Y-factor

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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_BT_RB, 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.