Preface

Fundamentals of Engineering
Electromagnetic Fields and Waves

Why Another Fields Book?

True, there are many EM field books on the market for undergraduate engineering students.  I personally have used many of them in my classes as texts and as occasional references.  I liked some for their simple presentation and readability and others for their thorough analysis and comprehensive coverage.  Whichever book I used, the students always had difficulty with the subject.  One reason is that many students lack adequate background preparation for the material (Math and Physics).  Available textbooks and most professors do not take that into account in their presentation. For this reason, this book is an attempt to address this issue and present the material with students’ realistic preparation in mind.

In addition, this book pays attention to material that always falls in the cracks between the courses students take and is vital to the comprehension of the overall picture. The book is written for both readability and adequate material coverage.  It focuses on tackling three major issues that are typically encountered in teaching EM fields:

First Issue:

Let us face it; our undergraduate education of electromagnetic (EM) fields leaves the majority of the students with more questions than answers.  Their biggest question is “Why are we studying this material?” In a way, they are right.  If we do not tell them what Coulomb’s law, Faraday’s experiment, or Maxwell’s equations mean to them, then this material is an unnecessary burden and a waste of their time.  Typically, all they get is a bunch of vector analysis exercises and complicated integrations; another “Math” course at best.

The fact of the matter is that EM fields is pivotal to all aspects of Electrical Engineering.  That should be our theme when teaching undergraduates the topic.  It is not just a matter of showing some practical applications for electrostatics or wave propagation; we need to go far beyond.  We should show them how Maxwell’s equations provide the foundation for the topics of circuit theory, electronics, communications, power generation and transmission, microwaves and antennas, just to name a few application areas. Borrowing from the computer community, EM fields is like the machine language and the way we deal with these EE topics is like writing the code in a higher-level language. 

Second Issue:

Teaching EM fields to undergraduates has the potential of arming them with “problem solving” skills.  It is a fringe benefit that comes naturally with the topic, far beyond what comes through from other courses in their curricula. This is manifested in the ability to take a physical problem through the steps of deriving a physically based model for which a mathematical model is then developed. Next, we do the math analysis and obtain results for which we find relevant explanations for physical phenomena.

Third Issue:

The other point is that the majority of our students lack adequate background preparation for the material required for the study of EM fields (in both Math and Physics).  The challenge is that the subject of EM fields requires good mastery of BOTH Math and Physics skills; Math being a coded language of expression of the physical phenomena and how things evolve.  It is just like language and culture; they are both critical to communication skills.  For successful communication, one needs a good appreciation of both the language of communication and the culture of the people we communicate with.  Neither language nor culture can work well by themselves; the same is the case for Math and Physics. Some of our students (and professors) are more skilled in one side and pay less attention to the other.  We need to be continually reminded that Math is just an abstract language of expression (a coded one) and we must constantly be mindful of the physical phenomena and their implications as we go through the mathematical derivations and analyses.

Fields is one of the toughest topics for UG EE students. The reason is twofold: 1. Lack of student preparation and 2. Inadequate textbooks and teaching of the material.  The topic requires a holistic presentation of the math and physics to ensure student comprehension of the topic and appreciation of its importance to their education. In the proposed text, we provide detailed explanation and always relate the math to the physics.  We simply write for the below-average student.  Moreover, the book has order of coverage flexibility and as much as it relates things to each other, we try to make topics as much independent as possible.

In this book, we recognize the need to keep the physics involved in the entire process of developing a mathematical model of a physical problem, in deciding the correct math analysis approach, successfully carrying out solutions, and finally in interpreting (decoding) the mathematical results and translating their implications in physical terms.  Unfortunately, most of our EM education does not give adequate emphasis to maintaining the physics insight and ignores the last and most important step in the process of translating the obtained mathematical results into physical phenomena.

So, in this book will shall attempt to keep both the students and professors mindful of the physics aspects of all topics.  Both will find many eye-opening conclusions as a result.  There will be many challenges as most of us are not accustomed to that.  But at the end of the day, the benefit of achieving lasting comprehension is worth much more than training to carry out procedures.

