Unit V-Electromagnetic Fields-Normal incidence at a plane dielectric boundary, Normal incidence at a plane conducting boundary

Normal incidence at a plane dielectric boundary
Normal incidence at a plane conducting boundary

1. ELECTROMAGNETIC FIELDS
Dr.K.G.SHANTHI
Professor/ECE
[email protected]
Normal incidence at a plane dielectric boundary
Normal incidence at a plane conducting boundary

2. REFLECTION OF A PLANE WAVE -Normal incidence
at a plane dielectric boundary
✘Whenaplanewavefromonemediummeetsadifferent
medium,itispartlyreflectedandpartlytransmitted.
✘Theproportionoftheincidentwavethatisreflectedor
transmitteddependsontheconstitutiveparameters
(Permittivityε,Permeabilityμ,Conductivityσ)ofthetwo
mediainvolved.
✘Supposethataplanewavepropagatingalongthe+z-
directionisincidentnormallyontheboundaryz=0
betweendielectricmedium1(z<0)characterizedby
ε
1,μ
1,σ
1anddielectricmedium2(z>0)characterizedby
ε
2,μ
2,σ
2.
2

3. 3
Inthe figure,
subscriptsi,r,andt
denote incident,
reflected, and
transmittedwaves,
respectively.
Incident
wave
Reflected
wave
Transmitted
wave
Z=0
Normal incidence at a plane dielectric boundary

4. ✘(E
i,H
i)istravelingalong+a
zinmedium1istheincidentwave.
✘LetE
ibeelectricfieldstrengthofincidentwave.H
ibeMagneticfield
strengthofincidentwave.
✘(E
r,H
r)istravelingalong-a
zinmedium1isthereflectedwave.
✘E
rbeelectricfieldstrengthofreflectedwave.H
rbeMagneticfield
strengthofreflectedwave.
✘(E
t,H
t)istravelingalong+a
zinmedium2isthetransmittedwave.
✘E
tbeelectricfieldstrengthoftransmittedwave.H
tbeMagneticfield
strengthofincidentwave.
✘Totalfieldsinmedium1comprisesboththeincidentandreflected
fieldsaregivenby
✘Thetotallyreflectedwavecombineswiththeincidentwavetoforma
standingwave.
4
E
1=E
i+E
r
H
1=H
i+H
r

5. ✘Total fields in medium 2 are given by
✘The transmitted wave in medium 2 is a purely traveling wave
and consequently there are no maxima or minima in this region.
✘Attheinterfacez=0,theboundaryconditionsrequirethatthe
tangentialcomponentsofEandHfieldsmustbecontinuous.
Sincethewavesaretransverse,EandHfieldsareentirely
tangentialtotheinterface.
✘Thus at the interface z = 0
✘Relation between E and H is given by
5
E
2=E
t
H
2=H
t
E
1tan=E
2tan
H
1tan=H
2tan
E
i+E
r=E
t andH
i+H
r=H
tH
E

As the direction of reflected wave is
opposite to that of incident wave

6. 6
Thereflectioncoefficient(Г):
Itistheratioofthecomplexamplitude
ofthereflectedwavetothat
oftheincidentwave.

7. 7
The transmission coefficient
Itisdefinedasratioof
transmittedvoltagewave
amplitudetoincidentvoltage
waveamplitude
i.e.E
t/E
i

8. Important results:
8
1.
2.
3.

9. ✘Considerthewhenmedium
1isaperfectdielectric
(lossless,σ
1=0)and
medium2isaperfect
conductor(σ
2=).
✘Foraperfectconductor,
bothmagneticandelectric
fieldarezero.Hence
intrinsicimpedanceiszero.
9REFLECTION OF A PLANE WAVE -Normal incidence
at a plane conducting boundary  0
2

t
t
H
E


10. ✘The transmission coefficient:
✘The reflection coefficient:
✘Theplanewaveincidentonaperfectconductorgetsentirely
reflectedbecausenofieldexistswithintheconductor.sothere
canbenotransmittedwave(E
2=0).
✘Thetotallyreflectedwavecombineswiththeincidentwaveto
formastandingwave.
10REFLECTION OF A PLANE WAVE -Normal incidence
at a plane conducting boundary

11. ✘Astandingwave"stands"anddoesnottravel;itconsistsoftwo
travelingwaves:E
i-incidentwaveandE
r-reflectedwave.Both
thewaveshavesameamplitudesbuttravelinopposite
directions.
✘Thestandingwaveinmedium1isdenotedas
✘Medium1isaperfectdielectric(lossless,σ
1=0)
✘ThePropagationConstantisgivenby
11

12. 12
Simplifying the above equation,
Hence the Electric field in Medium 1 is given by
The magnetic field component of the wave in Medium 1 is given by
Thestandingwaveinmedium1isdenotedas

13. Theelectricfieldmagnitudevariessinusoidallywithrespecttodistance
fromthereflectingplane.Itiszeroatthesurfaceandatmultiplesofhalf
wavelength.
1322
0sin0








nnn
z
nz
zatE



|E| is maximum at odd multiples of quarter wavelength.4
)12(
2
2
)12(
2
)12(
2
)12(
1sin

















n
nn
z
nz
zatEE
xam
Where n=0,1,2…….
Where n=0,1,2…….
|H| minimum occurs whenever there is |E| maximum and vice versa.

14. Standing waves curves
14

15. Standing-wave ratio -S
✘The ratio of |E
1|
maxto |E
1|
min(or) | H
1|
maxto |H
1|
minis called the
standing-wave ratio
15

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THANK YOU

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