# Effective area of a phased array

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 $$A_e=\frac{\lambda^2}{4\pi}GN$$ 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?

• Hello and welcome to ham.stackexchange.com! – rclocher3 Jul 14 at 13:25

If the elements are isotropic then as you've written it, $$G=1$$
And the effective aperture increases by $$N$$.
• Really thank for your answer! So, does $N$ equal to the maximum directivity (When mainlobe is steered at the direction of signal ) of the array? Then, for any fixed angle $(\theta,\phi)$, the result is $\frac{\lambda^2}{4 \pi}G(\theta,\phi)$? ($G(\theta,\phi)$ is the directivity of the array for the angle $(\theta,\phi)$) – tyrela Jul 14 at 17:44
• You should include efficiency too, but in an ideal antenna $\eta=1$ so Gain = Directivity. – tomnexus Jul 14 at 20:26