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Antenna directivity is the ratio of maximum radiation intensity (power per unit surface) radiated by the antenna in the maximum direction divided by the intensity radiated by a hypothetical isotropic antenna radiating the same total power as that antenna. For example, a hypothetical antenna which had a radiated pattern of a hemisphere (1/2 ...
As frequency increases, the directivity of an antenna of a given physical size will increase. In order to keep receiver antenna directivity constant in the formula, the antenna size must be reduced, and a smaller size antenna results in less power being received as it is able to capture less power with a smaller area.
The Deep Space Network has been able to maintain the link at a higher than expected bitrate through a series of improvements, such as increasing the antenna size from 64 m to 70 m for a 1.2 dB gain, and upgrading to low noise electronics for a 0.5 dB gain in 2000–2001.
This result could be further generalized if we allow the integral over frequency to be more general. Then we find that A eff for the same antenna must vary with frequency according to that same formula, using λ = c/f. Moreover, the integral over solid angle can be generalized for an antenna that is not isotropic (that is, any real antenna).
The fundamental resonance of a thin linear conductor occurs at a frequency whose free-space wavelength is twice the wire's length; i.e. where the conductor is 1 / 2 wavelength long. Dipole antennas are frequently used at around that frequency and thus termed half-wave dipole antennas. This important case is dealt with in the next section.
The Foltz drawing pin like antenna from 1998 size 0.62 and 22% bandwidth. The Rogers cone from 2001 is size 0.65 and right on the limit. Lina and Choo planar spirals in size ratios range from 0.2 to 0.5; The fractal Koch curve antenna approaches the limit. [5] A meander line antenna optimizes the size for narrower bandwidths of the order 10%. [11]
Applying the above formula to the 25-meter-diameter antennas often used in radio telescope arrays and satellite ground antennas at a wavelength of 21 cm (1.42 GHz, a common radio astronomy frequency), yields an approximate maximum gain of 140,000 times or about 52 dBi (decibels above the isotropic level).
For the relationship between the electric and magnetic fields, see the impedance of free space. For a 50 Ω load, knowing that P D A e = P r = V 2 /R and E 2 = μ 0 ε 0 {\displaystyle {\sqrt {\frac {\mu _{0}}{\varepsilon _{0}}}}} P D ~ 377P D (E and V noted here are the RMS values averaged over time), the antenna factor is developed as: