feat: conclusion, first pass

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Martin Kennedy 2025-02-18 00:13:10 -05:00
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@ -253,6 +253,9 @@ 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.
Note: our use of the oscilloscope for magnitude measurements will
later be identified as a key source of error.
\subsection{Experiment ~\ref{type:ac} (sinusoidal AC)}
Given a read period of $T$ seconds, we calculate the frequency as
@ -465,7 +468,27 @@ As for the second question:
the DMM is showing the true RMS regardless of the waveform.
\end{quote}
We have arrived independently at RMS voltage values multiple ways, and
have discovered that no waveform yields a particularly higher error
for RMS voltage than any other; in fact, more specifically, the
highest error values are associated only with our analytical
derivation, which relies on an oscilloscope-derived magnitude reading.
I'll review the oscilloscope-derived magnitude problem in a moment,
but I wanted to finish my point abaout the suitability of the DMM to
produce RMS voltage measurements: the lack of particularly high error
values when comparing experimental (DMM) RMS values for any of our
various waveforms indicates that the DMM's suitability does not,
within reason, depend on the waveform it's measuring.
As for our error: our largest cases of error are when comparing our
experimental and numerical results to our analytical results for 2V
square-wave AC. Despite setting the function generator to 2V, our
oscilloscope nevertheless read a peak-to-peak magnitude of 4.22 and
4.26V (so, a peak-magnitude 2.11V of 2.13V, respectively). This likely
has to do with how the oscilloscope regisers peak-to-peak voltages,
relying on hazy extremes; but also, notably, because we had our
oscilloscope in 10X mode, reducing its signal sensitivity / resolution.
\nocite{*}
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