Fundamentals of Electromagnetics
for Teaching and Learning:
A Two-Week Intensive Course for Faculty in
Electrical-, Electronics-, Communication-, and
Computer- Related Engineering Departments in
Engineering Colleges in India
by
Nannapaneni Narayana Rao
Edward C. Jordan Professor Emeritus
of Electrical and Computer Engineering
University of Illinois at Urbana-Champaign, USA
Distinguished Amrita Professor of Engineering
Amrita Vishwa Vidyapeetham, India
Program for Hyderabad Area and Andhra Pradesh Faculty
Sponsored by IEEE Hyderabad Section, IETE Hyderabad
Center, and Vasavi College of Engineering
IETE Conference Hall, Osmania University Campus
Hyderabad, Andhra Pradesh
June 3 – June 11, 2009
Workshop for Master Trainer Faculty Sponsored by
IUCEE (Indo-US Coalition for Engineering Education)
Infosys Campus, Mysore, Karnataka
June 22 – July 3, 2009
Introductory Presentation
Part 2
2
Terminology
Because I will be using the term “electrical and
computer engineering” it is of interest to elaborate
upon this terminology. In engineering departments
in the United States educational institutions,
electrical and computer engineering is generally
one academic department, although not in all
institutions. The name, ECEDHA, Electrical and
Computer Engineering Department Heads
Association, reflects this situation. In the College
of Engineering at the University of Illinois at
Urbana-Champaign (UIUC), the Department of
Electrical and Computer Engineering (ECE) offers
two undergraduate programs leading to the
Bachelor of Science degrees: Electrical
Engineering and Computer Engineering.
3
The Scope of Electrical Engineering
“A list of the twenty greatest engineering achievements of
the twentieth century compiled by the National Academy of
Engineering includes ten achievements primarily related to
the field of electrical engineering: electrification,
electronics, radio and television, computers, telephone,
internet, imaging, household appliances, health
technologies, and laser and fiber optics. The remaining
achievements in the list - automobile, airplane, water
supply and distribution, agricultural mechanization, air
conditioning and refrigeration, highways, spacecraft,
petroleum/petrochemical technologies, nuclear
technologies, and high-performance materials - also
require knowledge of electrical engineering to differing
degrees. In the twenty-first century the discipline of
electrical engineering continues to be one of the primary
drivers of change and progress in technology and
standards of living around the globe.”
4
NAE’s List of Greatest Engineering
Achievements of the 20th Century
•
•
•
•
•
•
•
•
•
•
Electrification
Automobile
Airplane
Water Supply &
Distribution
Electronics
Radio & Television
Agricultural
Mechanization
Computers
Telephone
Air Conditioning &
Refrigeration
Red indicates areas where ECE
at UIUC has had influence.
•
•
•
•
•
•
•
Highways
Spacecraft
Internet
Imaging
Household Appliances
Health Technologies
Petroleum/Petrochemical
Technologies
• Laser & Fiber Optics
• Nuclear Technologies
• High-Performance
Materials
5
The Scope of Computer Engineering
“Computer engineering is a discipline that applies principles
of physics and mathematics to the design, implementation,
and analysis of computer and communication systems. The
discipline is broad, spanning topics as diverse as radio
communications, coding and encryption, computer
architecture, testing and analysis of computer and
communication systems, vision, and robotics. A defining
characteristic of the discipline is its grounding in physical
aspects of computer and communication systems.
Computer engineering concerns itself with development of
devices that exploit physical phenomena to store and
process information, with the design of hardware that
incorporates such devices, and with software that takes
advantage of this hardware's characteristics. It addresses
problems in design, testing, and evaluation of system
properties, such as reliability, and security. It is an exciting
area to work in, one that has immediate impact on the
6
technology that shapes society today.”
The Illinois Curriculum in Electrical
Engineering
For the electrical engineering program at Illinois,
the core curriculum focuses on fundamental
electrical engineering knowledge: circuits, systems,
electromagnetics, solid state electronics, computer
engineering, and design. A rich set of elective
courses permits students to select from collections
of courses in seven areas of electrical and
computer engineering: bioengineering, acoustics,
and magnetic resonance engineering; circuits and
signal processing; communication and control;
computer engineering; electromagnetics, optics,
and remote sensing; microelectronics and quantum
electronics; power and energy systems.
7
The Illinois Curriculum in Computer
Engineering
For the computer engineering program, the core
curriculum focuses on fundamental computer
engineering knowledge: circuits, systems,
electromagnetics, computer engineering, solid state
electronics, and computer science. A rich set of
elective courses permits students to concentrate in
any sub-discipline of computer engineering
including: computer systems; electronic circuits;
networks; engineering applications; software,
languages, and theory; and algorithms and
mathematical tools.
8
Electromagnetics is all around us!
In simple terms, every time we turn
a switch on for electrical power or
for an electronic equipment, every
time we press a key on our
computer key board or on our cell
phone, or every time we perform a
similar action involving an everyday
electrical device, electromagnetics
comes into play.
9
Some modern applications of EM
(Courtesy of Weng C. Chew)
Biomedical
Engineering
& BioTech
Wireless
Comm. &
Propagation
RCS Analysis,
Design, ATR
& Stealth
Technology
Physics Based
Signal
Processing &
Imaging
Computer
Chip Design
& Circuits
ELECTROMAGNETICS
Antenna
Analysis &
Design
EMC/EMI
