Y-factor
# 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 $P_J$ = $k_BT_RB,$ 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.

