math

calc.tex

@@ -0,0 +1,117 @@
+\documentclass[a4paper,10pt]{article}
+%\documentclass[a4paper,10pt]{scrartcl}
+
+\usepackage[utf8]{inputenc}
+\usepackage{datetime2}
+\usepackage{amsmath}
+
+\title{Wheatstone Bridge Amplifier Calculations}
+\author{Willow Herron\\Katherine Sarna, Tarik Fawal}
+
+\pdfinfo{%
+  /Title    (Wheatstone Bridge Amplifier Calculations)
+  /Author   (Willow Herron)
+  /Creator  (Willow Herron)
+  /Producer (Willow Herron)
+  /Subject  ()
+  /Keywords ()
+}
+
+\begin{document}
+	\maketitle
+	\section{Ohm's Law}
+		\subsection{Wheatstone Bridge}
+			\subsubsection{Case 1}
+				\begin{align*}
+					I_{4} &= \frac{3.3-V_{S-}}{2000}\\
+					I_{6} &= \frac{V_{S-}}{2000}\\
+					I_{5} &= \frac{3.3-V_{S+}}{2000}\\
+					I_{7} &= \frac{V_{S+}}{2000}
+				\end{align*}
+			\subsubsection{Case 2}
+				\begin{align*}
+					I_{4} &= \frac{3.3-V_{S-}}{2020}\\
+					I_{6} &= \frac{V_{S-}}{1980}\\
+					I_{5} &= \frac{3.3-V_{S+}}{2020}\\
+					I_{7} &= \frac{V_{S+}}{1980}
+				\end{align*}
+		\subsection{Op-Amp}
+			\begin{align*}
+				I_{11} &= \frac{V_{S+}-V_{OPA+}}{R_{11}}\\
+				I_9 &= \frac{V_{S-}-V_{OPA-}}{R_{9}}\\
+				I_8 &= \frac{V_{OPA+}}{R_{8}}\\
+				I_{10} &= \frac{V_{OUT}-V_{OPA+}}{R_{10}}
+			\end{align*}
+	\section{Assertions}
+		\begin{align*}
+			V_{OUT_1} &= 1\\
+			V_{OUT_2} &= 2.3\\
+			R_{IN} &= R_9 = R_{11} = 1000
+		\end{align*}
+	\section{Kirchoff's Current Law}
+		\begin{align*}
+			I_{S-} = 0 &= I_4 - I_6 - I_9\\
+			I_{S+} = 0 &= I_5 - I_7 - I_{11}\\
+			I_{OPA-} = 0 &= I_9 + I_{10} + I_{OPA-}\\
+			I_{OPA+} = 0 &= I_{11} - I_8 + I_{OPA+}
+		\end{align*}
+	\section{Ideal Op-Amp Model}
+		\begin{align*}
+			0 &= I_{OPA+} = I_{OPA-}\\
+			V_{OPA} &= V_{OPA+} = V_{OPA-}
+		\end{align*}
+	\section{Combine}
+		\subsection{Case 1}
+			\begin{align*}
+				0 &= \frac{3.3-V_{S-}}{2000} - \frac{V_{S-}}{2000} - \frac{V_{S-}-V_{OPA}}{1000}\\
+				0 &= \frac{3.3-V_{S+}}{2000} - \frac{V_{S+}}{2000} - \frac{V_{S+}-V_{OPA}}{1000}\\
+				0 &= \frac{V_{S-}-V_{OPA}}{1000} + \frac{1-V_{OPA}}{R_{10}}\\
+				0 &= \frac{V_{S+}-V_{OPA}}{1000} - \frac{V_{OPA}}{R_{8}}
+			\end{align*}
+		\subsection{Case 2}
+			\begin{align*}
+				0 &= \frac{3.3-V_{S-}}{2020} - \frac{V_{S-}}{1980} - \frac{V_{S-}-V_{OPA}}{1000}\\
+				0 &= \frac{3.3-V_{S+}}{1980} - \frac{V_{S+}}{2020} - \frac{V_{S+}-V_{OPA}}{1000}\\
+				0 &= \frac{V_{S-}-V_{OPA}}{1000} + \frac{2.3-V_{OPA}}{R_{R10}}\\
+				0 &= \frac{V_{S+}-V_{OPA}}{1000} - \frac{V_{OPA}}{R_{8}}
+			\end{align*}
+	\section{Reduce}
+		\subsection{Case 1}
+			\subsubsection{Node S}
+				\begin{align*}
+					0 &= \frac{3.3-2V_{S-}}{2000}-\frac{V_{S-}-V_{OPA}}{1000}\\
+					0 &= \frac{3300 - (2000-2000)V_{S-}}{2000}+V_{OPA}\\
+					V_{OPA} &= 1.65
+				\end{align*}
+			\subsubsection{Node OPA}
+				\begin{align*}
+					0 &= R_{10}V_{S-}-R_{10}V_{OPA}+1000-1000V_{OPA}\\
+					0 &= R_{10}V_{S-}+1000-(R_{10}+1000)V_{OPA}\\
+					V_{OPA} &= \frac{R_{10}V_{S-}+1000}{R_{10}+1000}\\
+					0 &= R_8V_{S+}-R_8V_{OPA}-1000V_{OPA}\\
+					V_{OPA} &= \frac{R_8V_{S+}}{R_8+1000}
+				\end{align*}
+		\subsection{Case 2}
+			\subsubsection{Node S}
+				\begin{align*}
+					0 &= 6534000-4000000V_{S-}-2181600V_{S-}+2181600V_{OPA}\\
+					V_{OPA} &= \frac{65340-18184V_{S-}}{21916}\\
+					0 &= 6666000-4000000V_{S+}-2181600V_{S+}+2181600V_{OPA}\\
+					V_{OPA} &= \frac{66660-18184V_{S+}}{21816}\\
+				\end{align*}
+			\subsubsection{Node OPA}
+				\begin{align*}
+					0 &= R_{10}V_{S-}-R_{10}V_{OPA}+2.31000-1000V_{OPA}\\
+					0 &= R_{10}V_{S-}+1000-(R_{10}+2.31000)V_{OPA}\\
+					V_{OPA} &= \frac{R_{10}V_{S-}+1000}{R_{10}+1000}\\
+					0 &= R_8V_{S+}-R_8V_{OPA}-1000V_{OPA}\\
+					V_{OPA} &= \frac{R_8V_{S+}}{R_8+1000}
+				\end{align*}
+	\section{Solve}
+		\subsection{$V_{S+}=V_{S-}$ (1)}
+		\subsection{$V_{S+}-V_{S-}$ (2)}
+			\begin{align*}
+				65340-18184V_{S-} &= 66660-18184V_{S+}\\
+				V_{S+}-V_{S-} &= \frac{165}{2273}
+			\end{align*}
+\end{document}

load-cell-test.kicad_pro

@@ -563,6 +563,14 @@
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@@ -578,6 +586,10 @@
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       "Root"
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