well, Antenna Gain is defined as the ratio of the radiation intensity of an antenna in a given direction, to the intensity of the same antenna as it radiates in all directions (isotropically). Since the radiation intensity of an isotropically radiated power is equal to the power into the antenna divided by 4п (360 degrees) we can express the following equation:
Gain = 4\pi\left(\frac{\mbox{Radiatio n Intensity}}{\mbox{Antenna Input Power}}\right)
Gain = 4\pi\left(\frac{\mbox{U}\left (\theta,\phi\right)}{\mbox{Pin }}\right) \qquad\qquad \mbox{Dimensionless Units}.
Although the gain of an antenna is directly related to its directivity, it is important to note that the antenna gain is a measure that takes into account the efficiency of the antenna as well as its directional capabilities. In contrast, directivity is defined as a measure that takes into account only the directional properties of the antenna and therefore it is only influenced by the antenna pattern. However, if we assumed an ideal antenna without losses then Antenna Gain will equal directivity as the antenna efficiency factor equals 1 (100% efficiency). In practice, the gain of an antenna is always less than its directivity.
D(\theta,\phi) = 4\pi\left(\frac{\mbox{U}\left (\theta,\phi\right)}{\mbox{Pra d}}\right)
D(\theta,\phi) = \epsilon_{cd}\left (4\pi\frac{\mbox{U}\left (\theta,\phi\right)}{\mbox{Pra d}}\right)
D(\theta,\phi) = \epsilon_{cd}\left (D(\theta,\phi)\right)
The formulas above show the relationship between antenna gain and directivity, where εcd is the antenna efficiency factor, D the directivity of the antenna and G the antenna gain. In the antenna world, we usually deal with a “relative gain” which is defined as the power gain ratio in a specific direction of the antenna, to the power gain ratio of a reference antenna in the same direction. The input power must be the same for both antennas while performing this type of measurement. The reference antenna is usually a dipole, horn or any other type of antenna whose power gain is already calculated or known.
Gain = \mbox{G(ref ant)}\left(\frac{\mbox{Pmax(AU T)}}{\mbox{Pmax(ref ant)}}\right)
In the case that the direction of radiation is not stated, the power gain is always calculated in the direction of maximum radiation. The maximum directivity of an actual antenna can vary from 1.76 dB for a short dipole, to as much as 50 dB for a large dish antenna. The maximum gain of a real antenna has no lower bound, and is often -10 dB or less for electrically small antennas[1].
Taking into consideration the radiation efficiency of an antenna, we can express a relationship between the antenna’s total radiated power and the total power input as:
Power Radiated = \mbox{(Antenna Radiation Efficiency)}\left(\mbox{Power Input}\right)
It is important to note that in the above formula, antenna radiation efficiency only includes conduction efficiency and dielectric efficiency and does not include reflection efficiency as part of the total efficiency factor. Moreover, the IEEE standards state that “gain does not include losses arising from impedance mismatches and polarization mismatches”.
Antenna Absolute Gain is another definition for antenna gain. However, Absolute Gain does include the reflection or mismatch losses.
G_{abs}(\theta,\phi)= \epsilon_{refl}G(\theta,\phi) = (1-\Gamma^2)\left(G(\theta,\ph i)\right)
= \epsilon_{refl}\epsilon_{cd}D( \theta,\phi) = \epsilon_{eff}\left(D(\theta,\ phi)\right)
In this equation, εrefl is the reflection efficiency, and εcd includes the dielectric and conduction efficiency. The term εeff is the total antenna efficiency factor.
Taking into account polarization effects in the antenna, we can also define the partial gain of an antenna for a given polarization as that part of the radiation intensity corresponding to a given
Answered by
Romi
, an ibibo Master,
at
9:46 AM on September 15, 2008