deletions | additions       diff --git a/subsection_Johnson_Noise_Johnson_noise__.tex b/subsection_Johnson_Noise_Johnson_noise__.tex  index 271cd58..e3c2b33 100644  --- a/subsection_Johnson_Noise_Johnson_noise__.tex  +++ b/subsection_Johnson_Noise_Johnson_noise__.tex 
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Johnson noise is the electric noise generated from small thermal fluctuations of the electrons through an electrical conductor. Thermal noise arises because the electrons create a random, and measurable, fluctuation in voltage. Johnson noise is also given the name "Nygquist noise" because it was correctly predicted and explained by H. Nyquist, but Johnson was the first to measure it.  As published in NYQUIST THING, NYQUIST,  the root mean square of ac voltage when no current is flowing is as follows: \begin{equation}  \label{eq:Equatoin} 
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V_{\textrm{Johnson noise, RMS}} = \sqrt{} = \sqrt{(4 R \Delta f) (k_B T) }  \end{equation}  where R is the resistance of the resistor, $\delta f$ is the equivolent equivalent  noise bandwidth (ENBW), $k_B$ is the Boltzmann constant (what we are hoping to reproduce), $T$ is the temperature of the room, and $\sqrt{}$ is the measured voltage from the preamp. The ENBW is what we use to represent the frequencies we use in order to vary the ac voltage that is generated from the random fluctuations of electrons within the resistor. We will be measuring the $\sqrt{}$, the $\delta f$, the $T$, and the $R$ in order to find the $k_B$.