Merge branch 'master' of dev:/home/robin/git/thesis

Conflicts:
	fmmd_concept/abstract.doc

noninvopamp/Makefile

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+DIA_IMAGES = dc1.png   fg1b.png  fgampa.png  fgamp.png noninv.png  opamp.png                             fg1a.png  fg1.png   fgampb.png  noninvampa.png  op1.png
+#
+#
+#
+
+%.png : %.dia
+	dia $< -e $@
+	echo source $< target $@
+
+#graphics: $(DIA_IMAGES)
+
+paper:	paper.tex noninvopamp_paper.tex $(DIA_IMAGES)
+	#latex paper.tex
+	#dvipdf paper     pdflatex cannot use eps ffs
+	pdflatex paper.tex
+	cp paper.pdf noninvopamp_paper.pdf
+	okular noninvopamp_paper.pdf
+
+
+# Remove the need for referncing graphics in subdirectories
+#
+noninvopamp_paper.tex: noninvopamp.tex paper.tex
+	cat noninvopamp.tex | sed 's/noninvopamp\///' > noninvopamp_paper.tex
+
+bib:	
+	bibtex paper
+

noninvopamp/noninvopamp.tex

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+
+\ifthenelse {\boolean{paper}}
+{
+\abstract{ 
+This paper analyses a non-inverting op-amp
+configuration, with the opamp and gain resistors using the FMMD 
+methodology.
+
+It has three base components, two resistors
+and one op-amp.
+
+The  two resistors are used as a potential divider to program the gain
+of the amplifier. We consider the two resistors as a functional group
+where the function is provides is to operate as a potential divider.
+
+The base component error modes of the 
+resistors are used to model the potential divider from
+a failure mode perspective.
+
+We determine the failure symptoms of the potential divider and 
+consider these as failure modes of a derived component.
+
+We can now create a functional group representing the amplifier,
+by bringing the failure modes from the potential divider and 
+the op-amp into a functional group.
+
+This can now be analysed and a derived component to represent the non inverting
+amplifier determined.
+}
+}
+{
+}
+
+\section{Introduction}
+
+A standard non inverting  op amp (from ``The Art of Electronics'' ~\cite{aoe}[pp.234]) is shown in figure \ref{fig:noninvamp}.
+
+\begin{figure}[h]
+ \centering
+ \includegraphics[width=200pt,keepaspectratio=true]{./noninvopamp/noninv.png}
+ % noninv.jpg: 341x186 pixel, 72dpi, 12.03x6.56 cm, bb=0 0 341 186
+ \caption{Standard non inverting amplifier configuration}
+ \label{fig:noninvamp}
+\end{figure}
+
+
+
+The functional of the resistors in this circuit is to set the amplifier gain.
+They operate as a potential divider and program the minus input on the op-amp
+to balance them against the positive input, giving the voltage gain ($G_v$)
+defined by $ G_v = 1 + \frac{R2}{R1} $ at the output.
+
+As the resistors work to provide a specific function, that of a potential divider,
+we can treat them as a functional group. This functional group has two members, R1 and R2,.
+Using the EN298 specification for resistor failure ~\cite{en298}[App.A]
+we can assign  failure modes of $OPEN$ and $SHORT$ to the resistors.
+Thus $R1$ has failure modes $\{R1\_OPEN, R1\_SHORT\}$ and $R2$ has failure modes $\{R2\_OPEN, R2\_SHORT\}$.
+
+\section{Failure Mode Analysis of the Potential Divider}
+
+Modelling this as a functional group, we can draw a circle to represent each failure mode
+in the potential divider, shown in figure \ref{fig:fg1}.
+
+
+\begin{figure}[h]
+ \centering
+ \includegraphics[width=200pt,keepaspectratio=true]{./noninvopamp/fg1.png}
+ % fg1.jpg: 430x271 pixel, 72dpi, 15.17x9.56 cm, bb=0 0 430 271
+ \caption{potential divider `functional group' failure modes}
+ \label{fig:fg1}
+\end{figure}
+
+We can now look at each of these base component failure modes,
+and determine how they will affect the operation of the potential divider.
+Each failure mode scenario we look at will be given a teat case number,
+which is represented on the diagram, with an asterisk marking 
+which failure modes is is modelling (see figure \ref{fig:fg1a}).
+
+\begin{figure}[h]
+ \centering
+ \includegraphics[width=200pt,keepaspectratio=true]{./noninvopamp/fg1a.png}
+ % fg1a.jpg: 430x271 pixel, 72dpi, 15.17x9.56 cm, bb=0 0 430 271
+ \caption{potential divider with test cases}
+ \label{fig:fg1a}
+\end{figure}
+
+
+\begin{table}[ht]
+\caption{Potential Divider: Failure Mode Effects Analysis: Single Faults} % title of Table
+\centering % used for centering table
+\begin{tabular}{||l|c|c|l|l||}
+\hline \hline
+ \textbf{Test} & \textbf{Pot.Div} & \textbf{  } & \textbf{General}   \\
+ \textbf{Case} &  \textbf{Effect} & \textbf{  } & \textbf{Symtom Description}   \\
+%   R         &    wire        & res +         & res -    & description
+\hline
+\hline
+ TC1: $R_1$ SHORT    &  LOW       &       &  LowPD \\ 
+ TC2: $R_1$  OPEN    &  HIGH        &       &  HighPD \\ \hline
