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Antenna gain-to-noise-temperature is a figure of merit in the characterization of antenna performance, where G is the antenna gain in decibels at the receive frequency, and T is the equivalent noise temperature of the receiving system in kelvins. The receiving system noise temperature is the summation of the antenna noise temperature and the RF chain noise temperature from the antenna terminals to the receiver output.
Antenna temperature is a parameter that describes how much noise an antenna produces in a given environment. Antenna noise temperature is not the physical temperature of the antenna but rather an expression of the available noise power at the antenna flange. Moreover, an antenna does not have an intrinsic "antenna temperature" associated with it; rather the temperature depends on its gain pattern and the thermal environment that it is placed in. Antenna temperature is also sometimes referred to as Antenna Noise Temperature.To define the environment, we'll introduce a temperature distribution - this is the temperature in every direction away from the antenna in spherical coordinates. For instance, the night sky is roughly 4 K; the value of the temperature pattern in the direction of the Earth's ground is the physical temperature of the Earth's ground. This temperature distribution will be written as TS. Hence, an antenna's temperature will vary depending on whether it is directional and pointed into space or staring into the sun.
For an antenna with a radiation pattern given by G, the noise temperature is mathematically defined as:
This states that the temperature surrounding the antenna is integrated over the entire sphere, and weighted by the antenna's radiation pattern. Hence, an isotropic antenna would have a noise temperature that is the average of all temperatures around the antenna; for a perfectly directional antenna , the antenna temperature will only depend on the temperature in which the antenna is "looking".