# Reciprocity Theorem

## 1 The Reciprocity Theorem

The Reciprocity Theorem, as applied to antennas, simply states that the transmitting and receiving antenna beams are the same. That is, the response of an antenna to radiation coming from any chosen direction, $A(\vec\Omega )$, at any frequency (i.e. the electric field that is coupled into the receiving electronics) is equal to the far-field radiation that would be transmitted in that direction, $G(\vec\Omega )$, to within a frequency-dependent constant of proportionality:

$\frac{G(\vec\Omega )}{A(\vec\Omega )}=\frac{4\pi }{\lambda ^2}, \,\!$

where λ is the wavelength of the radiation in question.