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CH5 pencil and edit session

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submission_thesis/CH5_Examples/copy.tex
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@ -20,7 +20,7 @@ hybrids.
%using an op-amp and two resistors; %using an op-amp and two resistors;
this demonstrates re-use of a potential divider {\dc} from section~\ref{subsec:potdiv}. this demonstrates re-use of a potential divider {\dc} from section~\ref{subsec:potdiv}.
This amplifier is analysed twice, using different compositions of {\fgs}. This amplifier is analysed twice, using different compositions of {\fgs}.
The two approaches, i.e. choice of membership for {\fgs}, are then discussed. The two approaches, i.e. effects of choice of membership for {\fgs} are then discussed.
% %
\item Section~\ref{sec:diffamp} analyses a circuit where two op-amps are used \item Section~\ref{sec:diffamp} analyses a circuit where two op-amps are used
to create a differencing amplifier. to create a differencing amplifier.
@ -31,7 +31,7 @@ not in the second.
% %
\item Section~\ref{sec:fivepolelp} analyses a Sallen-Key based five pole low pass filter. \item Section~\ref{sec:fivepolelp} analyses a Sallen-Key based five pole low pass filter.
It demonstrates re-use of the first Sallen-Key analysis, %encountered as a {\dc} It demonstrates re-use of the first Sallen-Key analysis, %encountered as a {\dc}
increasing test efficiency. This example also serves to show a deep hierarchy of {\dcs}. increasing test efficiency. This example also serves to show a deeper hierarchy of {\dcs}.
% %
\item Section~\ref{sec:bubba} shows FMMD applied to a \item Section~\ref{sec:bubba} shows FMMD applied to a
loop topology---using a `Bubba' oscillator---demonstrating how FMMD differs from fault diagnosis techniques. loop topology---using a `Bubba' oscillator---demonstrating how FMMD differs from fault diagnosis techniques.
@ -266,7 +266,7 @@ and analyse it as such; see table~\ref{tbl:pdneg}.
% %
We assume a valid range for the output value of this circuit. We assume a valid range for the output value of this circuit.
Thus negative or low voltages can be considered as LOW Thus negative or low voltages can be considered as LOW
and voltages higher than this range considered as HIGH. and voltages higher than a given threshold considered as HIGH.
% %
\begin{table}[h+] \begin{table}[h+]
\caption{Inverted Potential divider: Single failure analysis} \caption{Inverted Potential divider: Single failure analysis}
@ -461,7 +461,8 @@ We can now express the failure modes for the {\dc} $INVAMP$ thus;
$$ fm(INVAMP) = \{ HIGH, LOW, LOW PASS \} .$$ $$ fm(INVAMP) = \{ HIGH, LOW, LOW PASS \} .$$
We can draw a DAG representing the failure mode behaviour of We can draw a DAG representing the failure mode behaviour of
this amplifier (see figure~\ref{fig:invdag1}). Note that this allows us this amplifier (see figure~\ref{fig:invdag1}). Note that this allows us
to traverse from system level, or top failure modes to base component failure modes. to trace failure symptoms back to causes, i.e.
to traverse from system level or top failure modes to base component failure modes.
%%%%% 12DEC 2012 UP to here in notes from AF email. %%%%% 12DEC 2012 UP to here in notes from AF email.
% %
\clearpage \clearpage
@ -913,7 +914,7 @@ This FMMD analysis also revealed an undetectable failure mode, $DiffAMPIncorrec
\begin{figure}[h] \begin{figure}[h]
\centering \centering
\includegraphics[width=200pt]{CH5_Examples/circuit2002.png} \includegraphics[width=300pt]{CH5_Examples/circuit2002.png}
% circuit2002.png: 575x331 pixel, 72dpi, 20.28x11.68 cm, bb=0 0 575 331 % circuit2002.png: 575x331 pixel, 72dpi, 20.28x11.68 cm, bb=0 0 575 331
\caption{Five Pole Low Pass Filter, using two Sallen~Key stages and three op-amps. \caption{Five Pole Low Pass Filter, using two Sallen~Key stages and three op-amps.
