Unit-1fundamentals of Electromagnetic

7/29/2019 Unit-1fundamentals of Electromagnetic

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FUNDAMENTALS

OFELECTROMAGNE

TICSPrepared by: Prof. K. K. SAWANT


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MAXWELL EQUATIONS

Electric Charges

Electric Currents

Electromotive Force

Within Material Media: Polarization and

Magnetization of charge

Lorentz force equation: for charge velocity


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James Clerk Maxwell (1831-1879)

ELECTROMAGNETIC THEORY


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MAXWELL EQUATIONS

Electric charges whose density are the sources of

electric field E . MKSA system: Gauss's law-

Electric charges

(1)


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Electric currents

If Field lines are closed..?

This is equivalent to the statement that there are no

magnetic monopoles.

Mathematically this is expressed by the equation

(2)

(3)


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The electromotive force around a closed field is proportional to

the rate of change of flux of the magnetic field B ( )

Electromotive Force: Faradays law

In differential form this law is expressed by the following formula:

Within material media having polarization ~P and magnetization ~M the above

laws still hold with the following replacements: as the density of , E & B

Within Material Media: Polarization and magnetization

..(4)

..(5)


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Polarization

Polarization is a property of wave that describes the

orientation of their oscillations.

EM wave: light wave, exhibit polarization;

When light travels in free space, in most cases it

propagates as a transverse wave the polarization is

perpendicular to the wave's direction of travel.

Acoustic waves: Sound waves in a gas or liquid do not

have polarization because the direction of vibration and

direction of propagation are the same.


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If EM wave is composed of two plane waves ofequal amplitude, and by 90 phase

difference, then the wave is said to be circularly polarized.

Circularly Polarization


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Circularly Polarization

Electric field of the passing wave does not change strength(constantmagnitude) but only changes direction in a rotary manner.

Click here: Animation

of a circularly polarized

wave as a sum of two

components

If wave is clockwise

rotation , then left-

circularly polarized wave

and vice versa


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Elliptically polarized wave consists of two perpendicular waves of unequal amplitude

which differ in phase by 90.

Elliptical Polarization

If electric field magnitude is not same or and the phase angle is other than 0, 90, 180.


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Elliptical Polarization

Elliptical

The electric field vector describes an ellipse in any fixed plane intersecting, and normal to, the

direction of propagation.

If two plane waves of differing amplitude are related in phase by 90, or if the relative phase is

other than 90 then the light is said to be elliptically polarized.


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.

Linear polarization


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Linear polarization

The orientation of a linearly polarized EM wave is defined by the direction of

the electric field vector.

- For example, if the electric field vector is vertical direction (alternately up

and down as the wave travels) the radiation is said to be vertically polarized.

A plane electromagneticwave is said to be linearly

polarized.


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Over long distances, the atmosphere can cause the polarization of a radio wave to

fluctuate, so the distinction between horizontal and vertical becomes lesssignificant.

Some wireless antennas transmit and receive EM waves whose polarization

rotates 360 degrees with each complete wave cycle. This type of polarization,

called elliptical or circular polarization,


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Thus, a vertical antenna receives and emits vertically

polarized waves, and a horizontal antenna receives or emits

horizontally polarized waves. The best short-range

communications is obtained when the transmitting and

receiving (source and destination) antennas have the same

polarization.

The physical orientation of a wireless antenna corresponds

to the polarization of the radio waves received or transmitted

by that antenna.
http://searchmobilecomputing.techtarget.com/definition/antennahttp://searchmobilecomputing.techtarget.com/definition/antenna


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Methods of achieving polarization
http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/polar.htmlhttp://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/polar.htmlhttp://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/polar.htmlhttp://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/polpri.html


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Electric field displacement

By polarization

Magnetic field by magnetization


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Lorentz force

1. The force(F) acting on a charge(e) , which is at

rest within an electric field(E), is:

F = Ee.(1)

2. The force acting on a small wire element(dl),

carrying electric current(I), which is placed in a

magnetic field(B), is:

F= I dl x B(2).


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Cont.

