Noise figure

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In telecommunication, noise figure (NF) is a measure of degradation of the signal to noise ratio (SNR), caused by components in the RF signal chain. The noise figure is the 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 $T 0$ (usually 290 K). The noise figure is thus the ratio of actual output noise to that which would remain if the device itself did not introduce noise. It is a number by which the performance of a radio receiver can be specified.

[edit] General

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.

Essentially, the noise figure is the difference in decibels 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 with identical temperatures. The noise power from a simple load is equal to kTB, where k is Boltzmann's constant, T is the absolute temperature of the load (for example a resistor), and B is the measurement bandwidth. See also noise level, signal-to-noise ratio.

[edit] Mathematics

Noise figure is given by

N F = S N R i n - S N R o u t

where everything is in dB.

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.

$F = \frac{{SNR}_{in}}{{SNR}_{out}}$

where everything is a ratio

$F = 10^{NF/10}, \quad NF = 10 \log(F)$

The noise factor of a device is related to its noise temperature via

$F = 1 + \frac{T_e}{T_0}$

Devices with no gain (e.g. attenuators) have noise figure equal to their attenuation L (in dB) when their physical temperature equals $T 0$ . More generally, for an attenuator at a physical temperature $T p h y s$ , the noise temperature is $T e = (L - 1) T p h y s$ , thus giving a noise factor of $F = 1 + \frac{(L-1)T_{phys}}{T_0}$