An example of FMMD applied to a multi-stage but linear signal path topology. } An example of FMMD applied to a multi-stage but linear signal path topology. }
@ -1038,9 +1039,10 @@ on the schematic as in figure~\ref{fig:circuit2002_LP1}.
\begin{figure}[h] \begin{figure}[h]
\centering \centering
\includegraphics[width=200pt,keepaspectratio=true]{CH5_Examples/circuit2002_LP1.png} \includegraphics[width=300pt,keepaspectratio=true]{CH5_Examples/circuit2002_LP1.png}
% circuit2002_LP1.png: 575x331 pixel, 72dpi, 20.28x11.68 cm, bb=0 0 575 331 % circuit2002_LP1.png: 575x331 pixel, 72dpi, 20.28x11.68 cm, bb=0 0 575 331
\caption{Circuit showing {\fgs} modelled so far.} \caption{Five Pole Sallen Key Filter: Circuit showing the first two {\fgs} modelled.
Shown as an Euler diagram super-imposed onto the electrical schematic.} % so far.}
\label{fig:circuit2002_LP1} \label{fig:circuit2002_LP1}
\end{figure} \end{figure}
@ -1107,21 +1109,21 @@ As the signal has to pass through each block/stage
in order to be `five~pole' filtered, we need to bring these three blocks together into a {\fg} 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. in order to get a failure mode model for the whole circuit.
We can index the Sallen Key stages, and these are marked on the circuit schematic in figure~\ref{fig:circuit2002_FIVEPOLE}. We can index the Sallen Key stages, and these are marked on the circuit schematic in figure~\ref{fig:circuit2002_FIVEPOLE}.
%
\begin{figure}[h]+ \begin{figure}[h]+
\centering \centering
\includegraphics[width=200pt]{CH5_Examples/circuit2002_FIVEPOLE.png} \includegraphics[width=300pt]{CH5_Examples/circuit2002_FIVEPOLE.png}
% circuit2002_FIVEPOLE.png: 575x331 pixel, 72dpi, 20.28x11.68 cm, bb=0 0 575 331 % circuit2002_FIVEPOLE.png: 575x331 pixel, 72dpi, 20.28x11.68 cm, bb=0 0 575 331
\caption{Functional Groupings in Five Pole Low Pass Filter: shown as an Euler diagram super-imposed onto the electrical schematic.} \caption{Functional Groupings in Five Pole Low Pass Filter. Shown as an Euler diagram super-imposed onto the electrical schematic.}
\label{fig:circuit2002_FIVEPOLE} \label{fig:circuit2002_FIVEPOLE}
\end{figure} \end{figure}
%
\pagebreak[4] \pagebreak[4]
%
So our final {\fg} will consist of the derived components $\{ LP1, SKLP_1, SKLP_2 \}$. So our final {\fg} will consist of the derived components $\{ LP1, SKLP_1, SKLP_2 \}$.
We represent the desired FMMD hierarchy in figure~\ref{fig:circuit2h}. We represent the desired FMMD hierarchy in figure~\ref{fig:circuit2h}.
%
%
% HTR 20OCT2012 \begin{figure}[h]+ % HTR 20OCT2012 \begin{figure}[h]+
% HTR 20OCT2012 \centering % HTR 20OCT2012 \centering
% HTR 20OCT2012 \includegraphics[width=300pt]{CH5_Examples/circuit2h.png} % HTR 20OCT2012 \includegraphics[width=300pt]{CH5_Examples/circuit2h.png}
@ -1137,18 +1139,18 @@ We represent the desired FMMD hierarchy in figure~\ref{fig:circuit2h}.
is an abstract version of figure~\ref{fig:circuit2002_FIVEPOLE}}. is an abstract version of figure~\ref{fig:circuit2002_FIVEPOLE}}.
\label{fig:circuit2h} \label{fig:circuit2h}
\end{figure} \end{figure}
%
%\pagebreak[4] %\pagebreak[4]
%
%
%
%
%
%
%
%$$ fm ( SKLP ) = \{ SKLPHigh, SKLPLow, SKLPIncorrect, SKLPnosignal \} $$ %$$ fm ( SKLP ) = \{ SKLPHigh, SKLPLow, SKLPIncorrect, SKLPnosignal \} $$
%$$ fm(LP1) = \{ LP1High, LP1Low, LP1ExtraLowPass, LP1NoLowPass \} $$ %$$ fm(LP1) = \{ LP1High, LP1Low, LP1ExtraLowPass, LP1NoLowPass \} $$
%
\begin{table}[ht]+ \begin{table}[ht]+
\caption{Five Pole Low Pass Filter: Failure Mode Effects Analysis($FivePoleLP$): Single Faults} % title of Table \caption{Five Pole Low Pass Filter: Failure Mode Effects Analysis($FivePoleLP$): Single Faults} % title of Table
\centering % used for centering table \centering % used for centering table
@ -1185,43 +1187,39 @@ We represent the desired FMMD hierarchy in figure~\ref{fig:circuit2h}.
