Worcester Polytechnic Institute Department of Electrical and Computer Engineering ECE 2112 ELECTROMAGNETIC THEORY C-term 2018 Professor: Dr. Reinhold Ludwig Office: AK 229, Tel.: 508-831-5315 Office hours: Mo, Tu, Th, Fr: 11 am 11:50 am email: ludwig@wpi.edu Teaching Assistants: Swarnadeep Majumder (smajumder@wpi.edu) Office in AK 014, Mo: 4 pm 6 pm. Mr. Siddhant Pandey (spandey2@wpi.edu) Office in AK 014, Th: noon 1:30 pm Lectures: Mo Fr, 10:00-10:50 am in AK 233 Grading: Homework: 20% Exams 1 and 2: 25% each Final Exam: 30% Prerequisite: Vector Calculus, ECE 2010. Textbook: F. T. Ulaby, Fundamentals of Applied Electromagnetics, Prentice-Hall, 7 th edition, 2015. Related Text: R. Ludwig and G. Bogdanov, RF Circuit Design: Theory and Applications, 2 nd edition, Prentice-Hall, 2009. 1
ECE 2112 GENERAL OBJECTIVES This course attempts to break new grounds in teaching you electromagnetics the core subject topic has created electrical engineering, and to this day is shaping our profession in profound ways. A typical approach to learning EM would start with a refresher of key mathematical terms (which you should know from your math courses), followed by electrostatic and magnetostatic fields, leading up to Faraday s induction law, and ultimately culminating in Maxwell s equations (gulp). The progression is thus 1) statics, 2) low frequency, and 3) high frequency. While this sequence undoubtedly has its merits, it suffers from two drawbacks: lack of immediate gratification (i.e. don t give me all the math, tell me instead what the stuff is useful for ), and important engineering applications you need to know in your professional career (like high-frequency circuits) are relegated to later courses. We will depart from this sequence, and commence our course with the second part in an effort to make the material more hands-on. Traditionally, relatively few students have been willing to take on electromagnetics and its follow-on course ECE3113, RF Circuit Design. Interestingly, these students today are well-paid specialists in such diverse areas as signal integrity, optical communication, sensors, microwave imaging, biomedicine, satellite communication, etc. The reason for this continued interest in electromagnetic field phenomena stems from today s highspeed, high-frequency engineering universe; examples include digital clock speeds exceeding 3 GHz, or car radar systems operating at 24 GHz and above. They have rendered many conventional, so-called lumped, circuit design techniques obsolete. Instead, transmission line principles that rely on traveling voltage and current waves are needed to build amplifiers, mixers, and oscillators at 1 GHz and above. There is little doubt that sooner or later you will be confronted with aspects of this highfrequency revolution, even as a digital design engineer. Consequently, you have to understand what makes RF so different, at least on a fundamental level. The engineering jobs being created in all types of high-frequency endeavors should be a very motivating factor. In light of this RF circuit migration, I decided to begin the first 14 classes of this course with high-frequency circuit principles, like voltage and current waves along transmission lines. This material, by the way, will also be the starting point of ECE 3113. You may be surprised to learn that transmission line theory answers a number of interesting questions, including what constitutes a 50Ω cable, how do voltages and currents get reflected and transmitted on a circuit board, what is a propagation 2
constant, how can we find the high frequency impedance of a copper trace? Many of these topics have counterparts in optics. After our high-frequency circuit exposure we will briefly review the subject of vector calculus. I would like to present you with the basics of three very different coordinate systems (rectangular, cylindrical, and spherical) and refresh your memory on how to carry out integration and differentiation in each system (i.e. gradient, divergence, and curl). So, after all your math and physics courses you will practice this stuff in an engineering context for a third and probably final time. We will then delve into electrostatics, a topic which rests on only three principles (existence of charge, Coulomb s law, spatial convolution). Here we will discuss the electric properties of materials; this is important when studying current flow in semiconductor devices diodes, transistors. Also, Ohm s and Joule s Laws, plus the behavior of dielectrics, are directly linked to electrostatics. Since the world is finite, we need to understand what happens at interfaces (the boundary conditions) before we can finish the subject of electrostatics with the important concepts of capacitance and energy storage. After the excursion into stationary charges, electric fields and voltages, we next will turn our attention to moving charges and currents they are responsible for magnetic effects as part of magnetostatics. You will discover how the magnetic field is created by a coil and how it is practically exploited. With the aid of Ampère s law we can quantify the magnetic field behavior inside and outside of a wire conductor. The topic of magnetic properties and their classification will conclude our course. You may find it surprising, but the biological response to applied magnetic fields in humans is widely exploited in medical imaging, for instance in magnetic resonance imaging (MRI) scanners. Let s be clear: we are going to cover quite a bit of theoretical and practical ground in this course, and you will gain a lot of knowledge. So, even if you possess a preconceived negative bias toward electromagnetics, please try to approach ECE2112 with the open mind it deserves. Drop your prejudices and give ELECTORMAGNETICS your best effort. I m convinced, you will enjoy it Make everything as simple as possible, but not simpler. A. Einstein 3
ECE 2112 SYLLABUS Class Date Topic Reading HW assign. 1 10 January Introduction 01 11 2 11 January Nature of Electromagnetism 12 18 3 12 January Traveling Wave Phenomena 18 30 15 January MLK day no classes 4 16 January EM-Frequency Spectrum, 30 44 Complex Numbers, Phasors 5 17 January RF Transmission Line Concepts 48 52 6 18 January Lumped-Element RF Model 52 55 HW 1 due 7 19 January Transmission Line Equations 56 57 8 22 January Voltage and Current Wave 57 59 Solutions 9 23 January Lossless Transmission Line, 65 69 Reflection Coefficient 24 January Summary/Review 01 69 HW 2 due 25 January Exam 1-10 26 January Standing Waves 70 75 11 29 January Input Impedance of a Lossless 75 78 Transmission Line 12 30 January Special Cases of the Lossless 78 84 Transmission Line 13 31 January Lambda-Quarter Transformer, 84 86 Summary of Parameters 14 01 February Power Flow and Signal 86 88 HW 3 due Integrity 15 02 February Vector Analysis (Review I) 134 154 16 05 February Vector Calculus (Review II) 154 170 17 06 February Maxwell s Equations 178 179 07 February Summary/Review 70 179 HW 4 due 08 February Exam 2-18 09 February Electrostatics, Coulomb s Law 180 187 19 12 February Gauss Law, Electric Potential 187 189 20 13 February Potential, Gradient, Dipole 189 192 21 14 February Dipole Field 192 194 15 February Advising day - NO CLASS 22 16 February Electric Properties of Materials 195 203 4
23 19 February Boundary Conditions and 203 222 HW 5 due Capacitance 24 20 February Magnetic Field 236 243 25 21 February Magnetic Field of a Coil 244 250 26 22 February Ampere s Law 252 260 23 February Reading Day NO CLASS 27 26 February Magnetic Materials 260 264 28 27 February Inductance/Faraday s Law 282-285 - 28 February Review of Course 1-285 HW 6 due - 01 March Final Exam - 02 March Celebration - Boynton 5