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Back To: Rao's Faculty Bio

Transmission Lines and Waveguides

by

Nannapaneni Narayana Rao
Edward C. Jordan Professor Emeritus of Electrical and Computer Engineering
University of Illinois at Urbana-Champaign (UIUC), USA
Distinguished Amrita Professor of Engineering
Amrita Vishwa Vidyapeetham, India

 

"Fill your heart with love and express it in everything you do." – Amma Mata Amritanandamayi Devi, Chancellor, Amrita Vishwa Vidyapeetham

To the young (and not so young) minds in my motherland, India, and everywhere else in the world, with love

 

“Everything comes to us that belongs to us if we create the capacity to receive it.”
– Rabindranath Tagore

In January 2007, I met a young faculty member in electronics in my motherland, India, where I was a presenter in a workshop.  Since then, she received her Ph.D., with specialization in communications and networking.  Somehow, she was assigned to teach the “much dreaded” electromagnetic theory (a subject she taught a couple of times earlier) class in the first semester of the academic year 2008-09.  So, she began communicating with me by e-mail in May 2008.  Since then, we have exchanged numerous e-mails.  Having taught the electromagnetic theory class in the first semester, she wanted to take up the challenge of teaching the “Transmission Lines and Waveguides” class for the first time, in the second semester, beginning in January 2009.  Although the syllabus for her course and the approach used differ from mine, she also wanted to learn the subject in my way, while teaching according to their requirements.  So, here I am pleased to tell you my story and offer to you these materials.

Falling in love with the teaching of “Transmission Lines”

 

Transmission-line theory can be studied by beginning with the distributed circuit equivalent for the line.  However, this treatment obscures the fact that the phenomenon is actually one of electromagnetic wave propagation, except that it is cast in term of circuit quantities.  Furthermore, one must return to the field equations for the study of waveguides.  For these reasons, I always employ the field approach in my treatment of the subject of “transmission lines.”

In fact, as I mentioned in the preface to the Indian edition of "Elements of Engineering Electromagnetics, Sixth Edition," and in the “Gratitude and Grattitude” section in "Fundamentals of Electromagnetics for Electrical and Computer Engineering," and its Indian Edition, while I was a graduate student at the University of Washington, I fell in love with the teaching of "Transmission Lines" from the electromagnetics aspect, which then extended beyond transmission lines and later led to the writing of my books.

Thus, although entitled, “Transmission Lines and Waveguides,” I consider the material made available here to be devoted to electromagnetic wave propagation along guiding systems, that is, transmission lines and waveguides.  Strictly speaking, both transmission lines and waveguides should be called waveguides.  However, the terminology, “transmission line,” is commonly used for those guiding systems which propagate the so-called transverse electromagnetic (TEM) waves or almost TEM waves, whereas “waveguide” is employed for those systems which propagate the higher order transverse electric (TE) and transverse magnetic (TM) waves, although higher order modes may exist on a transmission line.

The study of transmission-line theory is essential to electrical and computer engineers not only because of the direct and widespread application of transmission lines in communications and computer systems, but also because many problems in unguided wave propagation can be solved by using transmission line analogies.  In addition, there are many problems in other branches of engineering which are analogous to wave propagation along transmission lines.

Transmission-line theory differs from ordinary (lumped) circuit theory in the following manner.  In ordinary circuit theory, when an excitation is applied in some branch of a circuit at some value of time, a response is considered to occur simultaneously in all other branches of the circuit. In transmission-line theory, when a system is excited at some location at some value of time, a response does not occur simultaneously at some other location in the system.  There is always a time delay between the application of the excitation at one location and the occurrence of the response at a different location.  This is because the situation in a transmission line is one of electromagnetic waves propagating along the line being guided by the conductors of the line, and it takes certain amount of time for the electromagnetic waves to travel from one location to another.  In fact, this time delay exists also in an ordinary circuit; however, it can be ignored, without any significant consequence, since the circuit is “electrically” small.  When the circuit is not electrically small, as in the case of high-frequency analog systems or high-speed digital systems, the time delay is of significant consequence to the system’s performance; hence, transmission-line theory comes into play.

Grateful to Adler, Chu, and Fano

 

“I am grateful for being here, for being able to think, for being able to see, for being able to taste, for appreciating love – for knowing that it exists in a world so rife with vulgarity, with brutality and violence, and yet love exists.  I am grateful to know that it exists.” – Celebrated author and poet Maya Angelou looking back on 80 years of blessings, in American Way Magazine of the American Airlines, November 15, 2008.

