  # Y-Factor

## What is the Y-Factor?

Y-Factor refers to a popular technique for measuring the gain and noise temperature of an amplifier. Appropriately named the Y-factor method, the technique is based upon the Johnson-Nyquist noise of a resistor at two different, but known, temperatures. The process allows for one to plot out the function of gain and noise to determine and predict changes from the amplifier.

## How does the Y-Factor method work?

To begin, the noise power at the output of the amplifier is measured at two different values of physical temperature, dubbed Tr. The output is then converted to an effective temperature in units of kelvin by dividing by Boltzmann's constant and the measurement of bandwidth. The resulting two values are then plotted as a function of Tr, notated in kelvin, and a line is drawn to fit to the points. The slope of the line is equivalent to the amplifier's power gain. The x-intercept of the line is equal to the negative of the amplifier noise temperature, also in kelvin. The amplifier noise temperature can also be calculated from the y-intercept by multiplying the noise temperature by the gain.
Note in the graphic, the Y-factor method produced two points in the space from which a line can be drawn to determine the amplifier's power gain. Tout is the effective output temperature, Tr is the physical temperature of the resistor, and -Tamp is the x-intercept representing the negative of the amplifier noise temperature. All temperatures are recorded in units of kelvin.