Noise figure (NF) and noise factor (F) are figures of merit that indicate degradation of the signal-to-noise ratio (SNR) that is caused by components in a signal chain. These figures of merit are used to evaluate the performance of an amplifier or a radio receiver, with lower values indicating better performance. The noise factor is defined as the unitless ratio of the output noise power of a device to the portion thereof attributable to thermal noise in the input termination at standard noise temperature T0 (usually 290 K). The noise factor is thus the ratio of actual output noise to that which would remain if the device itself did not introduce noise, which is equivalent to the ratio of input SNR to output SNR. The noise figure is the power level of the noise factor, calculated in terms of the logarithm of noise factor and expressed in scale of decibels (dB).
General The noise figure is the difference in decibel (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 matched sources at the standard noise temperature T0 (usually 290 K). The noise power from a simple load is equal to kTB, where k is the Boltzmann constant, T is the absolute temperature of the load (for example a resistor), and B 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 receiver 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 low-noise amplifiers. In heterodyne systems, output noise power includes spurious contributions from image-frequency transformation, but the portion attributable to thermal noise in the input termination at standard noise temperature includes only that which appears in the output via the principal frequency transformation of the system and excludes that which appears via the image frequency transformation.
Definition The noise factor F of a system is defined as
where SNRi and SNRo are the input and output signal-to-noise ratios respectively. The SNR quantities are unitless power ratios. Note that this specific definition is only valid for an input signal of which the noise is Ni=kT0B. The noise figure NF is defined as the noise factor in units of decibels (dB):
where SNRi, dB and SNRo, dB are in units of (dB). These formulae are only valid when the input termination is at standard noise temperature T0 = 290 K, although in practice small differences in temperature do not significantly affect the values. The noise factor of a device is related to its noise temperature Te:
F = 1 + T e T 0 . {\displaystyle F=1+{\frac {T_{\text{e}}}{T_{0}}}.}
Attenuators have a noise factor F equal to their attenuation ratio L when their physical temperature equals T0. More generally, for an attenuator at a physical temperature T, the noise temperature is Te = (L − 1)T, giving a noise factor
F = 1 + ( L − 1 ) T T 0 . {\displaystyle F=1+{\frac {(L-1)T}{T_{0}}}.}
Noise factor of cascaded devices
If several devices are cascaded, the total noise factor can be found with Friis' formula:
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