\end{tabular} \end{tabular}
\label{tbl:fivepole} \label{tbl:fivepole}
\end{table} \end{table}
%
We now can create a {\dc} to represent the circuit in figure~\ref{fig:circuit2}, we call this We now can create a {\dc} to represent the circuit in figure~\ref{fig:circuit2}, we call this
$FivePoleLP$: applying the $fm$ function (see table~\ref{tbl:fivepole}) $FivePoleLP$: applying the $fm$ function (see table~\ref{tbl:fivepole})
yields $$fm(FivePoleLP) = \{ HIGH, LOW, FilterIncorrect, NO\_SIGNAL \}.$$ yields $$fm(FivePoleLP) = \{ HIGH, LOW, FilterIncorrect, NO\_SIGNAL \}.$$
%
%
%\pagebreak[4] %\pagebreak[4]
%
The failure modes for the low pass filters are very similar, and the propagation of the signal The failure modes for the low pass filters are very similar, and the propagation of the signal
is simple (as it is never inverted). The circuit under analysis is -- as shown in the block diagram (see figure~\ref{fig:blockdiagramcircuit2}) -- is simple (as it is never inverted). The circuit under analysis is -- as shown in the block diagram (see figure~\ref{fig:blockdiagramcircuit2}) --
three op-amp driven non-inverting low pass filter elements. It is not surprising therefore that they have very similar failure modes. three op-amp driven non-inverting low pass filter elements. It is not surprising therefore that they have very similar failure modes.
From a safety point of view, the failure modes $LOW$, $HIGH$ and $NO\_SIGNAL$ From a safety point of view, the failure modes $LOW$, $HIGH$ and $NO\_SIGNAL$
could be easily detected; the failure symptom $FilterIncorrect$ may be less observable. could be easily detected; the failure symptom $FilterIncorrect$ may be less detectable.
%
\subsection{Conclusion} \subsection{Conclusion}
This example shows the analysis of a linear signal path circuit with three easily identifiable This example shows the analysis of a linear signal path circuit with three easily identifiable
{\fgs} and re-use of the Sallen-Key {\dc}. {\fgs} and re-use of the Sallen-Key {\dc}.
%
%
%
%
%
\clearpage \clearpage
% %
% BUBBAOSC % BUBBAOSC
% %
%
\section{Quad Op-Amp Oscillator} \section{Quad Op-Amp Oscillator}
\label{sec:bubba} \label{sec:bubba}
%
\begin{figure}[h] \begin{figure}[h]
\centering \centering
\includegraphics[width=200pt]{CH5_Examples/circuit3003.png} \includegraphics[width=300pt]{CH5_Examples/circuit3003.png}
% circuit3003.png: 503x326 pixel, 72dpi, 17.74x11.50 cm, bb=0 0 503 326 % circuit3003.png: 503x326 pixel, 72dpi, 17.74x11.50 cm, bb=0 0 503 326
\caption{Circuit diagram for the Quad Op-Amp `Bubba' Oscillator} \caption{Circuit diagram for the Quad Op-Amp `Bubba' Oscillator}
\label{fig:circuit3} \label{fig:circuit3}
@ -1325,10 +1323,11 @@ Initially we use the first identified {\fgs} to create our model without further
\subsection{FMMD Analysis using initially identified {\fgs}} \subsection{FMMD Analysis using initially identified {\fgs}}
\label{sec:bubba1} \label{sec:bubba1}
Our {\fg} for this analysis can be expressed thus: By indexing the re-used {\dcs}
the {\fg} for this analysis can be expressed thus:
% %
%$$ G^1_0 = \{ PHS45^1_1, NIBUFF^0_1, PHS45^1_2, NIBUFF^0_2, PHS45^1_3, NIBUFF^0_3 PHS45^1_4, INVAMP^1_0 \} ,$$ %$$ G^1_0 = \{ PHS45^1_1, NIBUFF^0_1, PHS45^1_2, NIBUFF^0_2, PHS45^1_3, NIBUFF^0_3 PHS45^1_4, INVAMP^1_0 \} ,$$
$$ G = \{ PHS45, NIBUFF, PHS45, NIBUFF, PHS45, NIBUFF PHS45, INVAMP \} ,$$ $$ G = \{ PHS45_1, NIBUFF_1, PHS45_2, NIBUFF_2, PHS45_3, NIBUFF_3, PHS45_4, INVAMP \} ,$$
or in Euler diagram format as in figure~\ref{fig:bubbaeuler1}. or in Euler diagram format as in figure~\ref{fig:bubbaeuler1}.
