diff --git a/opamp_circuits_C_GARRETT/Makefile b/opamp_circuits_C_GARRETT/Makefile index 933e7ca..d75d01d 100644 --- a/opamp_circuits_C_GARRETT/Makefile +++ b/opamp_circuits_C_GARRETT/Makefile @@ -1,6 +1,6 @@ -PNG_DIA = circuit1_dag.png mvampcircuit.png pd.png invamp.png shared_component.png tree_abstraction_levels.png three_tree.png +PNG_DIA = circuit1_dag.png mvampcircuit.png pd.png invamp.png shared_component.png tree_abstraction_levels.png three_tree.png blockdiagramcircuit2.png circuit2h.png diff --git a/opamp_circuits_C_GARRETT/blockdiagramcircuit2.dia b/opamp_circuits_C_GARRETT/blockdiagramcircuit2.dia new file mode 100644 index 0000000..f1f67f2 Binary files /dev/null and b/opamp_circuits_C_GARRETT/blockdiagramcircuit2.dia differ diff --git a/opamp_circuits_C_GARRETT/circuit2002.png b/opamp_circuits_C_GARRETT/circuit2002.png index 7e96b90..060df96 100644 Binary files a/opamp_circuits_C_GARRETT/circuit2002.png and b/opamp_circuits_C_GARRETT/circuit2002.png differ diff --git a/opamp_circuits_C_GARRETT/circuit2h.dia b/opamp_circuits_C_GARRETT/circuit2h.dia new file mode 100644 index 0000000..624df33 Binary files /dev/null and b/opamp_circuits_C_GARRETT/circuit2h.dia differ diff --git a/opamp_circuits_C_GARRETT/opamps.tex b/opamp_circuits_C_GARRETT/opamps.tex index 13ece3e..6a0942a 100644 --- a/opamp_circuits_C_GARRETT/opamps.tex +++ b/opamp_circuits_C_GARRETT/opamps.tex @@ -250,35 +250,36 @@ We begin by identifying functional groups from the components in the circuit. \subsection{Functional Group: Potential Divider} +Here we can re-use the potential divider from section~\ref{potdivfmmd}. -R1 and R2 perform as a potential divider. -Resistors can fail OPEN and SHORT (according to GAS burner standard EN298 Appendix A). -$$ fm(R) = \{ OPEN, SHORT \}$$ +%R1 and R2 perform as a potential divider. +%Resistors can fail OPEN and SHORT (according to GAS burner standard EN298 Appendix A). +%$$ fm(R) = \{ OPEN, SHORT \}$$ -\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. +% \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 with $fm(PD) = \{PDHigh,PDLow\}$. @@ -406,7 +407,7 @@ two derived components of the type $NI\_AMP$ and $SEC\_AMP$. \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} \\ + \textbf{Case} & \textbf{Effect} & \textbf{ } & \textbf{Symptom Description} \\ % R & wire & res + & res - & description \hline \hline @@ -468,6 +469,164 @@ wihen it becomes a V2 follower). \end{figure} + + +The circuit in figure~\ref{fig:circuit2} shows a five pole low pass filter. +Starting at the input, we have a first order low pass filter buffered by an op-amp, +the output of this is passed to a Sallen~Key~\cite{aoe}[p.267] second order lowpass filter. +The output of this is passed into another Sallen~Key filter (which although it may have different values +for its resistors/capacitors and thus a different frequency response) is idential from a failure mode perspective. +Thus we can analyse the first Sallen~Key low pass filter and re-use the results. + +\paragraph{First Order Low Pass Filter.} +We begin with the first order low pass filter formed by $R10$ and $C10$. +% +This configuration (or {\fg}) is very commonly +used in electronics to remove unwanted high frequencies/interference +form a signal; Here it is being used as a first stage of +a more sophisticated low pass filter. +% +R10 and C10 act as a potential divider, with the crucial difference between a purely resistive potential divider being +that the impedance of the capacitor is lower for higher frequencies. +Thus higher frquencies are attenuated at the point that we +read its output signal. +However, from a failure mode perspective we can analyse it in a very similar way +to a potential divider. +Capacitors generally fail OPEN but some types fail OPEN and SHORT. +We will consider the latter type for this analysis. + + + +\begin{table}[h+] +\begin{tabular}{|| l | l | c | c | l ||} \hline + \textbf{Failure Scenario} & & \textbf{First Order} & & \textbf{Symptom} \\ + & & \textbf{Low Pass Filter} & & \\ + \hline + FS1: R10 SHORT & & $No Filtering$ & & $LPnofilter$ \\ \hline + FS2: R10 OPEN & & $No Signal$ & & $LPnosignal$ \\ \hline + FS3: C10 SHORT & & $No Signal$ & & $LPnosignal$ \\ \hline + FS4: C10 OPEN & & $No Filtering$ & & $LPnofilter$ \\ \hline +\hline +\end{tabular} +\end{table} + + +We can collect the symptoms $\{ LPnofilter,LPnosignal \}$ and create a derived component +called $FirstOrderLP$. Applying the $fm$ function yields $$ fm(FirstOrderLP) = \{ LPnofilter,LPnosignal \}.