THE GRADUATE COURSE IN
ELECTROMAGNETICS: INTEGRATING
THE PAST, PRESENT, AND FUTURE
David A. Rogers & Benjamin D. Braaten
Electrical and Computer Engineering
North Dakota State University
Fargo, ND
First Graduate Course in
Electromagnetics
• 30-50 years ago – textbooks by Plonsey and
Collin and Collin
• Emphasized:
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Maxwell’s Equations
Analytical Solutions: open- and closed structures
Followed undergrad cousin with increased rigor
Theoretical emphasis increased following
Sputnik
• Thorough vector calculus descriptions
Typical outline 50 years ago
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Gauss’s flux and divergence theorems
Poisson’s equation
Three common coordinate systems
Curvilinear coordinates
Green’s identities
Dirichlet and Neumann conditions
Uniqueness Theorem
In essence, quite theoretical/mathematical
Early Textbook Details
• Plonsey, R. and Collin, R. E. (1961). Principles
and Applications of Electromagnetic Fields.
New York, NY: McGraw-Hill.
• Collin, R. E. (2001). Foundations for
Microwave Engineering. New York, NY: IEEE
Press.
Grad Course in Electromagnetics
20-30 years ago.
• Textbooks by Pozar, Balanis, Ishimaru
• Advanced electromagnetics
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Boundary value problems
Reflection and transmission
Microwave device design and analysis
Microstrip design techniques
Microwave filters
Microwave networks
20-30 years ago (continued)
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Waveguides using vector potential methods
Magneto-ionic media
Propagation in the neutral atmosphere
Cavities
Intermediate mathematics of electromagnetics
Classical Textbook Details
• Balanis, C. A. (2012). Advanced Engineering
Electromagnetics. Hoboken, NJ: Wiley.
• Ishimaru, A. (1991). Electromagnetic Wave
Propagation, Radiation, and Scattering.
Englewood Cliffs, NJ: Prentice Hall.
• Pozar, D. M. (2005). Microwave Engineering.
Hoboken, NJ: Wiley.
A Contemporary Course
• Maxwell’s equations review
• Plane waves, lossy media, reflection and
transmission
• Transmission-line theory, losses, matching stubs
• Microstrip design
• Microstrip devices: couplers, splitters, matching
devices
• Metallic waveguides
• General solutions for guided-wave structures
• Human effects of electromagnetic waves/ethics
A Contemporary Course (Continued)
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Microwave network theory
Antennas, gain, noise, and systems studies
Radio propagation and scattering
Magneto-ionic theory
Fiber optics
Matrix method in networks
Project presentations
Contemporary Textbook Details
• Pozar, D. M. (2012). Microwave Engineering.
Hoboken, NJ: Wiley.
• 2012 edition is scheduled for release in
November 2011.
What will our students need?
• Course should serve grad students specializing in
electromagnetics.
• Should attract non-specialists.
• Serve those working with high-speed or very
small devices—material science, nanoscale
science/engineering, certain areas of applied
physics, and specialists in optics.
What do the students
bring to the course?
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An undergraduate electromagnetics course.
Phasor analysis of AC circuits.
Transmission line theory.
Plane wave background.
The usual physics and math common to
undergrad engineering and physics students.
Computer and laboratory work
• Early in the semester students begin a project,
groups of two or three students.
• Design a microwave device.
• Layout and simulate on the computer.
• Forward to ProtoMat S62 milling machine.
(www.lpkf.com )
• Measure using Agilent E5071C (4.5 GHz) network
analyzer.
• Compare to Advanced Design System (ADS) and
Matlab simulations.
• Present oral and written reports.
Have we had an impact on the
students?
• Gets students involved in:
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Literature searches
Reproducing published results
New designs, new frequencies
ADS layouts and simulations
Testing
• In the course:
• Reduce routine homework in favor of the above.
• Require student bi-weekly written progress reports and
oral presentations.
• Final report to be ready for submission to a conference.
Student Project Procedure:
Example: 90o Hybrid Coupler
• Design device based on Pozar or other
literature/research.
