# dipolo infinitesimal

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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. - PowerPoint PPT Presentation

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• Dipolo Infinitesimal

Sandra Cruz-Pol, Ph. D.INEL 5305ECE UPRMMayagez, PR

• OutlineMaxwells equationsWave equations for A and for FPower: Poynting VectorDipole antenna

• Potencial Magntico Vectorial A

Si lo sustituimos en la Ley de Faraday:F is the Electric Scalar Potential

• Usando Ley de Ampere:

• Lorentz conditionSi escogemos

Queda la Ecuacion de Onda

donde J es la densidad de una fuente de corriente, si hay.

• de la Ec. de Gauss Elctrica

• Wave equationFor sinusoidal fields (harmonics):

where

• OutlineMaxwells equationsWave equations for A and for FPower: Poynting VectorDipole antenna

• Poynting Vector

• Average SPara medios sin prdidas:

• OutlineMaxwells equationsWave equations for A and for FPower: Poynting VectorInfinitesimal Dipole antenna

• Find A from Dipole with current JLine charge w/uniform charge density, rL xzqrr0JzAzAssume the simplest solution Az(r):

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

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

• Apply B.C.If radiated wave travels outwards from the source:

To find C2, lets examine what happens near the source. (in that case k tends to 0)

So the wave equation reduces to

• Now we integrate the volume around the dipole:

And using the Divergence Theorem

• Comparing both, we get:

• Now from A we can find E & H

Using the Victoria IDENTITY:

And

Substitute:

• The magnetic filed intensity from the dipole is:

• Now the E field:

• The electric field from infinitesimal dipole:

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

• Power :Hertzian Dipole

• Resistencia de RadiacionLa potencia tiene parte real y parte reactiva