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| '''Noise figure''' (NF) and '''noise factor''' (''F'') are measures of degradation of the [[signal-to-noise ratio]] (SNR), caused by components in a [[radio frequency]] (RF) [[Signal_chain_(signal_processing_chain)|signal chain]]. It is a number by which the performance of a radio receiver can be specified.
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| The noise factor is defined as 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''<sub>0</sub> (usually 290 [[Kelvin|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, or the ratio of input SNR to output SNR.
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| The noise ''figure'' is simply the noise ''factor'' expressed in [[decibel]]s (dB).<ref>http://www.satsig.net/noise.htm</ref>
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| == General ==
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| 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 matched sources at the standard [[noise temperature]] ''T''<sub>0</sub> (usually 290 K). The noise power from a simple [[Electrical load|load]] is equal to ''k T B'', where ''k'' is [[Boltzmann's constant]], ''T'' is the [[absolute temperature]] of the load (for example a [[resistor]]), and ''B'' is the measurement bandwidth.
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| 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.<ref>{{Harvnb|Agilent|2010|p=7}}</ref> 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 input noise temperature|effective noise temperature]]'' is therefore often used instead of the noise figure for characterizing satellite-communication receivers and [[low noise amplifier]]s.
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| 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.
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| == Definition ==
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| The '''noise factor''' ''F'' of a system is defined as:<ref>{{Harvnb|Agilent|2010|p=5}}</ref>
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| :<math>F = \frac{\mathrm{SNR}_\mathrm{in}}{\mathrm{SNR}_\mathrm{out}}</math> | |
| where SNR<sub>in</sub> and SNR<sub>out</sub> are the input and output [[signal-to-noise ratio]]s, respectively. The SNR quantities are power ratios.
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| The noise figure NF is defined as:
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| :<math>\mathrm{NF} = 10 \log(F) = 10 \log\left(\frac{\mathrm{SNR}_\mathrm{in}}{\mathrm{SNR}_\mathrm{out}}\right) = \mathrm{SNR}_\mathrm{in, dB} - \mathrm{SNR}_\mathrm{out, dB}</math>
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| where SNR<sub>in, dB</sub> and SNR<sub>out, dB</sub> are in [[decibel]]s (dB). The noise figure is the noise factor, given in dB:
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| :<math>\mathrm{NF} = 10 \log \left(F\right)</math> | |
| These formulae are only valid when the input termination is at standard [[noise temperature]] ''T''<sub>0</sub>, although in practice small differences in temperature do not significantly affect the values.
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| The noise factor of a device is related to its [[noise temperature]] ''T''<sub>e</sub>:<ref>{{Harvnb|Agilent|2010|p=7}} with some rearrangement from ''T''<sub>e</sub>=''T''<sub>0</sub>(''F''-1).</ref>
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| :<math>F = 1 + \frac{T_e}{T_0}</math>
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| [[Attenuator (electronics)|Attenuators]] have a noise factor ''F'' equal to their attenuation ratio ''L'' when their physical temperature equals ''T''<sub>0</sub>. More generally, for an attenuator at a physical temperature ''T'', the noise temperature is <math>T_\mathrm{e} = (L-1)T</math>, giving a noise factor of: | |
| :<math>F = 1 + \frac{(L-1)T}{T_0}</math>
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| If several devices are cascaded, the total noise factor can be found with [[Friis formulas for noise|Friis' Formula]]:<ref>{{Harvnb|Agilent|2010|p=8}}</ref>
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| :<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>
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| where ''F''<sub>''n''</sub> is the noise factor for the ''n''-th device and ''G''<sub>n</sub> is the [[power gain]] (linear, not in dB) of the ''n''-th device. The first amplifier in a chain has the most significant effect on the total noise figure than any
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| other amplifier in the chain. The lower noise figure amplifier should usually go first in a line of
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| amplifiers (assuming all else is equal).
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| == See also ==
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| * [[Noise]]
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| * [[Noise (electronic)]]
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| * [[Noise figure meter]]
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| * [[Noise level]]
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| * [[Thermal noise]]
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| * [[Signal-to-noise ratio]]
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| * [[Y-factor]]
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| ==References==
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| {{Reflist}}
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| *{{Citation |last=Agilent |title=Fundamentals of RF and Microwave Noise Figure Measurements |date=August 5, 2010 |url=http://cp.literature.agilent.com/litweb/pdf/5952-8255E.pdf |series=Application Note |id=57-1 |doi= }}
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| ==External links==
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| * [http://www.emtalk.com/tools/noise-figure-calculator.php Noise Figure Calculator] 2- to 30-Stage Cascade
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| * [http://testrf.com/2011/noise-figure-uncertainties-y-factor-method/ Noise Figure and Y Factor Method Basics and Tutorial]
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| {{Noise}}
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| {{FS1037C MS188}}
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| [[Category:Noise]]
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| [[Category:Radar signal processing]]
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Name: Salvatore Hersom
My age: 34
Country: Norway
Home town: Moss
ZIP: 1535
Street: Bukkespranget 25
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