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

electromagnetic wave

Technology

e wave equation

wave equation e

plane wave lp

tx line theory

wave propagation assumption

whys em wave

transmission incident

h wave equation proof