As I mentioned above, while I was a graduate student at the University of Washington, I fell in love with the teaching of "Transmission Lines" from the electromagnetics aspect, which then extended beyond transmission lines and later led to the writing of my books.  For this, I am grateful to the late professors Lan Jen Chu and Richard B. Adler, and Professor Emeritus Robert M. Fano, of the Massachusetts Institute of Technology, for their book, "Electromagnetic Energy Transmission and Radiation.”  This book and the companion book, "Electromagnetic Fields, Energy, and Forces," by Fano, Chu, and Adler were both published in 1960, when I was a graduate student at the University of Washington. 

I had the good fortune of meeting Professor Adler, while he was an Associate Head of the EECS Department at MIT, at the ECEDHA (Electrical and Computer Engineering Department Heads Association, previously NEEDHA, National Electrical Engineering Department Heads Association) annual conferences, which I attended as Associate Head of my department at Illinois, before he, unfortunately, passed away at the age of 67, when he was accidentally hit by a car while jogging in Concord, Massachusetts, in 1990.  And I had the pleasure of meeting Professor Fano once when I visited MIT.  Professor Chu passed away in 1973 at the age of 60, before I had the opportunity to meet him. 

Teaching EE 411, “Energy Transmission,” at the University of Washington

 

I am not sure how much of the subject of “Transmission Lines and Waveguides” I learned before I came to the United States in 1958 to pursue my graduate studies at the University of Washington, because all I remember is that I learned “Transmission Lines” to my satisfaction from the book, "Electromagnetic Energy Transmission and Radiation” by Adler, Chu, and Fano, which has since then become my favorite book.  I learned the material by reading the chapters and solving the chapter-end problems, many of which were challenging, and derived great satisfaction from it, since I did not have the benefit of having a solution manual for the book.

In the first quarter (Spring 1963) I was involved in teaching EE 411 (Energy Transmission), the Adler, Chu, and Fano book was only a reference book and the textbook was a different one.  Yet, I was so inspired by that book that I made up sets of supplementary problems, many of which were based on problems from the chapters in it, and assigned some of them as homework, along with problems from the textbook.  In the next quarter (Autumn 1963), I taught the course again, this time with the Adler, Chu, and Fano Book as the textbook. 

Teaching EE 350, “Lines, Fields, and Waves,” at the University of Illinois

 

To continue the story, when I came to Illinois in 1965, I requested for teaching the then EE 350, “Lines, Fields, and Waves,” for which I was well prepared, from the experience of teaching the subject at the University of Washington. I was also determined to write a book on "Transmission Lines."  I began writing my own chapters and in 1968, I sent the material to Prentice Hall.  After reviewing it, they said they were interested in publishing it but wanted me to add some material on fields in the front.  So, I began writing that material, which soon grew and grew to become a book by itself, "Basic Electromagnetics With Applications," published in 1972, using the inductive approach.  The material on transmission lines was still there for a second book, but instead of publishing it, curriculum changes in the department took me in a different direction to write "Elements of Engineering Electromagnetics," published in 1977, for a one-semester course using the deductive approach.
  
In the second edition of "Elements of Engineering Electromagnetics," published in 1987, I added much of the unused material on transmission lines and waveguides, so that "Elements of Engineering Electromagnetics," in its sixth edition now, became the textbook for a second course on "Lines, Fields, and Waves," in addition to being the textbook for the first course on "Introduction to Electromagnetic Fields."   In the years until around 1987, when I became the Associate Head of the department, I taught EE 350 (which later became ECE 350 and still later ECE 450) somewhat regularly, using my notes to support the lectures delivered orally.  See the article, “EM course is gateway to many career paths” in the Spring 2005 issue of ECE Alumni News.  Read also a related article and the sidebar in the November 2004 issue of INGENUITY on the present sixth edition of "Elements of Engineering Electromagnetics."  Note that both articles quote Tony Zuccarino, a student in my EE 350 class in Summer 1983, pictured with me in both publications. In addition, the Alumni News article also quotes John Cioffi, the inventor of DSL technology.

As I was preparing this write-up, I contacted Tony Zuccarino for a copy of the handwritten class notes, mentioned by him.  Graciously, he obliged to my request by searching for the notes from among things stored in boxes in his house, locating it and making a copy of it, and sending me the copy.  When he found the notes on December 3, 2008, he exclaimed in his e-mail to me: “FOUND! The only notes I seem to have kept... are those from your EE 350 class summer of 1983!”  I am pleased to make available to you here Tony’s copy of the notes.

