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1259312..aa4e02c 100644 --- a/opamp_circuits_C_GARRETT/opamps.tex +++ b/opamp_circuits_C_GARRETT/opamps.tex @@ -21,10 +21,12 @@ \begin{abstract} Circuits from email conversation. + Not a document to be proof read. + Proof of analysis concept. -Function fm() applied to a component returns its failure modes. +Function $fm$ applied to a component returns its failure modes. \end{abstract} \clearpage \section{Op-Amp circuit 1} @@ -39,7 +41,7 @@ Function fm() applied to a component returns its failure modes. The amplifier in figure~\ref{fig:circuit1} amplifies the difference between -the voltages $+V1$ and $+V2$. +the input voltages $+V1$ and $+V2$. It would be desirable to represent this circuit as a derived component called say $DiffAMP$. We begin by identifying functional groups from the components in the circuit. @@ -47,7 +49,7 @@ We begin by identifying functional groups from the components in the circuit. \subsection{Functional Group: Potential Divider} R1 and R2 perform as a potential divider. -Resistors can fail OPEN and SHORT. +Resistors can fail OPEN and SHORT (according to GAS burner standard EN298 Appendix A). $$ fm(R) = \{ OPEN, SHORT \}$$ @@ -71,18 +73,18 @@ $$ fm(R) = \{ OPEN, SHORT \}$$ \label{tbl:pdfmea} \end{table} -By collecting the symptoms in table~ref{tbl:pdfmea} we can create a derived +By collecting the symptoms in table~\ref{tbl:pdfmea} we can create a derived component $PD$ to represent the failure mode behaviour of a potential divider. Thus for single failure modes, a potential divider can fail -$fm(PD) = \{PDHigh,PDLow\}$. +with $fm(PD) = \{PDHigh,PDLow\}$. The potential divider is used to program the gain of IC1. -IC1 and PD1 provide the function of buffering +IC1 and PD provide the function of buffering /amplifying the signal $+V1$. -We can treat IC1 and PD1 as a functional group. +We can now examine IC1 and PD as a functional group. \subsection{Functional Group: Amplifier} @@ -100,7 +102,7 @@ a functional group we can analyse its failure mode behaviour. \begin{table}[ht] -\caption{Non Inverting Amplifier: Failure Mode Effects Analysis: Single Faults} % title of Table +\caption{Non Inverting Amplifier $NI\_AMP$: Failure Mode Effects Analysis: Single Faults} % title of Table \centering % used for centering table \begin{tabular}{||l|c|c|l|l||} \hline \hline @@ -124,7 +126,7 @@ a functional group we can analyse its failure mode behaviour. Collecting the symptoms we can see that this amplifier fails in 3 ways $\{ AMPHigh, AMPLow, LowPass \}$. -We can now create a derived component, $NONINVAMP$, to represent it. +We can now create a derived component, $NI\_AMP$, to represent it. $$ fm(NI\_AMP) = \{ AMPHigh, AMPLow, LowPass \} $$ @@ -138,7 +140,8 @@ The second stage of this amplifier, following the signal path, is the amplifier consisting of $R3,R4,IC2$. This is in exactly the same configuration as the first amplifier. -Its failure mode are therefore the same. +Its failure modes are therefore the same. We can therefore re-use +the derived component for $NI\_AMP$ \pagebreak[4] \subsection{Modelling the circuit} @@ -161,9 +164,9 @@ two derived components of the type $NI\_AMP$. TC1: $NI\_AMP1$ AMPHigh & opamp 2 driven high & & DiffAMPLow \\ TC2: $NI\_AMP1$ AMPLow & opamp 2 fdriven low & & DiffAMPHigh \\ TC3: $NI\_AMP1$ LowPass & opamp 2 driven with lag & & DiffAMP\_LP \\ \hline - TC4: $NI\_AMP2$ AMPHigh & dual amplifier high & & DiffAMPHigh\\ - TC5: $NI\_AMP2$ AMPLow & dual amplifier low & & DiffAMPLow \\ - TC6: $NI\_AMP2$ LowPass & dual amplifier lag/lowpass & & DiffAMP\_LP \\ \hline + TC4: $NI\_AMP2$ AMPHigh & Diff amplifier high & & DiffAMPHigh\\ + TC5: $NI\_AMP2$ AMPLow & Diff amplifier low & & DiffAMPLow \\ + TC6: $NI\_AMP2$ LowPass & Diff amplifier lag/lowpass & & DiffAMP\_LP \\ \hline %TC7: $R_2$ OPEN & LOW & & LowPD \\ \hline \hline \end{tabular} @@ -180,11 +183,20 @@ We now create a derived component to represent the circuit in figure~\ref{fig:ci $$ fm (DiffAMP) = \{DiffAMPLow, DiffAMPHigh, DiffAMP\_LP\} $$ -Its interesting here to note that we can draw a directed graph -of the failure modes and derived components here. -By doing this we can trace any top level fault back to +Its interesting here to note that we can draw a directed graph (figure~\ref{fig:circuit1_dag}) +of the failure modes and derived components. +Using this we can trace any top level fault back to a component failure mode that could have caused it. +In fact we can re-construct an FTA diagram from the information in this graph. +We merely have to choose a top level event and work down using or gates. +\begin{figure}[h] + \centering + \includegraphics[width=400pt]{./circuit1_dag.png} + % circuit1_dag.png: 797x1145 pixel, 72dpi, 28.12x40.39 cm, bb=0 0 797 1145 + \caption{Directed Acyclic Graph of Circuit1 failure modes} + \label{fig:circuit1_dag} +\end{figure}