Dipolo Infinitesimal Sandra CruzPol Ph D INEL 5305

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

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

Maxwell Equations Ampere: Faraday: Gauss:

Relaciones de Continuidad

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

Usando Ley de Ampere:

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

de la Ec. de Gauss Eléctrica

Wave equation n For sinusoidal fields (harmonics): where

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

Poynting Vector

Average S Para medios sin pérdidas:

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

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

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

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

Apply B. C. n If radiated wave travels outwards from the source: n To find C 2, let’s examine what happens near the source. (in that case k tends to 0) n So the wave equation reduces to

Now we integrate the volume around the dipole: n And using the Divergence Theorem

Comparing both, we get:

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

The magnetic filed intensity from the dipole is:

Now the E field:

The electric field from infinitesimal dipole:

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

Power : Hertzian Dipole

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