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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.^{[1]}

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*_{R}, then the Johnson–Nyquist noise power coupled to the amplifier input is *P*_{J} = *k*_{B}*T*_{R}*B*, where *k*_{B} 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*_{out} = *Gk*_{B}(*T*_{R} + *T*_{amp})*B*, where *G* is the amplifier power gain, and *T*_{amp} is the amplifier noise temperature. In the Y-factor technique, *P*_{out} is measured for two different, known values of *T*_{R}. *P*_{out} is then converted to an effective temperature *T*_{out} (in units of kelvin) by dividing by *k*_{B} and the measurement bandwidth *B*. The two values of *T*_{out} are then plotted as a function of *T*_{R} (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*_{amp} in kelvins. The amplifier noise temperature can also be determined from the *y* intercept, which is equal to *T*_{amp} multiplied by the gain.

**^***Noise Figure Measurement Accuracy – The Y-Factor Method*(PDF), Application Note 57-2, Keysight Technologies, 2010, retrieved 2 September 2011