Effective area of a phased array

Question

For a $N$-element planar phased array, all the elements are same isotropic antennas. Then, what is the effective area of this array? Is it
$$A_e=frac{lambda^2}{4pi}GN$$
where $G$ is the directivity of a fixed angle $(theta,phi)$.

Meanwhile, as the antennas are isotropic, is the beamforming cause the $G$ times change in effective area?

tomnexus · Accepted Answer

Yes, that's correct.
If the elements are isotropic then as you've written it, $G=1$
And the effective aperture increases by $N$.
Of course this new aperture is only effective in the direction of the peak(s) of the response, elsewhere it will be less. And this assumes that the elements are far enough apart that there's no coupling between them.

Effective area of a phased array

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