Lect 2.1

# Lect 2.1 - Department of Electrical and Computer...

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Department of Electrical and Computer Engineering ECSE 352 Electromagnetic Waves and Optics 2.1 EM Wave propagation in free space References: Section 12.1 2.1-1 Overview In this class we will investigate the way that electromagnetic waves arise from axwell's equations e ill llow e derivation of the source- ee wave Maxwell s equations. We will follow the derivation of the source free wave equations from Maxwell's equations. In many cases of practical interest, the frequency of a wave-source remains constant and this leads to the concept of harmonic waves that have a single well-defined frequency. This assumption greatly simplifies the mathematical treatment of EM waves and results in a time- independent formulation of the wave equations called the vector Helmholtz equation. We will investigate the concept of phasor representation of EM waves and will see that simple cosine functions are solutions of this equation. Finally we pq y will examine the relationship between the electric and the magnetic fields. ©AGK ECSE 352 2.1-2 Concept Map ©AGK ECSE 352 2.1-3 Module 2: The Uniform Plane Wave Module 1: Transmission Lines Module 2: The Uniform Plane Wave ave propagation in free space 1. Wave propagation in free space 2. Wave propagation in lossy media 3. Waves in conductors 4. Wave power and the Poynting vector 5. The skin effect ave polarization 6. Wave polarization Module 3: Waves at boundaries ©AGK ECSE 352 2.1-4 Module 4: Waveguides and antennas

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Learning outcomes After taking this class you should be able to: • Describe an electromagnetic plane wave • Explain the relationship between electric and agnetic elds for a plane wave and sketch the form magnetic fields for a plane wave and sketch the form of a typical transverse electromagnetic wave • Define the propagation constant and wavenumber , and use them to calculate the propagation of a wave through space efine the pedance of free space Define the impedance of free space ©AGK ECSE 352 2.1-5 Contents • Review of Maxwell’s equations • Origins of EM waves • Derivation of the source-free wave equation l t t i Transverse electromagnetic waves ©AGK ECSE 352 2.1-6 James Clerk Maxwell (1831 James Clerk Maxwell (1831-1879) 1879) Professor of Physics at Aberdeen and subsequently Maxwell’s Equations Cambridge University. Unified theories of electricity and magnetism t ∇× = + D HJ Predicted the existence of EM waves 20 years before Hertz observed them t =− B E 0 ρ ⋅= D H Constitutive relations: D = ε E , ©AGK ECSE 352 2.1-7 H = B / μ The Electromagnetic Spectrum Source: ©AGK ECSE 352 2.1-8 Harvard-Smithsonian Center for Astrophysics ( http://chandra.harvard.edu ).
Outline 1. Introduction to EM wave generation: oscillating dipoles 2. Derivation of source-free wave equations from

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## This note was uploaded on 02/14/2011 for the course ECSE 352 taught by Professor Mi during the Fall '10 term at McGill.

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Lect 2.1 - Department of Electrical and Computer...

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