These two equations suggest that for a charge(e) moving

with velocity(u) , the total force(F) acting on it is(at once

charge movement/velocity from one-2-other point):

F= e (E + u + B).(3)

e e

For a continuous charge() and current(J) distribution, it

is convenient to define the force density (f) is

f= E+ J B(4)e e e e e e

This is the (3&4)well known Lorentz forceequation.


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Concluding Remark


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Thanks !


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ELECTROMAGNETIC WAVE

PROPAGATION


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ELECTROMAGNETIC WAVE PROPAGATION

Electromagnetic waves are propagated in:

1. Vacuum/air/outer space

2. Conducting media

3. Non-conducting media



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1. Vacuum/air/outer space

EM wave transports its energy through a vacuum at a speed of light c= 3.00 x 108 m/s.

The propagation of an EM wave through a material medium occurs at a net speed

which is less than 3.00 x 108 m/s.

CLICK: Animation

The mechanism of energy transport through a medium involves the absorptionand reemission of the wave energy by the atoms of the material.

M h i f EM h h di


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Mechanism of EM energy transport through a medium

EM wave impinges

upon the atoms of a

material

Energy of that

wave is

absorbed

causes the electrons

within the atoms to

undergo vibrations

After a short period

of vibrational

motion

The vibrating

electrons create a

new EM wave

Frequency of

new EM wave is

same as 1st EM

wave.

These vibrations

occur for only a

very short time

Then they delay the

motion of the wave

through the medium

Energy of the EM

wave is reemitted

by an atom

It travels through

a small region of

space between

atoms.

It reaches

the next

atom

Then it is known as

EM wave is

absorbed,

transformed into

electron vibrations

and then reemittedas an EM wave.

*At last speedof EM wave to

be less than c

* See next slide.


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OBSERVATIONS

The actual speed of an EM wave through a material medium isdependent upon the optical density of that medium.

Different materials cause a different amount of delay due to the

absorption and reemission process.

Different materials have their atoms more closely packed and thus the

amount of distance between atoms is less.

These two factors are depend upon the nature of the material throughwhich the EM wave is traveling.


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Simple Demo

They have the motion, but we cant see

or feel them, but they are around us!

That means, detector placed anywhere

in this room will indicate that the

waves have propagated.


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Diagram of Demonstration

key

Power

Source/Battery

+-

EM wave

Radiator

Detector


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EM Wave equation in vaccum

Assume Maxwell simple equation:

------------- For Electric Field

----------- For Magnetic Field

Assumptions that , charge density and current density J were zero, and

that the permeability and permittivity were constants.

We found that the above equations had plane-wave solutions with velocity:

EM wave travels in free space at the speed of light

0=vaccume permittivity

0=vaccume permeability


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We can derive from the Maxwell laws following equation:

In a nonconducting media/regions where there are nocharge and no current distributions,

------------- (1) For Electric Field

----------- (2) For Magnetic Field

Then !

Propagation in nonconducting media ( = 0) =conductivity, constant

PROPAGATION OF ELECTROMAGNETIC WAVES

Medium with values: =dielectric constant(permittivity); =magnetic

permeability, r= relative permittivity


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Absent

Their right hand sides are absent**, and

Medium with values: =dielectric constant(permittivity); =magnetic

permeability

Then !

We can derive from the Maxwell laws following equation:

------------- (1) For Electric Field

----------- (2) For Magnetic Field


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Electric and magnetic fields E and B,

satisfy the free space wave equations. Thewaves travels with velocityu.

Electric and magnetic fields of a plane

wave are perpendicular to each other and

both perpendicular to the direction of the

propagation.

**In regions, where there are nonvanishing

charge and current distributions the right

hand sides of eqs. are non-vanishing too

and are the sources of the electromagnetic

waves#.

C=

wave propagating

------ (3)


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#Theplane waves are particular solutions of (eqn.1,2) in regions where

sources are absent.

In the following we shall use complex notation and write the electric

component of a plane wave as:

------ (4)

Similar expression holds for the magnetic field too with E, E0 replaced by B, B0

respectively.

