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Dipolo Infinitesimal

Dipolo Infinitesimal. Sandra Cruz-Pol, Ph. D. INEL 5305 ECE UPRM Mayagüez, PR. Outline. Maxwell’s equations Wave equations for A and for F Power: Poynting Vector Dipole antenna. Maxwell Equations. Ampere:. Faraday:. Gauss:. Relaciones de Continuidad. Potencial Magnético Vectorial A.

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Dipolo Infinitesimal

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  1. Dipolo Infinitesimal Sandra Cruz-Pol, Ph. D. INEL 5305 ECE UPRM Mayagüez, PR

  2. Outline • Maxwell’s equations • Wave equations for A and for F • Power: Poynting Vector • Dipole antenna

  3. Maxwell Equations Ampere: Faraday: Gauss:

  4. Relaciones de Continuidad

  5. Potencial Magnético Vectorial A • Si lo sustituimos en la Ley de Faraday: F is the Electric Scalar Potential

  6. Usando Ley de Ampere:

  7. Lorentz’ condition • Si escogemos • Queda la Ecuacion de Onda donde J es la densidad de una fuente de corriente, si hay.

  8. de la Ec. de Gauss Eléctrica

  9. Wave equation • For sinusoidal fields (harmonics): where

  10. Outline • Maxwell’s equations • Wave equations for A and for F • Power: Poynting Vector • Dipole antenna

  11. Poynting Vector

  12. Average S Para medios sin pérdidas:

  13. Outline • Maxwell’s equations • Wave equations for A and for F • Power: Poynting Vector • Infinitesimal Dipole antenna

  14. Find A from Dipole with current J • Line charge w/uniform charge density, rL Assume the simplest solution Az(r): z Az r r q Jz x 0

  15. To find…. Assume the simplest solution Az(r):

  16. Fuera de la Fuente (J=0) Which has general solution of:

  17. Apply B.C. • If radiated wave travels outwards from the source: • To find C2, let’s examine what happens near the source. (in that case k tends to 0) • So the wave equation reduces to

  18. Now we integrate the volume around the dipole: • And using the Divergence Theorem

  19. Comparing both, we get:

  20. Now from A we can find E & H • Using the Victoria IDENTITY: • And • Substitute:

  21. The magnetic filed intensity from the dipole is:

  22. Now the E field:

  23. The electric field from infinitesimal dipole:

  24. General @Far field r> 2D2/l Note that the ratio of E/H is the intrinsic impedance of the medium.

  25. Power :Hertzian Dipole

  26. Resistencia de Radiacion • La potencia tiene parte real y parte reactiva • La potencia irradiada es: • Comparando con la P total, se halla la Impedancia • COmparando cno la Prad, halla la Rrad.

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