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= Área efectiva del dipolo: =
<math>A_{dip}</math>=<math>\frac{P_r}{P_0}=\frac{3\lambda ^2}{8\pi}= 0.1193\lambda ^2</math>[0.3cm] <math>P_o=E^2/120\pi</math>
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<math>Pr=\frac{E^2 a^2}{4(80\pi^2 a^2/ \lambda ^2 )}</math> = <math>\frac{\lambda^2 E^2 a^2}{320\pi a^2}</math>= <math>\frac{\lambda^2 E^2}{320\pi^2}</math><br />
<math>A_{dip}=\frac{\frac{\lambda^2 E^2}{320\pi^2}}{\frac{E^2}{120\pi}} = \frac{ 120 \pi \lambda^2 E^2}{320\pi^2E^2}=\frac{3\lambda^2}{8\pi}</math><br />

[[File:Area efectiva de una circunferencia.png|centro|miniaturadeimagen|400x400px|Área efectiva de una circunferencia]]

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= Small Dipole with No Heat Loss =
For a small uniform current element the available output power is equal to the induced voltage squared divided by four times the radiation resistance. Thus<br />


<math>P_r=\frac{E^2a^2}{4R_{rad}}</math><br />


where<br />
E=effective value of the electric field of the wave.<br />
a=length of the current element.<br />
Rrad. = radiation resistance of the current element<br />
<math>R_{rad}=80\pi ^2a^2/\lambda ^2</math> Since the power flow per unit area is equal to the electric field squared divided by the impedance of free space,<br />
i.e., <math>P_o=E^2/120\pi</math>, we have<br />

<math>A_{dip}=\frac{P_r}{P_0}=\frac{3\lambda ^2}{8\pi}=0.1193\lambda ^2</math><br />

The effective area of a half-wavelength dipole with no heat loss is only 9.4 per cent, 0.39 decibels,2 larger than the effective area of the small dipole. Therefore<br />

<math>A_{0.5\lambda }=0.1305\lambda ^2</math>

 The area of a rectangle with one-half wavelength and one-quarter wavelength sides is <math>0.125\lambda ^2 </math> and it is, therefore, a good approximation for the effective areas of small dipoles and half-wavelength dipoles.


<math>A_{0.5}=0.1305\lambda^2</math><br />
<math>0.1305\lambda^2 = \pi r^2</math><br />
<math>\frac{0.1305}{\pi} \lambda^2 = r^2</math><br />
<math>0.04154 \lambda^2 = r^2 </math><br />
<math>\sqrt{0.04152 \lambda^2} =\sqrt{r^2}</math><br />
<math>r=0.2038\lambda</math>

[[Categoría:Artículo de Friis]]