E0=amplitude of electric field,

k= its wave vector, k=wave no

w=its frequency

k=number of wavelengths per unit distance

K= it helps to describe the magnitude and direction of wave- wavenumberorangular wavenumberanddirection ofwave propagation resp.
http://en.wikipedia.org/wiki/Wavenumberhttp://en.wikipedia.org/wiki/Angular_wavenumberhttp://en.wikipedia.org/wiki/Wave_propagationhttp://en.wikipedia.org/wiki/Wave_propagationhttp://en.wikipedia.org/wiki/Angular_wavenumberhttp://en.wikipedia.org/wiki/Wavenumber


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2. Propagation within a conductor ( 0)

For times much larger than the relaxation time there are practically no

charges inside the conductor, All of them have moved to its surface where

they form a charge density

Charge move almost instantly to the surface of the conductor.

=conductivity, constant


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We shall restrict our analysis to the case of conductors, which are defined by:

Where, is a constant, the conductivity of the material.

J is the current density


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Cont.


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PROPAGATION OF EMWAVES INWAVE

GUIDES

Thanks!


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1

2

The Equations of Electromagnetism

E dAq

0

B dA 0

..monopole..

?...theres no

magnetic monopole....!!

Gausss Laws


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4


E dld

dtB

B dl I 0

3

.. if you change a

magnetic f ield you

induce an electr ic

field.........

.......is the reverse

true..?

Faradays Law

Amperes Law

lets take a look at charge f lowing into a capacitor


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...lets take a look at charge f lowing into a capacitor...

...when we derived Amperes Law

we assumed constant current...

EB

B dl I 0

lets take a look at charge f lowing into a capacitor


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...lets take a look at charge f lowing into a capacitor...

E

...when we derived Amperes Law

we assumed constant current...

.. i f the loop encloses one

plate of the capacitor..there

is a problem I = 0

B

Side view:(Surface

is now l ike a bag:)

EB

B dl I 0

Maxwell solved this problem


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by realizing that....

B EInside the capacitor there mustbe an induced magnetic field...

How?.



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B E

x

x x x x

x x x x x

x x

A changing

electric field

induces a

magnetic field

Inside the capacitor there mustbe an induced magnetic field...

How?. Inside the capacitor there is a changing E

E

B



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B E

x

x x x x

x x x x x

x x

A changing

electric field

induces a

magnetic field



where Id

is cal led the

displacement cur rent

B dld

dtIE d 0 0 0

E

B

Changed from previous eqn. instead constant current I



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B E

B dl Id

dt

E 0 0 0

x

x x x x

x x x x x

x x

A changing

electric field

induces a

magnetic field



where Id

is cal led the

displacement cur rent

Therefore, Maxwells revision

of Amperes Law becomes....

B dld

dtIE d 0 0 0

E

B



Derivation of Displacement Current


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Derivation of Displacement Current

q EA I dq

dt

d EA

dt 0 0

( )For a capacitor, and .

Id

dtE 0

( )Now, the electric flux is given by EA, so: ,where this current , not being associated with charges, is

called the Displacement current, Id.

Hence:

and: B ds I I

B ds Id

dt

d

E

0

0 0 0

( )

Id

dtdE 0 0

Again the previous equation becomes

Maxwells Equations of Electromagnetism


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(with charge & masses)

E dA q 0

B dA

0

E dld

dtB

Gauss Law for Electrostatics

Gauss Law for Magnetism

Faradays Law of Induction

Amperes Law B dl Id

dtE 0 0 0



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Maxwell s Equations of Electromagnetism

in Vacuum (no charges, no masses)

Consider these equations in a vacuum...........no mass, no charges. no currents.....

B dld

dtE 0 0

E dl ddt

B

E dA

q

0

B dA 0

B dl Id

dt

E 0 0 0

E dA

0

E dl ddt

B

B dA 0Faradays Law of Induction

Amperes Law


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X E = - B /t

X H = D/t + J

. D =

. B = 0

Where,

= 1/0 BD = 0 E

0 = 4 X 10-7 h/m

0 = 8.854 X 10-12 farad/m


(at this point )



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(in general form at this point )

E dAq

0B dA

0

E dld

dtB

B dl I 0

Gauss Law for Electrostatics

Gauss Law for Magnetism

Faradays Law of Induction

Amperes Law


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Permittivity is the measure of the resistance that is encounteredwhen forming an electric field in a medium. i.e.

