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en:electronics:antenna-theory:dipole-derivation [2014/10/20 22:45] alex |
en:electronics:antenna-theory:dipole-derivation [2014/10/20 23:04] (current) alex |
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| \begin{eqnarray*} | \begin{eqnarray*} | ||
| E_\theta &=& -j \omega 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 \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. | ||