To analyze this data, we made a plot of resistance (ohms) versus \(V^2\) so that we could analyze the slope. The equation used to understand why we did this is: \[\label{eq:boltzmann} V^2 = 4 K T R \Delta f\] where K is the Boltzmann Constant we are looking for, T is the temperature in Kelvin, R is the resistance in ohms, and \(\Delta f\) is the “equivalent noise bandwidth” (ENBW) that we varied by changing the values on the low and high pass filters.

This would be a good place to point out that the reason to find the slope is that it is proportional to \(k_B\) or, if you prefer, equal to \(k_B T \Delta f\).

In order to find the bandwidth, we had to use values that came from the Noise Fundamentals Test Data (Table 2), which gave us the measured values from the filters. You can see the values we used in Table 2, and as you can see, the measured values are different from the nominal values. After using the measured values from the Noise Fundamentals test data, we had to calculate the Equivolent Noise Bandwidth (ENBW) in order to find \(\Delta f\). To do this, we used an equation: \[\label{eq:ENBW} ENBW = \left(\frac{\pi}{2} \ Q\right) f_c\]

what is \(f_c\)? This needs to be defined.

Since you’ve just made a point of the fact that the ENBW \(\Delta f \neq f_2 - f_1\), this would be a good place for a table listing \(R\), \(f_1\), \(f_2\), and ENBW values for each of the three measurements.