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Electric far field for an arbitrary current through arbitrary antenna

  1. Nov 17, 2013 #1
    If we consider an arbitrary time varying current [itex]I\left(t\right)[/itex] flowing through an arbitrary antenna, then is the following a plausible expression for the electric field [itex]\vec{\mathrm{E}}\left(\vec{\mathrm{r}},t\right)
    [/itex] in the far field region:
    = \frac{1}{4\pi \epsilon_0 c^2 r} \;
    \vec{\mathrm{a}}_i\left(\hat{\mathrm{r}}\right) \;
    \frac {d^i}{dt^i}I\left(t - \frac {r} {c}\right)
    where the integer value [itex]n[/itex] and all vector functions [itex]\vec{\mathrm{a}}_i\left(\hat{\mathrm{r}}\right)[/itex] depend only on the antenna geometry (i.e. not on any characteristic of the input excitation), and [itex]
    \hat{\mathrm{r}} = 0
    [/itex] for all [itex]i[/itex]?

    And if this can indeed be done, what kind of expression can be deduced when the same antenna is receiving radiation -- converting the electric field into a current or voltage?

    I am trying to understand if it is possible to characterize an arbitrary arrangement of conductors as an antenna purely in the time domain -- as opposed to parameters like radiation resistance, gain, antenna aperture and radiation pattern that depend on frequency/wavelength.

  2. jcsd
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