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