% HTR 23SEP2012 \begin{figure}[h+] % HTR 23SEP2012 \begin{figure}[h+]
% HTR 23SEP2012 \centering % HTR 23SEP2012 \centering
@ -1566,7 +1565,7 @@ The following example is used to demonstrate FMMD analysis of a mixed analogue a
% %
\begin{figure}[h] \begin{figure}[h]
\centering \centering
\includegraphics[width=300pt,keepaspectratio=true]{./CH5_Examples/sigma_delta_block.png} \includegraphics[width=350pt,keepaspectratio=true]{./CH5_Examples/sigma_delta_block.png}
% sigma_delta_block.png: 828x367 pixel, 72dpi, 29.21x12.95 cm, bb=0 0 828 367 % sigma_delta_block.png: 828x367 pixel, 72dpi, 29.21x12.95 cm, bb=0 0 828 367
\caption{Electrical signal path Block diagram: \sd} % Analogue to Digital Converter } \caption{Electrical signal path Block diagram: \sd} % Analogue to Digital Converter }
\label{fig:sigmadeltablock} \label{fig:sigmadeltablock}
@ -1643,12 +1642,12 @@ The feedback voltage for the ADC is supplied via $R1$, we term this voltage as $
%The input voltage is supplied via $R2$ and we term this voltage as $V_{in}$. %The input voltage is supplied via $R2$ and we term this voltage as $V_{in}$.
$R2$ and $R1$ form a summing junction to IC1: they balance the integrator provided $R2$ and $R1$ form a summing junction to IC1: they balance the integrator provided
by the capacitor C1 and the opamp IC1. by the capacitor C1 and the opamp IC1.
This can be our first {\fg} and we analyse it in table~\ref{detail:SUMJINT}%{tbl:sumjint}. This can be our first {\fg} and we analyse it in table~\ref{detail:SUMJINT}: %{tbl:sumjint}.
%For the symptoms, we have to think in terms of the effect %For the symptoms, we have to think in terms of the effect
%on its performance as a summing junction and not be %on its performance as a summing junction and not be
%distracted by the integrator formed by $C_1$ and $IC1$. %distracted by the integrator formed by $C_1$ and $IC1$.
% %
$$FG = \{R1, R2, IC1, C1 \}$$ $$FG = \{R1, R2, IC1, C1 \} .$$
That is, the failure modes (see FMMD analysis at~\ref{detail:SUMJINT}) of our new {\dc} That is, the failure modes (see FMMD analysis at~\ref{detail:SUMJINT}) of our new {\dc}
$SUMJINT$ are $$\{ V_{in} DOM, V_{fb} DOM, NO\_INTEGRATION, HIGH, LOW \} .$$ $SUMJINT$ are $$\{ V_{in} DOM, V_{fb} DOM, NO\_INTEGRATION, HIGH, LOW \} .$$
@ -1662,20 +1661,24 @@ This presents a high impedance to the circuit driving it.
This prevents electrical loading, and thus interference with, the SUMJINT stage. This prevents electrical loading, and thus interference with, the SUMJINT stage.
This is simply an op-amp This is simply an op-amp
with the input connected to the +ve input and the -ve input grounded. with the input connected to the +ve input and the -ve input grounded.
It therefore has the failure modes of an Op-amp. %% \end{table}
%
%
This is an OpAmp in a signal buffer configuration
and therefore simply has the failure modes of an Op-amp.
%
% %
% \end{tabular} % \end{tabular}
% \end{table} %
This is an OpAmp in a signal buffer configuration. %
As it is performing one particular function As it is performing one particular function
we may consider it as a derived component, that of a High Impedance Signal Buffer (HISB). we may consider it as a derived component, that of a High Impedance Signal Buffer (HISB).
This is analysed using FMMD in section~\ref{detail:HISB}. This is analysed using FMMD in section~\ref{detail:HISB}.
