Noise figure 41417 220884382 2008-06-22T01:56:43Z CosineKitty 1750493 more nonbreaking space between numbers and units. linked first usage of Kelvin. In [[telecommunication]], '''noise figure''' ('''NF''') is a measure of degradation of the signal to noise ratio ([[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 [[standardization|standard]] [[noise temperature]] <math>T_0</math> (usually 290&nbsp;[[Kelvin|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. == 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 [[decibel]]s (dB) between the noise output of the actual receiver to the noise output of an “ideal” receiver with the same overall [[gain]] and [[Bandwidth (signal processing)|bandwidth]] when the receivers are connected to sources at the [[standardization|standard]] [[noise temperature]] <math>T_0</math> (usually 290&nbsp;K). The noise power from a simple [[Electrical load|load]] is equal to <math>k T B</math>, where ''<math>k</math>'' is [[Boltzmann's constant]], ''<math>T</math>'' is the [[absolute temperature]] of the load (for example a [[resistor]]), and ''<math>B</math>'' 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&nbsp;K. In this case, one receiver with a noise figure say 2&nbsp;dB better than another, will have an output signal to noise ratio that is about 2&nbsp;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&nbsp;K. In these cases a 2&nbsp;dB improvement in receiver noise figure will result in more than a 2&nbsp;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. == Mathematics == Noise figure is given by :<math>\mathrm{NF} = \mathrm{SNR}_\mathrm{in} - \mathrm{SNR}_\mathrm{out}</math> where every variable is a [[decibel|dB]] figure. The previous formula is only valid when the [[input]] termination is at [[standardization|standard]] [[noise temperature]] <math>T_0</math>. 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 [[standardization|standard]] [[noise temperature]] <math>T_0</math>. :<math> F = \frac{\mathrm{SNR}_\mathrm{in}}{\mathrm{SNR}_\mathrm{out}}</math> where everything is a ratio :<math>F = 10^\mathrm{NF/10}, \quad \mathrm{NF} = 10 \log(F)</math> The noise factor of a device is related to its [[noise temperature]] via :<math>F = 1 + \frac{T_\mathrm{e}}{T_0}</math> Devices with no gain (e.g., [[Attenuator (electronics)|attenuators]]) have a noise figure equal to their attenuation ''L'' (in dB) when their physical temperature equals <math>T_0</math>. More generally, for an attenuator at a physical temperature <math>T_\mathrm{phys}</math>, the noise temperature is <math>T_\mathrm{e} = (L-1)T_\mathrm{phys}</math>, thus giving a noise factor of <math>F = 1 + \frac{(L-1)T_\mathrm{phys}}{T_0}</math> If several devices are cascaded, the total noise factor can be found with [[Friis formula|Friis' Formula]]: :<math>F = F_1 + \frac{F_2 - 1}{G_1} + \frac{F_3 - 1}{G_1 G_2} + \frac{F_4 - 1}{G_1 G_2 G_3} + \cdots + \frac{F_n - 1}{G_1 G_2 G_3 \cdots G_{n-1}},</math> where <math>F_n</math> is the noise factor for the ''n''-th device and <math>G_n</math> is the [[power gain]] (numerical, not in dB) of the ''n''-th device. == See also == * [[Noise]] * [[Noise (electronic)]] * [[Noise level]] * [[Thermal noise]] * [[Signal-to-noise ratio]] ==External links== * [http://www.analog.com/library/analogDialogue/archives/42-06/noise_figure.html Noise Figure and Logarithmic Amplifiers] Analog Dialogue article by Barrie Gilbert {{FS1037C MS188}} [[Category:Noise]] [[ca:Factor de soroll]] [[de:Rauschzahl]] [[es:Factor de ruido]] [[fr:Facteur de bruit]] [[it:Cifra di rumore]]