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
since the dawn of the industrial age~\cite{indacc01}~\cite{steamboilers}.
The philosophy behind safety measure has progressed
@ -27,12 +27,6 @@ and, using contract programmed software, allows the modelling of integrated
software/electrical systems.
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.
}
\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,
\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;
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.
%
\item Section~\ref{sec:diffamp} analyses a circuit where two op-amps are used
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}
is examined,
where re-use is appropriate in the first stage and
not in the second.
%
\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}
increasing test efficiency. This example also serves to show a deep hierarchy of {\dcs}.
%
\item Section~\ref{sec:bubba} shows FMMD applied to a
loop topology---using a `Bubba' oscillator---demonstrating how FMMD differs from fault diagnosis techniques.
%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
{\dcs} showing
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
by analysing a sigma delta ADC.
by applying FMMD to a sigma delta ADC.
%shows FMMD analysing the sigma delta
%analogue to digital converter---again with a circular signal path---which operates on both
%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}}
We cannot simply re-use the {\dc} $PD$ from section~\ref{subsec:potdiv}, not just because
the potential divider is floating. That is the polarity of
Ideally we would like to re-use {\dcs} the the $PD$ from section~\ref{subsec:potdiv}, at first
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 circuit schematic stipulates that the input is positive.
What we have then, in normal operation, is an inverted potential divider.
%, but in addition, it facilitates the
@ -633,7 +645,7 @@ What we have then, in normal operation, is an inverted potential divider.
%symptoms.
%Were the input to be guaranteed % the input will only be
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.
Thus negative or low voltages can be considered as LOW
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+]
\caption{Inverted Potential divider: Single failure analysis}
\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
FS1: R1 SHORT & & $HIGH$ & & $PDHigh$ \\ \hline
FS2: R1 OPEN & & $LOW$ & & $PDLow$ \\ \hline
FS3: R2 SHORT & & $LOW$ & & $PDLow$ \\ \hline
FS4: R2 OPEN & & $HIGH$ & & $PDHigh$ \\ \hline
FC1: R1 SHORT & & $HIGH$ & & $PDHigh$ \\ \hline
FC2: R1 OPEN & & $LOW$ & & $PDLow$ \\ \hline
FC3: R2 SHORT & & $LOW$ & & $PDLow$ \\ \hline
FC4: R2 OPEN & & $HIGH$ & & $PDHigh$ \\ \hline
\hline
\end{tabular}
\label{tbl:pdneg}
@ -695,9 +707,10 @@ and voltages higher than this range considered as HIGH.
\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+]
\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} \\
\hline
FS1: INVPD LOW & & NEGATIVE on -input & & $ HIGH $ \\
FS2: INVPD HIGH & & Positive on -input & & $ LOW $ \\ \hline
FC1: INVPD LOW & & NEGATIVE on -input & & $ HIGH $ \\
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
\end{tabular}
\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
%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;
$$ fm(INVAMP) = \{ {lowpass}, {high}, {low} \}.$$
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}}