Madeline Horn edited subsection_Method_for_Johnson_Noise__.tex  over 8 years ago

Commit id: 5f10df317ccce54196e0c94823aa86d8b137d6e8

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To get the best measurement of Johnson Noise, we wanted to vary the $R_{in}$ from $10 \textrm{ k}\Omega$, $1 \textrm{ k}\Omega$ and $1 \Omega$. This is important because if our apparatus and measurements are correct, all of the different $R_{in}$ should generate the same value for the Johnson Noise, $k_B$. The $10 \textrm{ k}\Omega$ and $1 \textrm{ k}\Omega$ were used to calculate the $k_B$ while the $1 \Omega$ measurement was used as an error source that needed to be subtracted. As with all electronics, there is some innate error associated with the device, in order to subtract this, we took data with the $1 \Omega$ resistor.  As seen in equation \ref{eq:NyquistPredictionForJohnsonNoise2}, we will be measuring the $<(V_J + V_{\textrm{other noise}})^2>$.  \textbf{YOU NEED SOME SORT OF preliminary explanation} of what you are doing here before showering us with specific examples. For example, why data at $10 \textrm{ k}\Omega$, $1 \textrm{ k}\Omega$ and $1 \Omega$? The reader needs to know this before you start giving her the results for each of these cases.   This should be a reasonably straightforward explanation to provide if you refer to what you expect from the Johnson noise equation and an additional equation explaining how what you measure is a combination of Johnson noise and other sources. That explanation should include an explanation of why the formula involves $$ and $$ as opposed to $$ and $$ or $<(V_J + V_{\textrm{other noise}})^2>$, for example.