Johnson noise in \(1k \Omega\) Resistor

Our settings for the Noise Fundamentals devices were as follows: \(1k \Omega\) resistor, we used a Gain 1 (\(G1\)) of \(\times600\) for all values that comes directly from the Noise Fundamental device, a Gain 2 (\(G2\)) of \(\times1000\) for all values, we used a room temperature of \(296\) degrees Kelvin, and we varied the high and low pass filters’ frequency for each data set in order to vary the bandwidth. In Table \ref{table:Johnson1}, you can see how we varied the low pass filter (\(f2\)) and the high pass filter (\(f1\)) in order to change the bandwidth. The values are taken from the multi-meter after going through the filters, gain, and multiplier - passing through the \(A \times A\) multiplier and then being divided by 10 Volts. All of the values are in mV; we took \(36\) sets of data points. You can see all these values in TABLE \ref{table:Johnson2}.

The values in TABLE \ref{table:Johnson2} are explained by the following equation:

\(V_{\textrm{meter}} = (<V_J>^2 + <V_{\textrm{amplifiers}}>^2) G_1 G_2 / (10 \textrm{Volts}) \textrm{ [mV]}\)

where the factor of \(10 \textrm{Volts}\) comes from the amplifier and the \(<V_J>^2 + <V_{\textrm{amplifiers}}>^2\) is the measured voltage from the multi-meter before the error has been subtracted.