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Page 1: rNow, we will study EM waves with the real field theory
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We studied waves with the transmission line theory. Now, we will study EM waves with the real field theory.
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Plane Waves
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In many situations, we cannot define even local voltages and currents.
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A major difference between the two is the following:
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Page 2: rNow, we will study EM waves with the real field theory
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(1D)
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E
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in
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(lossless)
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Page 4: rNow, we will study EM waves with the real field theory

E

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Take-home messages: 1. The EM plane wave is transverse 2. E H
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The loop integral of E is not 0.
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Page 5: rNow, we will study EM waves with the real field theory
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If a field is constant in the xy-plane, any loop integral in the plane is zero.
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(What's the integral form?)
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(Talk about two types of "1D")
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Not all EM waves are transverse.
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Again, if a field is constant in the xy-plane, any loop integral in the plane is zero.
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Again, what's the integral form?
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(We have yet to prove E H.)
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Page 8: rNow, we will study EM waves with the real field theory
Page 9: rNow, we will study EM waves with the real field theory
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General EM wave equation in 3D
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Snapshot @ t=t
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0
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Waveform
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Back to our plane wave:
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=Re
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(Partial differential eq. to ordinary differential eq.)
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complex amplitudes
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Page 13: rNow, we will study EM waves with the real field theory
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(for the lossless case)
Page 14: rNow, we will study EM waves with the real field theory
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Mismatch ==> reflection at interface between media
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Relation between wave impedance and refractive index
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For a medium,
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Page 15: rNow, we will study EM waves with the real field theory
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The wave impedance is the intrinsic impedance of the medium, similar to the characteristic impedance of the transmission line.
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Do Homework 12 Problems 1& 2.
Page 16: rNow, we will study EM waves with the real field theory
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Page 17: rNow, we will study EM waves with the real field theory
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(We studied the 1D case in detail)
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(non-zero current)
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Page 18: rNow, we will study EM waves with the real field theory
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gamma <==> jk
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gamma^2 <==> -k^2
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exp(-gamma*z) <==> exp(-jkz)
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Page 19: rNow, we will study EM waves with the real field theory
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Finish Homework 12

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