Please note that not all courses listed in this catalogue and/or on ACORN/ROSI will be offered each year.
This course is intended to benefit graduate students with interest in Electromagnetics and Photonics. It revisits and expands some of the more fundamental electromagnetic laws and theories. The course provides the students with the necessary foundation and specific knowledge of electromagnetic theory and the dynamics of wave propagation and interaction with materials and structures.
Topics covered in the course:
Maxwell equations in differential and integral forms; constitutive relations; electric field and electrostatic potential, electric and magnetic polarization; boundary conditions, energy and power, material dispersion (electric response), material dispersion (magnetic response), conductors and conductivity, Multipole expansion, Maxwell-Helmholtz wave equations, solutions to Maxwell-Helmholtz wave equations, plane waves, polarization, reflection and transmission at interfaces, beam optics (time permitting), the other wave equation (Schrödinger wave equation), electron-photon analogies, waveguides, optical multilayers and transfer matrix method, dynamics of wave propagation (phase velocity, group velocity, energy velocity, forerunners), dispersive effects, introduction to waves in periodic structures, wave equation as operator, operator calculus and bases, anisotropic and bi-anisotropic medium, electromagnetic principles and theorems (duality, uniqueness, reciprocity theorem), and if time permits Green functions and Hamilton-Jacobi canonical equations.
Prerequisites: ECE 320 or ECE 357.
ECE1229H Advanced Antenna Theory
Professor G. Eleftheriades
This course deals with the analysis and design of a range of antennas. Topics addressed include: definitions of antenna parameters; vector potentials; solutions to the inhomogeneous wave equation; principles of duality and reciprocity; wire antennas; antenna arrays; phased arrays; synthesis techniques for discrete and continuous line sources; integral equations and solutions using the method of moments; field equivalence principle; aperture antennas; antenna measurement techniques; diffraction; horn antennas; reflector antennas; microstrip antennas; reflectarrays; electrically small antennas; and broadband antennas. Prerequisite: ECE320 or ECE357.
ECE1236H Microwave and Millimetre-Wave Techniques
Professor S. Hum
This course intends to provide a broad but firm exposure to the fundamental and practical aspects of modern microwave/mm-wave design of circuits, guiding structures and antennas. The emphasis will be placed on planar structures in the context of current wireless commercial, space and scientific applications. Planar antennas will also be treated since they have become increasingly important in many emerging wireless applications. Projects will be assigned tailored to the interests of each participant with emphasis placed on using modern CAD tools. Course Outline: Waveguide Concepts (potential theory, modal expansions, losses, slab waveguide and surface-wave modes), Transverse Resonance Technique, Transmission Line and Resonator Concepts, Planar Lines (stripline, microstrip, coplanar waveguide, asymmetric coupled lines, high-frequency limitations), Antennas and Antenna Array Concepts (radiation from dipoles and slots, directivity and gain, reciprocity and receiving antennas, Friis transmission equation, antenna arrays, Schelkunoff polynomial method, microstrip antennas), Active Circuits and Antennas (mixers, oscillators, active planar antennas and quasi-optical power combining). Prerequisites: ECE 320 or ECE 357 and permission of the instructor.
ECE1243H Topics in EM Waves: Advanced Engineering Electromagnetics
Professor G. Eleftheriades
The course builds on undergraduate electromagnetics to systematically develop advanced concepts in electromagnetic theory for engineering applications from dc to light. The following topics are covered. Maxwell’s equations, constitutive relations, wave equation; power flow, Poynting vector; field sources and representations, potentials; Green’s functions; plane waves: homogeneous and inhomogeneous waves, radiation from sources on a plane, plane wave transmission and reflection at boundaries, guided waves; rectangular waveguides and cavities: parallel-plate, rectangular and slab waveguides; wave equation in cylindrical coordinates; cylindrical waveguides (circular, coaxial waveguides and optical fibers); scattering from cylindrical objects and cylindrical waves; wave equation in spherical coordinates, spherical waves; electromagnetic theorems and concepts: duality, uniqueness, image theory, equivalence, reciprocity, induction.
ECE 1252H Introduction to Computational Electrodynamics
Professor C.D. Sarris
This course is an introduction to computational methods for the solution of operator problems in microwave, millimeter-wave and optical engineering. It presents a unified, field-theoretical approach to the derivation of numerical techniques, based on the application of the Method of Moments for the discretization of Maxwell’s equations. Emphasis is given in the Finite Difference Time Domain method, by providing a thorough study of such concepts as order of accuracy, stability, dispersion, convergence and error propagation. Theoretical derivation and practical implementation of source, material and absorbing boundary conditions is pursued. Higher order, multi-step, ADI and operator splitting methods are explained. Applications to wave propagation (including propagation in complex media and shock waves), antenna and circuit modeling are presented.
