lec28 - ) , ( z t Ae t z E z y Left and right propagating...

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Lecture Notes for C-term 2009 Lecture 28 Prof. R. Ludwig Department of Electrical and Computer Engineering Worcester Polytechnic Institute Worcester, MA ECE 2112 Electromagnetic Theory Copyright, 2000 © R. Ludwig
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ECE2112_28 2 Lecture 28 Objectives • How does a wave combine space and time? • How do waves propagate? • What is a lossy wave? • What is the time-harmonic form of Maxwell’s theory?
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ECE2112_28 3 ECE 2112 - Lecture 28 Traveling wave concept 0 2 2 ) , ( z T t x t Phase velocity )] , ( cos[ ) , ( z t A z t E r p c f T dt z d u  1 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 x 10 -8 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 0 ) , ( z t z t E(t,z 0 ) E(t,z 1 ) t 0 
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ECE2112_28 4 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 ECE 2112 - Lecture 28 • Attenuated Waves ) cos(
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Unformatted text preview: ) , ( z t Ae t z E z y Left and right propagating waves ) cos( ) cos( ) , ( z t B z t A t z E y E(z,t) x 5 . p u Right propagation Left propagation ECE2112_28 5 ECE 2112 -Lecture 28 Maxwell equations in time harmonic form } ) ( Re{ ) , ( t j e t r E r E / V E E E J H ) ( j j H E j H Spatial phasor Maxwell equations Benefit of time harmonic form: Time derivatives are eliminated...
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lec28 - ) , ( z t Ae t z E z y Left and right propagating...

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