The Y-factor method is a widely used technique for measuring the gain and noise temperature of an amplifier. It is based on the JohnsonâÂÂNyquist noise of a resistor at two different, known temperatures.
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 JohnsonâÂÂNyquist 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>âÂÂ+âÂÂT<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 âÂÂT<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.