feat: Compile experimental results in one place

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Martin Kennedy 2025-02-17 17:36:39 -05:00
parent 9908777345
commit 0a48d33888
2 changed files with 85 additions and 6 deletions

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

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