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Electromagnetic Theorems & Principles

Electromagnetic Theorems & Principles. INEL 6216 Dr. Sandra X-Pol. Theoremas que ayudan a resolver problemas de EM. Dualidad Unicidad Imágenes Reciprocidad Equivalencia de Volumen Equivalencia de superficie: Principio de Huygen Inducción. Dualidad.

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Electromagnetic Theorems & Principles

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  1. Electromagnetic Theorems & Principles INEL 6216 Dr. Sandra X-Pol

  2. Theoremas que ayudan a resolver problemas de EM • Dualidad • Unicidad • Imágenes • Reciprocidad • Equivalencia de Volumen • Equivalencia de superficie: • Principio de Huygen • Inducción

  3. Dualidad Electric source (J) Magnetic source (M) Same mathematical form Sustematic interchange of symbols

  4. Uniqueness theorem • Solution is unique given certain conditions: If you find two solutions, E1 & E2, H1 & H2, then over a surface S,

  5. Image Theory • When the ground, corner reflector or other obstacle is close to a radiating element, there will be reflections from it. • This can be accounted for by image. • Earth is more lossy at high frequency and moisture • Assume ground is a perfect electric conductor, flat, and infinite in extent

  6. Vertical (electric) Dipole Real source direct reflection h h The direction of the Image is such that the E tangent to perfect conductor is zero. image

  7. Horizontal (electric) Dipole Real source direct reflection The direction of the Image is such that the E tangent to perfect conductor is zero. image

  8. Electric perfect conductor electric magnetic h sources image h Infinite losser

  9. Magneticperfect conductor electric magnetic h sources Magnetic conductor image h

  10. Reciprocity Theorem Related to transmitting and receiving properties of radiating systems. • Fields for sources J1, M1 • Fields for sources J2, M2 • By reciprocity then,

  11. Volume Equivalence Th. Used to find the fields scattered by dielectric obstacles. If in free-space ( )we have: But then, the same sources find anothermedium ( ): We define the difference as the scattered fields:

  12. Volume Equivalence (cont.) Using this, we can derive: Where the volume equivalent current densities sources

  13. Huygen's Principle • predicts the future position of a wave when its earlier position is known. “Every point on a wave front can be considered as a source of tiny wavelets that spread out in the forward direction at the speed of the wave itself. The new wave front is the envelope of all the wavelets - that is, tangent to them."

  14. Volume Equivalence (Huygen’s Principle) • Used mostly for aperture radiation • Here actual sources are replaced by equivalent sources (J,M) within a region to simplify solution • An imaginary closed surface is chosen (usually so that it coincides with conducting structure) but fields outside are the same. • Chosen current densities source on the surface create the same fields outside.

  15. Perfect conductor surface Perfect magnetic conductor

  16. Love’s Principle • If inside field are zero

  17. Equivalent model for magnetic source radiating near perfect conductor Solution valid only on this side Remove plate

  18. Induction Theorem[similar to Huygen’s] • Used mostly for scattering from obstacles

  19. Homework problems- Ch.7 • 5 • 11 • 13

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