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Lucy Liang added subsubsection_Johnson_noise_in_1k__1.tex
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\subsubsection{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 \ref{table:Johnson2}.
The values in \ref{table:Johnson2} are explained by the following equation:
$V_{\textrm{meter}} = (^2 + ^2) G_1 G_2 / (10 \textrm{Volts}) \textrm{ [mV]}$
where the factor of $10 \textrm{Volts}$ comes from the amplifier and the $^2 + ^2$ is the measured voltage from the multi-meter before the error has been subtracted.
