# Electric far field for an arbitrary current through arbitrary antenna

1. Nov 17, 2013

### avjt

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

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.

Thanks...