fall 2013 notes 2 ece 6340 intermediate em waves prof. david r. jackson dept. of ece 1
TRANSCRIPT
Fall 2013
Notes 2
ECE 6340 Intermediate EM Waves
Prof. David R. JacksonDept. of ECE
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Constitutive Relations
Free Space:
0
0
0 0
1
c
D E
B H
Since 1983,
82.99792458 10 m/sc
70 4 10 H/m Also,
(exact value)
(exact value)
2
Constitutive Relations
Lorentz Force law (review):
q v F E B
C
i d l F B
Particle
Wire
C
The current i is the current flowing on the wire in the direction of the contour C.
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Constitutive Relations (cont.)
I
I
d
Fx
20 2
2 0 2
2[N/m]
2x
x
I d FF
d I
72 2 10 N/m when 1 mxF d Definition of I =1 Amp:
Hence
x
# 1
# 2
70 4 10 [H/m]
Two infinite wires carrying DC currents
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Constitutive Relations (cont.)
Phasor Domain:
120 8.85418781762039 10 F/m
0
0
D E
B H
0 20
1
c
5
Simple Linear Media
Atomic picture:
0
0
r
r
D E E
B H H
er
Dipoles
-q q
d ˆq d ppDipole moment of single molecule:
p̂
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There is a simple linear relationship between the fields in the time domain, and there is thus no loss due to molecular or atomic friction.
Simple Linear Media (cont.)
Applied electric field:
Dipole moment per unit volume:
1i
VV
P p
ET p ETorque on dipole:
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ˆET qr qr q p d E E p E
+++++++
-------
er
Electric dipoles
E
r
r
Simple Linear Media (cont.)
1i
VV
P p
Simple linear media:
so
Then
Definition of D vector:
Dipole moment per unit volume:
0 e P E
0 D E P
0 1 e D E
0 r D E Note that usually e > 0
1r 1r e
Define:
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Note: E is the average electric field inside the
material (what we would use to calculate macroscopic
voltage drop).
so
2ˆm n i A A a a
n̂i
1i
VV
M m
Simple Linear Media (cont.)
Magnetic media:
Definition of H vector:
Magnetic moment per unit volume:
mr i
BT m BTorque on dipole:
Magnetic dipoles
0
1
H B M
0 0 B H M9
Each magnetic dipole acts like a small bar magnet.
N
S
n̂
0
0
0
0
0
0
1
1
1
1
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1
m
m
m
m
m
m
m
M B
B H B
B H
B H
H
H
Simple linear media:
so
Simple Linear Media (cont.)
or
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Note: B is the average magnetic
field inside the material.
0 1 m B H
Then
Simple Linear Media (cont.)
0 r B H
1r m Define:
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Summary
Phasor Domain:
0
0
r
r
D E E
B H H
0
0
r
r
D E E
B H H
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Simple Linear Media
Note: For simple linear media the relative permittivity and permeability are real.
Generalized Linear Media
Phasor Domain:
2
0 1 2 2...
a a a
t t
E ED E
2
0 1 2
20 1 2
...
...
D a E j a E a E
a j a a E
Define: 20 2 1... ...a a j a
D EThen:
Similarly: B H
(complex)
j
j
friction term
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We still have a linear relationship
in the phasor domain.
This accounts for molecular or atomic friction, which results in material loss.
Anisotropic Media
D E
B
x xx xy xz x
y yx yy yz y
z zx zy zz z
D E
D E
D E
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Anisotropic Media (cont.)
Isotropic:
0,
0 0
0 0
0 0
xx yy zz
ij i j
Uniaxial:
0 0
0 0
0 0
h
h
z
Teflon
Fibers15
Anisotropic Media (cont.)
Biaxial:
Ferrite:
0
0
0
0 0 1
j
j
is not symmetric!
0 0
0 0
0 0
x
y
z
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Summary of Possible Media
x xx xy xz x
y yx yy yz y
z zx zy zz z
D E
D r E
D E
D E
D E
D E E
Linear, isotropic, homogeneous (simple or generalized):
Inhomogeneous:
Anisotropic:
Nonlinear:
Simple: The permittivity is real.Generalized: The permittivity is complex.
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