Analysis
Lasers &
Optoelectronics
MEMS &
Microwave
Engineering
Remote
Sensing &
Subsurface
Sensing & NDE
10
Fundamental to the Study of ECE
It is the foundation for the
technologies of electrical and
computer engineering, spanning
the entire electromagnetic
spectrum, from dc to light. As such,
in the context of engineering
education, it is fundamental to the
study of electrical and computer
engineering.
11
Foundation for the technologies of
electrical and computer engineering
12
Fundamental to the Study of ECE
In 1963, the American Institute of Electrical Engineers
(AIEE) and the Institute of Radio Engineers (IRE) were
merged into the Institute of Electrical and Electronics
Engineers (IEEE), a global nonprofit organization with
over 375,000 members, and “the world's leading
professional association for the advancement of
technology.” The IEEE logo or badge is a merger of the
badges of the two parent organizations. It contains a
vertical arrow surrounded by a circular arrow, within a
kite-shaped border. No letters clutter the badge because
a badge without letters can be read in any language. The
AIEE badge had the kite shape which was meant to
symbolize the kite from Benjamin Franklin’s famous kite
experiment to study electricity. The IRE badge had the
two arrows that symbolize the right hand rule of
electromagnetism.
13
Fundamental to the Study of ECE
Alternatively, the vertical arrow can be thought of as
representing one of the two fields, electric or magnetic,
and the circular arrow surrounding it representing the
second field, produced by it, so that together they
represent an electromagnetic field.
14
Fundamental to the Study of ECE
Whether this logo of IEEE was intended to be a
recognition of the fact that electromagnetics is
fundamental to all of electrical and computer engineering,
it is a fact that all electrical phenomena are governed by
the laws of electromagnetics, and hence, the study of
electromagnetics is essential to all branches of electrical
and computer engineering, and indirectly impacts many
other branches.
15
EM is so fundamental that even Mac “Circuits”
Van Valkenburg was caught having fun
“communicating” the RH Rule to Robert
“Communications” Lucky! Wonderful picture!
An amusing incident
One of the earliest postwar programs to be
established at UIUC was a program in radio
direction finding (RDF). It was intended as a
basic research program, sponsored by the
Office of Naval Research. When the sponsor
was asked by the research supervisor,
Edward Jordan, what facets of the field might
be of particular interest, the answer received
was: “Look, you know Maxwell’s equations,
the Russians know Maxwell’s equations; you
take it from there.” Jordan was amused that it
would be difficult to get more basic than that.
17
Wullenweber Array at Bondville Road Field
Station of the RDF Laboratory
•
•
•
•
Used in Radio Direction Finding Laboratory
In operation 1955-1980
Used 120 antennas and was 1000 ft in diameter
Operated in frequency range of 4-16 MHz
18
Wullenweber array of the RDF
Laboratory (1955 – 1980)
19
Discovering Wullenweber while riding the Pineapple Express at
the Dole Plantation on the island of Oahu, Hawaii, with family on
June 4, 2005, as a reminder
20
Wullenweber and Bananas (My favorite slide)
21
So, what is Electromagnetics?
By the very nature of the word,
electromagnetics implies having to do with
a phenomenon involving both electric and
magnetic fields and furthermore coupled.
This is indeed the case when the situation
is dynamic, that is, time-varying, because
time-varying electric and magnetic fields
are interdependent, with one field
producing the other.
22
What is Electromagnetics?
In other words, a time-varying electric field
or a time-varying magnetic field cannot
exist alone; the two fields coexist in time
and space, with the space-variation of one
field governed by the time-variation of the
second field. This is the essence of
Faraday’s law and Ampere’s circuital law,
the first two of the four Maxwell’s equations
resulting in wave propagation.
23
About Electromagnetics (Continued)
Only when the fields are not changing with
time, that is, for the static case, they are
independent; a static electric field or a
static magnetic field can exist alone, with
the exception of one case in which there is
a one-way coupling, electric field resulting
in magnetic field, but not the other way.
24
About Electromagnetics (Continued)
Thus, in the entire frequency spectrum,
except for dc, all electrical phenomena are,
in the strictest sense, governed by
interdependent electric and magnetic
fields, or electromagnetic fields.
Statics
Dynamics
dc
Frequency, f
Light
25
Quasistatic Approximation
However, at low frequencies, an
approximation, known as the “quasistatic
approximation,” can be made in which the
time-varying fields in a physical structure
are approximated to have the same spatial
variations as the static fields in the
structure obtained by setting the source
frequency equal to zero.
26
Quasistatic Approximation (Continued)
Thus, although the actual situation in the
structure is one of electromagnetic wave
nature, it is approximated by a dynamic but
not wavelike nature. As the frequency
becomes higher and higher, this
approximation violates the actual situation
more and more, and it becomes
increasingly necessary to consider the
wave solution.
27
Statics
Quasistatics
Dynamics
dc
Frequency, f
Light
Statics: f = 0;   t  0; dc
Dynamics: No restriction; complete Maxwell’s equations;
Electromagnetic waves
Quasistatics: Low-frequency extension of statics, or
low-frequency approximation of
dynamics; l  2
28
Maxwell’s Equations are elegant and beautiful.
As profound as they are, they are actually
quite simple to explain and understand.
29
Maxwell’s Equations
d
E  dl  –
B  dS
C
dt S
Electric field
intensity
V m
S
C m3 
Wb m2 
A m
Current
density
A m2
V
r dv
Charge density
Magnetic
flux density
d
H
dl
J
dS
D
dS

