Electromagnetic Wave
Microwave EngineeringMicrowave EngineeringCHO, Yong HeuiCHO, Yong Heui
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
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EM Wave EM Wave LabLab
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Wave propagation
Propagation direction: z-direction
: simplified wave equation02
2
2
2
Etz
Cartesian coordinate system
1. Wave equation
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EM Wave EM Wave LabLab
4
Wave propagation
Assumption:
Propagation: constant wavefront
)cos(ˆ zvtxE
zvt
1. Wave equation
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EM Wave EM Wave LabLab
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Wave velocity
Substitution:
Wave velocity:
Uniqueness theorem
fv 1
0ˆ)cos(1 2 xzvtv
1. Wave equation
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EM Wave EM Wave LabLab
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Why’s EM wave propagate?
Movement, variance
Importance of two curl equations
Bt
E
Dt
JH
1. Wave equation
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EM simulators
Ansoft: Ensemble
HP: ADS
CST: MWS
Ansoft: HFSS
1. Wave equation
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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
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1. Wave equation
Signal representation using phasor
tjtj ejet
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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 )
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EM Wave EM Wave LabLab
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Wave impedance
Ratio of E and H
-
Resistance-
HE /
RIV /
2. Plane 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
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EM Wave EM Wave LabLab
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2. Plane wave
Visualization of reflection, transmission
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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
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Transparency ( 투명 )
No reflection: transparency-
Total reflection- : PEC (Electric Conductor) - : PMC (Magnetic Conductor)
00
10 1
2. Plane wave
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Lossy media
Ohm’s law: induced current density-
Complex permittivity- -
IRVEJ ,
EjEjH
ImRe1 jj
Stealth
2. Plane wave
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Skin depth
Conductor-
Skin depth:- Wavenumber: -
j
1,
jk
1
2
Water
2. Plane 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
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