diff --git a/temperature_measurement_error/AMS_T_error.pdf b/temperature_measurement_error/AMS_T_error.pdf new file mode 100644 index 0000000..3c2fcd1 Binary files /dev/null and b/temperature_measurement_error/AMS_T_error.pdf differ diff --git a/temperature_measurement_error/AMS_T_error.tex b/temperature_measurement_error/AMS_T_error.tex new file mode 100644 index 0000000..e75955b --- /dev/null +++ b/temperature_measurement_error/AMS_T_error.tex @@ -0,0 +1,117 @@ +\documentclass[paper=A4]{article} +\usepackage[utf8]{inputenc} + +\usepackage[a4paper, left=2cm, right=2cm, top=2cm, bottom=2cm]{geometry} + +\usepackage{siunitx} +\sisetup{ + group-separator = {.}, + input-decimal-markers={.}, +% output-decimal-marker = {,}, + group-minimum-digits=4} +\usepackage{graphicx} +\usepackage{fancyhdr} +\usepackage{lastpage} +\usepackage{subfigure} +\usepackage{float} +\usepackage{multicol} +\usepackage{amsmath, amssymb} +\usepackage{csvsimple} +\usepackage{pgfplotstable} + +\pagestyle{fancy} +\fancyhf{} + +\rhead{\includegraphics*[scale=0.03]{bilder/Fasttube-Logo.png}} +\rfoot{Page \thepage \hspace{1pt} of \pageref{LastPage}} + +\begin{document} + +\lhead{Car 313, 06.03.2025, Rev. 1} +\chead{\large Temperature Measurement Error Calculation} + +\hfill \break + +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. + +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. + +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. + +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: + +\begin{align*} + & V_{REF2} * \frac{R_{NTC}}{R_{NTC}+R_1} + V_{err} \\ + = & 3.006V * \frac{3086.8}{3086.8+9990} + 0.0028V \\ + \approx & 712.4V +\end{align*} + +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: + +\begin{align*} + & V_{REF2} * \frac{R_{NTC}}{R_{NTC}+R_1} + V_{err} \\ + = & 2.994V * \frac{R_{NTC}}{R_{NTC}+10010} - 0.0028V = 712.4V \\ + & R_{NTC} \approx 3141.6 +\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}. + +\begin{figure}[H] + \centering + \includegraphics[width=\textwidth]{./bilder/aux.png} + \caption{AUX-ADC Specifications} + \label{fig:aux} +\end{figure} + +\begin{figure}[H] + \centering + \includegraphics[width=\textwidth]{./bilder/v_ref2.png} + \caption{$V_{REF2}$ Specifications} + \label{fig:vref2} +\end{figure} + +\begin{table}[h!] + \centering + \caption{NTC Look Up Table} + \label{tab:lut} + \begin{tabular}{||c c c c c c||} + \hline + Temp. [\SI{}{\celsius}] & $R_{nom}$ [\Omega] & $R_{min}$ [\Omega] & $R_{max}$ [\Omega] & \Delta R/R [\%] & \Delta T [\SI{}{\celsius}] \\ + \hline\hline + 58 & 3214.99 & 3145.6 & 3284.4 & 2.16 & 0.69 \\ + 58.1 & 3204.88 & 3135.6 & 3274.2 & 2.16 & 0.69 \\ + 58.2 & 3194.81 & 3125.6 & 3264.0 & 2.17 & 0.69 \\ + 58.3 & 3184.78 & 3115.7 & 3253.9 & 2.17 & 0.69 \\ + 58.4 & 3174.78 & 3105.8 & 3243.7 & 2.17 & 0.69 \\ + 58.5 & 3164.81 & 3096.0 & 3233.7 & 2.18 & 0.69 \\ + 58.6 & 3154.89 & 3086.2 & 3223.6 & 2.18 & 0.69 \\ + 58.7 & 3145.00 & 3076.4 & 3213.6 & 2.18 & 0.69 \\ + 58.8 & 3135.15 & 3066.7 & 3203.6 & 2.18 & 0.70 \\ + 58.9 & 3125.33 & 3056.9 & 3193.7 & 2.19 & 0.70 \\ + 59 & 3115.55 & 3047.3 & 3183.8 & 2.19 & 0.70 \\ + 59.1 & 3105.80 & 3037.7 & 3173.9 & 2.19 & 0.70 \\ + 59.2 & 3096.09 & 3028.1 & 3164.1 & 2.20 & 0.70 \\ + 59.3 & 3086.41 & 3018.5 & 3154.3 & 2.20 & 0.70 \\ + 59.4 & 3076.77 & 3009.0 & 3144.6 & 