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 years ago – textbooks by Plonsey and Collin and Collin Emphasized: 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 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 years ago. Textbooks by Pozar, Balanis, Ishimaru Advanced electromagnetics Boundary value problems Reflection and transmission Microwave device design and analysis Microstrip design techniques Microwave filters Microwave networks

20-30 years ago (continued) 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) 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 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? 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. ( ) 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: 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: 90 o 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 90 o Hybrid Coupler

ProtoMat S62 PCB milling machine

Waiting for the Grad Assistant

90 o Hybrid Coupler

Network Analyzer

Network Analyzer close-up

Test Results: 90 o Hybrid Coupler Design f o = 3Ghz

More Student Project Results Power dividers “Rat race” coupler Quasi-Yagi antenna Quasi-Landstorfer antenna Bow-tie slot antenna

Student Projects: Power Dividers

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 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. M. A. Aziz, S. Roy and B. D. Braaten, "A New Printed Quasi- Lanstorfer Antenna," Accepted for publication in the IEEE Transactions on Antennas and Propagation.

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, He continues to be an inspiration for our work.

Questions? Thank you for listening!