128 lines
4.3 KiB
TeX
128 lines
4.3 KiB
TeX
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\ifthenelse {\boolean{paper}}
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{
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\abstract{
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This paper analyses a non-inverting op-amp
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configuration, with the opamp and gain resistors using the FMMD
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methodology.
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It has three base components, two resistors
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and one op-amp.
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The two resistors are used as a potential divider to program the gain
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of the amplifier. We consider the two resistors as a functional group
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where the function is provides is to operate as a potential divider.
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The base component error modes of the
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resistors are used to model the potential divider from
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a failure mode perspective.
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We determine the failure symptoms of the potential divider and
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consider these as failure modes of a derived component.
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We can now create a functional group representing the amplifier,
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by bringing the failure modes from the potential divider and
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the op-amp into a functional group.
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This can now be analysed and a derived component to represent the non inverting
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amplifier determined.
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}
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}
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{
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}
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\section{Introduction}
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Standard non inv op amp from ``art of electronics'' ~\cite{aoe}[pp.234] shown in figure \ref{fig:noninvamp}.
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\begin{figure}[h]
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\centering
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\includegraphics[width=200pt,keepaspectratio=true]{./noninvopamp/noninv.jpg}
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% noninv.jpg: 341x186 pixel, 72dpi, 12.03x6.56 cm, bb=0 0 341 186
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\caption{Standard non inverting amplifier configuration}
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\label{fig:noninvamp}
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\end{figure}
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The functional of the resistors in this amplifier is to set the gain.
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They operate as a potential divider and program the minus input on the op-amp
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to balance them against the positive input, giving the voltage gain ($G_v$)
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defined by $$ G_v = 1 + \frac{R2}{R1} $$ at the output.
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As the resistors work to provide a specific function, that of a potential divider,
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we can treat them as a functional group.
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Using the EN298 specification for resistor failure ~\cite{en298}[App.A]
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we can assign failure modes of $OPEN$ and $SHORT$ to the resistors.
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Thus $R1$ has failure modes $\{R1\_OPEN, R1\_SHORT\}$ and $R2$ has failure modes $\{R2\_OPEN, R2\_SHORT\}$.
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Modelling this as a functional group, we can draw a circle to represent each failure mode
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in the potential divider, shown in figure \ref{fig:fg1}.
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\begin{figure}[h]
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\centering
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\includegraphics[width=200pt,keepaspectratio=true]{./noninvopamp/fg1.jpg}
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% fg1.jpg: 430x271 pixel, 72dpi, 15.17x9.56 cm, bb=0 0 430 271
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\caption{potential divider `functional group' failure modes}
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\label{fig:fg1}
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\end{figure}
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We can now look at each of these base component failure modes,
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and determine how they will affect the operation of the potential divider.
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Each failure mode scenario we look at will be given a teat case number,
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which is represented on the diagram, with an asterisk marking
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which failure modes is is modelling (see figure \ref{fig:fg1a}).
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\begin{figure}[h]
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\centering
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\includegraphics[width=200pt,keepaspectratio=true]{./noninvopamp/fg1a.jpg}
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% fg1a.jpg: 430x271 pixel, 72dpi, 15.17x9.56 cm, bb=0 0 430 271
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\caption{potential divider with test cases}
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\label{fig:fg1a}
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\end{figure}
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\begin{table}[ht]
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\caption{Potential Divider: Failure Mode Effects Analysis: Single Faults} % title of Table
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\centering % used for centering table
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\begin{tabular}{||l|c|c|l|l||}
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\hline \hline
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\textbf{Test} & \textbf{Pot.Div} & \textbf{ } & \textbf{General} \\
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\textbf{Case} & \textbf{Effect} & \textbf{ } & \textbf{Symtom Description} \\
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% R & wire & res + & res - & description
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\hline
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\hline
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TC1: $R_1$ SHORT & LOW & & Low PD \\
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TC2: $R_1$ OPEN & HIGH & & High PD \\ \hline
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TC3: $R_2$ SHORT & HIGH & & High PD \\
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TC4: $R_2$ OPEN & LOW & & Low PD \\ \hline
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\hline
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\end{tabular}
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\label{pdfmea}
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\end{table}
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We can now collect the symptoms of failure. From the four base component failure modes, we now
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have two symptoms, $LOW\;PD, HIGH\;PD$.
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We can represent the collection of these symptoms by drawing connecting lines between
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the test cases and naming them (see figure \ref{fig:fg1b}).
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\begin{figure}[h]
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\centering
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\includegraphics[width=200pt,keepaspectratio=true]{./noninvopamp/fg1b.jpg}
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% fg1b.jpg: 430x271 pixel, 72dpi, 15.17x9.56 cm, bb=0 0 430 271
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\caption{Collection of potential divider failure mode symptoms}
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\label{fig:fg1b}
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\end{figure}
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\vspace{60pt}
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$$ \int_{0\-}^{\infty} f(t).e^{-s.t}.dt \; | \; s \in \mathcal{C}$$
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\today
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$$\frac{-b\pm\sqrt{ {b^2-4ac}}}{2a}$$
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\today
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