2.20 & 0.70 \\ + 59.5 & 3067.17 & 2999.5 & 3134.9 & 2.21 & 0.71 \\ + 59.6 & 3057.60 & 2990.0 & 3125.2 & 2.21 & 0.71 \\ + 59.7 & 3048.06 & 2980.6 & 3115.5 & 2.21 & 0.71 \\ + 59.8 & 3038.56 & 2971.2 & 3105.9 & 2.22 & 0.71 \\ + 59.9 & 3029.09 & 2961.9 & 3096.3 & 2.22 & 0.71 \\ + 60 & 3019.66 & 2952.5 & 3086.8 & 2.22 & 0.71 \\ + 60.1 & 3010.26 & 2943.3 & 3077.3 & 2.23 & 0.71 \\ + \hline + \end{tabular} +\end{table} + +\bibliographystyle{plain} +%\nocite{*} + +\renewcommand\refname{Reference} +\begin{thebibliography}{00} + + \bibitem{datasheet} \textit{Data Sheet ADBMS6830B Rev.0 page 5}. analog.com, 01.2024. + +\end{thebibliography} + +\end{document} diff --git a/temperature_measurement_error/NTC.csv b/temperature_measurement_error/NTC.csv new file mode 100644 index 0000000..dc3ca92 --- /dev/null +++ b/temperature_measurement_error/NTC.csv @@ -0,0 +1,23 @@ +T [celsius], Rnom [ohms], Rmin [ohms], Rmax [ohms], delta R/R [+-\%], delta T [+- celsius], alpha [\%/K] +"58","3214.99","3145.6","3284.4","2.16","0.69","-3.15" +"58.1","3204.88","3135.6","3274.2","2.16","0.69","-3.15" +"58.2","3194.81","3125.6","3264.0","2.17","0.69","-3.15" +"58.3","3184.78","3115.7","3253.9","2.17","0.69","-3.15" +"58.4","3174.78","3105.8","3243.7","2.17","0.69","-3.14" +"58.5","3164.81","3096.0","3233.7","2.18","0.69","-3.14" +"58.6","3154.89","3086.2","3223.6","2.18","0.69","-3.14" +"58.7","3145.00","3076.4","3213.6","2.18","0.69","-3.14" +"58.8","3135.15","3066.7","3203.6","2.18","0.70","-3.14" +"58.9","3125.33","3056.9","3193.7","2.19","0.70","-3.14" +"59","3115.55","3047.3","3183.8","2.19","0.70","-3.13" +"59.1","3105.80","3037.7","3173.9","2.19","0.70","-3.13" +"59.2","3096.09","3028.1","3164.1","2.20","0.70","-3.13" +"59.3","3086.41","3018.5","3154.3","2.20","0.70","-3.13" +"59.4","3076.77","3009.0","3144.6","2.20","0.70","-3.13" +"59.5","3067.17","2999.5","3134.9","2.21","0.71","-3.13" +"59.6","3057.60","2990.0","3125.2","2.21","0.71","-3.12" +"59.7","3048.06","2980.6","3115.5","2.21","0.71","-3.12" +"59.8","3038.56","2971.2","3105.9","2.22","0.71","-3.12" +"59.9","3029.09","2961.9","3096.3","2.22","0.71","-3.12" +"60","3019.66","2952.5","3086.8","2.22","0.71","-3.12" +"60.1","3010.26","2943.3","3077.3","2.23","0.71","-3.12" diff --git a/temperature_measurement_error/bilder/Fasttube-Logo.png b/temperature_measurement_error/bilder/Fasttube-Logo.png new file mode 100644 index 0000000..b958efb Binary files /dev/null and b/temperature_measurement_error/bilder/Fasttube-Logo.png differ diff --git a/temperature_measurement_error/bilder/aux.png b/temperature_measurement_error/bilder/aux.png new file mode 100644 index 0000000..8bf9a70 Binary files /dev/null and b/temperature_measurement_error/bilder/aux.png differ diff --git a/temperature_measurement_error/bilder/v_ref2.png b/temperature_measurement_error/bilder/v_ref2.png new file mode 100644 index 0000000..e597f93 Binary files /dev/null and b/temperature_measurement_error/bilder/v_ref2.png differ diff --git a/temperature_measurement_error/grade.csv b/temperature_measurement_error/grade.csv new file mode 100644 index 0000000..0004dc9 --- /dev/null +++ b/temperature_measurement_error/grade.csv @@ -0,0 +1,4 @@ +name,givenname,matriculation,gender,grade +Maier,Hans,12345,m,1.0 +Huber,Anna,23456,f,2.3 +Weisbaeck,Werner,34567,m,5.0