Date post: | 31-Dec-2015 |
Category: |
Documents |
Upload: | maite-hamilton |
View: | 55 times |
Download: | 1 times |
ENE428
Syllabus
•Asst. Prof. Dr. Rardchawadee Silapunt, [email protected]•Lecture: 9:30pm-12:20pm Tuesday, CB41004
12:30pm-3:20pm Wednesday, CB41002 •Office hours : By appointment•Textbook: Applied Electromagnetics by Stuart M. Wentworth (Wiley, 2007)
ENE428
Homework 20% Midterm exam 40% Final exam 40%
Grading
Vision Providing opportunities for intellectual growth in the context of an engineering discipline for the attainment of professional competence, and for the development of a sense of the social context of technology.
ENE428
Course overview
• Maxwell’s equations and boundary conditions for electromagnetic fields
• Uniform plane wave propagation• Waveguides• Antennas• Microwave communication systems
ENE428
Introduction
• From Maxwell’s equations, if the electric field is changing with time, then the magnetic field varies spatially in a direction normal to its
orientation direction
• A uniform plane wave, both electric and magnetic fields lie in the transverse plane, the plane whose normal is the direction of propagation
• Both fields are of constant magnitude in the transverse plane, such a wave is sometimes called a transverse electromagnetic (TEM) wave.
BBBBBBBBBBBBBBEBBBBBBBBBBBBBBH
http://www.phy.ntnu.edu.tw/ntnujava/viewtopic.php?t=52
ENE428
Maxwell’s equations
0
BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB
BBBBBBBBBBBBBBBBBBBBBBBBBBBB
BBBBBBBBBBBBBBBBBBBBBBBBBBBB
v
DH J
t
BE
t
D
B
(1)
(2)
(3)
(4)
ENE428
Maxwell’s equations in free space
= 0, r = 1, r = 1
0
0
BBBBBBBBBBBBBBBBBBBBBBBBBBBB
BBBBBBBBBBBBBBBBBBBBBBBBBBBB
EH
t
HE
t
Ampère’s law
Faraday’s law
ENE428
General wave equations
• Consider medium free of charge where• For linear, isotropic, homogeneous, and
time-invariant medium,
(1)
(2)
BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB EH E
t
BBBBBBBBBBBBBBBBBBBBBBBBBBBB HE
t
ENE428
General wave equations
Take curl of (2), we yield
From
then
For charge free medium
( )
BBBBBBBBBBBBBBBBBBBBBBBBBBBB HE
t
2
2
( )
BBBBBBBBBBBBBBBBBBBBBBBBBBBB BBBBBBBBBBBBBBBBBBBBBBBBBBBB
BBBBBBBBBBBBBBE
E E EtEt t t
2 BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB
A A A
22
2
BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB
E EE E
t t
0 BBBBBBBBBBBBBBE
ENE428
Helmholtz wave equation
22
2
BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB E EE
t t
22
2
BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB H HH
t t
For electric field
For magnetic field
ENE428
Time-harmonic wave equations
• Transformation from time to frequency domain
Therefore
j
t
2 ( ) BBBBBBBBBBBBBBBBBBBBBBBBBBBBs sE j j E
2 ( ) 0 BBBBBBBBBBBBBBBBBBBBBBBBBBBBs sE j j E
2 2 0 BBBBBBBBBBBBBBBBBBBBBBBBBBBBs sE E
ENE428
Time-harmonic wave equations
or
where
This term is called propagation constant or we can write
= +j
where = attenuation constant (Np/m) = phase constant (rad/m)
2 2 0 BBBBBBBBBBBBBBBBBBBBBBBBBBBBs sH H
( ) j j
ENE428
Solutions of Helmholtz equations
• Assuming the electric field is in x-direction and the wave is propagating in z- direction
• The instantaneous form of the solutions
• Consider only the forward-propagating wave, we have
• Use Maxwell’s equation, we get
0 0cos( ) cos( )
BBBBBBBBBBBBBBz z
x xE E e t z a E e t z a
0 cos( )
BBBBBBBBBBBBBBz
xE E e t z a
0 cos( )
BBBBBBBBBBBBBBz
yH H e t z a
ENE428
Solutions of Helmholtz equations in phasor form
• Showing the forward-propagating fields without time-harmonic terms.
• Conversion between instantaneous and phasor form
Instantaneous field = Re(ejtphasor field)
0
BBBBBBBBBBBBBB
z j zs xE E e e a
0
BBBBBBBBBBBBBB
z j zs yH H e e a
ENE428
Propagating fields relation
1
BBBBBBBBBBBBBBBBBBBBBBBBBBBB
BBBBBBBBBBBBBBBBBBBBBBBBBBBBs s
s s
H a E
E a H
where represents a direction of propagationa
ENE428
Propagation in lossless-charge free media
• Attenuation constant = 0, conductivity = 0
• Propagation constant
• Propagation velocity
– for free space up = 3108 m/s (speed of light)
– for non-magnetic lossless dielectric (r = 1),
1
pu
p
r
cu
ENE428
Ex1 A 9.375 GHz uniform plane wave is propagating in polyethelene (r = 2.26). If the amplitude of the electric field intensity is 500 V/m and the material is assumed to be lossless, finda) phase constant
b) wavelength in the polyethelene
ENE428
Propagation in dielectrics• Cause
– finite conductivity– polarization loss ( = ’-j” )
• Assume homogeneous and isotropic medium
' "( ) BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBH E j j E
" '[( ) ] BBBBBBBBBBBBBBBBBBBBBBBBBBBBH j E
ENE428
Loss tangent
• A standard measure of lossiness, used to classify a material as a good dielectric or a good conductor
"
' 'tan
eff
ENE428
Low loss material or a good dielectric (tan « 1)
• If or < 0.1 , consider the material
‘low loss’ , then
1
2
(1 ).2
jand
ENE428
Low loss material or a good dielectric (tan « 1)
• propagation velocity
• wavelength
1
pu
2 1
f
ENE428
High loss material or a good conductor (tan » 1)
• In this case or > 10, we can
approximate
1
2 f
45 .
jje
therefore
2
1 1)
and
ENE428
High loss material or a good conductor (tan » 1)
• depth of penetration or skin depth, is a distance
where the field decreases to e-1 or 0.368 times of
the initial field
• propagation velocity
• wavelength
1 1 1m
f
pu
22
ENE428
Ex2 Given a nonmagnetic material having r = 3.2 and = 1.510-4 S/m,
at f = 3 MHz, find a) loss tangent
b) attenuation constant
ENE428
Ex3 Calculate the followings for the wave with the frequency f = 60 Hz propagating in a copper with the conductivity, = 5.8107 S/m: a) wavelength
b) propagation velocity