Electromagnetic Wave

Electromagnetic Wave

Antenna Antenna EngineeringEngineering

CHO, Yong HeuiCHO, Yong Heui


EM Wave LabEM Wave Lab2

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



Wave propagation

Propagation direction: z-direction

: simplified wave equation02

2

2

2

Etz

Cartesian coordinate system

1. Wave equation



Wave propagation

Assumption:

Propagation: constant wavefront

)cos(ˆ zvtxE

zvt

1. Wave equation



Wave velocity

Substitution:

Wave velocity:

Uniqueness theorem

fv 1

0ˆ)cos(1 2 xzvtv

1. Wave equation



Why’s EM wave propagate?

Movement, variance

Importance of two curl equations

Bt

E

Dt

JH

1. Wave equation



Complex number: time

Circuit theory-

EM theory-

fe tj 2,

),sin()cos()( kztjkzte kztj

tjtj ejet

2

k

1. Wave equation



2. Plane wave

EM power

Poynting vector-

EM power-

Example of plane wave:

kkSHE ˆ

PVIPSdHES

,

)cos(ˆ zvtxE

Approximation ( 근사 )



Wave impedance

Ratio of E and H

-

Resistance-

HE /

RIV /

2. Plane wave



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



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



Transparency ( 투명 )

No reflection: transparency-

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

00

10 1

2. Plane wave



Lossy media

Ohm’s law: induced current density-

Complex permittivity- -

IRVEJ ,

EjEjH

ImRe1 jj

Stealth

2. Plane wave



Skin depth

Conductor-

Skin depth:- Wavenumber: -

j

1,

jk

1

2

Water

2. Plane wave



Polarization: direction of E field

2. Plane wave

LP: Linear Polarization, co and cross CP: Circular Polarization, AR (Axial Ratio) EP: Elliptic Polarization

Vertical LP Horizontal LP



Wave propagation

}Re{

}Re{

)cos(),()(

tjzjjo

ztjo

o

eeeV

eV

ztVtzV

3. Tx Line Theory



Distributed element

Lumped element: R, L, C

Distributed element: tx line

3. Tx Line Theory



Transmission line equation

)()()(

zILjRdz

zdVs

s

)()()(

zVCjGdz

zdIs

s

Tx line

Tx line modeling

3. Tx Line Theory



Wave solution

Traveling wave solution- Voltage:

- Current:

zzs eVeVzV 00)(

zzs eIeIzI 00)(

)())(()(

2

2

zVCjGLjRdz

zVds

s

))(( CjGLjRj

3. Tx Line Theory



Characteristic impedance

Important parameter in tx line:

-

-

CjG

LjRZ

0

0

0

0

00 I

V

I

VZ

0Z

3. Tx Line Theory



Reflection coefficient

0

0

011 ||

ZZ

ZZ

V

Ve

L

Loj

Voltage wave continuity conditions Current wave continuity conditions

3. Tx Line Theory



Comparison with circuit theory

3. Tx Line Theory




3. Tx Line Theory




3. Tx Line Theory

Technology

Electromagnetic Wave