ECE 1100 Introduction to Electrical and Computer Engineering

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ECE 6340 Intermediate EM Waves
Fall 2006
Prof. Donald R. Wilton ECE Dept.
Notes 26
Based on Notes by Prof. David R. Jackson
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Equivalence Principle
Basic idea We can replace the actual sources in
a region by equivalent sources at the boundary.
Keep original fields E , H outside S. Put zero
fields inside S.
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Equivalence Principle (cont.)
Ea E
Ha H
Note (Ea , Ha) and (Eb , Hb) both satisfy
Maxwells equations.
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Equivalence Principle (cont.)
The B.C.s on S are violated. Use equivalent
sources to make B.C.s valid.
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Equivalence Principle (cont.)
Hence
Equivalent sources
Outside S, these sources radiate the same fields
as the original antenna, and produce zero fields
inside S. This is justified by the uniqueness
theorem.
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Equivalence Principle (cont.)
Note If there are zero fields throughout a
region, it doesnt matter what material is placed
there (or removed).
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Scattering by a PEC
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Scattering by a PEC
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Example (cont.)
Conclusion The conductor can be removed.
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Example (cont.)
Integral equation for the unknown current
(E , H)
(0 ,0)
source
Electric Field Integral Equation (EFIE)
so
This integral equation has to be solved
numerically.
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Example Scattering by Dielectric Body
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Exterior Equivalence
Replace body by free space (since material
doesnt matter in zero-field region).
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Summary for Exterior
Original problem
Free-space problem
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Interior Equivalence
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Summary for Interior
Original problem
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Integral Equation
The means calculate the fields inside the
surface, assuming an infinite dielectric region.
Note The means calculate the fields outside
the surface, radiated by the sources in free
space.
Boundary conditions
Hence
PMCHWT Integral Equation
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Fields in a Half Space
Equivalent sources
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Fields in a Half Space (cont.)
Put PEC in zero-field region
The electric surface current on the PEC does not
radiate.
Hence, we have
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Fields in a Half Space (cont.)
Now use image theory
(E , H)
correct fields
incorrect fields
Note fields are not correct for z lt 0 (the image
method gives incorrect fields in this region).
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Fields in a Half Space Summary
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Fields in a Half Space (cont.)
Alternative (better when H is known)
Mse does not radiate on PMC, and is therefore not
included.
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Example Radiation from Waveguide
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Example (cont.)
Step 1
Step 2
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Example (cont.)
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Example (cont.)
Apply Duality
Solve this problem first
Then use