+



C
S
dt S
Magnetic
field intensity
D  dS 
S
B  dS  0
Displacement
flux density
2
C m


30
Faraday’s Law, the first EMantra
d
C E • dl  – dt S B • dS
B
S
C
dS
Electromotive Force (emf) or voltage around C
= Negative of the time rate of increase of the
magnetic flux crossing S bounded by C.
31
C E • dl = Voltage around C, also known as
electromotive force (emf) around C
(but not really a force),
V
m  m, or V.
S B • dS = Magnetic flux crossing S,
 Wb
m2   m2 , or Wb.
d
– S B • dS = Time rate of decrease of
dt
magnetic flux crossing S,
Wb s, or V.
32
Ampere’s Circuital Law, the
second EMantra
d
C H • dl  S J • dS + dt S D • dS
J, D
S
C
dS
Magnetomotive force (mmf) around C
= Current due to flow of charges crossing S bounded by C
+ Time rate of increase of electric (or displacement) flux
crossing S
33
C H • dl = Magnetomotive force (only by
analogy with electromotive
force),
 A m  m, or A.
S J • dS = Current due to flow of charges
crossing S,
 Amp
m2   m2 , or A.
S D • dS = Displacement flux, or electric
flux, crossing S,
2
2
C
m

m

 , or C.
34
d
D • dS = Time rate of increase of

S
dt
displacement flux crossing S,
or, displacement current
crossing S,
C s, or A.
35
Gauss’ Law for the Electric Field, the
third EMantra
 C

