# Electromagnetics Course Catalogue

Note: The course catalogues, the SGS Calendar, and ACORN list all graduate courses associated with ECE – please note that not all courses will be offered every year.

### ECE1228H Electromagnetic Theory

##### Prerequisites: ECE320 or ECE357.

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.

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### ECE1229H Advanced Antenna Theory

##### Prerequisite: ECE320 or ECE357.

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.

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### ECE1252H Introduction to Computational Electrodynamics

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.

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### ECE1254H Modeling of Multiphysics Systems

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.

Topics:
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).

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### ECE1256H Microwave Circuits

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.

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