% %
We create the {\dc} $HISB$ and its failure modes may be stated as $$fm(HISB) = \{HIGH, LOW, NOOP, LOW_{SLEW} \}.$$ We create the {\dc} $HISB$ and its failure modes may be stated as: $$fm(HISB) = \{HIGH, LOW, NOOP, LOW_{SLEW} \}.$$
\subsubsection{Digital level to analogue level conversion ($DL2AL$).} \subsubsection{Digital level to analogue level conversion ($DL2AL$).}
The integrator is implemented in digital electronics, but the output from the D type flip flop is a digital signal. The integrator is implemented in analogue electronics, but the output from the D type flip flop is a digital signal.
A conversion stage is required to interface these stages. A conversion stage is required to interface these stages.
Digital level to analogue level conversion is performed by IC3 in conjunction with a potential divider formed by R3,R4. Digital level to analogue level conversion is performed by IC3 in conjunction with a potential divider formed by R3,R4.
The potential divider provides a mid rail reference voltage The potential divider provides a mid rail reference voltage
@ -1714,27 +1717,27 @@ $$ fm (DL2AL) = \{ LOW, HIGH, LOW\_{SLEW} \} $$
The digital element of the {\sd}, is a `one~bit~memory', or D type flip flop. This The digital element of the {\sd}, is a `one~bit~memory', or D type flip flop. This
buffers the feedback result and provides the output bit stream. buffers the feedback result and provides the output bit stream.
We create a {\fg} from the CLOCK and IC4 to model this digital buffer. We create a {\fg} from the CLOCK and IC4 to model this digital buffer,
%
$$FG = \{ IC4, CLOCK \}$$ $$FG = \{ IC4, CLOCK \} . $$
%
%
%% DIGBUF --- Digital Buffer %% DIGBUF --- Digital Buffer
%
We now analyse this {\fg} (see section~\ref{detail:DIGBUF}). We now analyse this {\fg} (see section~\ref{detail:DIGBUF}).
%in table~\ref{tbl:digbuf}. %in table~\ref{tbl:digbuf}.
%
%
We can now derive a new component to represent the digital buffer and call it $DIGBUF$. We can now derive a new component to represent the digital buffer and call it $DIGBUF$, .
%
%
$$ fm (DIGBUF) = \{ LOW, STOPPED \} $$ $$ fm (DIGBUF) = \{ LOW, STOPPED \} . $$
%
%
%%% END DIGBUF %%% END DIGBUF
%
\subsection{First {\fgs} analysed} \subsection{First {\fgs} analysed}
%
We have analysed the initial {\fgs} and We have analysed the initial {\fgs} and
have created our first {\dcs}. %and can now take stock of the situation have created our first {\dcs}. %and can now take stock of the situation
%and see what is now required. %and see what is now required.
@ -1752,11 +1755,11 @@ These {\dcs} follow the signal path shown in figure~\ref{fig:sigmadeltablock}.
We now use these {\dcs} to create higher level {\fgs}. We now use these {\dcs} to create higher level {\fgs}.
%to represent the failure mode %to represent the failure mode
%behaviour of the $\Sigma \Delta ADC$. %behaviour of the $\Sigma \Delta ADC$.
We represent this We represent these in the Euler diagram in figure~\ref{fig:eulersd}.
in the Euler diagram in figure~\ref{fig:eulersd}. %
The next stage is to create {\fgs} from these initial {\dcs} They are later used to create {\fgs} to %from these initial {\dcs}
and make a complete failure mode for the {\sd}. make a complete failure mode for the {\sd}.
%
\begin{figure}[h] \begin{figure}[h]
\centering \centering
\includegraphics[width=400pt]{./CH5_Examples/eulersd.png} \includegraphics[width=400pt]{./CH5_Examples/eulersd.png}
@ -1764,7 +1767,7 @@ and make a complete failure mode for the {\sd}.
\caption{Euler diagram showing the initial {\dcs} used to model the $\Sigma \Delta ADC$} \caption{Euler diagram showing the initial {\dcs} used to model the $\Sigma \Delta ADC$}
\label{fig:eulersd} \label{fig:eulersd}
\end{figure} \end{figure}
%
% %
% \begin{figure}[h+] % \begin{figure}[h+]
% \centering % \centering
@ -1773,14 +1776,14 @@ and make a complete failure mode for the {\sd}.
% \caption{First stage of FMMD analysis: Sigma delta Converter} % \caption{First stage of FMMD analysis: Sigma delta Converter}
% \label{fig:sigdel1} % \label{fig:sigdel1}
% \end{figure} % \end{figure}
%
%
%\clearpage %\clearpage
%
%
%
\subsubsection{Buffered Integrating Summing Junction (BISJ): {\fg} of $HISB$ and $SUMJINT$} \subsubsection{Buffered Integrating Summing Junction (BISJ): {\fg} of $HISB$ and $SUMJINT$}
%
We now form a {\fg} with the two derived components $HISB$ and $SUMJINT$. We now form a {\fg} with the two derived components $HISB$ and $SUMJINT$.
This forms a buffered integrating summing junction. We analyse this using FMMD This forms a buffered integrating summing junction. We analyse this using FMMD
(see section~\ref{detail:BISJ}). (see section~\ref{detail:BISJ}).
@ -1792,31 +1795,28 @@ Using the $fm$ function we define the failure modes of
our derived component BISJ thus: our derived component BISJ thus:
% %
$$ fm(BISJ) = \{ OUTPUT STUCK , REDUCED\_INTEGRATION \} . $$ $$ fm(BISJ) = \{ OUTPUT STUCK , REDUCED\_INTEGRATION \} . $$
%
%
%
%
%
\subsubsection{Flip Flop Buffer (FFB): {\fg} of $DL2AL$ and $DIGBUF$} \subsubsection{Flip Flop Buffer (FFB): {\fg} of $DL2AL$ and $DIGBUF$}
%
%$$ fm (DL2AL^2) = \{ LOW, HIGH, LOW\_SLEW \} $$ %$$ fm (DL2AL^2) = \{ LOW, HIGH, LOW\_SLEW \} $$
%$$ fm ( CD4013B) = \{ HIGH, LOW, NOOP \} $$ %$$ fm ( CD4013B) = \{ HIGH, LOW, NOOP \} $$
%
The {\fg} formed by $DIGBUF$ and $DL2AL$ takes the flip flop clocked and buffered The {\fg} formed by $DIGBUF$ and $DL2AL$ takes the flip flop clocked and buffered
value, and outputs it at analogue voltage levels for the summing junction. value, and outputs it at analogue voltage levels for the summing junction.
%
$ FG = \{ DIGBUF, DL2AL \} $ $ FG = \{ DIGBUF, DL2AL \} $
%
We analyse the buffered flip flop circuitry (see table~\ref{detail:FFB}) We analyse the buffered flip flop circuitry (see table~\ref{detail:FFB})
and create a {\dc} $FFB$, and create a {\dc} $FFB$,
where $$fm (FFB) = \{OUTPUT STUCK, LOW\_SLEW\}$$. where $$fm (FFB) = \{OUTPUT STUCK, LOW\_SLEW\} .$$
%\clearpage %\clearpage
\subsection{Final, top level {\fg} for sigma delta Converter} \subsection{Final, top level {\fg} for sigma delta Converter}
%
%
We now have two {\dcs}, $FFB$ and $BISJ$. We now have two {\dcs}, $FFB$ and $BISJ$.
These together represent all base components within this circuit. These together represent all base components within this circuit.
We form a final {\fg} with these: We form a final {\fg} with these:
@ -1827,10 +1827,10 @@ We analyse the buffered {\sd} circuit using FMMD (see section~\ref{detail:SDADC}
% FFB^3 $\{OUTPUT STUCK, LOW\_SLEW\}$ % FFB^3 $\{OUTPUT STUCK, LOW\_SLEW\}$
% BISJ^2 $\{ OUTPUT STUCK , REDUCED\_INTEGRATION \}$ % BISJ^2 $\{ OUTPUT STUCK , REDUCED\_INTEGRATION \}$
% %
We now have a {\dc} $SDADC$ which provides a failure mode model for the \sd. We now have a {\dc} $SDADC$ which provides a failure mode model for the \sd:
$$fm(SSDADC) = \{OUTPUT\_OUT\_OF\_RANGE, OUTPUT\_INCORRECT\}$$ $$fm(SSDADC) = \{OUTPUT\_OUT\_OF\_RANGE, OUTPUT\_INCORRECT\} . $$
We now show the final {\dc} hierarchy in figure~\ref{fig:eulersdfinal}. We now show the final {\dc} hierarchy in figure~\ref{fig:eulersdfinal}.
