= Gaussian antenna beam solid angle
{c}
{title2=$\Omega_A\simeq2\pi\alpha^2$}
For a narrow angular <power> pattern $\exp[-(u^2+w^2)/(2\alpha^2)]$ about an equatorial beam centre, the <solid angle> measure is locally $du\,dw$. Extending the small lobe to the plane gives its beam <solid angle> $\Omega_A\simeq2\pi\alpha^2$. Both sides of the azimuthal lobe must be included. A lossless <antenna> then has peak <antenna gain> $G_0\simeq2/\alpha^2$ and peak <antenna effective area> $A_0\simeq\lambda^2/(2\pi\alpha^2)$.
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