Permittivity: it is a measure of how an electric field affects, and

is affected by, a dielectric medium.

Permittivity relates to a material's ability to transmit (or "permit") an

electric field.

It Describes how much electric field (more correctly, flux) is

'generated' per unit charge.

Permeability is the measure of the ability of a material to

support the formation of a magnetic field within itself.

It is the degree of magnetization that a material obtains inresponse to an applied magnetic field.

Forces


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The term ndiactes power density

(watts per meter squared) that the transmitter produces at the target

Or Total power intercepted by the target.

Forces


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Forces


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Brief review:

Water and sound waves transfer energy

from one place to another- they require a

medium through which to travel. They are

mechanical waves.

Electric field-region in which charged

particles can be pushed or pulled.


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Nature of Electromagnetic Waves

They are Transverse waves without a medium. (Theycan travel through empty space)

They travel as vibrations in electrical and magneticfields.

Have some magnetic and some electrical properties tothem.

Speed of electromagnetic waves = 300,000,000

meters/second (Takes light 8 minutes to move from thesun to earth {150 million miles} at this speed.)


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When an electric field changes, so does the

magnetic field. The changing magnetic field causes

the electric field to change. When one fieldvibratesso does the other.

RESULT-An electromagnetic wave.

Click hereAnimation: Interaction of vibratingcharges

Waves or Particles
http://www.colorado.edu/physics/2000/waves_particles/wavpart4.htmlhttp://www.colorado.edu/physics/2000/waves_particles/wavpart4.htmlhttp://www.colorado.edu/physics/2000/waves_particles/wavpart4.htmlhttp://www.colorado.edu/physics/2000/waves_particles/wavpart4.html


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Waves or Particles

Electromagnetic radiation has properties of waves but

also can be thought of as a stream of particles.

Example: Light

Light as a wave: Light behaves as a transverse wave

which we can filter using polarized lenses.

Light as particles (photons)

When directed at a substance light can knock electronsoff of a substance (Photoelectric effect)

PROPAGATION OF EM WAVES


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PROPAGATION OF EM WAVES

Power density is intercepted by the target, has

Cross section , which has units of area (meters squared).

= Cross section of Power density .

3.


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B. Waves of the Electromagnetic Spectrum


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B. Waves of the Electromagnetic Spectrum Electromagnetic Spectrumname for the range of

electromagnetic waves when placed in order of increasing frequency

Click here (AnimationSize of EMwaves)

RADIO

WAVES

MICROWAVES

INFRARED

RAYS

VISIBLE LIGHT

ULTRAVIOLET

RAYS

X-RAYS

GAMMA

RAYS
http://www.colorado.edu/physics/2000/waves_particles/index.htmlhttp://www.colorado.edu/physics/2000/waves_particles/index.htmlhttp://www.colorado.edu/physics/2000/waves_particles/index.htmlhttp://www.colorado.edu/physics/2000/waves_particles/index.html


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RADIO WAVES

A. Have the longest wavelengths and lowestfrequencies of all the electromagnetic waves.

B. A radio picks up radio waves through an antenna andconverts it to sound waves.

C. Each radio station in an area broadcasts at a differentfrequency. # on radio dial tells frequency.

D. MRI (MAGNETIC RESONACE IMAGING)

Uses Short wave radio waves with a magnet to create an

image


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MRI of the Brain

AM=Amplitude modulationwaves bounce off ionosphere can


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p ppick up stations from different cities.

(535kHz-1605kHz= vibrate at 535 to 1605 thousand times/second)

+

FM=Frequency modulationwaves travel in a straight line &


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q y gthrough the ionosphere--lose reception when you travel out of range.

(88MHz-108MHz = vibrate at 88million to 108million times/second)

+

INFRARED RAYS


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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.

