ECEN 5114
Waveguides and Transmission Lines
Spring, 2016         2:00-3:15 T Th         ECEE 1B32

Prof. E. F. Kuester                    
ECOT 248                                                      (303) 492-5173

Office Hours: M 3:00-4:00 PM, Tu 3:30-4:30 PM, W 9:30-11:00 AM, or by appointment

Page last updated 25 April 2016
Links and Downloadable Files                Download Course Notes                Homework Assignments                General Course Information                Class Lectures on D2L                                        


My office hours have been set and listed above. Please note that my Monday office hour will not take place on January 18 (due to the Martin Luther King holiday), nor on January 25 (when I will be on travel).

I plan to hold a final lecture from 4:30-5:45 PM on Tuesday May 3, to make up for the one that was cancelled when campus was closed due to the snowstorm.
Material in this lecture will not be included on the final exam, but the lecture will be archived for use in future years.

Homework Assignments (and Final Exam)
Problems not found in the notes, and all of the solutions, are in PDF format; download the Acrobat Reader to read them.

Problems Assigned Date Due Solutions
p1-2, p1-5
21 January 2016
p1-2 p1-5
p1-21, p1-22
28 January 2016
p1-21 p1-22
p2-12, p2-15, p2-23
9 February 2016
p2-12 p2-15 p2-23
p3-2, p3-15
16 February 2016
p3-2 p3-15
18 February 2016

p4-3(a,c only), p4-14

25 February 2016
p4-3 p4-14
p5-3, p5-11
3 March 2016
p5-3 p5-11
p5-20, p5-28
10 March 2016
p5-20 p5-28
Midterm Exam
17 March 2016
Midterm Exam Solutions
p6-7, p7-1
31 March 2016
p6-7 p7-1
p8-2, p8-6 (see section C.3 of Appendix C for elliptic integrals)
7 April 2016
p8-2 p8-6
p8-26, p9-25
14 April 2016
p8-26 p9-25
p9-26, p10-2
21 April 2016
p9-26 p10-2
Final Exam
10:00 AM MST, 4 May 2016

General Course Information:

This course is divided into three main parts. In the first part (corresponding to the first four chapters of the course notes), we will examine most of the basic concepts of guided waves through their simplest prototypes: the properties of the classical (distributed-network) transmission line with lumped elements connected to it. In the next part (chapters 5-8 of the notes) we will deal with various types of electromagnetic waveguides and transmission lines—particularly their mode properties. These types include traditional hollow waveguides, dielectric (including optical) waveguides, printed transmission lines such as microstrip, and more. As we do so, the features common to all varieties of waveguide will begin to be apparent, and this will set the stage for the final third of the course, in which we will study the problems of excitation and scattering of waveguide modes; that is, how they act as interconnecting parts of real systems.

The lectures are recorded and are made available on D2L. Log in, go to the page for this course, and on the left side of the gold bar along the top is a button that says "Lecture Access"; click on this to view the lectures.

Your grade will consist (in roughly equal weights) of three parts. The first is your grade on the homework problems, which are assigned once a week and are due one week later. The second is the mid-term exam, which is a take-home exam due in class on Thursday March 17, 2016. The third part of your course grade is the final exam, which is a take-home exam due at 10:00 AM on Wednesday May 4, 2016: (slightly after the nominal date of the in-class final exam). The exams will consist of problems similar to those given as homework during the semester.

There is bound to be a certain amount of informal discussion of the homework problems among students in the class. As long as this discussion does not entail solving the problem for someone else, I have no objection to it. In particular, I do expect that solutions to the same or similar problems which may be floating around from previous semesters are not to be consulted. I expect that any work turned in to me with your name on it represents your unique write-up and understanding of the solution to a problem, rather than a copy of some collective or collaborative effort. For the midterm exam and the take-home final exam, there is to be absolutely no consultation between students, past or present. I will be available to answer any questions on interpretation of the problems on the exams.

Some of the homework problems will require (or at least be considerably facilitated by) the use of mathematical software. There are many such programs available, and I don't really care which one you use. You can consider MathCAD, Matlab, Mathematica or Excel among the commercial programs, or the freeware programs Euler and Scilab (see below). Remember, however, that I am not an expert in all such programs (I have used MathCAD the most for my own work), so the help I can give you in making any given program work may be limited. I am always willing to give you what assistance I can within those limits.

The notes for this course are available for download here. You must use the username


and the password given out in class or otherwise communicated to you. If nothing else works, I can email the pdf file to you directly. Be aware that the file is large (about 6 MB); it can be read and printed using the free Adobe Acrobat Reader software. Only the 2016 version of the course notes should be used—significant changes from previous versions have been made. They are intended to be essentially self-contained, but other books can offer a different perspective on a topic that might be more illuminating for some people than the one given in the notes. I have therefore arranged to have the following books put on reserve in the Engineering Library for this course: Also useful are portions of the online text Electromagnetic Waves and Antennas by Sophocles J. Orfanidis at Rutgers University.

