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The effective area of an antenna or aperture is based upon a receiving antenna. However, due to reciprocity, an antenna's directivity in receiving and transmitting are identical, so the power transmitted by an antenna in different directions (the radiation pattern) is also proportional to the effective area .
It can be shown that its effective area averaged over all directions must be equal to λ 2 /4π, the wavelength squared divided by 4π. Gain is defined such that the average gain over all directions for an antenna with 100% electrical efficiency is equal to 1. Therefore, the effective area A eff in terms of the gain G in a given direction is ...
There are critical differences in how various authors and IEEE define antenna efficiency and effective area of an antenna. IEEE defines the antenna efficiency of an aperture-type antenna as, "For an antenna with a specified planar aperture, the ratio of the maximum effective area of the antenna to the aperture area." [1]
For a given frequency, the antenna's effective area is proportional to the gain. An antenna's effective length is proportional to the square root of the antenna's gain for a particular frequency and radiation resistance. Due to reciprocity, the gain of any antenna when receiving is equal to its gain when transmitting.
where and are the antenna gains (with respect to an isotropic radiator) of the transmitting and receiving antennas respectively, is the wavelength representing the effective aperture area of the receiving antenna, and is the distance separating the antennas. [1]
Shaped-beam antennas – Modern reflector antennas can be designed to produce a ... is the area of the antenna ... which has an effective aperture of about 300 meters ...