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Antenna efficiency, efficiency of antenna radiation

Antenna efficiency is defined as a ratio of a radiated power and a supplied one. Efficiency can be evaluated exploiting the following relation:

(R_Σvst is radiation resistance related to input current, and R_ztr is lossy resistance related to input current). Good antenna efficiency is conditioned by a small lossy resistance and (or) by a high radiation resistance. On the contrary, low efficiency is exhibited by antennas of small radiation resistance, which is typical for antennas much shorter that the wavelength.

Computing radiation efficiency, a lossles antenna is assumed (lossy resistance is zero). Then radiation efficiency is given as a ratio of a real power radiated by the antenna (we integrate Poynting vector in the far-field region over the whole half-space) and a real power at the input terminal of the antenna.