add temperature calculation
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temperature_measurement_error/AMS_T_error.pdf
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temperature_measurement_error/AMS_T_error.pdf
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temperature_measurement_error/AMS_T_error.tex
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temperature_measurement_error/AMS_T_error.tex
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\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=4}
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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{multicol}
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\usepackage{amsmath, amssymb}
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\usepackage{csvsimple}
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\usepackage{pgfplotstable}
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\pagestyle{fancy}
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\fancyhf{}
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\rhead{\includegraphics*[scale=0.03]{bilder/Fasttube-Logo.png}}
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\rfoot{Page \thepage \hspace{1pt} of \pageref{LastPage}}
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\begin{document}
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\lhead{Car 313, 06.03.2025, Rev. 1}
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\chead{\large Temperature Measurement Error Calculation}
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\hfill \break
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Since the Look Up Table provided by Vishay is used for the calculation in the AMS Software, the following calculation is also based on it.
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As the characteristic curve is not linear, it is relatively trivial to find the absolute maximum measurement error, therefore, the maximum error at \SI{60}{\celsius} is calculated here.
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Our Voltage measurement system is based on a NTC (NTCLE413E2103F102L from Vishay) and a 10k 0.1\% resistor (name as $R_1$ here) froming a voltage divider, and the output voltage is then feed to an ADC after passing through a RC-filter.
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To calculate the error, the highest possible measured voltage at \SI{60}{\celsius} is worked out here, since according to the design of our voltage divider, the lower the temperature, the higher the voltage. As shown in Fig. \ref{fig:vref2}, the supply voltage $V_{REF2}$ of the voltage divider can have a maximum value of \SI{3.006}{\volt}, while the total measurement error of the GPIO is $\pm$ \SI{2.8}{mV}. (Fig \ref{fig:aux}) In addition, the maximum resistance from the NTC can be \SI{3086.8}{\ohm} according to the LUT (Tab. \ref{tab:lut}). the maximum possible voltage recorded is therefore:
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\begin{align*}
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& V_{REF2} * \frac{R_{NTC}}{R_{NTC}+R_1} + V_{err} \\
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= & 3.006V * \frac{3086.8}{3086.8+9990} + 0.0028V \\
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\approx & 712.4V
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\end{align*}
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to find the largest possible error, the lowest possible matching temperature should be calculated, that theoretically can produce the same voltage output. The calculation is as below:
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\begin{align*}
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& V_{REF2} * \frac{R_{NTC}}{R_{NTC}+R_1} + V_{err} \\
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= & 2.994V * \frac{R_{NTC}}{R_{NTC}+10010} - 0.0028V = 712.4V \\
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& R_{NTC} \approx 3141.6
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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]{./bilder/aux.png}
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\caption{AUX-ADC Specifications}
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\label{fig:aux}
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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]{./bilder/v_ref2.png}
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\caption{$V_{REF2}$ Specifications}
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\label{fig:vref2}
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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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\renewcommand\refname{Reference}
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\begin{thebibliography}{00}
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\bibitem{datasheet} \textit{Data Sheet ADBMS6830B Rev.0 page 5}. analog.com, 01.2024.
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\end{thebibliography}
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\end{document}
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temperature_measurement_error/NTC.csv
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temperature_measurement_error/NTC.csv
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T [celsius], Rnom [ohms], Rmin [ohms], Rmax [ohms], delta R/R [+-\%], delta T [+- celsius], alpha [\%/K]
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"58","3214.99","3145.6","3284.4","2.16","0.69","-3.15"
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"58.1","3204.88","3135.6","3274.2","2.16","0.69","-3.15"
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"58.2","3194.81","3125.6","3264.0","2.17","0.69","-3.15"
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"58.3","3184.78","3115.7","3253.9","2.17","0.69","-3.15"
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"58.4","3174.78","3105.8","3243.7","2.17","0.69","-3.14"
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"58.5","3164.81","3096.0","3233.7","2.18","0.69","-3.14"
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"58.6","3154.89","3086.2","3223.6","2.18","0.69","-3.14"
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"58.7","3145.00","3076.4","3213.6","2.18","0.69","-3.14"
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"58.8","3135.15","3066.7","3203.6","2.18","0.70","-3.14"
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"58.9","3125.33","3056.9","3193.7","2.19","0.70","-3.14"
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"59","3115.55","3047.3","3183.8","2.19","0.70","-3.13"
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"59.1","3105.80","3037.7","3173.9","2.19","0.70","-3.13"
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"59.2","3096.09","3028.1","3164.1","2.20","0.70","-3.13"
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"59.3","3086.41","3018.5","3154.3","2.20","0.70","-3.13"
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"59.4","3076.77","3009.0","3144.6","2.20","0.70","-3.13"
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"59.5","3067.17","2999.5","3134.9","2.21","0.71","-3.13"
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"59.6","3057.60","2990.0","3125.2","2.21","0.71","-3.12"
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"59.7","3048.06","2980.6","3115.5","2.21","0.71","-3.12"
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"59.8","3038.56","2971.2","3105.9","2.22","0.71","-3.12"
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"59.9","3029.09","2961.9","3096.3","2.22","0.71","-3.12"
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"60","3019.66","2952.5","3086.8","2.22","0.71","-3.12"
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"60.1","3010.26","2943.3","3077.3","2.23","0.71","-3.12"
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temperature_measurement_error/bilder/Fasttube-Logo.png
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temperature_measurement_error/bilder/Fasttube-Logo.png
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temperature_measurement_error/bilder/aux.png
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temperature_measurement_error/bilder/aux.png
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temperature_measurement_error/bilder/v_ref2.png
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temperature_measurement_error/bilder/v_ref2.png
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temperature_measurement_error/grade.csv
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temperature_measurement_error/grade.csv
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name,givenname,matriculation,gender,grade
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Maier,Hans,12345,m,1.0
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Huber,Anna,23456,f,2.3
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Weisbaeck,Werner,34567,m,5.0
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