%
\begin{figure}[h] \begin{figure}[h]
\centering \centering
\includegraphics[width=400pt]{./CH5_Examples/eulersdfinal.png} \includegraphics[width=400pt]{./CH5_Examples/eulersdfinal.png}
@ -1845,7 +1845,7 @@ We now show the final {\dc} hierarchy in figure~\ref{fig:eulersdfinal}.
% \caption{FMMD Analysis hierarchy for the {\sd}} % \caption{FMMD Analysis hierarchy for the {\sd}}
% \label{fig:sdadc} % \label{fig:sdadc}
% \end{figure} % \end{figure}
%
%\clearpage %\clearpage
% ] % ]
% into % into
@ -1866,9 +1866,11 @@ We now show the final {\dc} hierarchy in figure~\ref{fig:eulersdfinal}.
% and IC3. % and IC3.
% The output from this is sent to the summing integrator as the signal summed with the input. % The output from this is sent to the summing integrator as the signal summed with the input.
\subsection{Conclusion} \subsection{Conclusion}
The {\sd} example, shows that FMMD can be applied to mixed digital and analogue circuitry. The {\sd} example, shows that FMMD can be applied to mixed digital and analogue circuitry:
which means the analogue/digital interface is also achieved. This
leads onto interfacing to software and digital~systems in the next chapter.
%
%
%\clearpage %\clearpage
\section{Pt100 Analysis: FMMD and Double Failure Mode Analysis} \section{Pt100 Analysis: FMMD and Double Failure Mode Analysis}
\label{sec:Pt100} \label{sec:Pt100}
@ -1897,7 +1899,7 @@ Applying FMMD lets us look at this circuit in a fresh light.
We analyse this for both single and double failures, We analyse this for both single and double failures,
in addition it demonstrates FMMD coping with component parameter tolerances. in addition it demonstrates FMMD coping with component parameter tolerances.
% %
The circuit is described traditionally and then analysed using the FMMD methodology. The circuit is described from a conventional safety perspective and then analysed using the FMMD methodology.
%A derived component, representing this circuit is then presented. %A derived component, representing this circuit is then presented.
@ -2017,24 +2019,32 @@ expected voltages for failure mode and temperature reading purposes.
V_{out} = V_{in}.\frac{Z2}{Z2+Z1} V_{out} = V_{in}.\frac{Z2}{Z2+Z1}
\end{equation} \end{equation}
\subsection{Safety case for 4 wire circuit} \subsection{Safety case for 4 wire circuit: Detailed calculations}
%
This sub-section looks at the behaviour of the $Pt100$ four wire circuit The following analysis of the Pt100 circuit
for the effects of component failures. firstly presents an FMEA analysis which is then supported by
All components have a set of known `failure modes'. detail and calculations of the type that would be submitted to an approval agency.
In other words we know that a given component can fail in several distinct ways. %
Studies have been published which list common component types Detailed potential divider calculations and the effect of component tolerances
and their sets of failure modes~\cite{fmd91}, often with MTTF statistics~\cite{mil1991}. are factored for each test case in the FMEA table~\ref{sec:singlePt100FMEA}.
Thus for each component, an analysis is made for each of its failure modes, The next section~\ref{sec:Pt100d}, extends this analysis for double failure scenarios.
with respect to its effect on the %{sec:Pt100d}
circuit. Each one of these scenarios is termed a `test case'. % This sub-section looks at the behaviour of the $Pt100$ four wire circuit
The resultant circuit behaviour for each of these test cases is noted. % for the effects of component failures.
The worst case for this type of % All components have a set of known `failure modes'.
analysis would be a fault that we cannot detect. % In other words we know that a given component can fail in several distinct ways.
Where this occurs a circuit re-design is probably the only sensible course of action. % Studies have been published which list common component types
% and their sets of failure modes~\cite{fmd91}, often with MTTF statistics~\cite{mil1991}.
% Thus for each component, an analysis is made for each of its failure modes,
% with respect to its effect on the
% circuit. Each one of these scenarios is termed a `test case'.
% The resultant circuit behaviour for each of these test cases is noted.
% The worst case for this type of
% analysis would be a fault that we cannot detect.
% Where this occurs a circuit re-design is probably the only sensible course of action.
%
\fmodegloss \fmodegloss
%
\paragraph{Single Fault FMEA Analysis of $Pt100$ Four wire circuit.} \paragraph{Single Fault FMEA Analysis of $Pt100$ Four wire circuit.}
\label{sec:singlePt100FMEA} \label{sec:singlePt100FMEA}
%\label{fmea} %\label{fmea}