updated the size of the Logo

temperature-measurement-error/AMS_T_error.tex

@@ -7,7 +7,7 @@
 \sisetup{
      group-separator = {.},
      input-decimal-markers={.},
-%     output-decimal-marker = {,},
+     output-decimal-marker = {.},
      group-minimum-digits=9}
 \usepackage{graphicx}
 \usepackage{fancyhdr}
@@ -18,60 +18,71 @@
 \usepackage{multicol}
 \usepackage{amsmath, amssymb}
 
+\hyphenpenalty=10000	%to stop cutting words in a paragraph
+
 \pagestyle{fancy}
 \fancyhf{}
 
-\rhead{\includegraphics*[scale=0.01]{./bilder/FaSTTUBe_Logo_ohneAuto.png}}
+\rhead{\includegraphics*[scale=0.015]{./bilder/FaSTTUBe_Logo_ohneAuto.png}}
 \rfoot{Page \thepage \hspace{1pt} of \pageref{LastPage}}
 \lhead{Car 313, 06.03.2025, Rev. 1}
 \chead{\large Temperature Measurement Error Calculation}
 
 \begin{document}
 
-\begin{wrapfigure}{l}{0.3\textwidth}
+\begin{wrapfigure}{l}{0.4\textwidth}
 	\includegraphics[width=1\linewidth]{./bilder/NTC-schematic.png} 
 	\caption{NTC Voltage Divider and Filter}
 	\label{fig:NTC-schematic}
 \end{wrapfigure}
 
-The following calculation is based on the Look-Up Table (LUT) provided by Vishay, which is used in the AMS software.
+The following calculation is based on the Look-Up Table (LUT) provided by Vishay\cite{vishay website}, which is used in the AMS software.
 
-Since the characteristic curve of the NTC thermistor is nonlinear, determining the absolute maximum measurement error is not straightforward. Therefore, we will calculate the maximum error specifically at 60\si\celsius.
+Since the characteristic curve of the NTC thermistor is nonlinear, determining the absolute maximum measurement error is not straightforward. 
+Therefore, we will calculate the maximum error specifically at \SI{60}{\celsius}.
 
-Our voltage measurement system consists of an NTC thermistor (NTCLE413E2103F102L) and a 10k 0.1 resistor (denoted as R1) forming a voltage divider. The output voltage is then passed through an RC filter before being fed to an ADC.
+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. 
+The output voltage is then passed through an RC filter before being fed to an ADC.
 
-To estimate the error, we calculate the highest possible measured voltage at 60\si\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 3.006V. Additionally, the total measurement error of the GPIO is ±2.8mV (as shown in Fig. \ref{fig:aux}). Furthermore, the maximum resistance of the NTC at 60\si\celsius, according to the LUT (Tab. \ref{tab:lut}), is 3086.8\si\ohm. The maximum possible voltage recorded is therefore:
+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. 
+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{3086.8}{3086.8+9990} + 0.0028V \\
-	&\approx 712.4mV
+	&= \SI{3.006}\volt \cdot \frac{\SI{3086.8}{\ohm}}{\SI{3086.8}{\ohm}+\SI{9990}{\ohm}} + \SI{0.0028}{\volt} \\
+	&\approx 0.7124\si\volt
 \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:
+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}  \\
-	712.4V &= 2.994V \cdot \frac{R_{NTC}}{R_{NTC}+10010} - 0.0028V \\
-	R_{NTC} &\approx 3141.6
+	\SI{0.7124}{\ohm} &= \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}.
-
-\begin{figure}[H]
-	\centering
-	\includegraphics[width=\textwidth]{./bilder/aux.png}
-	\caption{AUX-ADC Specifications}
-	\label{fig:aux}
-\end{figure}
+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/v_ref2.png}
-	\caption{$V_{REF2}$ Specifications}
+	\caption{Voltage Reference Specifications}
 	\label{fig:vref2}
 \end{figure}
 
+\begin{figure}[H]
+	\centering
+	\includegraphics[width=\textwidth]{./bilder/aux.png}
+	\caption{Auxiliary (AUX) ADC DC Specifications}
+	\label{fig:aux}
+\end{figure}
+
+
 \begin{table}[h!]
 	\centering
 	\caption{NTC Look Up Table}
@@ -109,11 +120,12 @@ since the LUT is used to match the voltage to the temperature, and the nominal r
 \bibliographystyle{plain}
 %\nocite{*}
 
+\newpage
 \renewcommand\refname{Reference}
 \begin{thebibliography}{00}
 	
-	\bibitem{ADBMS6830B datasheet AUX} \textit{Data Sheet ADBMS6830B Rev.0 page 5}. analog.com, 01.2024
-	\bibitem{ADBMS6830B datasheet VREF} \textit{Data Sheet ADBMS6830B Rev.0 page 5}. analog.com, 01.2024
+	\bibitem{ADBMS6830B datasheet AUX} \textit{Table 3 AUX Data Sheet ADBMS6830B Rev.0 page 5}. analog.com, 01.2024
+	\bibitem{ADBMS6830B datasheet VREF} \textit{Table 5 VREF Data Sheet ADBMS6830B Rev.0 page 5}. analog.com, 01.2024
 	\bibitem{vishay website} \textit{NTC RT Calculation Tool}. www.vishay.com, 03.2025
 
 \end{thebibliography}