feat: Compile experimental results in one place
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Lab1.tex
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Lab1.tex
@ -178,9 +178,43 @@ $(v_{\ref{type:squarewave}}(t))^{2}={V_{m}}^{2}$:
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We will reference these three derivations in our ``Experimental Results'' section below.
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\section{Numerical Modeling Results}
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\section{Experimental Results}
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\section{Data Comparison}
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\section{Conclusions}
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\begin{figure}[h]
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\caption{Breadboard, with resistor $R$ connected to our DMM, scope and function generator}
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\label{fig:breadboard}
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\centering
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\includegraphics[width=\textwidth]{lab1breadboard}
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\end{figure}
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The circuit we implemented can be seen in
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Figure~\ref{fig:breadboard}. This configuration connects one resistor
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leg with the signal lead of the oscilloscope, the positive lead each
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of the function generator and DMM; repeat the same with the other
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resistor leg, the ground lead of the scope, and the negative leads of
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each the DMM and function generator. In effect, all pieces of
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equipment are placed in parallel, consistent with any other procedure
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for measuring the facets of a signal's voltage.
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(Our circuit builder was Peyton; our checker was Will; I was grouped
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with these two as there were an odd number of students.)
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We used this configuration for the entire lab procedure, and adjusted
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both our function generator and oscilloscope through the variations of
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the three different signal types; in all three cases, we first used
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the oscilloscope to read the period and magnitude of the signal, and
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then used the DMM to measure the signal's RMS voltage.
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\subsection{Experiment ~\ref{type:ac} (sinusoidal AC)}
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Given a read period of $T$ seconds, we calculate the frequency as
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$\frac{1}{T}$ Hz. For the RMS voltage, we use the formula derived at
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Equation ~\ref{deriv:ac}:
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\begin{equation*}
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V_{\ref{type:ac}RMS} = \frac{V_{m}}{\sqrt{2}}
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\end{equation*}
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\begin{longtable}[]{@{}lllllllll@{}}
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\toprule
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@ -188,12 +222,57 @@ We will reference these three derivations in our ``Experimental Results'' sectio
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\bottomrule
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\endlastfoot
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Set Mag. & Set Freq. & Read Mag. & Read Period & Calc. Freq. & Calc. RMS & Meas. RMS \\
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2V & 100 Hz & 2.10 V & 9.994 ms & XXXXXHz & .....V & 1.4236 V \\
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2V & 50 kHz & 2.05 V & 19.947 us & a & d & 1.4112 V \\
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5V & 100 Hz & 5.11 V & 10.007 ms & b & e & 3.5522 V \\
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5V & 50 kHz & 5.11 V & 20.005 us & c & f & 3.5451 V \\
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2V & 100 Hz & 2.10 V & 9.994 ms & 100.1 Hz & 1.48 V & 1.4236 V \\
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2V & 50 kHz & 2.05 V & 19.95 us & 50.13 kHz & 1.45 V & 1.4112 V \\
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5V & 100 Hz & 5.11 V & 10.01 ms & 99.90 Hz & 3.61 V & 3.5522 V \\
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5V & 50 kHz & 5.11 V & 20.01 us & 49.98 kHz & 3.61 V & 3.5451 V \\
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\end{longtable}
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\subsection{Experiment ~\ref{type:acoffset} (sinusoidal AC with DC offset)}
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Given a read period of $T$ seconds, we calculate the frequency as
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$\frac{1}{T}$ Hz. For this signal's RMS voltage, we use the formula derived at
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Equation ~\ref{deriv:acoffset}:
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\begin{equation*}
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V_{\ref{type:acoffset}RMS} = \sqrt{\frac{V_{m}^{2}}{2} + V_{b}^{2}}
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\end{equation*}
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TODO NOTE ERROR could not check dc offset voltage bias
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\begin{longtable}[]{@{}lllllllll@{}}
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\toprule
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\endhead
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\bottomrule
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\endlastfoot
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Set Mag. & Set Freq. & DC bias & Read Mag. & Read Period & Calc. Freq. & Calc. RMS & Meas. RMS \\
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2V & 100 Hz & 2V & 2.13 V & 10.00 ms & 100.0 Hz & 2.50 V & 2.44 V \\
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2V & 100 Hz & -5V & 2.11 V & 9.996 ms & 100.0 Hz & 5.22 V & 5.19 V \\
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5V & 100 Hz & 2V & 5.15 V & 9.998 ms & 100.0 Hz & 4.15 V & 4.05 V \\
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5V & 100 Hz & -5V & 5.20 V & 9.997 ms & 100.0 Hz & 6.21 V & 6.16 V \\
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\end{longtable}
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\subsection{Experiment ~\ref{type:squarewave} (square wave)}
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Given a read period of $T$ seconds, we calculate the frequency as
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$\frac{1}{T}$ Hz. As we saw when deriving Equation
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~\ref{deriv:squarewave}, this signal's RMS voltage is the same as its
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magnitude.
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\begin{longtable}[]{@{}lllllllll@{}}
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\toprule
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\endhead
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\bottomrule
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\endlastfoot
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Set Mag. & Set Freq. & Duty & Read Mag. & Read Period & Calc. Freq. & Calc. RMS & Meas. RMS \\
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2V & 100 Hz & 25\% & 2.11 V & 10.00ms & 100.0 Hz & 2.11 V & 2.02 V \\
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2V & 100 Hz & 50\% & 2.13 V & 10.00ms & 100.0 Hz & 2.13 V & 2.01 V \\
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5V & 100 Hz & 25\% & 5.20 V & 9.998ms & 100.0 Hz & 5.20 V & 5.04 V \\
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5V & 100 Hz & 50\% & 5.20 V & 9.999ms & 100.0 Hz & 5.20 V & 5.01 V \\
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\end{longtable}
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\section{Data Comparison}
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\section{Conclusions}
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\nocite{*}
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\printbibliography
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lab1breadboard.jpg
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