{{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 and noise temperature of an amplifier. It is based on the Johnson–Nyquist noise of a 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 amplifier with a 50-ohm impedance with a 50-ohm resistor connected to the amplifier input. If the resistor is at a physical 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, 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. 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) 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