic field
When an electric field changes, so does the magnetic field. The changing magnetic field causes the electric field to change. When one field vibrates—so does the other. electromagnetic wave.

Importance of EM Waves Each wavelength of electro-magnetic radiation (light) brings us unique information Almost everything we know about the Universe comes from the study of the electromagnetic radiation emitted or reflected by objects in space Objects in space send out electromagnetic radiation at all wavelengths - from gamma rays to radio waves.

Electromagnetic Spectrum
EM waves when placed in order of increasing frequency Band width and frequency

RADIO WAVES Longest wavelengths and lowest frequencies
A radio picks up radio waves through an antenna and converts it to sound waves Each radio station in an area broadcasts at a different frequency

MICROWAVES Used in microwave ovens. Used by cell phones and pagers
Waves transfer energy to the water in the food causing them to vibrate which in turn transfers energy in the form of heat to the food Used by cell phones and pagers RADAR (Radio Detection and Ranging) Used to find the speed of an object by sending out radio waves and measuring the time it takes them to return.

INFRARED RAYS Infrared= below red
Shorter wavelength and higher frequency than microwaves. You can feel the longest ones as warmth on your skin Heat lamps give off infrared waves. Warm objects give off more heat energy than cool objects. Thermogram—a picture that shows regions of different temperatures in the body. Temperatures are calculated by the amount of infrared radiation given off. Therefore people give off infrared rays.

VISIBLE LIGHT Shorter wavelength and higher frequency than infrared rays. Electromagnetic waves we can see. Longest wavelength= red light Shortest wavelength= violet (purple) light When light enters a new medium it bends (refracts). Each wavelength bends a different amount allowing white light to separate into it’s various colors ROYGBIV.

ULTRAVIOLET RAYS Shorter wavelength and higher frequency than visible light Carry more energy than visible light Used to kill bacteria. (Sterilization of equipment) Causes your skin to produce vitamin D (good for teeth and bones) Used to treat jaundice ( in some new born babies. Too much can cause skin cancer. Use sun block to protect against (UV rays)

X- RAYS Shorter wavelength and higher frequency than UV-rays
Carry a great amount of energy Can penetrate most matter. Bones and teeth absorb x-rays. (The light part of an x-ray image indicates a place where the x-ray was absorbed) Too much exposure can cause cancer Used by engineers to check for tiny cracks in structures.

GAMMA RAYS Shorter wavelength and higher frequency than X-rays
Carry the greatest amount of energy and penetrate the most. Used in radiation treatment to kill cancer cells. Can be very harmful if not used correctly.

Using the EM waves to view the Sun
At different wavelengths

They all have different wavelength and different frequencies.
Brief SUMMARY All electromagnetic waves travel at the same speed. (300,000,000 meters/second in a vacuum. They all have different wavelength and different frequencies. Long wavelength-lowest frequency Short wavelength highest frequency The higher the frequency the higher the energy.

Electromagnetic Spectrum Quiz
Which of the following is correct in order of lowest to highest frequency? [A] X-rays, Visible Light, Microwave [B] Ultraviolet, Visible Light, Gamma-rays [C] Microwave, Visible Light, Gamma-rays Answer: C

Gas in space emits radio waves.
[A] True [B] False Answer: A

This type of emission can come from radioactive materials.

Applications of EM Waves
Transmission Lines High frequency circuits Satellite Communication Antenna Fiber Optic Communication Mobile Communication EMI and EMC

Transmission Lines Carry EM energy Eg: Coaxial cable
Low frequency and high frequency LOW Freq HIGH Freq . Discrete Components-RLC .Physical size has no effect .KVL KCL .V and I . Distributed .Length of the connecting wire .Maxwell .Waves

High frequency circuits
Discontinuity in ckt path – Radiation Computer Satellite Communication C band (6/4 GHz) Remote sensing Antenna EMI/EMC Tempest

Transmission Media Twisted Pair Coaxial Cable Wave Guide Low Data Rate
Telephone lines-avoid common interference Coaxial Cable Few Mbps LAN Wave Guide High frequency Center conductor loss- Skin effect

Q.1 A plane wave propagating in a lossless dielectric medium has n electric field given as E= 10 cos(1.5x 1010 t z). Determine the wavelength , phase velocity and wave impedance for this wave and the dielectric constant of the medium.

E=E0 cos(wt-kz) Angular velocity w= Wavenumber / Phase constant k=

E=E0 cos(wt-kz) Angular velocity w=1.5x 1010 rad/sec Wavenumber / Phase constant k= 61.6 m-1

Wave length λ = 2π/k Phase Velocity Vp= w/k εr = (c/ Vp )2 η= η0 / √εr

Wave length λ = 2π/k =0.102 m Phase Velocity Vp= w/k = 2.45 x 108 m/sec εr = (c/ Vp )2= 1.5 η= η0 / √εr = Ω

Q. 2 A plane wave incident on a medium having εr = 9 and incident power is 45 w/m2.Find reflection coefficient reflected power and power transmitted through the medium?

Reflection coefficient, R= (1- √εr )/(1+ √εr )
Reflected Power=lRl2 x Incident Power Transmitted Power= (1-lRl2 )x Incident Power

Q. 3 A radio transmitter is connected to an antenna having an impedance 80+j40 Ω with a 50 Ω coaxial cable. If the 50 Ω transmitter can deliver 30 W when connected to a 50 Ω load, how much power is delivered to the antenna.

R= (Zl - Zo)/ (Zl +Zo) PLoad =PIncident – Preflected Pload = (1-lRl2 )x PIncident

R= (Zl - Zo)/ (Zl +Zo) = 0.367<360

Q. 4 A transmission line has the following per unit length parameters: L=0.2 µ H/m, C= 300 pF/m, R= 5 Ω/m and G=0.01 S/m. Calculate the propagation constant and characteristic impedance of this line at 500 MHz. Recalculate these quantities in the absence of loss

r = √((R+jwL)(G+jwC)) = α + j β Zo = √((R+jwL)/(G+jwC))
Propagation Constant r = √((R+jwL)(G+jwC)) = α + j β Zo = √((R+jwL)/(G+jwC)) Absence of loss (R=G=0) α=0 r =w √(LC) Zo = √(L/C)

r = √((R+jwL)(G+jwC)) = α + j β =0.23+j24.3 rad/m
Propagation Constant r = √((R+jwL)(G+jwC)) = α + j β =0.23+j24.3 rad/m Zo = √((R+jwL)/(G+jwC)) = 25.8+j 0.03 Ω Absence of loss (R=G=0) α=0 r =w √(LC)=24.3 rad/m Zo = √(L/C)=25.8 Ω

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