Electrical & Computer Engineering Department
National University of Singapore
EE2011 Engineering Electromagnetics
Tutorial 4: Electric Fields
(for week beginning 30 September 2013)
The tutorial discussion will focus on Questions 2-4 (which are marked by a

Engineering Electromagnetics
EE2011
LECTURE 0
Chen Xudong
Dept. of Electrical and Computer Engineering
National University of Singapore
NUS/ECE
EE2011
Introduction: Waves and Phasors
1. Review of Complex Numbers
Complex Number
z x jy
Where x and y are the

Engineering Electromagnetics
EE2011
LECTURE 1
Chen Xudong
Dept. of Electrical and Computer Engineering
National University of Singapore
NUS/ECE
EE2011
Transmission Lines Basic Theories
1. Introduction
Transmission Line (T-Lines) may encompass all
structur

Engineering Electromagnetics
EE2011
Recap: Transmission Line
Chen Xudong
Dept. of Electrical and Computer Engineering
National University of Singapore
NUS/ECE
EE2011
Fundamental questions regarding T-Lines
What is the key difference between T-Line theory

Engineering Electromagnetics
EE2011, Part CXD
LECTURE 5
Chen Xudong
Dept. of Electrical and Computer Engineering
National University of Singapore
NUS/ECE
EE2011
Plane Wave Reflection and Transmission
1 Normal Incidence at a lossless Dielectric Boundary
Me

Engineering Electromagnetics
EE2011
LECTURE 3
Chen Xudong
Dept. of Electrical and Computer Engineering
National University of Singapore
NUS/ECE
EE2011
Plane Wave Propagation in Lossless Media
1. Maxwells Equations
Equations for electricity and magnetism

Engineering Electromagnetics
EE2011
Introduction
Chen Xudong
Dept. of Electrical and Computer Engineering
National University of Singapore
1
Outline
What is electromagnetics?
Basic Information of Module
2
What is electromagnetics?
Electromagnetic Freque

Engineering Electromagnetics
EE2011, Part CXD
LECTURE 2
Chen Xudong
Dept. of Electrical and Computer Engineering
National University of Singapore
NUS/ECE
EE2011
Transmission Lines Smith Chart &
Impedance Matching
1 Smith Chart
Smith chart is a graphical p

EE2011 Engineering Electromagnetics
(Semester I of Academic Year 2013/2014)
Professor Yeo Swee Ping (eleyeosp@nus.edu.sg)
Electrical & Computer Engineering Department
A
NUS EE2011 Engineering Electromagnetics
Magnetic Fields
Lorentz Force
force on charge

EE2011 Engineering Electromagnetics
Semester I of Academic Year 2013/2014
Professor Yeo Swee Ping (eleyeosp@nus.edu.sg)
Electrical & Computer Engineering Department
NUS EE2011 Engineering Electromagnetics
Electric Fields
Coulombs Law
quantitative observat

Plane Wave Reflection and Transmission
(Intensive Reading)
1 Normal incidence on a conducting boundary
Up to this point, we have discussed the propagation of plane waves in an unbounded
homogeneous medium. In practice, waves usually propagate in regions w

Plane Wave Propagation in Lossless Media
(Intensive Reading)
1 Maxwell's equations
James Clark Maxwell (1831-1879) postulated a set of laws which define the relationship
between the electric field E, the magnetic field H and the sources of these fields: (

NUS/ECE
EE2011
Plane Wave Reflection and Transmission
1 Normal Incidence at a Conducting Boundary
Medium 1 air or dielectric medium
(1 = 0)
(1 , 1 )
Medium 2 perfect conductor
Er
k r
Hr
E2 (z ) = H 2 (z ) = 0
y
Ei
k i
z
Js
+
Hi
(2 = )
x
s
z=0
Hon Tat Hui

Transmission Lines Basic Theories
(Intensive Reading)
1 Introduction
In previous sections on plane waves, we have developed an electromagnetic model with
which we can analyse electromagnetic actions that occur at a distance and which are caused
by time-va

Engineering Electromagnetics
EE2011, Part CXD
LECTURE 4
Chen Xudong
Dept. of Electrical and Computer Engineering
National University of Singapore
NUS/ECE
EE2011
Plane Wave Propagation in Lossy Media
1 Plane Waves in Lossy Media
In a lossy medium, conducti

