Madeline Horn edited untitled.tex  over 8 years ago

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In order to find the Boltzmann constant and the charge of the electron, we had to perform the Johnson Noise Experiment and the Shot Noise Experiment. We performed the Johnson Noise Experiment in order to find the Boltzman Constant: $1.38064852 × 10^{-23} \textrm{ m}^2 \textrm{ kg} \textrm{ s}^{-2} \textrm{ K}^{-1}$. We performed the Shot Noise Experiment in order to find the charge of an electron: 1.60217662 × 10-19 coulombs.  To analyze this data, we made a plot of resistance (ohms) versus $V^2$ so that we could analyze the slope. The equation used to understand why we did this is: $V^2 = 4 K T R \Delta f$, where K is the Boltzmann Constant we are looking for, T is the temperature in Kelvin, R is the resistance in ohms, and $\Delta f$ is the bandwidth that we varied by changing the values on the low and high pass filters. After plotting $V^2$ versus Bandwidth ($\Delta f$), we were able to find the slope. Because of how we plotted the data, the slope is therefore: $4 K R T$ and we know the values of R and T because we kept them constant. After solving for K, we found the Boltzmann Constant for our data to be $1.908 * 10^{-23} \textrm{ m}^2 \textrm{ kg} \textrm{ s}^{-2} \textrm{ K}^{-1}$. This is close to the actual Boltzmann Constant, but we still need to subtract error in order to see if we got a better value.  \textit{Shot Noise}  To perform the Shot Noise Experiment, we used the Noise Fundamentals devices and two digital multi-meters. Our settings for the Noise Fundamentals devices were as follows: we used the trans-impedance amplifier with a resistance of 10K ohm, a Gain (G1) of 100 through the preamp, we used a bandwidth of 100K Hz which has an equivalent noise bandwidth of 115.303K Hz, and we varied the voltage across the photo-diode from 0 to -120 mV. To avoid saturating the values of Vsq (read from the multimeter attached after the signal (Vsq) went through the filter, the gain, and the multiplier) we had to vary the gain (G2) from 5000, to 4000, and finally to 3000. Our multiplier had a setting of AxA because we needed to square the signal. We recorded the Vsq values in Volts and we recorded the V across the photo-diode in mV. Vsq is the signal that has been filtered.