3
D
d
S

r
dv

m
,
or
C
 3

S
V
m

D
r
•
V
S
dS
Displacement flux emanating from a closed surface S
= charge contained in the volume V bounded by S
= charge enclosed by S
36
Gauss’ Law for the Magnetic Field, the
fourth EMantra
S B • dS = 0
B
dS
S
Magnetic flux emanating from a closed surface S = 0.
37
Out of the four EMantras, only the first
two, Faraday’s and Ampere’s circuital
laws are independent. The fourth Mantra,
Gauss’ law for the magnetic field, follows
from Faraday’s law, and the third Mantra,
Gauss’ law for the electric field, follows
from Ampere’s circuital law, with the aid of
an auxiliary equation, the law of
conservation of charge.
38
Law of Conservation of Charge, an
auxiliary EMantra
S J • dS +
d
r dv  0

V
dt
r(t)
V
S
J
dS
Current due to flow of charges emanating from a
closed surface S
= Time rate of decrease of charge enclosed by S.
39
Maxwell’s Equations in Differential Form
and the Continuity Equation
B
xE= –
t
D
x H  J+
t
Faraday’s Law
Ampere’s Circuital Law
 D  r
Gauss’ Law for the Electric Field
B  0
Gauss’ Law for the Magnetic Field
r
J +
0
t
Continuity Equation
40
E y
Ez
Bx
–
–
y
z
t
By
Ez
E x
–
–
z
x
t
E y
Bz
E x
–
–
x
y
t
Lateral space
derivatives of the
components of E
Time derivatives of
the components of B
Dy Dz
Dx
+
+
r
x
y
z
Longitudinal derivatives
of the components of D
Charge
density
41
The “Mahatmyam (Greatness)” of
Maxwell’s Equations
d
C E • dl = – dt S B • dS
d
C H • dl = S J • dS + dt S D • dS
42
The “Mahatmyam (Greatness)” of
Maxwell’s Equations
+
J
+
Law of Conservation
of Charge
r
Gauss’ Law
for E
Ampere’s
Circuital Law
H ,B
Faraday’s
Law
D,E
43
The “Mahatmyam (Greatness)” of
Maxwell’s Equations
Thus, Faraday's law says that a time-varying magnetic
field gives rise to an electric field, the space-variation of
which is related to the time-variation of the magnetic
field. Ampere's circuital law tells us that a time-varying
electric field produces a magnetic field, the space
variation of which is related to the time-variation of the
electric field. Thus, if one time-varying field is generated,
it produces the second one, which in turn gives rise to the
first one, and so on, which is the phenomenon of
electromagnetic wave propagation, characterized by time
delay of propagation of signals. In addition, Ampere’s
circuital law tells us that an electric current produces a
magnetic field, so that a time-varying current source
results in a time-varying magnetic field, beginning the
process of one field generating the second.
44
Hertzian Dipole
I(t)
I(t)
H(t)
E(t)
45
Radiation from Hertzian Dipole
46
Hertzian dipole and radiation pattern on the
covers of the U.S. and Indian Editions of
“Fundamentals of Electromagnetics”
The Contribution of Maxwell
You will have noted that none of the four equations
are named after Maxwell. So, the question arises
as to why they are known as Maxwell’s equations.
It is because of a purely mathematical contribution
of Maxwell. This mathematical contribution is the
second term on the right side of Ampere’s circuital
law. Prior to that, Ampere’s circuital law consisted
of only the first term on the right side.
48
The Contribution of Maxwell
Without the second term on the right side of
Ampere’s circuital law, the loop is not complete
and hence there is no interdependence of timevarying electric and magnetic fields and no EM
waves!
d
C E • dl = – dt S B • dS
d
C H • dl = S J • dS + dt S D • dS
49
Unifying Electricity and Magnetism
Thus, the purely mathematical contribution
of Maxwell in 1864 unified electricity and
magnetism and predicted the generation of
EM waves owing to the interdependence of
time-varying electric and magnetic fields.
Only 23 years later in 1887, eight years after
his death in 1879, the theory was proved
correct by the experimental discovery of EM
waves by Heinrich Hertz.
50
Parallel with Principles from Upanishads
In fact, Maxwell’s Equations are as fundamental
to the science of all electrical phenomena and
hence to modern living as the Guiding Principles,
from the Taittriyopanishad are to spirituality.
51
The Guiding Principles from Upanishads
52
The Guiding Equations of
Electromagnetics
53
Maxwell’s Equations
parallel to the
Principles in Upanishads!
Isn’t it fascinating!
54
So, why are these poor little guys so perplexed
at the sight of Maxwell’s Equations?
55
Why is the teaching and learning of EM so
dreaded, as implied by this mnemonic?
HOW I WANT A DRINK,
3. 1 4
1 5
ALCOHOLIC, OF COURSE,
9
2
6
AFTER THE HEAVY LECTURES
5
3
5
8
INVOLVING ELECTRO-MAGNETICS!
9
7
9
56
Incomplete list of reasons given
