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