# Y-factor

> Mediated Wiki article. Canonical URL: https://mediated.wiki/source/Y-factor
> Markdown URL: https://mediated.wiki/source/Y-factor.md
> Source: https://en.wikipedia.org/wiki/Y-factor
> Source revision: 1305556210
> License: Creative Commons Attribution-ShareAlike 4.0 International (https://creativecommons.org/licenses/by-sa/4.0/)

{{Short description|Method for determining noise temperature}}
{{One source|date=August 2025}}
The '''Y-factor''' method is a widely used technique for measuring the [gain](/source/Gain_(electronics)) and [noise temperature](/source/noise_temperature) of an [amplifier](/source/Electronic_amplifier). It is based on the [Johnson–Nyquist noise](/source/Johnson%E2%80%93Nyquist_noise) of a [resistor](/source/resistor) at two different, known temperatures.<ref>{{Citation|title=Noise Figure Measurement Accuracy – The Y-Factor Method|url=http://literature.cdn.keysight.com/litweb/pdf/5952-3706E.pdf|year=2010|series=Application Note 57-2|publisher=Keysight Technologies|access-date=2 September 2011}}</ref>

thumb|alt=Plot used in the Y-factor method for determining the gain and noise temperature of an amplifier.|Plot used in the Y-factor method for determining the gain and noise temperature of an amplifier 

Consider a [microwave](/source/microwave) amplifier with a 50-[ohm](/source/ohm) [impedance](/source/Electrical_impedance) with a 50-ohm resistor connected to the amplifier input. If the resistor is at a physical [temperature](/source/temperature) ''T''<sub>R</sub>, then the Johnson–Nyquist noise power coupled to the amplifier input is ''P''<sub>J</sub> = ''k''<sub>B</sub>''T''<sub>R</sub>''B'', where ''k''<sub>B</sub> is the [Boltzmann constant](/source/Boltzmann_constant), and ''B'' is the bandwidth. The noise power at the output of the amplifier (i.e. the noise power coupled to an impedance-matched load that is connected to the amplifier output) is ''P''<sub>out</sub> = ''Gk''<sub>B</sub>(''T''<sub>R</sub> + ''T''<sub>amp</sub>)''B'', where ''G'' is the amplifier power gain, and ''T''<sub>amp</sub> is the amplifier [noise temperature](/source/noise_temperature). In the Y-factor technique, ''P''<sub>out</sub> is measured for two different, known values of ''T''<sub>R</sub>. ''P''<sub>out</sub> is then converted to an effective temperature ''T''<sub>out</sub> (in units of [kelvin](/source/kelvin)) by dividing by ''k''<sub>B</sub> and the measurement bandwidth ''B''. The two values of ''T''<sub>out</sub> are then plotted as a function of ''T''<sub>R</sub> (also in units of kelvin), and a line is fit to these points (see figure). The slope of this line is equal to the amplifier power gain. The ''x'' intercept of the line is equal to the negative of the amplifier noise temperature −''T''<sub>amp</sub> in kelvins. The amplifier noise temperature can also be determined from the ''y'' intercept, which is equal to ''T''<sub>amp</sub> multiplied by the gain.

== References ==
{{reflist}}

Category:Microwave technology
Category:Radio technology
Category:Electrical engineering
Category:Electronic engineering

---
Adapted from the Wikipedia article [Y-factor](https://en.wikipedia.org/wiki/Y-factor) by Wikipedia contributors ([contributor history](https://en.wikipedia.org/wiki/Y-factor?action=history)). Available under [Creative Commons Attribution-ShareAlike 4.0 International](https://creativecommons.org/licenses/by-sa/4.0/). Changes may have been made.