forgot to commit last nighe...

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
 
 
 

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.
+%R1 and R2 perform as a potential divider.
-Resistors can fail OPEN and SHORT (according to GAS burner standard EN298 Appendix A).
+%Resistors can fail OPEN and SHORT (according to GAS burner standard EN298 Appendix A).
-$$ fm(R) = \{ OPEN, SHORT \}$$
+%$$ fm(R) = \{ OPEN, SHORT \}$$
 
 
 
-\begin{table}[ht]
+% \begin{table}[ht]
-\caption{Potential Divider $PD$: Failure Mode Effects Analysis: Single Faults} % title of Table
+% \caption{Potential Divider $PD$: Failure Mode Effects Analysis: Single Faults} % title of Table
-\centering % used for centering table
+% \centering % used for centering table
-\begin{tabular}{||l|c|c|l|l||}
+% \begin{tabular}{||l|c|c|l|l||}
-\hline \hline
+% \hline \hline
- \textbf{Test} & \textbf{Pot.Div} & \textbf{  } & \textbf{General}   \\
+%  \textbf{Test} & \textbf{Pot.Div} & \textbf{  } & \textbf{General}   \\
- \textbf{Case} &  \textbf{Effect} & \textbf{  } & \textbf{Symtom Description}   \\
+%  \textbf{Case} &  \textbf{Effect} & \textbf{  } & \textbf{Symtom Description}   \\
-%   R         &    wire        & res +         & res -    & description
+% %   R         &    wire        & res +         & res -    & description
-\hline
+% \hline
-\hline
+% \hline
- TC1: $R_1$ SHORT    &  LOW       &       &  LowPD \\ 
+%  TC1: $R_1$ SHORT    &  LOW       &       &  LowPD \\ 
- TC2: $R_1$  OPEN    &  HIGH        &       &  HighPD \\ \hline
+%  TC2: $R_1$  OPEN    &  HIGH        &       &  HighPD \\ \hline
- TC3: $R_2$ SHORT    &  HIGH        &      &  HighPD \\  
+%  TC3: $R_2$ SHORT    &  HIGH        &      &  HighPD \\  
- TC4: $R_2$ OPEN     &  LOW         &      &  LowPD \\ \hline
+%  TC4: $R_2$ OPEN     &  LOW         &      &  LowPD \\ \hline
-\hline
+% \hline
-\end{tabular} 
+% \end{tabular} 
-\label{tbl:pdfmea}
+% \label{tbl:pdfmea}
-\end{table}
+% \end{table}
-
+% 
-By collecting the symptoms in table~\ref{tbl:pdfmea} we can create a derived
+% By collecting the symptoms in table~\ref{tbl:pdfmea} we can create a derived
-component $PD$ to represent the failure mode behaviour
+% component $PD$ to represent the failure mode behaviour
-of a potential divider.
+% 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}