From 19c75e38831b4a92a7018635b10624c843e18a58 Mon Sep 17 00:00:00 2001
From: Johnny Hsu <j.hsu@fasttube.de>
Date: Sun, 23 Mar 2025 01:16:23 +0100
Subject: [PATCH] small changes to clear out error

---
 temperature_measurement_error/AMS_T_error.pdf | Bin 308767 -> 308545 bytes
 temperature_measurement_error/AMS_T_error.tex |  60 +++++++++---------
 2 files changed, 29 insertions(+), 31 deletions(-)

diff --git a/temperature_measurement_error/AMS_T_error.pdf b/temperature_measurement_error/AMS_T_error.pdf
index 3c2fcd14a4a6fc9817532929adeff72592fb4f75..ff452d7246a83a8fdfa0f64bcd1fef8dd23965bc 100644
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diff --git a/temperature_measurement_error/AMS_T_error.tex b/temperature_measurement_error/AMS_T_error.tex
index e75955b..7110c21 100644
--- a/temperature_measurement_error/AMS_T_error.tex
+++ b/temperature_measurement_error/AMS_T_error.tex
@@ -16,8 +16,6 @@
 \usepackage{float}
 \usepackage{multicol}
 \usepackage{amsmath, amssymb}
-\usepackage{csvsimple}
-\usepackage{pgfplotstable}
 
 \pagestyle{fancy}
 \fancyhf{}
@@ -36,21 +34,21 @@ Since the Look Up Table provided by Vishay is used for the calculation in the AM
 
 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.
+Our Voltage measurement system is based on a NTC (NTCLE413E2103F102L from Vishay) and a 10k 0.1\% resistor (named $R_1$ 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:
+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    \\
+	        & V_{REF2} \cdot \frac{R_{NTC}}{R_{NTC}+R_1} + V_{err} \\
+	=       & 3.006V \cdot \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 \\
+	  & V_{REF2} \cdot \frac{R_{NTC}}{R_{NTC}+R_1} + V_{err}          \\
+	= & 2.994V \cdot \frac{R_{NTC}}{R_{NTC}+10010} - 0.0028V = 712.4V \\
 	  & R_{NTC} \approx 3141.6
 \end{align*}
 
@@ -76,30 +74,30 @@ since the LUT is used to match the voltage to the temperature, and the nominal r
 	\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}] \\
+		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                       \\
+		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}