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en:electronics:antenna-theory:dipole-derivation [2013/03/23 23:21] alexen:electronics:antenna-theory:dipole-derivation [2014/10/20 21:04] (current) alex
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 \begin{eqnarray*} \begin{eqnarray*}
-E_\theta &=& -j \omega \eta A_T \\+E_\theta &=& -j \omega A_T \\
 A_T &=& A_z \sin \theta \\ A_T &=& A_z \sin \theta \\
-E_\theta &=& \frac{-j \omega \eta \mu I_0 e^{-jkr}}{2\pi r k \sin \theta} \left [ \cos \left (\frac{kL}{2} \cos \theta \right ) - \cos \left( \frac{kL}{2} \right) \right ]+E_\theta &=& \frac{-j \omega \mu I_0 e^{-jkr}}{2\pi r k \sin \theta} \left [ \cos \left (\frac{kL}{2} \cos \theta \right ) - \cos \left( \frac{kL}{2} \right) \right ]
 \end{eqnarray*} \end{eqnarray*}
  
 This equation for $E_\theta$ is the general form for the theta component in spherical coordinates of the far-field E field of a dipole antenna of any length oriented along the z-axis.  The r component is zero due to the far-field assumption and the phi component is zero due to the electric field's orientation along the z-axis.   This equation for $E_\theta$ is the general form for the theta component in spherical coordinates of the far-field E field of a dipole antenna of any length oriented along the z-axis.  The r component is zero due to the far-field assumption and the phi component is zero due to the electric field's orientation along the z-axis.