From 1ad4d0889bbe447b26553273231e1fc21d5f74d7 Mon Sep 17 00:00:00 2001 From: Robin Clark Date: Fri, 7 Oct 2011 17:08:37 +0100 Subject: [PATCH] reasoning for diff dual op-amp example circuit --- opamp_circuits_C_GARRETT/opamps.tex | 153 ++++++++++++++++++++++++++++ 1 file changed, 153 insertions(+) diff --git a/opamp_circuits_C_GARRETT/opamps.tex b/opamp_circuits_C_GARRETT/opamps.tex index 8c2aae6..f7fdd30 100644 --- a/opamp_circuits_C_GARRETT/opamps.tex +++ b/opamp_circuits_C_GARRETT/opamps.tex @@ -23,6 +23,8 @@ 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. \end{abstract} \clearpage \section{Op-Amp circuit 1} @@ -36,6 +38,157 @@ Proof of analysis concept. \end{figure} +The amplifier in figure~\ref{fig:circuit1} amplifies the difference between +the 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. + + +\subsection{Functional Group: Potential Divider} + +R1 and R2 perform as a potential divider. +Resistors can fail OPEN and SHORT. +$$ fm(R) = \{ OPEN, SHORT \}$$ + + + +\begin{table}[ht] +\caption{Potential Divider $PD$: 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{Pot.Div} & \textbf{ } & \textbf{General} \\ + \textbf{Case} & \textbf{Effect} & \textbf{ } & \textbf{Symtom Description} \\ +% R & wire & res + & res - & description +\hline +\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{tbl:pdfmea} +\end{table} + +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 +$fm(PD) = \{PDHigh,PDLow\}$. + + +The potential divider is used to program the gain of IC1. +IC1 and PD1 provide the function of buffering +/amplifying the signal $+V1$. +We can treat IC1 and PD1 as a functional group. + + +\subsection{Functional Group: Amplifier} + +Let use now consider the op-amp. According to +FMD-91~\cite{fmd91}[3-116] an op amp may have the following failure modes: +latchup(12.5\%), latchdown(6\%), nooperation(31.3\%), lowslewrate(50\%). + + +$$ fm(OPAMP) = \{L\_{up}, L\_{dn}, Noop, L\_slew \} $$ + + +By bringing the $PD$ derived component and the $OPAMP$ into +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 +\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 : Low gain& & 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 : Low Gain& & AMPLow \\ \hline + %TC7: $R_2$ OPEN & LOW & & LowPD \\ \hline +\hline +\end{tabular} +\label{ampfmea} +\end{table} + + +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. + + +$$ fm(NI\_AMP) = \{ AMPHigh, AMPLow, LowPass \} $$ + + + + +\subsection{The second Stage of the amplifier} + +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. + +\pagebreak[4] +\subsection{Modelling the circuit} + +For the final stage of this we can create a functional group consisting of +two derived components of the type $NI\_AMP$. + + + +\begin{table}[ht] +\caption{Difference Amplifier $DiffAMP$ : 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{Dual Amplifier} & \textbf{ } & \textbf{General} \\ + \textbf{Case} & \textbf{Effect} & \textbf{ } & \textbf{Symtom Description} \\ +% R & wire & res + & res - & description +\hline +\hline + 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 + %TC7: $R_2$ OPEN & LOW & & LowPD \\ \hline +\hline +\end{tabular} +\label{ampfmea} +\end{table} + + + +Collecting the symptoms, we can determine the failure modes for this circuit, $\{DiffAMPLow, DiffAMPHIGH, DiffAMP\_LP\}$. + + +We now create a derived component to represent the circuit in figure~\ref{fig:circuit1}. + +$$ fm (DiffAMP) = \{DiffAMPLow, DiffAMPHIGH, DiffAMP\_LP\} $$ + + +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 +a component failure mode that could have caused it. + + + + + \clearpage \section{Op-Amp circuit 2}