EE2011 Part CXD Tutorial 2: Solutions
EE2011 Engineering Electromagnetics - Part CXD
Tutorial 2 - Solutions
Q1
Successive voltage minima = / 2 25 (cm),
(a) S 2 L
50
cm .
S 1 1
S 1 3
First voltage minimum occurs at m
5
0.1
50
L 2n 1
with n 0
4
4
L

Electrical & Computer Engineering Department
National University of Singapore
EE2011 Engineering Electromagnetics
Tutorial 6: Electric Potential and Currents
(for week beginning 7 October 2013)
The tutorial discussion will focus on Questions 2-4 (which ar

Electrical & Computer Engineering Department
National University of Singapore
EE2011 Engineering Electromagnetics
Tutorial 5: Electric Potentials and Currents
Q1(a) Two small spheres (carrying charges q1 and q2) are connected by a metallic wire as
E
r
dep

EE2011, Part CXD, Tutorial 1
EE2011 Engineering Electromagnetics - Part CXD
Tutorial 1
Q1*
Consider a coaxial line with a dielectric constant of r = 2.9 for the material filling the
space between the inner and the outer conductors.
The characteristic impe

EE2011, Part CXD, Tutorial 1: Solutions
EE2011 Engineering Electromagnetics - Part CXD
Tutorial 1 - Solutions
Q1
(i) r = 2.9
Z0 = 75
ZL = 300
l = 38 mm = 0.038 m
since u p
k
c
k
c
r
, we have
r 71.33 rad/m
Zin Z 0
Z L jZ 0 tan kl
Z 0 jZ L tan kl
82

EE2011, Part CXD, Tutorial 2
EE2011 Engineering Electromagnetics - Part CXD
Tutorial 2
Q1*
In an experiment conducted on a lossless 50 transmission line terminated in an
unknown load impedance, it is found that the standing-wave ratio is 2.0. Successive
v

EE2011, Part CXD, Tutorial 7
EE2011 Engineering Electromagnetics - Part CXD
Tutorial 7
Q1*
The electric field of a plane wave in free space is given by:
E x, t y50cos 108 t kx
V/m
(i)
Find the direction of the wave propagation.
(ii)
Calculate the wave num

EE2011, Part CXD, Tutorial 8
EE2011 Engineering Electromagnetics - Part CXD
Tutorial 8
Q1*
A team of scientists is designing a radar as a probe for measuring the depth of the ice
layer over the Antarctic land mass. In order to measure a detectable echo du

Electrical & Computer Engineering Department
National University of Singapore
EE2011 Engineering Electromagnetics
Tutorial 6: Magnetic Fields
(for week beginning 21 October 2013)
The tutorial discussion will focus on Questions 2-4 (which are marked by ast

EE2011, Part CXD, Tutorial 7: Solutions
EE2011 Engineering Electromagnetics - Part CXD
Tutorial 7 - Solutions
Q1
(ii) From the expression of the electric field, we have:
108 rad/s, k / c 1/ 3 m
Then,
t1
2
6
k
/2
c
m,
31.42 ns.
(iii) The wave has only

EE2011, Part CXD, Tutorial 8: Solutions
EE2011 Engineering Electromagnetics - Part CXD
Tutorial 8 - Solutions
Q1
Q2
(i)
It is easy to see that 1010
4
is not small
10
0.18 . In this case, the ratio
12
10 80 8.854 10
enough to warrant the use of the low

Electrical & Computer Engineering Department
National University of Singapore
EE2011 Engineering Electromagnetics
Tutorial 3: Vector Operators
(for week beginning 16 September 2013)
The tutorial discussion will focus on Questions 2, 3 and 4 (which are mar

EE2011, Part CXD, Tutorial 9
EE2011 Engineering Electromagnetics - Part CXD
Tutorial 9
Q1*
A uniform plane wave in air with Ei ( z ) x10 e j 6 z is incident normally on an
interface at z 0 with a medium having a dielectric constant of 2.56 and relative
pe

NUS/ECE
EE2011
Plane Wave Propagation in Lossless Media
See animation Plane Wave Viewer
1 Plane Waves in Lossless Media
In a source free lossless medium, J = = = 0.
Maxwells equations:
H
E = -
t
E
H =
t
E = 0
J =current density
=charge density
=condu