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Robin P. Clark 2013-09-17 13:48:34 +01:00
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38
submission_thesis/CH5_Examples/copy.tex
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@ -22,7 +22,7 @@ this examines re-use of the potential divider {\dc} from section~\ref{subsec:pot
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. effects of choice of membership for {\fgs} are then discussed. The two approaches, i.e. effects of choice of membership for {\fgs} are then discussed.
%\ %\
fmmdglossOPAMP \fmmdglossOPAMP
\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}
@ -53,6 +53,11 @@ by analysing a sigma delta ADC.
safety critical temperature sensor circuit, analysed for single and double failure mode scenarios. safety critical temperature sensor circuit, analysed for single and double failure mode scenarios.
\end{itemize} \end{itemize}
\clearpage \clearpage
\section{Example Analysis: Inverting OPAMP} \section{Example Analysis: Inverting OPAMP}
% %
@ -66,6 +71,19 @@ safety critical temperature sensor circuit, analysed for single and double failu
\label{fig:invamp} \label{fig:invamp}
\end{figure} \end{figure}
% %
Figure~\ref{fig:invamp} shows a standard configuration inverting amplifier.
A valid range for the output value of this circuit is assumed.
%
%Thus negative or low voltages can be considered as LOW
%and voltages higher than a given threshold considered as HIGH.
%
Because the amplifier inverts and the input is guaranteed positive any
output voltage above or equal to zero would be erroneous.
%
This would be an `$AMP_{HIGH}$' failure symptom.
%
A threshold would be determined for an `$AMP_{LOW}$' failure symptom (i.e. the output voltage more negative than expected). % error given the expected input range.
%
%This configuration is interesting from methodology pers. %This configuration is interesting from methodology pers.
There are two obvious ways in which this circuit can be modelled. There are two obvious ways in which this circuit can be modelled.
% %
@ -100,17 +118,6 @@ In normal operation then, this is an inverted potential divider.
It must therefore be viewed as an inverted potential divider It must therefore be viewed as an inverted potential divider
and analysed as such; see table~\ref{tbl:pdneg}. and analysed as such; see table~\ref{tbl:pdneg}.
% %
A valid range for the output value of this circuit is assumed.
%
%Thus negative or low voltages can be considered as LOW
%and voltages higher than a given threshold considered as HIGH.
%
Because the amplifier inverts and the input is guaranteed positive any
output voltage above or equal to zero would be erroneous.
%
This would be an $AMP_{HIGH}$ failure symptom.
%
A threshold would be determined for an $AMP_{LOW}$ failure symptom (i.e. the output voltage more negative than expected). % error given the expected input range.
% %
\begin{table}[h+] \begin{table}[h+]
\caption{Inverted Potential divider: Single failure analysis} \caption{Inverted Potential divider: Single failure analysis}
@ -199,6 +206,7 @@ by forming a {\fg} with the OpAmp and the new {\dc} $IPD$.
\end{table} \end{table}
% %
% %
\clearpage
%%This gives the same results as the analysis from figure~\ref{fig:invampanalysis}. %%This gives the same results as the analysis from figure~\ref{fig:invampanalysis}.
% %
% %
@ -303,7 +311,7 @@ by forming a {\fg} with the OpAmp and the new {\dc} $IPD$.
Failure modes for the {\dc} $INVAMP$ can be expressed thus; Failure modes for the {\dc} $INVAMP$ can be expressed thus;
%% $$ fm(INVAMP) = \{ {lowpass}, {high}, {low} \}.$$ %% $$ fm(INVAMP) = \{ {lowpass}, {high}, {low} \}.$$
$$ fm(INVAMP) = \{ HIGH, LOW, LOW PASS \} .$$ $$ fm(INVAMP) = \{ HIGH, LOW, LOW PASS \} .$$
% \clearpage
A DAG is drawn representing the failure mode behaviour of A DAG is drawn representing the failure mode behaviour of
this amplifier (see figure~\ref{fig:invdag1}). this amplifier (see figure~\ref{fig:invdag1}).
% %
@ -311,8 +319,8 @@ Note that this allows failure symptoms to be traced back to causes, i.e.
to traverse from system level or top failure modes to base component failure modes. 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
\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}}
\label{subsec:invamp2} \label{subsec:invamp2}
@ -368,7 +376,7 @@ This concern is re-visited in the differencing amplifier example in the next sec
\label{tbl:invamp} \label{tbl:invamp}
\end{table} \end{table}
\clearpage %\clearpage
\subsection{Comparison between the two approaches} \subsection{Comparison between the two approaches}
\label{sec:invampcc} \label{sec:invampcc}