and Transmission Lines
T Th ECEE 1B32
E. F. Kuester
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
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
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
Problems not found in the notes, and all of the
solutions, are in PDF format; download the
Acrobat Reader to read them.
|28 January 2016
|9 February 2016
|16 February 2016
|18 February 2016
p4-3(a,c only), p4-14
|25 February 2016
|3 March 2016
|10 March 2016
|Midterm Exam Solutions
|31 March 2016
|p8-2, p8-6 (see
section C.3 of Appendix C for elliptic integrals)
|7 April 2016
|14 April 2016
|21 April 2016
AM MST, 4 May 2016
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.
General Course Information:
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.
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
(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
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
and Antennas by Sophocles J. Orfanidis at Rutgers University.
- P. A. Rizzi, Microwave Engineering: Passive Circuits. Englewood
Cliffs, NJ: Prentice-Hall, 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.
Please read the information on
disabilities, religious observances, standards of behavior and
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
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.
is an animation I made from the equations in Pocklington's
article on the
propagation of a backward wave after the source has been
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.
"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.
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, ...).
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.
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:
data structures (polynomial, rational and string matrices, lists,
multivariable linear systems,...).
interpreter and programming language with Matlab-like syntax.
of built-in math functions (new primitives can easily be added).
graphics (2d, 3d, animation).
structure (easy interfacing with Fortran and C via online dynamic
Algebra (including sparse matrices, Kronecker form, ordered
(Classical, LQG, H-infinity,...).
for LMI (Linear Matrix Inequalities) optimization.
(various ode's, dassl,...).
(differentiable and non-differentiable, LQ solver).
an interactive environment for modeling and simulation of
(network analysis and optimization).
capabilities through Maple interface.
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
atlc - Arbitrary Transmission Line
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
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
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
- Finite Element Method Magnetics
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
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.
- Multilayer Multiconductor Transmission Line Electromagnetic
Freeware tool for
generating transmission parameters and SPICE models
from descriptions of electronics interconnect
(transmission line) dimensions and materials
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
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
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,
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 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:
Grounded coplanar WG
TX-Line has an easy-to-use interactive graphical user interface and
runs on Microsoft Windows 2000/XP and later.