EMLAB

1

Introduction to EM theory 2

EMLAB

2

IdC

sH

(?)0C dsH

IdC

sHI

Displacement current

Sd

tI a

DJ

With the help of displacement cur-rent, magnetic fields are also gen-erated around the capacitor.

EMLAB

3

dt

dVCd

dt

d

dt

I

S

S

aE

aD

J

0

Displacement current

dt

dVCI

The time-varying displacement vector and charged particles in motion form current flow. Despite their origin, magnetic fields are generated.

EMLAB

4

Faraday’s law

The time-varying magnetic field generates electric field nearby.

EMLAB

5

The induced electric field forces current to flow along the loop. The induction current generates a magnetic field that decreases the external magnetic flux change.

Induced mag-netic field

EMLAB

6Transformer

dt

diL

dt

diL

N

Ni

N

L

dt

dN

dt

dN 1

211

11

21

1

1222

The current flowing through the primary circuit generates magnetic flux, which influences the secondary circuit. Due to the magnetic flux, a repulsive voltage is induced on the secondary circuit.

EMLAB

7

Basic laws – Maxwell equations

0

B

D

DJH

BE

t

t

1. Electromagnetic phenomena are explained by the four Maxwell equations.

2. Through the equations, electric field and magnetic field are coupled to each other.

3. Quantities on the right hand side are the source terms.

4. Quantities on the left side are the resulting phenomena.

5. The independent variables are current den-sity vector J and charge density .

Maxwell equations

EMLAB

8

Ampere’s law

Current or increase of electric field strength

t

E

JH

E , J

H

EMLAB

9

t

H

E

E

H Increase of mag-netic field

Faraday’s law

EMLAB

10

Gauss’ law

/ E

+Q+Q -Q-Q

EE

Electric field lines emanate from positive charges and sink into negative charges.

EMLAB

11

0 H

Magnetic field lines always form closed loops

EMLAB

12Example – Hertzian dipole antenna

Heinrich Hertz (1857-1894)

spheres for storing electric charges

arc monitoring

EMLAB

13Schematic diagram of Hertz experiment

Transformer for high voltage generation

EMLAB

14

Electric field : red

Magnetic field : blue

Propagation of electromagnetic wave

EMLAB

15Radio communication

EMLAB

16

V

Reception of EM wave

current

Transmitting antenna Receiving an-

tenna

E

The charges on the receiving antenna move toward the antenna terminal, which causes voltage drop across them.

EMLAB

17

t

H

E

t

E

JH

E

ZL

H-field due to mov-ing charges

Example – Signal propagation over a line trace

H

V

t

V

EMLAB

18Example – PCB line trace

EMLAB

19EM field of a simple circuit

R R

L

L

C

In circuit theory, capacitances and inductances of wires are ig-nored

The inductor L models the ef-fect of magnetic field. The ca-pacitor C models that of electric field.

EMLAB

20

dt

diLVL

Increasing current

Increase of current

A line inductance blocks the variation of current in that it generates opposing voltage across its terminals.

)(ti

Line inductance

EMLAB

21

)0()(1

0 C

t

C diC

V )(ti

The voltage difference between wires are always accompanied by a capacitor.

Capacitance

direction of current

EMLAB

22

i (z, t)

v (z, t)+

-

z

L zC z

i (z+z, t)

v (z+ z,t)+

-

i (z, t)

z

v (z, t)+

-

Transmission line

tC

z

it

iL

z

),(

),(),( tzz

t

tzizLtz

),(),(

),( tzzit

tzzzCtzi

EMLAB

23Transmission line eq. solution

tC

z

i

t

iL

z

, 0,02

2

2

2

2

2

2

2

tLC

z

i

tLC

z

)()(),(

)()(),(

ctzIctzItzi

ctzVctzVtz

IILc

VV

t

iL

z

IIc

t

i

VV

z

ctzV

z

ctzV

z

,

)()(

C

LZ0)()(),()( 00 tIZtVtIZtV

LCc

1

IC

LVI

C

LV ,

)(z

z

)( ctz

z

)( ctz

z

EMLAB

24V and I in a transmission line

H

E

propagation direction

H

0ZI

V

I

V

0ZI

V

I

V)(tV

SZLZ

1. The ratio of E+/H+ propagating in the same direction is kept constant.

2. The ratio of V+/I+ wave is also constant, which is called characteristic impedance (Z0) of the line.

3. If the ratio is broken at a certain point, reflections oc-cur.

EMLAB

LZ+V-

SZ

20 40 60 800 100

0

1

-1

2

time, nsec

Vin

, VV

out,

V

20 40 60 800 100

0

1

-1

2

time, nsec

Vin

, VV

out,

V

20 40 60 800 100

0

1

-1

2

time, nsec

Vin

, VV

out,

V

20 40 60 800 100

0

1

-1

2

time, nsec

Vin

, VV

out,

V

20 40 60 800 100

0

1

-1

2

time, nsec

Vin

, VV

out,

V

LZ+V-

SZ

LZ+V-

SZ

LZ+V-

SZ

LZ+V-

SZ

Zs = 20

Z0= 50

ZL= 1k

0.5m

Line 길이에 따른 반사파 영향

rc

LT

/delay

[ns]250 T

[ns]6d T

[ns]3d T

[ns]5.1

[ns]375.0

[ns]75.0

Impedance mismatched

Vin VoutRR2R=1k Ohm

MLINRR1R=20 Ohm

VtPulseSRC1

t

Z0= 50

43.05020

50200

ZZ

ZZ

s

ss

9.05020

50200

ZZ

ZZ

L

LL

EMLAB

26Electromagnetic problem