robin/Robin_PHD
1
0
Fork 0
Code Issues Pull Requests Actions Packages Projects Releases Wiki Activity

started on CH5 AF comments

Browse Source
This commit is contained in:
Robin P. Clark 2012-12-12 18:26:04 +00:00
parent 056d759258
commit beb0a727ac
2 changed files with 39 additions and 27 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

8
submission_thesis/CH1_introduction/copy.tex
View File

@ -1,5 +1,5 @@
\abstract{ \paragraph{Abstract}{
The ability to assess the safety of man made equipment has been a concern The ability to assess the safety of man made equipment has been a concern
since the dawn of the industrial age~\cite{indacc01}~\cite{steamboilers}. since the dawn of the industrial age~\cite{indacc01}~\cite{steamboilers}.
The philosophy behind safety measure has progressed The philosophy behind safety measure has progressed
@ -27,12 +27,6 @@ and, using contract programmed software, allows the modelling of integrated
software/electrical systems. software/electrical systems.
This is followed by two chapters showing examples of the new modular FMEA analysis technique (Failure Mode Modular De-Composition FMMD) This is followed by two chapters showing examples of the new modular FMEA analysis technique (Failure Mode Modular De-Composition FMMD)
firstly looking at electronic circuits and then at electronic/software hybrid systems. firstly looking at electronic circuits and then at electronic/software hybrid systems.
} }
\section{Introduction} \section{Introduction}

