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Johnny Hsu 2025-03-27 16:46:25 +01:00
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temperature-measurement-error/temperature-measurement-error.pdf
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temperature-measurement-error/temperature-measurement-error.tex
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@ -32,7 +32,7 @@
\begin{document}
\begin{wrapfigure}{l}{0.4\textwidth}
\includegraphics[width=1\linewidth]{./Pictures/NTC-schematic.png}
\includegraphics[width=1\linewidth]{./Pictures/NTC-schematic.png}
\caption{NTC Voltage Divider and Filter}
\label{fig:NTC-schematic}
\end{wrapfigure}
@ -48,23 +48,23 @@ The output voltage is then passed through an RC filter before being fed to an AD
To estimate the error, we calculate the highest possible measured voltage at \SI{60}{\celsius}.
According to the design of the voltage divider, the lower the temperature, the higher the output voltage.
As shown in Fig. \ref{fig:vref2}, the supply voltage VREF2 for the voltage divider can reach a maximum value of \SI{3.006}\volt.
As shown in Fig. \ref{fig:vref2}, the supply voltage $V_{REF2}$ for the voltage divider can reach a maximum value of \SI{3.006}\volt.
Additionally, the total measurement error of the GPIO is $\pm\SI{0.0028}{\volt}$ (as shown in Fig. \ref{fig:aux}).
Lastly, the maximum resistance of the NTC at \SI{60}{\celsius}, according to the LUT (Tab. \ref{tab:lut}), is \SI{3086.8}{\ohm}.
The maximum possible voltage measurement can then be calculated as such:
\begin{align}
V_{worstcase} &= V_{REF2} \cdot \frac{R_{NTC}}{R_{NTC}+R_1} + V_{err} \\
&= \SI{3.006}\volt \cdot \frac{\SI{3086.8}{\ohm}}{\SI{3086.8}{\ohm}+\SI{9990}{\ohm}} + \SI{0.0028}{\volt} \\
&\approx \SI{0.7124}{\volt}
V_{worstcase} & = V_{REF2} \cdot \frac{R_{NTC}}{R_{NTC}+R_1} + V_{err} \\
& = \SI{3.006}\volt \cdot \frac{\SI{3086.8}{\ohm}}{\SI{3086.8}{\ohm}+\SI{9990}{\ohm}} + \SI{0.0028}{\volt} \\
& \approx \SI{0.7124}{\volt}
\end{align}
To find the largest possible error, the lowest possible matching temperature should be calculated, which theoretically can produce the same voltage output. The calculation is as follows:
\begin{align}
V_{worstcase} &= V_{REF2} \cdot \frac{R_{NTC}}{R_{NTC}+R_1} + V_{err} \\
\SI{0.7124}{\volt} &= \SI{2.994}{\volt} \cdot \frac{R_{NTC}}{R_{NTC}+\SI{10010}{\ohm}} - \SI{0.0028}{\volt} \\
R_{NTC} &\approx \SI{3141.6}{\ohm}
V_{worstcase} & = V_{REF2} \cdot \frac{R_{NTC}}{R_{NTC}+R_1} + V_{err} \\
\SI{0.7124}{\volt} & = \SI{2.994}{\volt} \cdot \frac{R_{NTC}}{R_{NTC}+\SI{10010}{\ohm}} - \SI{0.0028}{\volt} \\
R_{NTC} & \approx \SI{3141.6}{\ohm}
\end{align}
Since the LUT is used to match the voltage to the temperature, and the nominal resistance from the LUT is used for the calculation, the closest matching temperature is \SI{58.7}{\celsius}.
@ -128,7 +128,7 @@ Since the LUT is used to match the voltage to the temperature, and the nominal r
\bibitem{ADBMS6830B datasheet} \textit{Table 3 Data Sheet ADBMS6830B Rev.0 page 6}. \hyperlink{https://www.analog.com/media/en/technical-documentation/data-sheets/adbms6830b.pdf}{www.analog.com}, 01.2024
\bibitem{ADBMS6830B datasheet} \textit{Table 5 Data Sheet ADBMS6830B Rev.0 page 7}. \hyperlink{https://www.analog.com/media/en/technical-documentation/data-sheets/adbms6830b.pdf}{www.analog.com}, 01.2024
\bibitem{vishay website} \textit{NTC RT Calculation Tool}. \hyperlink{https://www.vishay.com/en/thermistors/ntc-rt-calculator/}{www.vishay.com}, 03.2025
\end{thebibliography}
\end{document}