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ECE303 Electromagnetic Fields and Waves

### Part I: Electroquasistatics

Applications of electromagnetic fields and waves in industry and research.

Maxwell’s equations in integral and differential forms, electrostatics and magnetostatics, electroquasistatics and magnetoquasistatics.

Electrostatics, applications of Gauss’ Law in problem solving, applications of the superposition principle in problem solving, some simple charge distributions.

Electric scalar potential, Poisson equation, Laplace equation, superposition principle, problem solving.

### Part II: Conductors and Dielectrics

Electrical conduction and perfect metals in electroquasistatics, solution of Laplace and Poisson equations with metal electrodes, boundary conditions, dielectric relaxation, image charges and method of images.

Capacitance, problems in Cartesian, Cylindrical and Spherical coordinates.

Material polarization, polarization charge and current densities, mathematics of polarization in electromagnetism, dielectrics vs conductors, boundary conditions.

Problems and examples involving material polarization, dielectrics, and boundary conditions.

### Part III: Magnetoquasistatics

Magnetoquasistatics, Ampere’s law, the vector potential, the vector Poisson equation, Biot-Savart law, magnetic fields of some simple current distributions, magnetic flux and the vector potential.

Magnetoquasistatics in the presence of perfect metals, boundary conditions, method of images, inductance, inductances of some simple structures.

### Part IV: Fields, Forces, and Energy

Faraday’s Law and electromagnetic Induction, non-uniqueness of voltages in magnetoquasistatics, current-charge continuity equation in electromagnetism, power-energy continuity equation in electromagnetism, Poynting’s vector, electromagnetic energy and power flow and connection with electrical circuit theory

Energy, forces, and work in electromagnetics, forces between charged dielectrics and conductors, electromagnetic energy, forces, and work in closed systems and systems connected to voltage sources.

### Part V: Electromagnetic Waves in Free-Space and in Media

Electromagnetic wave equation, uniform plane wave solutions, Poynting vector.

Time-harmonic electromagnetic fields, phasors, complex version of Maxwell’s equations, complex Poynting vector.

Polarization states of plane waves, linearly polarized waves, circularly polarized waves, elliptically polarized waves, left-hand and right-hand circularly (or elliptically) polarized waves.

Wave propagation in isotropic media – dielectrics and conductors.

Wave propagation in isotropic media – plasmas, dispersive media, wave packets, phase and group velocities.

Wave propagation in anisotropic media, biaxial media, uniaxial media, half-wave plates, quarter-wave plates, birefringence.

Wave reflection and transmission at media interfaces, reflection and transmission coefficients, standing waves and standing wave ratio.

Non-normal incidence of waves at media interfaces, phase matching condition, reflection, refraction, Snell’s law, critical angle and evanescent waves, Brewster’s angle.

### Part VI: Guided Electromagnetic Waves

Transmission lines, types of transmission lines, fields, voltages and currents on transmission lines, transmission line equations, transmission line dispersion relations, transmission line impedances

Impedance transformations in transmission line RF and microwave circuits, equivalent circuit models, short load, open load, matched load, Thevenin equivalent circuit models, power dissipation.

G-Plane and Smith Charts, load matching and stub tuning, quarter wave transformers.

Reflection and transmission for multilayer structures, AR and HR coatings, 1-dimensional photonic bandgap structures, multilayer structures for non-normal incidence (TE and TM waves).

Time domain analysis of transmission lines, transients.

Guided waves in parallel plate metal waveguides, TE and TM modes, dispersion characteristics and cut-off frequencies.

Guided waves in dielectric slab waveguides, TE and TM modes, dispersion characteristics and cut-off frequencies.

Guided waves in rectangular metal waveguides, TE and TM modes, dispersion characteristics and cut-off frequencies.

### Part VII: Radiation Emission and Antennas

Radiation by time-varying currents and charges, retarded potentials in time-domain and for time-harmonic fields, wave equations for vector and scalar potentials, Hertzian dipoles, near- and far-fields, Poynting vector.

Hertzian dipoles, near- and far-fields, Poynting vector, antenna gain, radiation pattern, radiation resistance.

Hertzian dipoles, superposition principle for more than one Hertzian dipoles, gain and radiation pattern for two-element array of Hertzian dipoles.

Radiation from linear wire antennas, short-dipole, half-wave dipole, three-half-wave dipole, radiation from wire loop antennas, electric vs magnetic dipole antennas.

Circuit properties of transmitting antennas, antenna self-impedance and trans-impedance, receiving and transmitting antennas, antenna effective area, reciprocity and antenna theorem.

Antenna arrays, element factor and array factor, linear antenna arrays, phase arrays, binomial arrays, radiation patterns.

Electromagnetic scattering, Rayleigh scattering, scattering from a dielectric sphere, scattering-cross section and scattered radiation, scattering of sunlight in the atmosphere (why the sky is blue), radars, radar range equation.

Aperture antennas and electromagnetic diffraction, Fraunhoffer diffraction, rectangular apertures - radiation pattern and gain.

Reflector antennas, dish antennas, parabolic dish antennas