• Abstract (not practical; ideal; theoretical; hard
to understand; difficult; abstruse)
• Mathematical complexity
• Vector notation
• Curl, divergence, and gradient
• Highly conceptual
57
The approach to the teaching of
electromagnetics
While these might be valid reasons to
differing degrees for different people,
depending on their background
preparations, let us look at the teaching of
EM.
58
The approach to the teaching of
electromagnetics
Historically, the development of major
technologies based on Maxwell’s equations
occurred in the sequence of electrically and
magnetically based technologies
(electromechanics and electrical power) in
the nineteenth century; electronics hardware
and software in the twentieth century; and
photonics technologies, entering into the
twenty-first century.
59
Progression of technologies
based on Maxwell’s Equations
60
The approach to the teaching of
electromagnetics
The teaching of electromagnetics evolved
following this sequence, that is, beginning
with a course on electrostatics,
magnetostatics, energy and forces, and in
some cases quasistatic fields, followed by
Maxwell’s equations for time-varying fields
and an introduction to electromagnetic
waves. This course was then followed by
one or more courses on transmission lines,
electromagnetic waves, waveguides and
antennas.
61
The historical, or, “inductive” approach
The teaching of the introductory course in this manner is
known as the “inductive” approach, that is, an approach
consisting of developing general principles from particular
facts, which in this case was developing complete set of
Maxwell’s equations from the particular laws of static fields.
Since generally much time is taken up for the coverage of
static fields before getting to the complete set of Maxwell’s
equations, the time is cut short (and in some cases not
available) for the more interesting and useful material,
centered on electromagnetic waves. This is the principal
drawback of the traditional, inductive, approach, which is
unnecessarily aggravating, because all the mathematics
and concepts taught in the context of static fields can not
only be taught but taught better and with less aggravation
with time-varying fields.
62
The “Deductive” Approach
In contrast to the “inductive” approach is the “deductive”
approach, that is, an approach in which one begins with
the general principles that are accepted as true and then
applies it to particular cases, which in this case is
beginning with the complete set of Maxwell’s equations
for time-varying fields and then developing their
applications, as well as considering special cases of
static and quasistatic fields. This approach permits the
structuring of the course so that (a) it constitutes the
foundation for students taking follow-on courses, as well
as (b) imparting the essentials for students taking this
course only in EM.
63
“Deduction” versus “Induction”
Deduction applies to the process in which one starts with
a general principle that is accepted as true and applies it
to a particular case, arrives at a conclusion that is true if
the starting principle was true, as in All animals die; this
is an animal; therefore this will die. Induction applies to
the process by which one collects many particular cases,
finds out by experiment what is common to all of them,
and forms a general rule or principle which is probably
true, as in Every animal I have tested died; probably all
animals die.
64
The “Deductive” Approach (Continued)
Since the deductive approach begins with
the complete Maxwell’s equations, it
provides an appreciation of the fact that
regardless of how low the frequency is, as
long as it is nonzero, the phenomenon is
one of electromagnetic waves, resulting
from the interdependence of time-varying
electric and magnetic fields. Then, statics
and quasistatics are treated as special
cases.
65
The “Deductive” Approach (Continued)
Furthermore, combining the deductive approach with the
thread of statics-quasistatics-waves makes it quite clear that,
along the frequency spectrum, the quasistatic behavior
approached from the static (zero frequency) limit as an
extension of the static behavior to dynamic behavior of first
order in frequency is the same as the low-frequency behavior
approached from the other (higher frequencies) side, by
approximating the exact dynamic solution for low frequencies.
This very important concept is not always clearly understood
or appreciated when the inductive approach is employed.
Statics
l
 2
Quasistatics
Dynamics
dc
Frequency, f
Light
66
