135 lines
7.8 KiB
TeX
135 lines
7.8 KiB
TeX
\documentclass[paper=A4]{article}
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\usepackage[utf8]{inputenc}
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\usepackage[a4paper, left=2cm, right=2cm, top=2cm, bottom=2cm]{geometry}
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\usepackage{siunitx}
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\sisetup{
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group-separator = {.},
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input-decimal-markers={.},
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output-decimal-marker = {.},
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group-minimum-digits=9}
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\usepackage{graphicx}
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\usepackage{fancyhdr}
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\usepackage{lastpage}
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\usepackage{subfigure}
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\usepackage{float}
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\usepackage{wrapfig}
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\usepackage{multicol}
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\usepackage{amsmath, amssymb}
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\usepackage{hyperref}
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\hyphenpenalty=10000 %to stop cutting words in a paragraph
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\pagestyle{fancy}
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\fancyhf{}
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\rhead{\includegraphics*[scale=0.013]{./Pictures/FaSTTUBe_Logo_ohneAuto.png}}
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\rfoot{Page \thepage \hspace{1pt} of \pageref{LastPage}}
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\lhead{Car 313, 06.03, Rev. 1}
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\chead{\large Temperature Measurement Error Calculation}
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\begin{document}
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\begin{wrapfigure}{l}{0.4\textwidth}
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\includegraphics[width=1\linewidth]{./Pictures/NTC-schematic.png}
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\caption{NTC Voltage Divider and Filter}
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\label{fig:NTC-schematic}
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\end{wrapfigure}
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The following calculation is based on the Look-Up Table (LUT) provided by Vishay\cite{vishay website}, which is used in the AMS software.
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Since the characteristic curve of the NTC thermistor is nonlinear, determining the absolute maximum measurement error is not straightforward.
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Therefore, we will calculate the maximum error specifically at \SI{60}{\celsius}.
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As seen in Fig.\ref{fig:NTC-schematic} our voltage measurement system consists of an NTC thermistor (NTCLE413E2103F102L) and a \SI{10}{\kilo\ohm} 0.1\% resistor forming a voltage divider.
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The output voltage is then passed through an RC filter before being fed to an ADC.
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To estimate the error, we calculate the highest possible measured voltage at \SI{60}{\celsius}.
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According to the design of the voltage divider, the lower the temperature, the higher the output voltage.
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As shown in Fig. \ref{fig:vref}, the supply voltage $V_{REF2}$ for the voltage divider can reach a maximum value of \SI{3.006}\volt.
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Additionally, the total measurement error of the GPIO is $\pm\SI{0.0028}{\volt}$ (as shown in Fig. \ref{fig:aux}).
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Lastly, the maximum resistance of the NTC at \SI{60}{\celsius}, according to the LUT (Tab. \ref{tab:lut}), is \SI{3086.8}{\ohm}.
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The maximum possible voltage measurement can then be calculated as such:
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\begin{align}
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V_{worstcase} & = V_{REF2} \cdot \frac{R_{NTC}}{R_{NTC}+R_1} + V_{err} \\
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& = \SI{3.006}\volt \cdot \frac{\SI{3086.8}{\ohm}}{\SI{3086.8}{\ohm}+\SI{9990}{\ohm}} + \SI{0.0028}{\volt} \\
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& \approx \SI{0.7124}{\volt}
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\end{align}
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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:
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\begin{align}
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V_{worstcase} & = V_{REF2} \cdot \frac{R_{NTC}}{R_{NTC}+R_1} + V_{err} \\
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\SI{0.7124}{\volt} & = \SI{2.994}{\volt} \cdot \frac{R_{NTC}}{R_{NTC}+\SI{10010}{\ohm}} - \SI{0.0028}{\volt} \\
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R_{NTC} & \approx \SI{3141.6}{\ohm}
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\end{align}
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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}.
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\begin{figure}[H]
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\centering
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\includegraphics[width=\textwidth]{./Pictures/Table 5. Voltage Reference Specifications.png}
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\caption{Voltage Reference Specifications}
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\label{fig:vref}
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\end{figure}
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\begin{figure}[H]
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\centering
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\includegraphics[width=\textwidth]{./Pictures/Table 3. Auxiliary (AUX) ADC DC Specifications.png}
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\caption{Auxiliary (AUX) ADC DC Specifications}
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\label{fig:aux}
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\end{figure}
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\begin{table}[h!]
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\centering
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\caption{NTC Look Up Table}
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\label{tab:lut}
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\begin{tabular}{||c c c c c c||}
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\hline
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Temp. [\SI{}{\celsius}] & $R_{nom} [\Omega]$ & $R_{min} [\Omega]$ & $R_{max} [\Omega]$ & $\Delta R/R [\%]$ & $\Delta T [\SI{}{\celsius}]$ \\
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\hline\hline
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58 & 3214.99 & 3145.6 & 3284.4 & 2.16 & 0.69 \\
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58.1 & 3204.88 & 3135.6 & 3274.2 & 2.16 & 0.69 \\
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58.2 & 3194.81 & 3125.6 & 3264.0 & 2.17 & 0.69 \\
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58.3 & 3184.78 & 3115.7 & 3253.9 & 2.17 & 0.69 \\
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58.4 & 3174.78 & 3105.8 & 3243.7 & 2.17 & 0.69 \\
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58.5 & 3164.81 & 3096.0 & 3233.7 & 2.18 & 0.69 \\
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58.6 & 3154.89 & 3086.2 & 3223.6 & 2.18 & 0.69 \\
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58.7 & 3145.00 & 3076.4 & 3213.6 & 2.18 & 0.69 \\
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58.8 & 3135.15 & 3066.7 & 3203.6 & 2.18 & 0.70 \\
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58.9 & 3125.33 & 3056.9 & 3193.7 & 2.19 & 0.70 \\
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59 & 3115.55 & 3047.3 & 3183.8 & 2.19 & 0.70 \\
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59.1 & 3105.80 & 3037.7 & 3173.9 & 2.19 & 0.70 \\
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59.2 & 3096.09 & 3028.1 & 3164.1 & 2.20 & 0.70 \\
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59.3 & 3086.41 & 3018.5 & 3154.3 & 2.20 & 0.70 \\
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59.4 & 3076.77 & 3009.0 & 3144.6 & 2.20 & 0.70 \\
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59.5 & 3067.17 & 2999.5 & 3134.9 & 2.21 & 0.71 \\
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59.6 & 3057.60 & 2990.0 & 3125.2 & 2.21 & 0.71 \\
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59.7 & 3048.06 & 2980.6 & 3115.5 & 2.21 & 0.71 \\
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59.8 & 3038.56 & 2971.2 & 3105.9 & 2.22 & 0.71 \\
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59.9 & 3029.09 & 2961.9 & 3096.3 & 2.22 & 0.71 \\
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60 & 3019.66 & 2952.5 & 3086.8 & 2.22 & 0.71 \\
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60.1 & 3010.26 & 2943.3 & 3077.3 & 2.23 & 0.71 \\
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\hline
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\end{tabular}
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\end{table}
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\bibliographystyle{plain}
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%\nocite{*}
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\newpage
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\renewcommand\refname{Reference}
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\begin{thebibliography}{00}
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\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
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\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
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\bibitem{vishay website} \textit{NTC RT Calculation Tool}. \hyperlink{https://www.vishay.com/en/thermistors/ntc-rt-calculator/}{www.vishay.com}, 03.2025
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\end{thebibliography}
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\end{document}
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