A receiver antenna aperture or effective area is measured as the area of a circle to incoming signal as the power density (watts per square metre) x aperture (square metres) = available power from antenna (watts).

Antenna gain is directly proportional to aperture and generally antenna gain is increased by focusing radiation in a single direction, while reducing all other directions. Since power cannot be created by the antenna the larger the aperture, the higher gain and narrower the beam-width.

The relation between gain and effective area is

G = 4 * PI * A / L2 or A = G * L2 / 4 / PI

Where G is gain (linear, not dB), A is the effective area, PI is 3.14... and L2 is wavelength squared. Units for A and L2 are not important, but both must be given in the same units. The same area means more gain at a higher frequency, and the same gain means less area at a higher frequency.

Simply increasing the size of antenna does not guarantee an increase in effective area; however, other factors being equal, antennas with higher maximum effective area are generally larger.

It seems obvious to optical astronomers that a parabolic dish antenna that is many wavelengths across, will have an aperture nearly equal to their physical area. However other antenna such as a Yagi and Collinear arrays my not look to be the same at first glance but they do achieve the same result using other means at radio frequencies.

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