Thermograma picture that shows regions of differenttemperatures in the body. Temperatures are calculated bythe amount of infrared radiation given off. Therefore

people give off infrared rays.
http://www.snellinfrared.com/library/_view_msg.asp?refid=19


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VISIBLE LIGHT
http://www.snellinfrared.com/library/_view_msg.asp?refid=19


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VISIBLE LIGHT

Shorter wavelength and higher frequency thaninfrared 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 itsvarious colors ROYGBIV.


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ULTRAVIOLET RAYS


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ULTRAVIOLET RAYS

Shorter wavelength and higher frequency thanvisible light

Carry more energy than visible light

Used to kill bacteria. (Sterilization of equipment)

Causes your skin to produce vitamin D (good forteeth 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


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X- RAYS

Shorter wavelength and higher frequency than UV-rays Carry a great amount of energy

Can penetrate most matter.

Bones and teethabsorb 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

(lead vest at dentist protects organs from unnecessary exposure)

Used by engineers to check for tiny cracks in structures.

The rays pass through the cracks and the cracks appear dark onfilm.


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GAMMA RAYS


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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.


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Using the EM waves to view the Sun

AnimationView a Galaxy at different wavelengths
http://www.classzone.com/books/earth_science/terc/content/visualizations/es2801/es2801page01.cfmhttp://www.classzone.com/books/earth_science/terc/content/visualizations/es2801/es2801page01.cfm


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Brief SUMMARY

A. All electromagnetic waves travel at thesame speed. (300,000,000 meters/second in avacuum.

B. They all have different wavelength anddifferent frequencies.

Long wavelength-lowest frequency

Short wavelength highest frequency

The higher the frequency the higher the energy.

MICROWAVES


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MICROWAVES

Microwaveshave the shortest wavelengths andthe highest frequency of the radio waves.

Used in microwave ovens.

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.


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What is radio frequency ?

Microwave Frequency

frequency: 1 GHz ~ 300 GHz

wave length: 30cm ~ 1mm

Radio Frequency

frequency: several hundred MHz to low

microwave frequency band


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IEEE frequency bandBand numbe Designation Aapplication

2 ELF 30-300 Hz 10-1 Mm

3 VF 300-3000 Hz 1-0.1 Mm

4 VLF 3-30 kHz 100-10 km Navigation,sonar

5 LF 30-300 kHz 10-1 km Radio beacons, navigation

6 MF 300-3000 kHz 1-0.1 km AM broadcast, Coast Guard

7 HF 3-30 MHz 100-10 m Telephone, telegraph

8 VHF 30-300 MHz 10-1 m TV, FM broadcast

9 UHF 300-3000 MHz 100-10 cm TV, satellite links

10 SHF 3-30 GHz 10-1 cm Radar, microwave links

11 EHF 30-300 GHz 1-0.1 cm Radar, experimental

12 Decimillimeter 300-3000 GHz 1-0.1 mm

P-band 0.23-1 GHz 130-30 cm

L-band 1-2 GHz 30-15 cm

S-band 2-4 GHz 15-7.5 cm

C-band 4-8 GHz 7.5-3.75 cm

X-band 8-12.5 GHz 3.75-2.4 cm

Ku-band 12.5-18 GHz 2.4-1.67 cm

K-band 18-26.5 GHz 1.67-1.13 cm

Ka-band 26.5-40 GHz 1.13-0.75 cm

Millimeter wave 40-300 GHz 7.5-1 mm

Submillimeter wave 300-3000 GHz 1-0.1 mm

Frequency Wavelength

Why use Microwaves?

I l C i i i l i di i


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In early century, Communication using electromagnetic radiation

(except for light) used very long wavelengths (low frequencies)

which traveled great distances.

Electronics were developed, including the vacuum tube

Microwaves are easier to control (than longer wavelengths) because

small antennas could direct the waves very well.

Energy could be easily confined to a tight beam.

This beam could be focused on another antenna of dozens of miles away.

Another characteristic is because of high frequency, greater amountsof information could be put on them.

Both of these advantages (narow beamwidth and modulation bandwidth)

k i f l f RADAR ll i i

Documents

Unit-1fundamentals of Electromagnetic