ECE1253H Active Microwave Circuits
Professor S.V. Hum
This course deals with the design of microwave circuit employing active devices. Topics addressed include a brief review of representation of two-port networks, scattering parameters, signal flow graphs, Smith charts, and matching networks; characteristics of microwave transistors (bipolar transistors, MOSFETS, MESFETS); microwave transistor linear amplifier design (gain equations, stability considerations, gain circles, unilateral and bilateral design cases, conjugate matching, bias considerations); low noise amplifiers (noise figure, noise circles), power amplifiers (amplifier classes, intermodulation and harmonic distortion, high efficiency topologies), broadband amplifiers; microwave mixers (mixer design and configurations: single-ended, balanced, double-balanced); and oscillators (feedback oscillators, reflection / negative resistance oscillators, dielectric resonator oscillators, tuning techniques). Lecture material will be strongly enforced using a laboratory which will teach students the use of industry standard RF/microwave CAD and simulation tools.
ECE1254H Modeling of Multiphysics Systems
Professor P. Triverio
The course deals with the modeling and simulation of physical systems. It introduces the fundamental techniques to generate and solve the equations of a static or dynamic system. Special attention is devoted to complexity issues and to model order reduction methods, presented as a systematic way to simulate highly-complex systems with acceptable computational cost. Examples from multiple disciplines are considered, including electrical/electromagnetic engineering, structural mechanics, fluid-dynamics. Students are encouraged to work on a project related to their own research interests.
Automatic generation of system equations (Tableau method, modified nodal analysis).
Solution of linear and nonlinear systems (LU decomposition, conjugate gradient method, sparse systems, Newton-Raphson method).
Solution of dynamical systems (Euler and trapezoidal rule, accuracy, stability).
Model order reduction of linear systems (proper orthogonal decomposition, Krylov methods, truncated balanced realization, stability/dissipativity enforcement).
Modeling from experimental data (system identification, the Vector Fitting algorithm, enforcement of stability and dissipativity).
If time permits, an overview of numerical methods to solve partial differential equations (Boundary element method, finite elements, FDTD).
ECE1256H Microwave Circuits
Professor G.V. Eleftheriades
This course outlines the principles of designing modern microwave and RF circuits. Signal-integrity issues in high-speed digital circuits are also examined. The wave equation, ideal transmission lines. Transients on transmission-lines. Planar transmission lines and introduction to MMIC’s. Designing with scattering parameters. Planar power dividers, directional couplers. Microwave filters. Solid-state microwave amplifiers, noise, diode-mixers, RF receiver chains, oscillators.
Electromagnetics-Related Courses Available from Other Groups and Departments
Course No. – Title
AER 1717H – Applied Plasma Physics I
AER 1720H – Applied Plasma Physics II
ECE 527H – Photonics I
ECE 530H – Analog Circuits
ECE 1336H – Semiconductor Physics
ECE 1364H – Selected Topics in Solid State Circuit Design: RF and MMIC Design
ECE 1435H – Applied Optics I
ECE 1448H – Quantum Mechanics for Engineers
ECE 1450H – Photonics II
ECE 1460H – Special Topics in Photonics
JEL 1704H – Introduction to Lasers
ECE 1041H – Numerical Solution of Field Problems
ECE 1080H – Application of Approximate Methods to Field Problems
ECE 1081H – Application of the Finite Element Method to Field Problems
ECE 1082H – Mathematics for Advanced Electromagnetics
ECE 1083H – Harmonic Balance and the Finite Element Method
ECE 1089H – Special Topics in Electromagnetics
ECE 1515H – Smart Antennas
ECE 1543H – Mobile Communications Systems
PHY 2102H – Theory of Nonlinear Waves
MAT 1001H – Complex Analysis
MAT 1005H – Fourier Analysis
MAT 1507H – Asymptotic and Perturbation Methods (also designated as APM 441F)
MAT 1508H – Applied Nonlinear Equations
MEC 1401H – Engineering Analysis III (variational calculus; integral equations)
MEC 1402H – Engineering Analysis IV (solution of nonlinear differential equations)