Book Plan

The plan is to allow maximum flexibility to enable a wide sector of the academic community to customize the book to their curriculum needs.  The book chapters will be arranged in four blocks (see the book outline below); each block can be taught independently of the others and as a result the textbook can be customized by rearranging the blocks.  Each block will have an introductory section to transition the learners into the material presented in that block. 

There are three typical approaches to EM coverage, which I believe this book can serve very well.  Referring to the outline table shown below (under product outline), the three approaches, and the corresponding proposed block coverage arrangement are:

• Early transmission line approach: Blocks A-B-C-D
• Classical Static-Dynamic approach: Blocks B-C-D/A
• Start with Maxwell’s Equation approach: Blocks D/A-B-C

 

Two other features of the book that add to the customization flexibility:

• A summary is provided at the beginning of each chapter to help the instructor and learner pick and choose relevant study material
• In addition, Chapter material is presented with “potentially distracting” material moved to addenda at the end of the chapter.  This allows the instructor and the learners decide which and how much of the material in these addenda to cover.

With these flexibility features, the book can be used for both one semester and two semester curricula.

WHY Transmission Lines First?

Traditionally, EM fields are taught starting with Electrostatics followed by Magnetostatics, after which dynamics, time varying fields, and EM propagation are introduced. This approach has been criticized by many as “dry,” as most of the interesting EM applications are not introduced until the dynamics part is covered. As a result, it is believed that many students are turned away from the subject because of the abstract nature of the “static” part.

The idea of reversing the order of coverage has been entertained by many educators in the past with varying degrees of success. The impeding factors are the difficulty in presenting the dynamics part without the prerequisite foundation established during the study of the statics part. The lack of a “good” textbook using this approach adds to the complexity.

As discussed earlier, this book can be taught in orders other than the way the chapters are ordered.  My personal preference is to start with TL analysis, as a topic close to the students’ familiarization with many applications encountered in their daily lives.  A logical question follows regarding the nature of the transmission line characteristic parameters: internal resistance, inductance, capacitance, and conductance (R, L, C, and G). What do these parameters physically imply, and what does it take to control their values, and hence control the performance of the transmission line. This question can be used to lead the students to the following electrostatic and dynamics chapters. 

So, we find ourselves in need of studying EM field topics that enable us to explain the physics of each of these “circuit” elements.  It is the only way to understand how they work, but also how can we design them, control their parameters, and make them do what we desire for them to do.  Some may wonder, is it the chicken and egg dilemma? We start with circuit theory and end up in fields.  The fact of the matter is that “fields” is the chicken that laid for us the “circuits” egg (and a few other eggs) that we encounter in our physics and electrical engineering studies.

Finally, we close the loop by coming back to the TL analysis based on field theory, thus demonstrating to the students the limitations of the use of the RLCG circuit theory model.

Acknowledgements:

I am deeply indebted to my dear friend, colleague, and office neighbor for more than 20 years, Dr. Ioannis Besieris. He supported this effort through many discussions and thorough review of the manuscript. He must have spent enormous amount of time reviewing every sentence and every equation I wrote. Simply put, I owe it to Ioannis for achieving the caliber of this book.

Also, I would like to acknowledge the support of my dear friend and former graduate assistant, Dr. Karim Said, who helped me in many aspects with the production of this manuscript. In particular, I would like to cite his help with many technical discussions, the lesson objectives, end of chapter problems and exercises, as well as converting the manuscript equations for proper web display.

 

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Introduction

Fundamentals of Engineering
Electromagnetic Fields and Waves

Why Study EM Fields?

Most certainly, the course of EM Fields is perceived as one of the toughest for UG engineering students. The typical reasons for this issue are 1) Lack of adequate background preparation and 2) Inadequate textbooks and teaching of the material.  The topic requires a holistic presentation of the math and physics to ensure student comprehension and appreciation of its importance to their education.

The fact of the matter is that EM fields are pivotal to all aspects of Electrical Engineering.  Maxwell’s equations provide the foundation for the topics of circuit theory, electronics, communications, power generation and transmission, microwaves and antennas, just to name a few application areas.  Borrowing from the computer community, EM fields is like the machine language and the way we deal with these EE topics is like writing the code in a higher-level language.

