Essentially, the noise figure is the difference in decibels (dB) between the noise output of the actual receiver to the noise output of an “ideal” receiver with the same overall gain and bandwidth when the receivers are connected to sources at the standard noise temperature (usually 290 K). The noise power from a simple load is equal to , where is Boltzmann's constant, is the absolute temperature of the load (for example a resistor), and is the measurement bandwidth.
This makes the noise figure a useful figure of merit for terrestrial systems where the antenna effective temperature is usually near the standard 290 K. In this case, one receiver with a noise figure say 2 dB better than another, will have an output signal to noise ratio that is about 2 dB better than the other. However, in the case of satellite communications systems, where the antenna is pointed out into cold space, the antenna effective temperature is often colder than 290 K. In these cases a 2 dB improvement in receiver noise figure will result in more than a 2 dB improvement in the output signal to noise ratio. For this reason, the related figure of effective noise temperature is therefore often used instead of the noise figure for characterizing satellite-communication receivers and LNA.
Sometimes the noise factor F is specified, which is the numerical ratio form of noise figure. Noise Factor is a straight ratio of SNR ratios. Noise Figure is the decibel equivalent of Noise Factor. The following formula is only valid when the input termination is at standard noise temperature .
The noise factor of a device is related to its noise temperature via
Devices with no gain (e.g., attenuators) have a noise figure equal to their attenuation L (in dB) when their physical temperature equals . More generally, for an attenuator at a physical temperature , the noise temperature is , thus giving a noise factor of
If several devices are cascaded, the total noise factor can be found with Friis' Formula: