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looking at circuit after email from C garret and discussiion with Darren

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Robin Clark 2011-10-11 10:58:26 +01:00
parent ab25a14bdc
commit b70e731859
1 changed files with 64 additions and 13 deletions
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77
opamp_circuits_C_GARRETT/opamps.tex
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@ -139,15 +139,61 @@ $$ fm(NI\_AMP) = \{ AMPHigh, AMPLow, LowPass \} $$
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 modes are therefore the same. We can therefore re-use
the derived component for $NI\_AMP$
This is in exactly the same configuration as the first amplifier, but it is being fed by the first amplifier.
The first amplifier was grounded and received as input `+V1' (presumably
a positive voltage).
This means the junction of R1 R3 is always +ve.
This means the input voltage `+V2' could be lower than this.
This means R3 R4 is not a potential divider with R4 being on the positive side.
It could be on either polarity (i.e. the other way around R4 could be the negative side).
Here it is more intuitive to model the resistors not as a potential divider, but individually.
%This means we are either going to
%get a high or low reading if R3 or R4 fail.
\begin{table}[ht]
\caption{Differencing Amplifier $D\_AMP$: 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: $R3\_open$ & +V2 follower & & AMPIncorrectOutput\\ \hline
TC6: $R3\_short$ & Undefined & & AMPIncorrectOutput \\
& (impedance of IC1 vs +V2) & & \\ \hline
TC5: $R4\_open$ & High or Low output & & AMPIncorrectOutput \\
& +V2$>$+V1 $\mapsto$ High & & \\
& +V1$>$+V2 $\mapsto$ Low & & \\ \hline
TC6: $R4\_short$ & +V2 follower & & AMPIncorrectOutput \\ \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 4 ways $\{ AMPHigh, AMPLow, LowPass, AMPIncorrectOutput\}$.
We can now create a derived component, $D\_AMP$, to represent it.
$$ fm(D\_AMP) = \{ AMPHigh, AMPLow, LowPass, AMPIncorrectOutput \} $$
%Its failure modes are therefore the same. We can therefore re-use
%the derived component for $NI\_AMP$
\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 $NI\_AMP$.
two derived components of the type $NI\_AMP$ and $D\_AMP$.
@ -161,13 +207,14 @@ two derived components of the type $NI\_AMP$.
% 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 & 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
TC1: $NI\_AMP$ AMPHigh & opamp 2 driven high & & DiffAMPLow \\
TC2: $NI\_AMP$ AMPLow & opamp 2 fdriven low & & DiffAMPHigh \\
TC3: $NI\_AMP$ LowPass & opamp 2 driven with lag & & DiffAMP\_LP \\ \hline
TC4: $D\_AMP$ AMPHigh & Diff amplifier high & & DiffAMPHigh\\
TC5: $D\_AMP$ AMPLow & Diff amplifier low & & DiffAMPLow \\
TC6: $D\_AMP$ LowPass & Diff amplifier lag/lowpass & & DiffAMP\_LP \\ \hline
TC7: $D\_AMP$ IncorrectOutput & Output voltage & & DiffAMPIncorrect \\
TC7: $D\_AMP$ & not difference of $V2 - V1$ & & \\ \hline
\hline
\end{tabular}
\label{ampfmea}
@ -175,12 +222,12 @@ two derived components of the type $NI\_AMP$.
Collecting the symptoms, we can determine the failure modes for this circuit, $\{DiffAMPLow, DiffAMPHigh, DiffAMP\_LP\}$.
Collecting the symptoms, we can determine the failure modes for this circuit, $\{DiffAMPLow, DiffAMPHigh, DiffAMP\_LP, DiffAMPIncorrect \}$.
We now create a derived component to represent the circuit in figure~\ref{fig:circuit1}.
$$ fm (DiffAMP) = \{DiffAMPLow, DiffAMPHigh, DiffAMP\_LP\} $$
$$ fm (DiffAMP) = \{DiffAMPLow, DiffAMPHigh, DiffAMP\_LP DiffAMPIncorrect\} $$
Its interesting here to note that we can draw a directed graph (figure~\ref{fig:circuit1_dag})
@ -190,6 +237,10 @@ 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.
This circuit performs poorly from a safety point of view.
Its failure modes could be indistinguishable from valid readings (especially
wihen it becomes a V2 follower).
\begin{figure}[h]
\centering
\includegraphics[width=400pt]{./circuit1_dag.png}