Madeline Horn edited untitled.tex  over 8 years ago

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To perform the Johnson Noise Experiment, we used the Noise Fundamentals devices and two digital multi-meters. Our settings for the Noise Fundamentals devices were as follows: 10K ohm resistor, we used a Gain of 1000 for all values, we used a room temperature of 295 degrees Kelvin, and we varied the high and low pass filters' frequency for each data set in order to vary the bandwidth. We varied our high pass filter one as follows: we started with 10 Hz, 30 Hz, 100 Hz, 300 Hz, 1000 Hz, and 3000 Hz. We varied our low pass filter as follows: we started with 0.33K Hz, 1K Hz, 3.3K Hz, 10K Hz, 33K Hz, and 100K Hz. We recorded all the values from the multi-meter for each combination of filters. For example, when we had a low pass of 0.33K Hz, a high pass of 10 Hz, our measured value was $5.13$ mV. In the end, we took 36 sets of data points.  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: $V^2 = 4*K*T*R*/Delta 4*K*T*R*\Delta  f$, where K is the Boltzmann Constant we are looking for, T is the temperature in Kelvin, R is the resistance in ohms, and $/Delta $\Delta  f$ is the bandwidth that we varied by changing the values on the low and high pass filters. After plotting $V^2$ versus Bandwidth ($/Delta ($\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 $1.908 * 10^-23 m^2 kg s^-2 K^-1$. 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.  When we recorded the data, we needed to find the error in the instruments in order to find the systematic error and eliminate it from our recorded values of both Vsq and the voltage across the photo-diode. In order to do this, every time we changed our gain, we had to drop the voltage across the photo-diode to 0V and record the systematic error in both multi-meters.  Once we had taken values across the photo-diode from 0 to 120 mV in steps of 10 mV, had our error in all the values, we were able to start calculating the current from both mulitmeters. In order to find the current from the voltage across the photo-diode, we only had to use Ohm's Law (V = IR) beause we knew the value of R, 10K ohms. Finding the current for Vsq was harder because we had to account for the change through the amplifiers and multiplier. The equation we used to find the filtered current was: 10 * Vsq = 2 * e *i_dc * \Delta f * (G1 * G2 * Resistance)^2, where e is the charge of the electron that we are looking for, R is the resistance of 10K ohms, and G2 varied