Download Tony Zuccarino’s copy of EE 350 class notes from Summer 1983 (PDF, 4.48 MB, 217 pages).    

EE 350 Video Course in 1983 at the University of Illinois

 

In 1983, the College of Engineering began offering an off-campus program, consisting of delivery of courses by videotape.  So, they requested me to videotape EE 350, "Lines, Fields, and Waves," which I accepted.  Forty-three lectures to an empty class, each of 50 minutes duration, were taped using a unique arrangement, consisting of a combination of electronic blackboards and an overhead camera for photographing handwritten cards as slides.  The tapes were used for a few years, after which the program was discontinued by the College.  Based on the materials used for this course, I give below the outline of the course and provide PowerPoint presentations for each of the six chapters, with each section in a given chapter corresponding to one lecture, and the video recordings for the lectures. Note that the copyright for the video recordings is owned by the Board of Trustees of the University of Illinois. They are provided courtesy of the College of Engineering of the University of Illinois at Urbana-Champaign for not-for-profit, academic and teaching purposes only. For other uses, please contact Director of Engineering Online Programs, College of Engineering, University of Illinois at Urbana-Champaign.

1.    REVIEW AND INTRODUCTION (PPT, 6.12 MB, 86 Slides)
1.1. Maxwell’s equations; Uniform plane waves in time domain in free space (video 240M mpg)
1.2. Sinusoidal traveling waves (frequency domain); review of phasor technique (video 303M mpg)
1.3. Uniform plane waves in material media (video 240M mpg)
1.4. Boundary conditions; Parallel-plate line; Transmission-line equations (video 240M mpg)
1.5. Transverse electromagnetic waves; Transmission line equations and solutions
       for lossless line; Line parameters for different lines (video 240M mpg)

2.    TIME DOMAIN ANALYSIS FOR LOSSLESS LINES (PPT, 8.45 MB, 145 Slides)
2.1. General solution; Semi-infinite line (video)
2.2. Line terminated by resistance (video)
2.3. Bounce diagram technique (video)
2.4. Bounce diagram technique (continued); Transmission-line discontinuity (video)
2.5. Three lines in cascade; Junction of three lines (video)
2.6. Lines with reactive elements (video)
2.7. Lines with initial conditions (video)
2.8. Lines with initial conditions, continued (video)
2.9. Lines with nonlinear terminations; Load line technique (video)

R.1. Review problems (video)
R.2. Review problems (video)

3.    FREQUENCY DOMAIN ANALYSIS FOR LOSSLESS LINES (PPT, 8.23 MB, 128 Slides)
3.1. General solution; Semi-infinite line (video)
3.2. Short-circuited line (video)
3.3. Natural oscillations; Resonance (video)
3.4. Line terminated by complex load (video)
3.5. Line impedance; Power flow (video)
3.6. Lines in cascade; Quarter-wave transformer matching (video)
3.7. Stub matching; Frequency response (video)
3.8. Multi-section quarter-wave transformer (video)

4.   THE SMITH CHART (PPT, 6.64 MB, 82 Slides)
4.1. Basis and construction of Smith chart (video)
4.2. Some basic procedures (video)
4.3. Quarter-wave transformer matching; Single stub matching (video)
4.4. Double stub matching (video)
4.5. Some other applications (video)

R.3. Review problems (video)
R.4. Review problems (video)

5.    LOSSLESS WAVEGUIDES (PPT, 6.45 MB, 90 Slides)
5.1. TM and TE waves in rectangular waveguides (video)
5.2. Characteristics of TM and TE waves (video)
5.3. Characteristics of TM and TE waves, Continued (video)
5.4. Transmission line analogy; Cavity resonator (video)
5.5. Dispersion and group velocity (video)

6.    LOSSY LINES AND GUIDES (PPT, 6.29 MB, 97 Slides)
6.1. Lossy line: Propagation constant and characteristic impedance (video)
6.2. Standing waves and power flow (video)
6.3. Use of the Smith chart for lossy lines (video)
6.4. Distortionless line; Diffusion (video)
6.5. Internal impedance of a plane conductor; Perturbation analysis of losses (video)
6.6. Attenuation constant of TE1,0 mode in a rectangular waveguide (video)

R.5. Review problems (video)

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University of Illinois at Urbana-Champaign
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