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.^[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 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 $P_{out} = Gk_{B}(T_{R}%2BT_{amp})B$ , where G is the amplifier power gain and $T_{amp}$ is the amplifier noise temperature. For 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 two points (see figure). The slope of this line is equal to the amplifier power gain. The x-intercept of the line is equal the negative of the amplifier noise temperature - $T_{amp}$ in kelvin.

References

^ Noise Figure Measurement Accuracy – The Y-Factor Method, Application Note 57-2, Agilent Technologies, 2010, http://cp.literature.agilent.com/litweb/pdf/5952-3706E.pdf, retrieved 2 September 2011