Please read the information on disabilities, religious observances, standards of behavior and academic integrity.

Links and files of possible interest:   

A Postscript file of a complete Smith chart. If you are a Postscript expert, you may be able to customize this to suit individual needs.


A Postscript file of only the impedance or admittance grids of a Smith chart (no captions or calibrations). Useful for programming directly for graphic output, if you are a Postscript expert.

Backward Wave Propagation

This is an animation I made from the equations in Pocklington's article on the propagation of a backward wave after the source has been switched on.

Agilent Interactive Model for S-Parameter Techniques 

Agilent (né Hewlett-Packard) Application Note 95-1, "S-Parameter Techniques for Faster, More Accurate Network Design", discusses S-parameter techniques for designing networks used in amplifiers and oscillators. The basic theory behind using S-parameters to characterize any two-port network is presented, and the measurements of s-parameters for a transistor are summarized. Examples of using S-parameters to optimize amplifier and oscillator performance are presented and the optimization of the power gain of a narrow-band amplifier is used to illustrate the use of S-parameters and the Smith Chart in network design. This application note is in Adobe Acrobat (PDF) format and is bundled with QuickTime animations. It is available for download for all major computing environments. There is also an interactive JavaTM model that illustrates basic techniques for using S-parameters in network design.

Engauge Digitizer

"This open source, digitizing software converts an image file showing a graph or map, into numbers. The image file can come from a scanner, digital camera or screenshot. The numbers can be read on the screen, and written or copied to a spreadsheet." Very handy for comparing your own calculations with those someone else has previously published only in the form of a graph.


Windows Freeware. From the website: "Create your graphs for scientific publication with XL-Plot. It reads ascii files and it outputs a vector drawing. XL-Plot is for Windows 2000 and later. The primary purpose of XL-Plot is to create a figure for scientific publication rapidly. It contains a few basic statistical functions, such as Students t-test and linear correlation of two sets of data (two columns in a spreadsheet). XL-Plot has a number of built-in functions that can be fitted to the data in columns on a spreadsheet or to a curve in a graph. The user can easily add fitting functions of his own design.Additional options are Fourier Transformation, (de-)convolution and Matrix inversion." It is a modest piece of software that does a surprising number of tasks well.


A portable command-line driven interactive data and function plotting utility for UNIX, IBM OS/2, MS Windows, DOS, Macintosh, VMS, Atari (!) and many other platforms. The software is copyrighted but freely distributed (i. e., you don't have to pay for it). It was originally intended as to allow scientists and students to visualize mathematical functions and data. It does this job pretty well, but has grown to support many non-interactive uses, including web scripting and integration as a plotting engine for third-party applications like Octave. Gnuplot supports many types of plots in either 2D and 3D. It can draw using lines, points, boxes, contours, vector fields, surfaces, and various associated text. It also supports various specialized plot types. Gnuplot supports many different types of output: interactive screen terminals (with mouse and hotkey functionality), direct output to pen plotters or modern printers (including postscript and many color devices), and output to many types of file (eps, fig, jpeg, LaTeX, metafont, pbm, pdf, png, postscript, svg, ...).


Another freeware plotting program for Windows, concentrating on the display of functions. This one can do 3D (surface) plots. It has some animation capabilities as well.


A freeware numerical mathematics program similar in many ways to Matlab. It is available for Windows, Linux, Unix and OS/2 (this latter is no longer maintained). May be worth a look, though I haven't really used it myself.


A free mathematical software package for various Unix flavors and for Windows, somewhat more advanced in capabilities than Euler. From its website: "Scilab is a scientific software package for numerical computations in a user-friendly environment. It features:
I have not used it myself.


Free from Hewlett-Packard. Their Website description: "AppCAD is an easy-to-use program that provides you with a unique suite of RF design tools and computerized Application Notes to make your wireless design job faster and easier. AppCAD's unique, interactive approach makes engineering calculations quick and easy for many RF, microwave, and wireless applications. AppCAD is useful for the design and analysis of many circuits, signals, and systems using products from discrete transistors and diodes to Silicon and GaAs integrated circuits. The keyword for AppCAD is easy - no circuit files, no manuals - just quick and easy."

atlc - Arbitrary Transmission Line Calculator

From their website: "Transmission lines, including directional couplers, of arbitrary cross section and an arbitrary number of dielectrics can be analysed with atlc. The impedance Zo of a two-conductor transmission line, as well as the odd-mode, even-mode, differential mode and common mode impedances of a directional coupler can all be computed with atlc. Tools to both analyse and synthesise directional couplers are available." atlc is primarily a UNIX or linux program, but ports to many other OSs have been made.

