From b70e731859f58dbe23983b1239d9fd2501032155 Mon Sep 17 00:00:00 2001 From: Robin Clark Date: Tue, 11 Oct 2011 10:58:26 +0100 Subject: [PATCH] looking at circuit after email from C garret and discussiion with Darren --- opamp_circuits_C_GARRETT/opamps.tex | 77 ++++++++++++++++++++++++----- 1 file changed, 64 insertions(+), 13 deletions(-) diff --git a/opamp_circuits_C_GARRETT/opamps.tex b/opamp_circuits_C_GARRETT/opamps.tex index aa4e02c..cd850fb 100644 --- a/opamp_circuits_C_GARRETT/opamps.tex +++ b/opamp_circuits_C_GARRETT/opamps.tex @@ -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}