ECEN 5114
Waveguides and Transmission Lines
Spring, 2008
M W F 3:00-3:50 PM: ECCR 133
Prof. E. F. Kuester
kuester@schof.colorado.edu
ECOT 248
(303) 492-5173
Office Hours:
M 10-11 AM, W F 10-11:30 AM
or by appointment
Page last updated 9 May 2008
Links
and Downloadable
Files
Download Course Notes
Homework Assignments
General Course Information
Announcements
- The take-home final exam is due on Wednesday May 7 at 4:00 PM.
- Office hour changes for the coming weeks:
- Monday, April 21: Due to a comprehensive exam, my office hour may start as late as 10:30 AM.
- Wednesday, April 23: Due to a comprehensive exam, my office hour will last from 10:00 - 10:50 AM only.
- Monday, April 28: No office hour at all.
- The solutions to the midterm exam are here.
- Some typographical errors in the solution of problem p5-18 have been corrected. You should download it again.
- A significant error in the notes has been called to my attention. In eqns. (6.13) and (6.14), everywhere E1 appears, it should be replaced by E2, and everywhere E2 appears, it should be replaced by E1.
If this is done, the plane waves in eqn. (6.13) are described correctly
by the picture of Fig. 5.3. All subsequent equations in this section
are unchanged.
- A correction to the first step in
the solution to problem p2-13 has been made. The final answers are all
correct, and the corrected version is now posted.
- The due date for problem p4-9 has been moved to Monday February 25.
- I had a few sign errors in my solution to problem p1-11. The corrected version is now posted.
- Remember,
if my office hours are not convenient for you, and
you'd like to see me, please feel free to ask for an appointment, and
I'll do
my best to accommodate you as soon as I can.
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 |
| p1-5, p1-11 |
25 January 2008 |
p1-5 p1-11 |
| p1-18 from
Supplementary Problems, p1-14 |
1 February 2008 |
p1-14 p1-18 |
| p2-13 from
Supplementary Problems, p2-10 (you can use the result of problem p2-11 to obtain an equivalent circuit) |
8 February 2008 |
p2-10 p2-13 |
| p3-3, p3-6 |
15 February 2008 |
p3-3 p3-6 |
| p4-3 |
22 February 2008 |
p4-3 |
| p4-9 from
Supplementary Problems |
25 February 2008 |
p4-9 |
| p5-17, p5-21 |
29 February 2008 |
p5-17 p5-21 |
| p5-14, p5-18 |
7 March 2008 |
p5-14 p5-18 |
| p6-17, p6-19 from
Supplementary Problems |
14 March 2008 |
p6-17 p6-19 |
| p7-4, p7-10, p8-19 |
4 April 2008 |
p7-4 p7-10 p8-19 |
| p8-5, p8-11 |
11 April 2008 |
p8-5 p8-11 |
| p9-18, p9-23 |
18 April 2008 |
p9-18 p9-23 |
| p9-24 from
Supplementary Problems, p10-2 |
25 April 2008 |
p9-24 p10-2 |
| Final Exam |
7 May 2008 |
Final Exam Solutions |
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.
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 an in-class exam scheduled for Friday March 21,
2008.
The third part of your course
grade is the final exam, which is a take-home exam which is due
at 4:00 PM on Wednesday, May 7, 2008: 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. I will be available to answer any questions on
interpretation of the problems on this exam.
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 the 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: the file is large (about 3 MB), and a fast
internet connection is recommended. The file can be read and printed
using the free
Adobe
Acrobat Reader software.
Please be mindful of conserving
paper
and other resources when using these notes: print only one copy
for yourself, and if at all possible, use a photocopier to make
multiple copies and share the cost with other members of the class to
keep costs down. Only the 2008 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 is 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: 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.
- C. C. Johnson, Field and Wave Electrodynamics . New
York:
McGraw-Hill, 1965.
- 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 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 95,98, 2000 and XP. 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, ...).
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
user-friendly environment. It features:
-
Elaborate data structures
(polynomial,
rational and string matrices, lists, multivariable linear systems,...).
-
Sophisticated interpreter
and
programming language with Matlab-like syntax.
-
Hundreds of built-in 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 built-in
libraries:
-
Linear
Algebra (including sparse
matrices, Kronecker form, ordered Schur,...).
-
Control
(Classical, LQG,
H-infinity,...).
-
Package
for LMI (Linear Matrix
Inequalities) optimization.
-
Signal
processing.
-
Simulation
(various ode's, dassl,...).
-
Optimization
(differentiable and
non-differentiable, 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.
Ansoft Student Software
Ansoft offers feature-limited
student versions of Ansoft Designer SV (high-frequency linear
circuit simulator) and Maxwell SV (AC/DC electromagnetic and
electrostatic-field simulator). From their web site: "Our free
downloads are feature-limited, student versions of some of our
commercially distributed software. Intended for electrical engineering
students studying topics in electronic design, our free software
fosters the development of engineering skills throughout the
electronic-design community. Each download comes with a set of examples
specially
designed for topics commonly studied at the junior, senior, and
graduate levels of study."
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.
Presents two useful Windows software
programs for microwave and RF modeling. Windows
FDTD 1.10 Software is Finite
Difference Time Domain
(FDTD) 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." 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 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 / SwitcherCAD III
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
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.
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 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:
Microstrip
Stripline
Coplanar waveguide
Grounded coplanar WG
Slotline
TX-Line has an easy-to-use interactive graphical user interface and runs on Microsoft Windows 2000/XP.
A
free (for noncommercial use) circuit
analysis program for UNIX
or Windows, slanted towards RF and microwave work. Its primary
advantage
(at least in its present state of development) over SPICE is that it
handles coupled transmission lines, and easily computes S-parameters
and plots on Smith charts. On the other hand, it does not presently
support nonlinear elements or other exotic things. From their web page:
"ViPEC is a powerful tool for the analysis of high frequency, linear
electrical networks. It takes a text based description of the
electrical
network and an analysis is performed in the frequency domain. The
output
is in the form of 2-port parameters (S,
Y or Z)
with results presented on a user
defined grid and Smith chart. It can
also be used to compute the input and output impedance/admittance as
well as amplifier stability factors (Linvill & Stern). ViPEC
supports various lumped elements (capacitors, resistors etc.) as well
as
distributed networks like transmission lines, microstrip and stripline
structures. Two port data files are also supported e.g. the 2-port
frequency parameters of various RF transistors as supplied by the
manufacturer. The component library is under constant development with
new elements added at regular intervals." Development seems to have come to a standstill in the last few years.