reasoning for diff dual op-amp example circuit
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Robin Clark
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@ -23,6 +23,8 @@
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Circuits from email conversation.
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Not a document to be proof read.
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Proof of analysis concept.
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Function fm() applied to a component returns its failure modes.
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\end{abstract}
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\clearpage
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\section{Op-Amp circuit 1}
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@ -36,6 +38,157 @@ Proof of analysis concept.
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\end{figure}
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The amplifier in figure~\ref{fig:circuit1} amplifies the difference between
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the voltages $+V1$ and $+V2$.
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It would be desirable to represent this circuit as a derived component called say $DiffAMP$.
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We begin by identifying functional groups from the components in the circuit.
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\subsection{Functional Group: Potential Divider}
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R1 and R2 perform as a potential divider.
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Resistors can fail OPEN and SHORT.
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$$ fm(R) = \{ OPEN, SHORT \}$$
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\begin{table}[ht]
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\caption{Potential Divider $PD$: 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 & & LowPD \\
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TC2: $R_1$ OPEN & HIGH & & HighPD \\ \hline
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TC3: $R_2$ SHORT & HIGH & & HighPD \\
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TC4: $R_2$ OPEN & LOW & & LowPD \\ \hline
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\hline
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\end{tabular}
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\label{tbl:pdfmea}
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\end{table}
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By collecting the symptoms in table~ref{tbl:pdfmea} we can create a derived
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component $PD$ to represent the failure mode behaviour
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of a potential divider.
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Thus for single failure modes, a potential divider can fail
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$fm(PD) = \{PDHigh,PDLow\}$.
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The potential divider is used to program the gain of IC1.
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IC1 and PD1 provide the function of buffering
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/amplifying the signal $+V1$.
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We can treat IC1 and PD1 as a functional group.
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\subsection{Functional Group: Amplifier}
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Let use now consider the op-amp. According to
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FMD-91~\cite{fmd91}[3-116] an op amp may have the following failure modes:
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latchup(12.5\%), latchdown(6\%), nooperation(31.3\%), lowslewrate(50\%).
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$$ fm(OPAMP) = \{L\_{up}, L\_{dn}, Noop, L\_slew \} $$
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By bringing the $PD$ derived component and the $OPAMP$ into
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a functional group we can analyse its failure mode behaviour.
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\begin{table}[ht]
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\caption{Non Inverting Amplifier: 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{Amplifier} & \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: $OPAMP$ LatchUP & Output High & & AMPHigh \\
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TC2: $OPAMP$ LatchDown & Output Low : Low gain& & AMPLow \\ \hline
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TC3: $OPAMP$ No Operation & Output Low & & AMPLow \\
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TC4: $OPAMP$ Low Slew & Low pass filtering & & LowPass \\ \hline
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TC5: $PD$ LowPD & Output High & & AMPHigh \\ \hline
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TC6: $PD$ HighPD & Output Low : Low Gain& & AMPLow \\ \hline
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%TC7: $R_2$ OPEN & LOW & & LowPD \\ \hline
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\hline
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\end{tabular}
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\label{ampfmea}
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\end{table}
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Collecting the symptoms we can see that this amplifier fails
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in 3 ways $\{ AMPHigh, AMPLow, LowPass \}$.
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We can now create a derived component, $NONINVAMP$, to represent it.
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$$ fm(NI\_AMP) = \{ AMPHigh, AMPLow, LowPass \} $$
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\subsection{The second Stage of the amplifier}
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The second stage of this amplifier, following the signal path, is the amplifier
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consisting of $R3,R4,IC2$.
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This is in exactly the same configuration as the first amplifier.
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Its failure mode are therefore the same.
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\pagebreak[4]
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\subsection{Modelling the circuit}
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For the final stage of this we can create a functional group consisting of
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two derived components of the type $NI\_AMP$.
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\begin{table}[ht]
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\caption{Difference Amplifier $DiffAMP$ : 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{Dual Amplifier} & \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: $NI\_AMP1$ AMPHigh & opamp 2 driven high & & DiffAMPLow \\
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TC2: $NI\_AMP1$ AMPLow & opamp 2 fdriven low & & DiffAMPHIGH \\
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TC3: $NI\_AMP1$ LowPass & opamp 2 driven with lag & & DiffAMP\_LP \\ \hline
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TC4: $NI\_AMP2$ AMPHigh & dual amplifier high & & DiffAMPHIGH \\
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TC5: $NI\_AMP2$ AMPLow & dual amplifier low & & DiffAMPLow \\
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TC6: $NI\_AMP2$ LowPass & dual amplifier lag/lowpass & & DiffAMP\_LP \\ \hline
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%TC7: $R_2$ OPEN & LOW & & LowPD \\ \hline
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\hline
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\end{tabular}
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\label{ampfmea}
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\end{table}
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Collecting the symptoms, we can determine the failure modes for this circuit, $\{DiffAMPLow, DiffAMPHIGH, DiffAMP\_LP\}$.
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We now create a derived component to represent the circuit in figure~\ref{fig:circuit1}.
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$$ fm (DiffAMP) = \{DiffAMPLow, DiffAMPHIGH, DiffAMP\_LP\} $$
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Its interesting here to note that we can draw a directed graph
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of the failure modes and derived components here.
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By doing this we can trace any top level fault back to
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a component failure mode that could have caused it.
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\clearpage
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\section{Op-Amp circuit 2}
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