Antenna Temperature () is a parameter that describes how much noise an
antenna produces in a given environment. This temperature is not the physical temperature of the antenna. 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 (and hence give the full definition of antenna temperature), we will 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 Kelvin; 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
. 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
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 (with a pencil beam), the antenna temperature will only depend on the temperature in which the antenna is "looking".
The noise power received from an antenna at temperature can be expressed in terms of
the bandwidth (B) the antenna (and its receiver) are
In the above, K is Boltzmann's constant (1.38 * 10^-23 [Joules/Kelvin = J/K]). The receiver also has a temperature associated
with it (), and the total system temperature (antenna plus receiver) has a
combined temperature given by . This temperature can be used in the above
equation to find the total noise power of the system. These concepts begin to illustrate how antenna engineers must understand
receivers and the associated electronics, because the resulting systems very much depend on each other.
A parameter often encountered in specification sheets for antennas that operate in certain environments is
the ratio of gain of the antenna divided by the antenna temperature
(or system temperature if a receiver is specified). This parameter is written as G/T, and has units of dB/Kelvin [dB/K].
Finally, note that many RF engineers like to use the term Noise Figure (or Noise Factor, NF) to describe systems. This is the ratio
of the input SNR (signal to noise ratio) to the output SNR. Basically, all RF devices (like mixers and amplifiers) add some noise.
Antenna temperature doesn't really relate to a Noise Figure, as the signal level power input varies greatly with the desired
signal's direction of arrival, while the noise added is a constant.
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