ECEN
5114
Waveguides
and Transmission Lines
Spring,
2015 2:003:15
T Th ECEE 1B32
Prof. E.
F. Kuester
kuester@schof.colorado.edu
ECOT
248
(303)
4925173
Office Hours: M 3:305:00, Tu 12:001:00, W 4:005:00, Th
10:0011:00 and 4:005:00, or by
appointment
Page last updated 26 February 2015
Announcements
It
has been pointed out to me that part (a) of problem p18 refers to a
result of the previous problem, but that previous problem is not
relevant to the solution of p18. In fact this is an error that arose
in my most recent editing of this chapter, and in fact you should be
using the result of problem p123 to solve part (a) of p18. I have
corrected this page (37) of the course notes here,
and you should substitute this for the old page 37.
Pocklington's article on propagation of a backward wave after the
source has been switched on can be found here.
And here is the movie I made from
Pocklington's equations.
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

p16, p18

20 January 2015

p16
p18

p114, p118

27 January 2015

p114
p118

p27

3 February 2015

p27

p217

5 February 2015

p217

p33

10 February 2015

p33

p313

12 February 2015

p313

p413

24 February 2015

p413

p59, p525

3 March 2015


p512

5 March
2015




















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
(distributednetwork) transmission line with lumped elements connected
to it. In the next part (chapters 58 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.
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 midterm exam, which is a takehome exam due
in class on Thursday March 19, 2015. The third part of your course
grade is the final exam, which is a takehome exam due at 4:00 PM on
Wednesday May 6, 2015: the nominal time and date of the inclass 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 writeup and understanding of
the solution to a problem, rather than a copy of some collective or
collaborative effort. For the midterm exam and the takehome 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
ecen_5114
and the password given out in class
or obtained from me during office hours. 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 2015 version of the course notes should be
used—significant changes from previous versions have been made. They
are intended to be essentially selfcontained, 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:
 P. A. Rizzi, Microwave Engineering: Passive Circuits. Englewood
Cliffs, NJ: PrenticeHall, 1988.
 S. Ramo, J. R. Whinnery and T. Van Duzer, Fields and Waves in
Communication Electronics. New York: Wiley, 1994.
 R. E. Collin, Foundations for Microwave Engineering. New York:
IEEE Press, 2001.
 D. M. Pozar, Microwave Engineering. Hoboken, NJ: Wiley, 2005.
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.
Agilent
(né HewlettPackard) Application Note 951, "SParameter Techniques
for Faster, More Accurate Network Design", discusses Sparameter
techniques for designing networks used in amplifiers and
oscillators. The basic theory behind using Sparameters to
characterize any twoport network is presented, and the measurements
of sparameters for a transistor are summarized. Examples of using
Sparameters to optimize amplifier and oscillator performance are
presented and the optimization of the power gain of a narrowband
amplifier is used to illustrate the use of Sparameters 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 Java^{TM} model that illustrates
basic techniques for using Sparameters in network design.
"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 XLPlot. It reads ascii files and it outputs a vector
drawing. XLPlot is for Windows 2000 and later. The primary
purpose of XLPlot is to create a figure for scientific publication
rapidly. It contains a few basic statistical functions, such as
Students ttest and linear correlation of two sets of data (two
columns in a spreadsheet). XLPlot has a number of builtin 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
commandline 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
noninteractive uses, including web scripting and integration as a
plotting engine for thirdparty 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, ...).
Winplot
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
userfriendly environment. It features:

Elaborate
data structures (polynomial, rational and string matrices, lists,
multivariable linear systems,...).

Sophisticated
interpreter and programming language with Matlablike syntax.

Hundreds
of builtin math functions (new primitives can easily be added).

Stunning
graphics (2d, 3d, animation).

Open
structure (easy interfacing with Fortran and C via online dynamic
link).

Many builtin
libraries:

Linear
Algebra
(including sparse matrices, Kronecker form, ordered Schur,...).

Control
(Classical,
LQG, Hinfinity,...).

Package
for
LMI (Linear Matrix Inequalities) optimization.

Signal
processing.

Simulation
(various
ode's, dassl,...).

Optimization
(differentiable
and nondifferentiable, LQ solver).

Scicos,
an
interactive environment for modeling and simulation of dynamical
systems.

Metanet
(network analysis and optimization).

Symbolic
capabilities through Maple interface.

Parallel
Scilab."
I
have not used it myself.
Free
from HewlettPackard. Their Website description: "AppCAD
is an easytouse 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
twoconductor transmission line, as well as the
oddmode, evenmode, 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.
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 threedimensional 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. behaviour of a
3D structure with SPICElike 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 twodimensional 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
quasiTEM 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
generalpurpose SPICE program, including
transmissionline 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
Puff is an MSDOS
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.
Qucs
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, Sparameter,
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. Longterm
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, featurelimited
version of 3D Planar HighFrequency Electromagnetic Software. From the
web site: "Sonnet's suites of
highfrequency 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
(zdirected strips), and any number of layers of metal traces
embedded in stratified dielectric material. The
Sonnet Suites develop precise RF models (S, Y, Zparameters 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 MethodofMoments EM analysis based on Maxwell's
equations that includes all parasitic, crosscoupling, 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."
TXLine is a free, easytouse,
Windowsbased interactive transmission line calculator from AWR. It can be used for the analysis and synthesis of transmission line structures.
TXLine enables users to enter either physical characteristics or
electrical characteristics for common transmission media such as:
Microstrip
Stripline
Coplanar waveguide
Grounded coplanar WG
Slotline
TXLine has an easytouse interactive graphical user interface and
runs on Microsoft Windows 2000/XP and later.