Y-factor

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.
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 Boltzmann’s 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.