The approach to the teaching of
electromagnetics
And the deductive approach is the way of
teaching Maxwell’s equations as “God said,” as
contrasted with the inductive approach, which is
the way in which they were evolved by human
intellect.
I am not a philosopher but it should not be
difficult to accept that Maxwell and others did
not create the equations; they only discovered
what “God said” in the first place, through a
series of ingenious steps over time!
67
Knowledge is inherent man; no
knowledge comes from outside.… We
say Newton discovered gravitation. Was
it sitting anywhere in a corner waiting for
him? It was in his own mind; the time
came and he found it out. All knowledge
that the world has ever received comes
from the mind; the infinite library of the
universe is in your own mind. The
external world is simply the suggestion,
the occasion, which sets you to study
your own mind – Swami Vivekananda
68
So, why is the teaching and learning of
EM so dreaded?
It is not entirely
because of EM, but
also because of the
way it is taught!
69
PoEM on why study EM!
To the students from all around the world
And to the students all over the world
EMpowered by the Jordan name
And inspired by the AMRITA name
I offer to you this book on EM
Beginning with this poem which I call PoEM
If you are wondering why you should study EM
Let me tell you about it by means of this PoEM
First you should know that the beauty of EM
Lies in the nature of its compact formalism
Through a set of four wonderful EMantras
Familiarly known as Maxwell's equations
They might be like mere four lines of mathematics to you
But in them lie a wealth of phenomena that surround you
Based on them are numerous devices
That provide you everyday services
Without the principles of Maxwell's equations
Surely we would all have been in the dark ages
Because there would be no such thing as electrical power
Nor would there be electronic communication or computer
Which are typical of the important applications of ECE
And so you see, EM is fundamental to the study of ECE.
70
PoEM on why study EM! (Continued)
So, you are curious about learning EM
Let us proceed further with this PoEM
First you should know that E means electric field
And furthermore that B stands for magnetic field
Now, the static E and B fields may be independent
But the dynamic E and B fields are interdependent
Causing them to be simultaneous
And to coexist in any given space
Which makes EM very illuminating
And modern day life most interesting
For it is the interdependence of E and B fields
That is responsible for electromagnetic waves
In your beginning courses you might have learnt circuit theory
It is all an approximation of electromagnetic field theory
So you see they put the cart before the horse
But it is okay to do that and still make sense
Because at low frequencies circuit approximations are fine
But at high frequencies electromagnetic effects are prime
So, whether you are an electrical engineer
Or you happen to be a computer engineer
Whether you are interested in high frequency electronics
Or may be high-speed computer communication networks
You see, electromagnetic effects are prime
Studying the fundamentals of EM is sublime.
71
PoEM on why study EM! (Continued)
If you still have a ProblEM with EM,
Because it is full of abstract mathematics,
I say, my dear ECE student who dislikes electromagnetics
Because you complain it is full of abstract mathematics
I want you to know that it is the power of mathematics
That enabled Maxwell’s prediction through his equations
Of the physical phenomenon of electromagnetic radiation
Even before its finding by Hertz through experimentation
In fact it was this accomplishment
That partly resulted in the entitlement
For the equations to be known after Maxwell
Whereas in reality they are not his laws after all
For example the first one among the four of them
Is Faraday’s Law expressed in mathematical form
You see, mathematics is a compact means
For representing the underlying physics
Therefore do not despair when you see mathematical derivations
Throughout your textbook on the Fundamentals of Electromagnetics
Instead look through the derivations to understand the concepts
Realizing that mathematics is only a means to extend the physics
Think of you as riding the horse of mathematics
To conquer the new frontier of electromagnetics
Let you and me together go on the ride
As I take you through the steps in stride, with grattitude!
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The End
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