In addition to developing the insight and appreciation to the roots of the different EE curriculum topics, we site two additional benefits of studying EM fields as an undergraduate.  In particular, we site the added skills in both the areas of design and problem solving.

Competent Design Skills?

As an Engineer, you are likely to get involved in the design, analysis, or testing of an electrical or electronic device (or circuit).  These devices and circuits are typically made of “conductors”, “dielectrics”, and possibly “magnetic” media.  These different materials are shaped and assembled (or integrated) together in specific manners as to perform certain functionality.  When powered up, the electrical charge distribution within the device structure is altered as to produce the desired device function.

Studying electromagnetic fields is about gaining the skill and acquiring the tools that enables the engineer to relate to the physics of electrical charge distributions and currents and their interaction with different materials.  In other words, this study is all about developing the appreciation to the properties and limitations of the elements and components we use in electrical and electronic devices.

Some would say that we learned how to design circuits by putting together passive and active components “wired” in certain fashions to produce the desired function.  The point is that the models we “claim” for the components we use in circuit design are approximate (simplified) ones that ignore “secondary” features of these components. These models are typically developed through an electromagnetic fields study of the components’ physical structures with certain degrees of approximations.

In other words, the “basic” models of passive components, such as resistors, capacitors, inductors, and even interconnecting wires (transmission lines), all are developed based on EM field studies of material structures and their interaction with charge distributions and currents. Similarly, the models of active components (devices), such as diodes, transistors, and various integrated circuits components, require an EM field analysis of how their physical structure and material properties react to different electromagnetic fields excitations.

Not only the models of these components are developed through an EM study of their physical structures, but also, the tools we use in circuit design are developed based on an electromagnetic study as well.  Even primary tools like Ohm’s law, Kirchhoff’s current and voltage laws have their roots in electromagnetic field studies.

To demonstrate, we take an example of a simple resistor component.  Typically, designers would use the simplified model of a “pure” resistance in the circuit schematic as well as in the circuit analysis or design equations.  The fact of the matter is that the “simple resistor” contains other features that may be ignored in some cases but would be critical to the circuit performance in others.  Those other features may include lead inductance, packaging capacitance, material nonlinearities and more. In fact, the model for other features as such requires a field analysis as well, and the resulting component is again an approximation to the actual physical performance of the structure.

Another example is the interconnecting “wires” in a circuit.  Typically, those are ignored as having no effect on the circuit performance other than connecting the circuit components to each other.  This simplification could lead to serious errors in some applications.  Connecting wires contribute to resistive, inductive, and capacitive circuit elements that could alter the circuit performance at high frequencies and high currents. 

From the above discussion, we can conclude that EM field studies are key to the development of component models we can use in circuit/device design and analysis. We can also conclude that several degrees of modeling “fidelity/accuracy” are possible, and in some cases, more approximations suffice than in the others.  Consequently, we can extrapolate to say that there will be cases where circuit models will not provide adequate representation of the physical devices, in which case, we must resort to the fundamental tool of EM field analysis.

In essence, a good designer needs to be in full appreciation of electromagnetic properties of different material.  Not only that, but a good designer needs to get into other interdisciplinary areas such as mechanical, thermal, and chemical properties, in addition to including environmental, economical, and human factors in the device design.

This book focuses on the basics of EM field studies.  It does not provide all the tools required for the learner to become a “good designer” in this regard.  However, it provides the foundations of EM field needed to build on with more advanced course work.  It certainly attempts to provide the student with the insight of what need to be learned to be a “good designer”.

Problem Solving Skills:

Studying EM fields has the potential of arming the learner with “problem solving” skills. This a fringe benefit that comes naturally with the topic, far beyond what comes through from other courses in his/her curricula. This is manifested in the ability to take a physical problem through the steps of deriving a physically based model for which a mathematical model is then developed. Next, we do the math analysis and obtain results for which we find relevant physical explanations and applications. 

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