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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{document}
\begin{wrapfigure}{l}{0.4\textwidth} \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} \caption{NTC Voltage Divider and Filter}
\label{fig:NTC-schematic} \label{fig:NTC-schematic}
\end{wrapfigure} \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}. 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. 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}). 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}. 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: The maximum possible voltage measurement can then be calculated as such:
\begin{align} \begin{align}
V_{worstcase} &= V_{REF2} \cdot \frac{R_{NTC}}{R_{NTC}+R_1} + V_{err} \\ 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} \\ & = \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} & \approx \SI{0.7124}{\volt}
\end{align} \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: 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} \begin{align}
V_{worstcase} &= V_{REF2} \cdot \frac{R_{NTC}}{R_{NTC}+R_1} + V_{err} \\ 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} \\ \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} R_{NTC} & \approx \SI{3141.6}{\ohm}
\end{align} \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}. 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 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{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 \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{thebibliography}
\end{document} \end{document}