diff --git a/Lab1.tex b/Lab1.tex index 171e52b..10c7e5c 100644 --- a/Lab1.tex +++ b/Lab1.tex @@ -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 diff --git a/lab1breadboard.jpg b/lab1breadboard.jpg new file mode 100644 index 0000000..b3f3309 Binary files /dev/null and b/lab1breadboard.jpg differ