diff --git a/submission_thesis/CH5_Examples/copy.tex b/submission_thesis/CH5_Examples/copy.tex index b3ac068..9b9385e 100644 --- a/submission_thesis/CH5_Examples/copy.tex +++ b/submission_thesis/CH5_Examples/copy.tex @@ -84,6 +84,7 @@ However, $PD$ cannot be directly re-used, and not just because the potential divider is floating i.e. that the polarity of the R2 side of the potential divider is determined by the output from the op-amp. +% \fmmdglossOPAMP % The circuit schematic stipulates that the input is positive. @@ -101,18 +102,25 @@ 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. +%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+] \caption{Inverted Potential divider: Single failure analysis} \begin{tabular}{|| l | l | c | c | l ||} \hline - \textbf{Failure Cause} & & \textbf{Inverted Pot Div Effect} & & \textbf{Symptom} \\ + \textbf{Failure Cause} & & \textbf{Inverted Pot Divider, $IPD$, Effect} & & \textbf{Symptom} \\ \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 + FC1: R1 SHORT & & $HIGH$ & & $IPDHigh$ \\ \hline + FC2: R1 OPEN & & $LOW$ & & $IPDLow$ \\ \hline + FC3: R2 SHORT & & $LOW$ & & $IPDLow$ \\ \hline + FC4: R2 OPEN & & $HIGH$ & & $IPDHigh$ \\ \hline \hline \end{tabular} \label{tbl:pdneg} @@ -145,8 +153,8 @@ and voltages higher than a given threshold considered as HIGH. % Potential divider failure modes % - \node[symptom] (PDHIGH) at (\layersep*2,-0.7) {$PD_{HIGH}$}; - \node[symptom] (PDLOW) at (\layersep*2,-2.2) {$PD_{LOW}$}; + \node[symptom] (PDHIGH) at (\layersep*2,-0.5) {$IPD_{HIGH}$}; + \node[symptom] (PDLOW) at (\layersep*2,-2.4) {$IPD_{LOW}$}; \path (R1OPEN) edge (PDLOW); \path (R2SHORT) edge (PDLOW); @@ -156,16 +164,16 @@ and voltages higher than a given threshold considered as HIGH. \end{tikzpicture} % - \caption{Failure symptoms of the `Inverted Potential Divider' $INVPD$} + \caption{Failure symptoms of the `Inverted Potential Divider' $IPD$} \label{fig:pdneg} \end{figure} % % A {\dc} can be formed from the analysis results in table~\ref{tbl:pdneg} %this, -and called an inverted potential divider $INVPD$. +and called an inverted potential divider ($IPD$). % The final stage of analysis for this amplifier, is made by -by forming a {\fg} with the OpAmp and our new {\dc} $INVPD$. +by forming a {\fg} with the OpAmp and the new {\dc} $IPD$. % \begin{table}[h+] \caption{Inverting Amplifier: Single failure analysis using the $PD$ {\dc}} @@ -175,8 +183,8 @@ by forming a {\fg} with the OpAmp and our new {\dc} $INVPD$. \textbf{cause} & & \textbf{ } & & \textbf{Failure Mode} \\ \hline - FC1: INVPD LOW & & NEGATIVE on -input & & $ HIGH $ \\ - FC2: INVPD HIGH & & Positive on -input & & $ LOW $ \\ \hline + FC1: IPD LOW & & Negative on -input & & $ HIGH $ \\ + FC2: IPD HIGH & & Positive on -input & & $ LOW $ \\ \hline FC5: AMP L\_DN & & $ INVAMP_{low} $ & & $ LOW $ \\ @@ -256,8 +264,8 @@ by forming a {\fg} with the OpAmp and our new {\dc} $INVPD$. % Potential divider failure modes % - \node[symptom] (PDHIGH) at (\layersep*2,-6) {$PD_{HIGH}$}; - \node[symptom] (PDLOW) at (\layersep*2,-7.6) {$PD_{LOW}$}; + \node[symptom] (PDHIGH) at (\layersep*2,-5.8) {$IPD_{HIGH}$}; + \node[symptom] (PDLOW) at (\layersep*2,-8.1) {$IPD_{LOW}$}; @@ -270,9 +278,9 @@ by forming a {\fg} with the OpAmp and our new {\dc} $INVPD$. - \node[symptom] (AMPHIGH) at (\layersep*3.4,-3) {$AMP_{HIGH}$}; - \node[symptom] (AMPLOW) at (\layersep*3.4,-5) {$AMP_{LOW}$}; - \node[symptom] (AMPLP) at (\layersep*3.4,-7) {$LOWPASS$}; + \node[symptom] (AMPHIGH) at (\layersep*4.4,-3) {$AMP_{HIGH}$}; + \node[symptom] (AMPLOW) at (\layersep*4.4,-5) {$AMP_{LOW}$}; + \node[symptom] (AMPLP) at (\layersep*4.4,-7) {$LOWPASS$}; \path (PDLOW) edge (AMPHIGH); \path (OPAMPLU) edge (AMPHIGH); @@ -299,8 +307,7 @@ Failure modes for the {\dc} $INVAMP$ can be expressed thus; A DAG is drawn representing the failure mode behaviour of this amplifier (see figure~\ref{fig:invdag1}). % -Note that this allows us -to trace failure symptoms back to causes, i.e. +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. %%%%% 12DEC 2012 UP to here in notes from AF email. % @@ -310,10 +317,12 @@ to traverse from system level or top failure modes to base component failure mod \label{subsec:invamp2} % -The problem above is analysed without using an intermediate $INVPD$ +The problem above is analysed without using an intermediate $IPD$ derived component. % If the input voltage was not constrained to being positive this one stage analysis would be necessary. +% +% This concern is re-visited in the differencing amplifier example in the next section. %We can view the failure mode mode produced with FMMD as a DAG %in figure~\ref{fig: @@ -336,13 +345,13 @@ This concern is re-visited in the differencing amplifier example in the next sec \textbf{cause} & & \textbf{ } & & \textbf{Failure Mode} \\ \hline - FS1: R1 SHORT & & NEGATIVE out of range & & $ HIGH $ \\ + FS1: R1 SHORT & & -ve in high gain & & $ LOW $ \\ % FS1: R1 SHORT -ve in & & POSITIVE out of range & & $ OUT OF RANGE $ \\ \hline - FS2: R1 OPEN & & zero output & & $ LOW $ \\ \hline + FS2: R1 OPEN & & zero volt follower & & $ HIGH $ \\ \hline % FS2: R1 OPEN -ve in & & zero output & & $ ZERO OUTPUT $ \\ \hline - FS3: R2 SHORT & & $INVAMP_{nogain} $ & & $ LOW $ \\ + FS3: R2 SHORT & & $INVAMP_{unitygain} $ & & $ HIGH $ \\ % FS3: R2 SHORT -ve in & & $INVAMP_{nogain} $ & & $ NO GAIN $ \\ \hline FS4: R2 OPEN & & NEGATIVE out of range $ $ & & $ LOW$ \\ \hline @@ -366,9 +375,9 @@ This concern is re-visited in the differencing amplifier example in the next sec The first analysis used two FMMD stages. % The first stage analysed an inverted potential divider %, analyses its failure modes, -giving the {\dc} (INVPD). +giving the {\dc} (IPD). % -The next stage analysed a {\fg} comprised of the INVPD and an OpAmp. +The next stage analysed a {\fg} comprised of the IPD and an OpAmp. % The second analysis (3 components) looked at the effects of each failure mode of each resistor and the op-amp. % circuit. @@ -1338,7 +1347,7 @@ This can be the first {\fg} and it is analysed in table~\ref{detail:SUMJINT}: %{ % $$FG = \{R1, R2, IC1, C1 \} .$$ % -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 the new {\dc} $SUMJINT$ are $$\{ V_{in} DOM, V_{fb} DOM, NO\_INTEGRATION, HIGH, LOW \} .$$ % %\clearpage