diff --git a/noninvopamp/noninvopamp.tex b/noninvopamp/noninvopamp.tex index a2f92f6..b1071c6 100644 --- a/noninvopamp/noninvopamp.tex +++ b/noninvopamp/noninvopamp.tex @@ -1,3 +1,4 @@ +\def\layersep{2.5cm} \ifthenelse {\boolean{paper}} { @@ -256,6 +257,12 @@ regions) see figure~\ref{fig:fgampa}. \label{ampfmea} \end{table} + +Let us consider, for the sake of example, that the voltage follower (very low gain of 1.0) +amplification chracteristics from +TC1 and TC6 can be considered as low output from the OPAMP for the application +in hand (say milli-volt signal amplification). + For this amplifier configuration we have three failure modes, $AMPHigh, AMPLow, LowPass$.%see figure~\ref{fig:fgampb}. We can now derive a `component' to represent this amplifier configuration (see figure ~\ref{fig:noninvampa}). @@ -276,12 +283,15 @@ We can now derive a `component' to represent this amplifier configuration (see f \section{Directed Acyclic Failure Mode Graph} +We can now represent the FMMD analysis as a directed graph, see figure \ref{fig:noninvdag0}. +With the information structured in this way, we can trace the high level failure mode symptoms +back to their potential causes. \begin{figure} \centering \begin{tikzpicture}[shorten >=1pt,->,draw=black!50, node distance=\layersep] \tikzstyle{every pin edge}=[<-,shorten <=1pt] - \tikzstyle{fmmde}=[circle,fill=black!25,minimum size=17pt,inner sep=0pt] + \tikzstyle{fmmde}=[circle,fill=black!25,minimum size=30pt,inner sep=0pt] \tikzstyle{component}=[fmmde, fill=green!50]; \tikzstyle{failure}=[fmmde, fill=red!50]; \tikzstyle{symptom}=[fmmde, fill=blue!50]; @@ -292,8 +302,10 @@ We can now derive a `component' to represent this amplifier configuration (see f % This is the same as writing \foreach \name / \y in {1/1,2/2,3/3,4/4} % \node[component, pin=left:Input \#\y] (I-\name) at (0,-\y) {}; - \node[component] (C-1) at (0,-1) {$C^0_1$}; - \node[component] (C-2) at (0,-3) {$C^0_2$}; + \node[component] (OPAMP) at (0,-6) {$OPAMP$}; + \node[component] (R1) at (0,-11) {$R_1$}; + \node[component] (R2) at (0,-15) {$R_2$}; + %\node[component] (C-3) at (0,-5) {$C^0_3$}; %\node[component] (K-4) at (0,-8) {$K^0_4$}; %\node[component] (C-5) at (0,-10) {$C^0_5$}; @@ -304,56 +316,100 @@ We can now derive a `component' to represent this amplifier configuration (see f %\foreach \name / \y in {1,...,5} % \path[yshift=0.5cm] - \node[failure] (C-1a) at (\layersep,-1) {a}; - \node[failure] (C-1b) at (\layersep,-2) {b}; - \node[failure] (C-2a) at (\layersep,-3) {a}; - \node[failure] (C-2b) at (\layersep,-4) {b}; - + \node[failure] (OPAMPLU) at (\layersep,-2) {latchup}; + \node[failure] (OPAMPLD) at (\layersep,-4) {latchdown}; + \node[failure] (OPAMPNP) at (\layersep,-6) {noop}; + \node[failure] (OPAMPLS) at (\layersep,-8) {lowslew}; + + \node[failure] (R1SHORT) at (\layersep,-11) {$R1_{SHORT}$}; + \node[failure] (R1OPEN) at (\layersep,-13) {$R1_{OPEN}$}; + + \node[failure] (R2SHORT) at (\layersep,-15) {$R2_{SHORT}$}; + \node[failure] (R2OPEN) at (\layersep,-17) {$R2_{OPEN}$}; + + + % Draw the output layer node - % Connect every node in the input layer with every node in the - % hidden layer. - %\foreach \source in {1,...,4} - % \foreach \dest in {1,...,5} - \path (C-1) edge (C-1a); - \path (C-1) edge (C-1b); - \path (C-2) edge (C-2a); - \path (C-2) edge (C-2b); - - %\node[symptom,pin={[pin edge={->}]right:Output}, right of=C-1a] (O) {}; - \node[symptom, right of=C-1a] (s1) {s1}; - \node[symptom, right of=C-2a] (s2) {s2}; - - - - \path (C-2b) edge (s1); - \path (C-1a) edge (s1); - - \path (C-2a) edge (s2); - \path (C-1b) edge (s2); - - %\node[component, right of=s1] (DC) {$C^1_1$}; - - %\path (s1) edge (DC); - %\path (s2) edge (DC); - - - - % Connect every node in the hidden layer with the output layer - %\foreach \source in {1,...,5} - % \path (H-\source) edge (O); - - % Annotate the layers - \node[annot,above of=C-1a, node distance=1cm] (hl) {Failure modes}; - \node[annot,left of=hl] {Base Components}; - \node[annot,right of=hl](s) {Symptoms}; +% % Connect every node in the input layer with every node in the +% % hidden layer. +% %\foreach \source in {1,...,4} +% % \foreach \dest in {1,...,5} + \path (OPAMP) edge (OPAMPLU); + \path (OPAMP) edge (OPAMPLD); + \path (OPAMP) edge (OPAMPNP); +\path (OPAMP) edge (OPAMPLS); + + \path (R1) edge (R1SHORT); + \path (R1) edge (R1OPEN); + + \path (R2) edge (R2SHORT); + \path (R2) edge (R2OPEN); + + + % Potential divider failure modes + % + \node[symptom] (PDHIGH) at (\layersep*2,-13) {$PD_{HIGH}$}; + \node[symptom] (PDLOW) at (\layersep*2,-15) {$PD_{LOW}$}; + + + + \path (R1OPEN) edge (PDHIGH); + \path (R2SHORT) edge (PDHIGH); + + + \path (R2OPEN) edge (PDLOW); + \path (R1SHORT) edge (PDLOW); + + + + \node[symptom] (AMPHIGH) at (\layersep*3,-9) {$AMP_{HIGH}$}; + \node[symptom] (AMPLOW) at (\layersep*3,-11) {$AMP_{LOW}$}; + \node[symptom] (AMPLP) at (\layersep*3,-13) {$LOWPASS$}; + + \path (PDLOW) edge (AMPHIGH); + \path (OPAMPLU) edge (AMPHIGH); + + \path (PDHIGH) edge (AMPLOW); + \path (OPAMPNP) edge (AMPLOW); + \path (OPAMPLD) edge (AMPLOW); + + \path (OPAMPLS) edge (AMPLP); +% %\node[symptom,pin={[pin edge={->}]right:Output}, right of=C-1a] (O) {}; +% \node[symptom, right of=C-1a] (s1) {s1}; +% \node[symptom, right of=C-2a] (s2) {s2}; +% +% +% +% \path (C-2b) edge (s1); +% \path (C-1a) edge (s1); +% +% \path (C-2a) edge (s2); +% \path (C-1b) edge (s2); +% +% %\node[component, right of=s1] (DC) {$C^1_1$}; +% +% %\path (s1) edge (DC); +% %\path (s2) edge (DC); +% +% +% +% % Connect every node in the hidden layer with the output layer +% %\foreach \source in {1,...,5} +% % \path (H-\source) edge (O); +% +% % Annotate the layers +% \node[annot,above of=C-1a, node distance=1cm] (hl) {Failure modes}; +% \node[annot,left of=hl] {Base Components}; +% \node[annot,right of=hl](s) {Symptoms}; %\node[annot,right of=s](dcl) {Derived Component}; \end{tikzpicture} % End of code - \caption{DAG representing failure modes and symptoms of $FG^0_1$} - \label{fig:dag0} + \caption{DAG representing failure modes and symptoms of the Non Inverting Op-amp Circuit} + \label{fig:noninvdag0} \end{figure} +\clearpage \section{Conclusion} We now have a derived component that represents the failure modes of a non-inverting @@ -366,12 +422,3 @@ statistical literature is available ~\cite{mil1991}~\cite{fmd91}. Software used to edit these diagrams, keeps the model in a directed acyclic graph data structure for this purpose. -%\clearpage % refs etc come next - - -%\vspace{60pt} -%$$ \int_{0\-}^{\infty} f(t).e^{-s.t}.dt \; | \; s \in \mathcal{C}$$ -%\today - -% $$\frac{-b\pm\sqrt{ {b^2-4ac}}}{2a}$$ -%\today