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. S tatics D ynam ics dc F requency , f L ight 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 S tatics Q uasistatics D ynam ics dc F requency , f L ight 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 S Wb V m m 2 C d H dl J dS D dS + C S dt S A m Current density A m 2 V r dv Charge density Magnetic flux density Electric field intensity Magnetic field intensity D dS S m 3 B dS 0 Displacement flux density C m 2 30 Faraday’s Law, the first EMantra C E • dl – d 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 – m 2 2 m , or W b. 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 C H • dl S J • dS + d dt S D • dS S J, D 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 m 2 2 m , or A. S D • dS = Displacement flux, or electric flux, crossing S, C m 2 2 m , or C . 34 d S D • dS = Time rate of increase of dt displacement flux crossing S, or, displacement current crossing S, C s , or A. 35 Gauss’ Law for the Electric Field, the third EMantra D S dS V C 3 r dv 3 m , or C 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 dt V r dv 0 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 z y E x z E y x E y – z – E z x E x – y Lateral space derivatives of the components of E D x x + D y y + D z L ongitudinal derivatives z – B x – t B y – t Bz t Time derivatives of the components of B r Charge density of the com ponents of D 41 The “Mahatmyam (Greatness)” of Maxwell’s Equations C E • d l = – d dt S B • dS C H • d l = S J • d S + d dt S D • d S 42 The “Mahatmyam (Greatness)” of Maxwell’s Equations + J H ,B + Law of Conservation of Charge r Gauss’ Law for E Ampere’s Circuital Law 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! C E • d l = – d dt S B • dS C H • d l = S J • d S + d dt S D • d S 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. S tatics l 2 Q uasistatics D ynam ics dc F requency , f L ight 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! 72 The End 73

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