58
submission_thesis/CH5_Examples/copy.tex
View File

@ -33,20 +33,24 @@ a variety of typical embedded system components including analogue/digital and e
% %
%This is followed by several example FMMD analyses, %This is followed by several example FMMD analyses,
\begin{itemize} \begin{itemize}
\item The first example applies FMMD to an operational amplifier inverting amplifier (see section~\ref{sec:invamp}), \item The first example applies FMMD to an operational amplifier inverting amplifier (see section~\ref{sec:invamp});
%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 inverting amplifier is analysed again, but this time with a different This inverting amplifier %is analysed again, but this time with a different
re-analysed with a different
composition of {\fgs}. The two approaches, i.e. choice of membership for {\fgs}, are then discussed. composition of {\fgs}. The two approaches, i.e. 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.
Building on the two approaches from section~\ref{sec:invamp}, re-use of the non-inverting amplifier {\dc} from section~\ref{sec:invamp} Building on the two approaches from section~\ref{sec:invamp}, re-use of the non-inverting amplifier {\dc} from section~\ref{sec:invamp}
is examined, is examined,
where re-use is appropriate in the first stage and where re-use is appropriate in the first stage and
not in the second. 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 deep 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.
%which uses %which uses
@ -55,8 +59,9 @@ Two analysis strategies are employed, one using
initially identified {\fgs} and the second using a more complex hierarchy of %{\fgs} and initially identified {\fgs} and the second using a more complex hierarchy of %{\fgs} and
{\dcs} showing {\dcs} showing
that a finer grained/more de-composed approach offers more re-use possibilities in future analysis tasks. that a finer grained/more de-composed approach offers more re-use possibilities in future analysis tasks.
%
\item Section~\ref{sec:sigmadelta} demonstrates FMMD can be applied to mixed analogue and digital circuitry \item Section~\ref{sec:sigmadelta} demonstrates FMMD can be applied to mixed analogue and digital circuitry
by analysing a sigma delta ADC. by applying FMMD to a sigma delta ADC.
%shows FMMD analysing the sigma delta %shows FMMD analysing the sigma delta
%analogue to digital converter---again with a circular signal path---which operates on both %analogue to digital converter---again with a circular signal path---which operates on both
%analogue and digital signals. %analogue and digital signals.
@ -620,9 +625,16 @@ Both approaches are followed in the next two sub-sections.
\subsection{First Approach: Inverting OPAMP using a Potential Divider {\dc}} \subsection{First Approach: Inverting OPAMP using a Potential Divider {\dc}}
We cannot simply re-use the {\dc} $PD$ from section~\ref{subsec:potdiv}, not just because Ideally we would like to re-use {\dcs} the the $PD$ from section~\ref{subsec:potdiv}, at first
the potential divider is floating. That is the polarity of glance, looks a good candidate for this.
%
However,
We cannot directly re-use $PD$ , and not just because
the potential divider is floating.
%
By floating, we mean that the polarity of
the R2 side of the potential divider is determined by the output from the op-amp. the R2 side of the potential divider is determined by the output from the op-amp.
%
The circuit schematic stipulates that the input is positive. The circuit schematic stipulates that the input is positive.
What we have then, in normal operation, is an inverted potential divider. What we have then, in normal operation, is an inverted potential divider.
%, but in addition, it facilitates the %, but in addition, it facilitates the
@ -633,7 +645,7 @@ What we have then, in normal operation, is an inverted potential divider.
%symptoms. %symptoms.
%Were the input to be guaranteed % the input will only be %Were the input to be guaranteed % the input will only be
We can therefore view it as an inverted potential divider We can therefore view it as an inverted potential divider
and analyse it as such, see table~\ref{tbl:pdneg}. 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 this range considered as HIGH.
@ -641,12 +653,12 @@ and voltages higher than this range considered as HIGH.
\begin{table}[h+] \begin{table}[h+]
\caption{Inverted Potential divider: Single failure analysis} \caption{Inverted Potential divider: Single failure analysis}
\begin{tabular}{|| l | l | c | c | l ||} \hline \begin{tabular}{|| l | l | c | c | l ||} \hline
\textbf{Failure Scenario} & & \textbf{Inverted Pot Div Effect} & & \textbf{Symptom} \\ \textbf{Failure Cause} & & \textbf{Inverted Pot Div Effect} & & \textbf{Symptom} \\
\hline \hline
FS1: R1 SHORT & & $HIGH$ & & $PDHigh$ \\ \hline FC1: R1 SHORT & & $HIGH$ & & $PDHigh$ \\ \hline
FS2: R1 OPEN & & $LOW$ & & $PDLow$ \\ \hline FC2: R1 OPEN & & $LOW$ & & $PDLow$ \\ \hline
FS3: R2 SHORT & & $LOW$ & & $PDLow$ \\ \hline FC3: R2 SHORT & & $LOW$ & & $PDLow$ \\ \hline
FS4: R2 OPEN & & $HIGH$ & & $PDHigh$ \\ \hline FC4: R2 OPEN & & $HIGH$ & & $PDHigh$ \\ \hline
\hline \hline
\end{tabular} \end{tabular}
\label{tbl:pdneg} \label{tbl:pdneg}
@ -695,9 +707,10 @@ and voltages higher than this range considered as HIGH.
\end{figure} \end{figure}
We can form a {\dc} from this, and call it an inverted potential divider $INVPD$. We can form a {\dc} from the analysis results in table~\ref{tbl:pdneg} %this,
and call it an inverted potential divider $INVPD$.
We can now form a {\fg} from the OpAmp and the $INVPD$ We can now progress the the final stage of analysis for this amplifier, by forming a {\fg} with the OpAmp and out new {\dc} $INVPD$.
\begin{table}[h+] \begin{table}[h+]
\caption{Inverting Amplifier: Single failure analysis using the $PD$ {\dc}} \caption{Inverting Amplifier: Single failure analysis using the $PD$ {\dc}}
@ -707,16 +720,16 @@ We can now form a {\fg} from the OpAmp and the $INVPD$
\textbf{cause} & & \textbf{ } & & \textbf{Failure Mode} \\ \textbf{cause} & & \textbf{ } & & \textbf{Failure Mode} \\
\hline \hline
FS1: INVPD LOW & & NEGATIVE on -input & & $ HIGH $ \\ FC1: INVPD LOW & & NEGATIVE on -input & & $ HIGH $ \\
FS2: INVPD HIGH & & Positive on -input & & $ LOW $ \\ \hline FC2: INVPD HIGH & & Positive on -input & & $ LOW $ \\ \hline
FS5: AMP L\_DN & & $ INVAMP_{low} $ & & $ LOW $ \\ FC5: AMP L\_DN & & $ INVAMP_{low} $ & & $ LOW $ \\
FS6: AMP L\_UP & & $INVAMP_{high} $ & & $ HIGH $ \\ FC6: AMP L\_UP & & $INVAMP_{high} $ & & $ HIGH $ \\
FS7: AMP NOOP & & $INVAMP_{nogain} $ & & $ LOW $ \\ FC7: AMP NOOP & & $INVAMP_{nogain} $ & & $ LOW $ \\
FS8: AMP LowSlew & & $ slow output \frac{\delta V}{\delta t} $ & & $ LOW PASS $ \\ \hline FC8: AMP LowSlew & & $ slow output \frac{\delta V}{\delta t} $ & & $ LOW PASS $ \\ \hline
\hline \hline
\end{tabular} \end{tabular}
\label{tbl:invamppd} \label{tbl:invamppd}
@ -824,8 +837,13 @@ We can now form a {\fg} from the OpAmp and the $INVPD$
%The differences are the root causes or component failure modes that %The differences are the root causes or component failure modes that
%lead to the symptoms (i.e. the symptoms are the same but causation tree will be different). %lead to the symptoms (i.e. the symptoms are the same but causation tree will be different).
We can now express the failure modes for the {\dc} $INVAMP$ thus;
$$ fm(INVAMP) = \{ {lowpass}, {high}, {low} \}.$$ $$ fm(INVAMP) = \{ {lowpass}, {high}, {low} \}.$$
We can draw a DAG representing the failure mode behaviour of
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.
%%%%% 12DEC 2012 UP to here in notes from AF email.
\subsection{Second Approach: Inverting OpAmp analysing with three components in one larger {\fg}} \subsection{Second Approach: Inverting OpAmp analysing with three components in one larger {\fg}}