EE523  Electromagnetic Wave Theory
Homework Assignment #1
Due date: November 9, 2010 till 17.00
Each student is viewed as a responsible professional in engineering,
and thus highest ethical standards
Ali Kemal KAZAR
1774249
Homework AssignmentI
1b) Figures of real and imaginary part of conductivity.
Imaginary Part of Conductivity
0.8
0.7
0.6
Q" (w)/ Q(0)
0.5
0.4
0.3
0.2
0.1
0
5
4
3
2
1
0
lo
EE 523
Electromagnetic Wave Theory
Course: 3 Credits, Fall 20092010, METU
Dept. of Electrical and Electronics Engineering
Instructor: zlem Aydn ivi (C202, [email protected])
Reference Books: 1. C.A.
Formulas (You may or may not need)
In spherical coordinates:
a r = a x sin cos + a y sin sin + a z cos
a = a x cos cos + a y cos sin a z sin
a = a x sin + a y cos
jk r r
3D Greens function:
E jA
EE523  Electromagnetic Wave Theory
Homework Assignment #3
Due date: December 23, 2010
1) Consider a rectangular waveguide with a
centered dielectric slab as shown in the
Figure. Derive characteristic
EE523  Electromagnetic Wave Theory
Homework Assignment #1
Due date: November 10, 2009 till 17.00
1. Use the KramersKrnig relation to find () for positive as
I ( ) = a[u ( 1 ) u ( 2 )]
where a is a p
EE523  Electromagnetic Wave Theory
Homework Assignment #4
Due date: January 6, 2011
1) Consider the following truncated wedge
waveguide. Assume that the structure is infinitely
long in the z directio
EE523  Electromagnetic Wave Theory
Homework Assignment #2
Due date: November 30, 2010 (till 17.00)
1) Electromagnetic fields in anisotropic media do not in general obey the
reciprocity relationship.
EE523 Electromagnetic Wave Theory
1st Midterm Examination (Home Take Part)
December 5, 2009
Due: December 15, 2009 (till 13.30)
Each student is viewed as a responsible professional in engineering, and
Ali Kemal KAZAR
1774249
Homework AssignmentI
1b) Figures of real and imaginary part of conductivity.
Imaginary Part of Conductivity
0.8
0.7
0.6
Q"(w)/Q(0)
0.5
0.4
0.3
0.2
0.1
0
5
4
3
2
1
0
log(
Dispersion (k) surfaces for
Ordinary and Extraordinary
Waves in a Uniaxial Medium
Assume zazis is the optical axis
Ordinary wave case
Dispersion relation for ord wave
k =
k 2 cos 2 k 2 sin 2
+2
=1
EE523 Electromagnetic Wave Theory
Final Examination (Home take Part)
January 14, 2011
Due: January 24, 2011 (till 12.00)
Each student is viewed as a responsible professional in engineering, and thus
h
Modal Expansion of the Fields
The modes propagating in a WG depend on the excitation of the
guide. The nonpropagating (evanescent) modes are of appreciable
magnitude only in the vicinity of sources o
Example on physical equivalent &
induction equivalent
A uniform plane wave in free space is
obliquely incident upon a rectangular,
flat, perfectly conducting plate as shown
in the following Figure. Fi
Circulating and Radial Waveguides
For waves traveling in z direction
= Bn (k )H (n )e jk z z
Equiphase surfaces are z=constant planes.
For waves traveling in direction
= Bn (k )H (k z z )e jn
Such w
Dielectric Waveguide
Consider 2D dielectric slab
y
0 , 0
2h
d , d

No variation with the x coordinate
0
x
Consider waves traveling +z direction
e jk z z
Modes TE and TM to either y or z can be found.
Time Harmonic Waves
Representation in phasor domain
B(r ) = A
Lorentz Condition
E (r ) = j A
A = j
Phasor potential satisfies + k 2 =
2
, k =
(5)
Consider charge density
(r , t ) = f (r ) cos(t
Wave Transformations and Addition
Theorems
It is often convenient to express wave functions of one coordinate
system in terms of wave functions of another coordinate system.
Such expressions are calle
Bessel Function of the First Kind, Jn(x)
Bessel Function of the Second Kind, Yn(x)
TM to z modes (in cylindrical coordiates)
Let
A = a z Az = az
and
F =0
2
E = j
z
1
1 2
E = j
z
1
1 2
2
Ez = j
+ k
TM to r modes (in spherical coordiates)
Let
A = ar Ar
and
F =0
1 2
2
Er = j
+ k Ar
r 2
Hr = 0
1 1 2 Ar
E = j
r r
1 Ar
H =
r sin
1 2 Ar
E = j
r sin r
1 1 Ar
H =
r
1
1
1
TE to r modes (in spher
ELECTROMAGNETIC
POTENTIALS
ELECTROMAGNETIC POTENTIALS
EM potentials are introduced to simplify
the solutions of EM problems.
Most common potentials
Scalar potential , and magnetic vector
potential
Time Harmonic Electromagnetic Fields
The wave at a single frequency is often called a time
harmonic or monochromatic wave and is most
conveniently described by phasor field:
cfw_
E (r , t ) = Re E (r
ELECTROMAGNETIC
THEOREMS AND
PRINCIPLES
Duality
Original Problem
J
Dual Problem
M
E
H
m
H
E
k
k
1/
Dual Problem
Original Problem
Uniqueness
Maxwells equations have a unique solution in a
finite regi
1
1
E j A j
A F
H
1
A j F j
1
F
TM to z modes
Lets choose A az Az x , y , z
and
F 0
2 Az k 2 Az 0
1 2 Az
Ex j
xz
1 2 Az
Ey j
yz
1 2
2
Ez j
k Az
z 2
Hx
1 Az
y
1 Az
Hy
x
Hz 0
A field wit
EE523 Electromagnetic Wave Theory
Homework Assignment #3
Due: December 24, 2009 (till 17.00)
Q1. Consider the coaxial to waveguide junction given in Figure. Only the TE01
mode propagates in the wavegu