deletions | additions       diff --git a/section_Experiment_on_Johnson_Noise__.tex b/section_Experiment_on_Johnson_Noise__.tex  index 27e0f72..4d4dd47 100644  --- a/section_Experiment_on_Johnson_Noise__.tex  +++ b/section_Experiment_on_Johnson_Noise__.tex 
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%but did three different trials where each trial had a different $R$ value. The values for $R$ are as follows: $10 \textrm{ k}\Omega$, $1 \textrm{ k}\Omega$, and $1 \Omega$. As with any resistor, there is error in the measurement and Table \ref{table:True_Resistance}, shows the true, measured value of the resistance. You can perform the Johnson Noise experiment by varying resistance for a given bandwidth ($\Delta f$), but we chose to vary $\Delta f$ and keep resistance constant.  We %We  chose to do this because if our apparatus and measurements are correct, all of the different $R_{in}$ should generate the same value for the Johnson Noise, $k_B$. We chose the three different resistances because 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. The goal is to find a ratio in which both the numerator and denominator get bigger as you increase $R_{in}$ (the resistor that is the source of the voltage fluctuations), so the slope $k_B$ remains the same. Nyquist %Nyquist  found theoretically that the ratio found in Equation \ref{eq:Equatoin} to produces $k_B$ if you change $R$ just as long as you don't change $T$ or $\Delta f$. That means the slope should also remain constant. Because %Because  we want to keep the $R$ the same, we decided to vary $\Delta f$, so we needed to have a set-up where there were both a low pass and a high pass filters. This way, we could vary $\Delta f$ with 36 different settings. We also used two amplifiers in order to amplify the desired signal. Those values were: $X600$ for the first gain and $X1000$ for the second gain. We also squared the signal (an amplifier of AxA) in order to measure the voltage as: $<(V_J + V_{\textrm{other noise}})^2>$. As seen in equation \ref{eq:NyquistPredictionForJohnsonNoise2}, we \ref{eq:NyquistPredictionForJohnsonNoise2} and since there is instrumental noise, our resulting signal $V_{mult}$  will bemeasuring the  $<(V_J + V_{\textrm{other noise}})^2>$. To obtain all of our voltage values for Johson Noise, we averaged 100 data points using the multi-meter. This reduced our error significantly as instead of 36 data points per resistance, there are actually 3,600 data points.