• Lay out and simulate device using ADS.
• Send gerber file to ProtoMat S62 PCB milling
machine.
• Add connectors and loads to the device.
• Determine the performance (scattering
parameters) using an Agilent E5071C spectrum
analyzer.
ADS Layout for 90o Hybrid Coupler
ProtoMat S62 PCB milling machine
http://sites.google.com/site/ndsuece/Home
Waiting for the Grad Assistant
90o Hybrid Coupler
Network Analyzer
Network Analyzer close-up
dB
1.50
1.58
1.65
1.73
1.80
1.88
1.95
2.03
2.10
2.18
2.25
2.33
2.40
2.48
2.55
2.63
2.70
2.78
2.85
2.93
3.00
3.08
3.15
3.23
3.30
3.38
3.45
3.53
3.60
3.68
3.75
3.83
3.90
3.98
4.05
4.12
4.20
4.28
4.35
4.42
4.50
Test Results: 90o Hybrid Coupler
S Parameters
0.00
-30.00
-35.00
-40.00
GHz
-3.97
-5.00
-5.33
-10.00
-15.00
S11
S12
-20.00
-21.43
S13
S14
-25.00
-28.92
Design fo = 3Ghz
More Student Project Results
• Power dividers
• “Rat race” coupler
• Quasi-Yagi antenna
• Quasi-Landstorfer antenna
• Bow-tie slot antenna
Student Projects: Power Dividers
Power divider without resistor
-15
Power divider with resistor
-3.0
-12
-3.5
-3.5
-4.0
-18
-4.0
-20
-30
(1.53, -29.33)
-35
S11-simulation
S11-measured
1.0
(1.486,-36.986)
1.2
1.4
1.6
Frequency (GHz)
1.8
-6.0
IS11I (dB)
IS11I (dB)
-5.5
-24
-5.0
-30
(1.549,-28.62)
-5.5
-6.0
-36
S11-Measured
S11-Simulated
-6.5
-42
(1.597,-44.206)
-7.0
2.0
-6.5
-7.0
1.0
1.2
1.4
1.6
Frequency (GHz)
1.8
2.0
IS12I, IS21I) (dB)
-5.0
-25
-4.5
IS21I, IS12I (dB)
-4.5
Student Project: “Rat Race” Coupler
Student Project: Metamaterial-based
Quasi-Yagi Antenna
Student Project: A Quasi-Landstorfer
Antenna
Student Project: Bow-tie Slot Antenna
Published/Accepted Results
J. Anderson, K. Johnson, C. Satterlee, A. Lynch and B. D. Braaten,
"A Reduced Frequency Printed Quasi-Yagi Antenna Symmetrically
Loaded with Meander Open Complementary Split Ring Resonator
(MOCSRR) Elements," Proceedings of the 2011 IEEE International
Symposium on Antennas and Propagation, Spokane, WA, July 2011.
M. A. Aziz, S. Roy and B. D. Braaten, "A New Printed QuasiLanstorfer Antenna," Accepted for publication in the IEEE
Transactions on Antennas and Propagation.
L. A. Berge, M. Reich and B. D. Braaten, “A Compact Dual-Band
Pseudo-Vivaldi Bowtie Slot Antenna for 900 and 2400 MHz ISM
Bands,” Submitted for review in the IEEE Antennas and Wireless
Propagation Letters – Accepted and under revision.
What are our plans for the
department?
• Recruit talented students to participate and be
student leaders.
• Integrate active research projects into teaching
(Dr. Braaten).
• Active interests: flexible antennas, printed
antennas, microwave devices.
• Leverage course activities to increase research in
department.
Conclusions
• The course has been an excellent research
initiation experience for our students.
• It has drawn students and faculty together in
ways that a straight lecture course couldn’t.
• It has been the first step towards several M.S.
degrees and a few Ph.D. degrees.
Acknowledgement
• Dr. Robert M. Nelson
of UW-Stout made
major contributions
to the Emag program
at NDSU, 1989-2008.
He continues to be an
inspiration for our
work.
Questions?
Thank you for listening!