Fabian Kung's Home Page

Presents two useful Windows software programs for microwave and RF modeling. Windows FDTD 1.10 Software is Finite Difference Time Domain software by F. Kung for printed circuit board (PCB) modeling.  "This software can model propagation of electromagnetic wave in a three-dimensional PCB structure, with lump components such as resistors, capacitors, inductors, diodes, and bipolar junction transistors.  Sinusoidal and pulse voltage sources model are also included.  The software runs on Windows platform (Win95 and above), and requires minimum 64 MByte RAM.  Included with this version are utilities to view the output data and to draw the model." (FDTD) Windows Smith Chart/Impedance Matching Tool (1.15) is a simple and intuitive tool for viewing an impedance value in Smith chart.  "The latest version also allows the user to perform L, T, Pi and single stub transmission line network interactive impedance matching/transformation.  It is a versatile tool, which can be used to teach engineers and students on transmission line and impedance matching theory."

Fast Field Solvers

Freeware Windows software for the solution of Maxwell's equations and extraction of circuit parasites (inductance and capacitance), thanks to which equivalent circuits can be derived for simulation of e.m. behavior of a 3D structure with SPICE-like simulators. Common usages include the analysis of connectors, strip lines, IC pacakges, ram cells, etc.

FEMM - Finite Element Method Magnetics

Freeware. From the reference manual: "FEMM is a suite of programs for solving low frequency electromagnetic problems on two-dimensional planar and axisymmetric domains. The program currently addresses linear/nonlinear magnetostatic problems, linear/nonlinear time harmonic magnetic problems, and linear electrostatic problems." FEMM is a Windows program, useful for getting numerical solutions of fields and line parameters for TEM and quasi-TEM modes on transmission lines, among many possible applications.

LTSpice IV

Free Windows high performance Spice III simulator, schematic capture and waveform viewer. Primarily intended for applications using the company's switching regulators, it is a very good general-purpose SPICE program, including transmission-line circuit elements.

MMTL - Multilayer Multiconductor Transmission Line Electromagnetic Modeling Tools

Freeware tool for generating transmission parameters and SPICE models from descriptions of electronics interconnect (transmission line) dimensions and materials properties.


Puff is an MS-DOS program for computer aided design and analysis of RF circuits. It was originally developed at California Institute of Technology (Caltech) by the research group of Prof. David Rutledge. You can freely download a copy of this program without a manual. More information is available at the Caltech website.


Quite Universal Circuit Simulator; an open source circuit simulator with graphical user interface (GUI). The GUI is based on Qt® by Trolltech®. The software aims to support all kinds of circuit simulation types, e.g. DC, AC, S-parameter, Harmonic Balance analysis, noise analysis, etc. It is available natively for GNU/Linux, but is also ported to many other platforms: MacOS, Windows, Solaris, NetBSD, FreeBSD, etc. Long-term ambitions are grand, but even now it has quite respectable capabilities. Documentation is not quite as complete as could be desired at this stage, however.

Sonnet Lite

Free, feature-limited version of 3D Planar High-Frequency Electromagnetic Software. From the web site: "Sonnet's suites of high-frequency electromagnetic (EM) Software are aimed at today's demanding design challenges involving predominantly planar (3D planar) circuits and antennas. Predominantly planar circuits include microstrip, stripline, coplanar waveguide, PCB (single and multiple layers) and combinations with vias, vertical metal sheets (z-directed strips), and any number of layers of metal traces embedded in stratified dielectric material. The Sonnet Suites develop precise RF models (S-, Y-, Z-parameters or extracted SPICE model) for planar circuits and antennas.  The software requires a physical description of your circuit (arbitrary layout and material properties for metal and dielectrics), and employs a rigorous Method-of-Moments EM analysis based on Maxwell's equations that includes all parasitic, cross-coupling, enclosure and package resonance effects. Sonnet maintains a single, dedicated focus on providing the industry's most accurate and reliable high frequency planar EM software.  Our aim to is make it easy for our customers to either develop and analyze designs within our software, or to incorporate our tools into their existing design processes and frameworks.  Customers need never commit to a proprietary framework in order to get the best in planar EM analysis."

TX-Line Transmission Line Calculator

TX-Line is a free, easy-to-use, Windows-based interactive transmission line calculator from AWR. It can be used for the analysis and synthesis of transmission line structures. TX-Line enables users to enter either physical characteristics or electrical characteristics for common transmission media such as:

Coplanar waveguide
Grounded coplanar WG

TX-Line has an easy-to-use interactive graphical user interface and runs on Microsoft Windows 2000/XP and later.