$$ + +\paragraph{Addition of Buffer Amplifier: first stage.} + +The opamp IC1 is being used simply as a buffer. By placing it between the next stages +on the signal path we remove the possibility of unwanted signal feedback. +The buffer is one of the simplest op-amp configurations. +It has no other components, and so we can now form a {\fg} +from the $FirstOrderLP$ and the OPAMP component. + +\begin{table}[ht] +\caption{First Stage LP1: 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{Symptom Description} \\ +% R & wire & res + & res - & description +\hline +\hline + TC1: $OPAMP$ LatchUP & Output High & & LP1High \\ + TC2: $OPAMP$ LatchDown & Output Low & & LP1Low \\ \hline + TC3: $OPAMP$ No Operation & Output Low & & LP1Low \\ + TC4: $OPAMP$ Low Slew & Unwanted Low pass filtering & & LP1ExtraLowPass \\ \hline + TC5: $LPnofilter $ & No low pass filtering & & LP1NoLowPass \\ \hline + TC6: $LPnosignal $ & No input signal & & LP1low \\ + \hline + +\hline +\end{tabular} +\label{tbl:firststage} +\end{table} + +From the table~\ref{tbl:firststage} we can see three symptoms of failure of +the first stage of this circuit (i.e. R10,C10,IC1). +We can create a derived component for it, lets call it $LP1$. + +$$ fm(LP1) = \{ LP1High, LP1Low, LP1ExtraLowPass, LP1NoLowPass \} $$ + + +\paragraph{Second order Sallen Key Low Pass Filter.} +The next two filters in the signal path are R1,R2,C2,C1,IC2 and R3,R4,C4,C3,IC3. +From a failure mode perspective these are identical. +We can analyse one and re-use the results for the second. + +\begin{table}[ht] +\caption{Sallen Key Low Pass Filter SKLP: 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{Symptom Description} \\ +% R & wire & res + & res - & description +\hline +\hline + TC1: $OPAMP$ LatchUP & Output High & & SKLPHigh \\ + TC2: $OPAMP$ LatchDown & Output Low & & SKLPLow \\ \hline + TC3: $OPAMP$ No Operation & Output Low & & SKLPLow \\ + TC4: $OPAMP$ Low Slew & Unwanted Low pass filtering & & SKLPIncorrect \\ \hline + TC5: $R1 OPEN$ & No input signal & & SKLPIncorrect \\ \hline + TC6: $R1 SHORT$ & incorrect low pass filtering & & SKLPIncorrect \\ + TC7: $R2 OPEN$ & No input signal & & SKLPnosignal \\ \hline + TC8: $R2 SHORT$ & incorrect low pass filtering & & SKLPIncorrect \\ + TC9: $C1 OPEN$ & reduced/incorrect low pass filtering & & SKLPIncorrect\\ \hline + TC10: $C1 SHORT$ & reduced/incorrect low pass filtering & & SKLPIncorrect \\ + TC11: $C2 OPEN$ & reduced/incorrect low pass filtering & & SKLPIncorrect \\ \hline + TC12: $C2 SHORT$ & No input signal, low signal & & SKLPnosignal \\ + \hline +\hline +\end{tabular} +\label{tbl:firststage} +\end{table} + +We now can create a derived component to represent the Sallen Key low pass filter, which we can call $SKLP$. + + +$$ fm ( SKLP ) = \{ SKLPHigh, SKLPLow, SKLPIncorrect, SKLPnosignal \} $$ + + +\paragraph{A failure mode model of Op-Amp Circuit 2.} + +We now have {\dcs} representing the three stages of this filter. +We represent this as a block diagram to represent the signal flow, in figure~\ref{fig:blockdiagramcircuit2}. + + +\begin{figure}[h] + \centering + \includegraphics[width=400pt,keepaspectratio=true]{./blockdiagramcircuit2.png} + % blockdiagramcircuit2.png: 689x83 pixel, 72dpi, 24.31x2.93 cm, bb=0 0 689 83 + \caption{Signal Flow though five pole low pass filter} + \label{fig:blockdiagramcircuit2} +\end{figure} + + + +As the signal has to pass though each block/stage +in order to be `five~pole' filtered, we need to bring these three blocks together into a {\fg} +in order to get a failure mode model for the whole circuit. + + +We can represent the desired FMMD hierarchy in figure~\ref{fig:circuit2h}. + + +\begin{figure}[h] + \centering + \includegraphics[width=300pt]{./circuit2h.png} + % circuit2h.png: 676x603 pixel, 72dpi, 23.85x21.27 cm, bb=0 0 676 603 + \caption{FMMD Hierarchy for five pole Low Pass Filter} + \label{fig:circuit2h} +\end{figure} + + +So out final {\fg} will consist of the derived components +$\{ LP1, SKLP_1, SKLP_2 \}$. + \clearpage \section{Op-Amp circuit 3}