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noninvopamp/noninvopamp.tex

@@ -33,7 +33,7 @@ amplifier determined.
 
 \section{Introduction}
 
-Standard non inv op amp from ``art of electronics'' ~\cite{aoe}[pp.234] shown in figure \ref{fig:noninvamp}.
+A standard non inverting  op amp (from ``The Art of Electronics'' ~\cite{aoe}[pp.234]) is shown in figure \ref{fig:noninvamp}.
 
 \begin{figure}[h]
  \centering
@@ -45,17 +45,19 @@ Standard non inv op amp from ``art of electronics'' ~\cite{aoe}[pp.234] shown in
 
 
 
-The functional of the resistors in this amplifier is to set the gain.
+The functional of the resistors in this circuit is to set the amplifier gain.
 They operate as a potential divider and program the minus input on the op-amp
 to balance them against the positive input, giving the voltage gain ($G_v$)
-defined by $$ G_v = 1 + \frac{R2}{R1} $$ at the output.
+defined by $ G_v = 1 + \frac{R2}{R1} $ at the output.
 
 As the resistors work to provide a specific function, that of a potential divider,
-we can treat them as a functional group.
+we can treat them as a functional group. This functional group has two members, R1 and R2,.
 Using the EN298 specification for resistor failure ~\cite{en298}[App.A]
 we can assign  failure modes of $OPEN$ and $SHORT$ to the resistors.
 Thus $R1$ has failure modes $\{R1\_OPEN, R1\_SHORT\}$ and $R2$ has failure modes $\{R2\_OPEN, R2\_SHORT\}$.
 
+\section{Failure Mode Analysis of the Potential Divider}
+
 Modelling this as a functional group, we can draw a circle to represent each failure mode
 in the potential divider, shown in figure \ref{fig:fg1}.
 
@@ -93,10 +95,10 @@ which failure modes is is modelling (see figure \ref{fig:fg1a}).
 %   R         &    wire        & res +         & res -    & description
 \hline
 \hline
- TC1: $R_1$ SHORT    &  LOW       &       &  Low PD \\ 
- TC2: $R_1$  OPEN    &  HIGH        &       &  High PD \\ \hline
- TC3: $R_2$ SHORT    &  HIGH        &      &  High PD \\  
- TC4: $R_2$ OPEN     &  LOW         &      &  Low PD \\ \hline
+ TC1: $R_1$ SHORT    &  LOW       &       &  LowPD \\ 
+ TC2: $R_1$  OPEN    &  HIGH        &       &  HighPD \\ \hline
+ TC3: $R_2$ SHORT    &  HIGH        &      &  HighPD \\  
+ TC4: $R_2$ OPEN     &  LOW         &      &  LowPD \\ \hline
 \hline
 \end{tabular} 
 \label{pdfmea}
@@ -104,7 +106,7 @@ which failure modes is is modelling (see figure \ref{fig:fg1a}).
 
 
 We can now collect the symptoms of failure. From the four base component failure modes, we now
-have two symptoms, $LOW\;PD, HIGH\;PD$. 
+have two symptoms, $LowPD, HighPD$. 
 
 We can represent the collection of these symptoms by drawing connecting lines between 
 the test cases and naming them (see figure \ref{fig:fg1b}).
@@ -118,7 +120,122 @@ the test cases and naming them (see figure \ref{fig:fg1b}).
  \label{fig:fg1b}
 \end{figure}
 
+We can now make a `derived component' to represent this potential divider.
+This {\dc} will have two failure failure modes.
+We can use the symbol $\bowtie$ to represent taking the analysed 
+{\fg} and creating from it, a {\dc}.
 
+%We could represent it algebraically thus: $ \bowtie(PotDiv) = 
+\begin{figure}[h]
+ \centering
+ \includegraphics[width=200pt,keepaspectratio=true]{./noninvopamp/dc1.jpg}
+ % dc1.jpg: 430x619 pixel, 72dpi, 15.17x21.84 cm, bb=0 0 430 619
+ \caption{From functional group to derived component}
+ \label{fig:dc1}
+\end{figure}
+
+Because the derived component is defined by its failure modes, we can use it
+as a building block for other {\fgs} in the same way as we used the resistors R1 and R2.
+
+\section{Failure Mode Analysis of the OP-AMP}
+
+
+
+Let use now consider the op-amp. According to 
+FMD-91~\cite{fmd91}[3-116] an op amp may have the follow failure modes
+latchup(12.5\%), latchdown(6\%), nooperation(31.3\%), lowslewrate(50\%).
+
+We can represent these failure modes on a diagram (see figure~\ref{fig:op1}).
+\clearpage
+\section{Bringing the OP amp and the potential divider together}
+
+We can now consider bringing the OP amp and the potential divider together to
+for an amplifier. We have the failure modes of the functional group for the potential divider, so we do not need to consider the individual resistor failure modes that define its behaviour.
+We can make a new functional group to represent the amplifier, by bringing the component opamp
+and the component potential divider into a new functional group.
+
+
+
+\begin{figure}[h]
+ \centering
+ \includegraphics[width=200pt,keepaspectratio=true]{./noninvopamp/op1.jpg}
+ % op1.jpg: 406x221 pixel, 72dpi, 14.32x7.80 cm, bb=0 0 406 221
+ \caption{Op Amp failure modes}
+ \label{fig:op1}
+\end{figure}
+
+
+This functional group has the failure modes from the op-amp component, and the failure modes
+from the potential divider {\dc} to analyse represented by figure~\ref{fig:fgamp}.
+
+
+\begin{figure}[h]
+ \centering
+ \includegraphics[width=200pt,keepaspectratio=true]{./noninvopamp/fgamp.jpg}
+ % fgamp.jpg: 430x330 pixel, 72dpi, 15.17x11.64 cm, bb=0 0 430 330
+ \caption{Amplifier Functional Group}
+ \label{fig:fgamp}
+\end{figure}
+
+
+
+We can now place test cases on this (note this analysis considers single failure modes only
+where we want to model multiple failures, we can over lap contours, and place the test cases in overlapping 
+regions) see figure~\ref{fig:fgampa}.
+
+
+
+
+\begin{figure}[h]
+ \centering
+ \includegraphics[width=200pt,keepaspectratio=true]{./noninvopamp/fgampa.jpg}
+ % fgampa.jpg: 430x330 pixel, 72dpi, 15.17x11.64 cm, bb=0 0 430 330
+ \caption{Amplifier Functional Group with Test Cases}
+ \label{fig:fgampa.jpg}
+\end{figure}
+
+
+
+\begin{table}[ht]
+\caption{Non Inverting Amplifier: Failure Mode Effects Analysis: Single Faults} % title of Table
+\centering % used for centering table
+\begin{tabular}{||l|c|c|l|l||}
+\hline \hline
+ \textbf{Test} & \textbf{Amplifier} & \textbf{  } & \textbf{General}   \\
+ \textbf{Case} &  \textbf{Effect} & \textbf{  } & \textbf{Symtom Description}   \\
+%   R         &    wire        & res +         & res -    & description
+\hline
+\hline
+ TC1: $OPAMP$ LatchUP    &  Output High          &      &  AMPHigh \\ 
+ TC2: $OPAMP$ LatchDown  &  Output Low           &      &  AMPLow \\ \hline
+ TC3: $OPAMP$ No Operation &  Output Low         &      &  AMPLow \\  
+ TC4: $OPAMP$ Low Slew     &  Low pass filtering &      &  LowPass \\ \hline
+ TC5: $PD$ LowPD         &   Output High          &      &  AMPHigh \\ \hline
+ TC6: $PD$ HighPD        &  Output Low          &      &  AMPLow \\ \hline 
+ %TC7: $R_2$ OPEN     &  LOW       &      &  LowPD \\ \hline
+\hline
+\end{tabular} 
+\label{ampfmea}
+\end{table}
+
+For this amplifier configuration we have three failure modes, $AMPHigh, AMPLow, LowPass$ see figure~\ref{fig:fgampb}.
+
+We can now derive a `component' to represent this amplifier configuration (see figure 
+and use it it to model higher level functional groups see figure\ref{fig:noninvampa}.
+
+
+
+\begin{figure}[h]
+ \centering
+ \includegraphics[width=200pt,keepaspectratio=true]{./noninvampa.jpg}
+ % noninvampa.jpg: 436x720 pixel, 72dpi, 15.38x25.40 cm, bb=0 0 436 720
+ \caption{Non Inverting Amplifier Derived Component}
+ \label{fig:noninvampa}
+\end{figure}
+
+
+%failure mode contours).
+\clearpage
 \vspace{60pt}
 $$ \int_{0\-}^{\infty}  f(t).e^{-s.t}.dt  \; | \; s \in \mathcal{C}$$
 \today