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Page 1: Electromagnetic Wave

Electromagnetic Wave

Microwave EngineeringMicrowave EngineeringCHO, Yong HeuiCHO, Yong Heui

Page 2: Electromagnetic Wave

Microwave Microwave EngineeringEngineering

EM Wave EM Wave LabLab

2

1. Wave equation

E and H wave equation

: E wave equation

: H wave equation

02

22

Et

02

22

Ht

Proof: Faraday’s law + curl operator

Bt

E

Sourceless system

Page 3: Electromagnetic Wave

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Wave propagation

Propagation direction: z-direction

: simplified wave equation02

2

2

2

Etz

Cartesian coordinate system

1. Wave equation

Page 4: Electromagnetic Wave

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EM Wave EM Wave LabLab

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Wave propagation

Assumption:

Propagation: constant wavefront

)cos(ˆ zvtxE

zvt

1. Wave equation

Page 5: Electromagnetic Wave

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Wave velocity

Substitution:

Wave velocity:

Uniqueness theorem

fv 1

0ˆ)cos(1 2 xzvtv

1. Wave equation

Page 6: Electromagnetic Wave

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Why’s EM wave propagate?

Movement, variance

Importance of two curl equations

Bt

E

Dt

JH

1. Wave equation

Page 7: Electromagnetic Wave

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EM simulators

Ansoft: Ensemble

HP: ADS

CST: MWS

Ansoft: HFSS

1. Wave equation

Page 8: Electromagnetic Wave

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Complex number: time

Circuit theory-

EM theory-

fe tj 2,

),sin()cos()( kztjkzte kztj

tjtj ejet

2

k

1. Wave equation

Page 9: Electromagnetic Wave

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1. Wave equation

Signal representation using phasor

tjtj ejet

Page 10: Electromagnetic Wave

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2. Plane wave

EM power

Poynting vector-

EM power-

Example of plane wave:

kkSHE ˆ

PVIPSdHES

,

)cos(ˆ zvtxE

Approximation ( 근사 )

Page 11: Electromagnetic Wave

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Wave impedance

Ratio of E and H

-

Resistance-

HE /

RIV /

2. Plane wave

Page 12: Electromagnetic Wave

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Reflection and transmission

Incident wave-

Reflected wave-

Transmitted wave-

0

0

0 ˆ,ˆ

zjk

izjk

i

eyHexE

0

0

0 ˆ,ˆ

zjk

rzjk

r

eyHexE

jkz

tjkz

t

TeyHTexE

ˆ,ˆ

TEEEE itir /,/

2. Plane wave

Page 13: Electromagnetic Wave

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2. Plane wave

Visualization of reflection, transmission

Page 14: Electromagnetic Wave

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Boundary conditions

E continuity at z = 0-

H continuity at z = 0-

Reflection and transmission coefficient-

tri EEE

tri HHH

1,0

0 T

2. Plane wave

Page 15: Electromagnetic Wave

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Transparency ( 투명 )

No reflection: transparency-

Total reflection- : PEC (Electric Conductor) - : PMC (Magnetic Conductor)

00

10 1

2. Plane wave

Page 16: Electromagnetic Wave

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Lossy media

Ohm’s law: induced current density-

Complex permittivity- -

IRVEJ ,

EjEjH

ImRe1 jj

Stealth

2. Plane wave

Page 17: Electromagnetic Wave

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Skin depth

Conductor-

Skin depth:- Wavenumber: -

j

1,

jk

1

2

Water

2. Plane wave

Page 18: Electromagnetic Wave

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Polarization: direction of E field

LP: Linear Polarization CP: Circular Polarization EP: Elliptic Polarization

Vertical LP Horizontal LP

2. Plane wave