+ TC3: $R_2$ SHORT    &  HIGH        &      &  HighPD \\  
+ TC4: $R_2$ OPEN     &  LOW         &      &  LowPD \\ \hline
+\hline
+\end{tabular} 
+\label{pdfmea}
+\end{table}
+
+
+We can now collect the symptoms of failure. From the four base component failure modes, we now
+have two symptoms, $LowPD, HighPD$. 
+
+We can represent the collection of these symptoms by drawing connecting lines between 
+the test cases and naming them (see figure \ref{fig:fg1b}).
+
+
+\begin{figure}[h]
+ \centering
+ \includegraphics[width=200pt,keepaspectratio=true]{./noninvopamp/fg1b.png}
+ % fg1b.jpg: 430x271 pixel, 72dpi, 15.17x9.56 cm, bb=0 0 430 271
+ \caption{Collection of potential divider failure mode symptoms}
+ \label{fig:fg1b}
+\end{figure}
+
+We can now make a `derived component' to represent this potential divider.
+This {\dc} will have two failure failure modes.
+We can use the symbol $\bowtie$ to represent taking the analysed 
+{\fg} and creating from it, a {\dc}.
+
+%We could represent it algebraically thus: $ \bowtie(PotDiv) = 
+\begin{figure}[h]
+ \centering
+ \includegraphics[width=200pt,keepaspectratio=true]{./noninvopamp/dc1.png}
+ % dc1.jpg: 430x619 pixel, 72dpi, 15.17x21.84 cm, bb=0 0 430 619
+ \caption{From functional group to derived component}
+ \label{fig:dc1}
+\end{figure}
+
+Because the derived component is defined by its failure modes, we can use it
+as a building block for other {\fgs} in the same way as we used the resistors R1 and R2.
+
+\section{Failure Mode Analysis of the OP-AMP}
+
+
+
+Let use now consider the op-amp. According to 
+FMD-91~\cite{fmd91}[3-116] an op amp may have the follow failure modes
+latchup(12.5\%), latchdown(6\%), nooperation(31.3\%), lowslewrate(50\%).
+
+We can represent these failure modes on a diagram (see figure~\ref{fig:op1}).
+\clearpage
+\section{Bringing the OP amp and the potential divider together}
+
+We can now consider bringing the OP amp and the potential divider together to
+for an amplifier. We have the failure modes of the functional group for the potential divider, so we do not need to consider the individual resistor failure modes that define its behaviour.
+We can make a new functional group to represent the amplifier, by bringing the component opamp
+and the component potential divider into a new functional group.
+
+
+
+\begin{figure}[h]
+ \centering
+ \includegraphics[width=200pt,keepaspectratio=true]{./noninvopamp/op1.png}
+ % op1.jpg: 406x221 pixel, 72dpi, 14.32x7.80 cm, bb=0 0 406 221
+ \caption{Op Amp failure modes}
+ \label{fig:op1}
+\end{figure}
+
+
+This functional group has the failure modes from the op-amp component, and the failure modes
+from the potential divider {\dc} to analyse represented by figure~\ref{fig:fgamp}.
+
+
+\begin{figure}[h]
+ \centering
+ \includegraphics[width=200pt,keepaspectratio=true]{./noninvopamp/fgamp.png}
+ % fgamp.jpg: 430x330 pixel, 72dpi, 15.17x11.64 cm, bb=0 0 430 330
+ \caption{Amplifier Functional Group}
+ \label{fig:fgamp}
+\end{figure}
+
+
+
+We can now place test cases on this (note this analysis considers single failure modes only
+where we want to model multiple failures, we can over lap contours, and place the test cases in overlapping 
+regions) see figure~\ref{fig:fgampa}.
+
+
+
+
+\begin{figure}[h]
+ \centering
+ \includegraphics[width=200pt,keepaspectratio=true]{./noninvopamp/fgampa.png}
+ % fgampa.jpg: 430x330 pixel, 72dpi, 15.17x11.64 cm, bb=0 0 430 330
+ \caption{Amplifier Functional Group with Test Cases}
+ \label{fig:fgampa.jpg}
+\end{figure}
+
+
+
+\begin{table}[ht]
+\caption{Non Inverting Amplifier: Failure Mode Effects Analysis: Single Faults} % title of Table
+\centering % used for centering table
+\begin{tabular}{||l|c|c|l|l||}
+\hline \hline
+ \textbf{Test} & \textbf{Amplifier} & \textbf{  } & \textbf{General}   \\
+ \textbf{Case} &  \textbf{Effect} & \textbf{  } & \textbf{Symtom Description}   \\
+%   R         &    wire        & res +         & res -    & description
+\hline
+\hline
+ TC1: $OPAMP$ LatchUP    &  Output High          &      &  AMPHigh \\ 
+ TC2: $OPAMP$ LatchDown  &  Output Low           &      &  AMPLow \\ \hline
+ TC3: $OPAMP$ No Operation &  Output Low         &      &  AMPLow \\  
+ TC4: $OPAMP$ Low Slew     &  Low pass filtering &      &  LowPass \\ \hline
+ TC5: $PD$ LowPD         &   Output High          &      &  AMPHigh \\ \hline
+ TC6: $PD$ HighPD        &  Output Low          &      &  AMPLow \\ \hline 
+ %TC7: $R_2$ OPEN     &  LOW       &      &  LowPD \\ \hline
+\hline
+\end{tabular} 
+\label{ampfmea}
+\end{table}
+
+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 
+and use it it to model higher level functional groups see figure~\ref{fig:noninvampa}.
+
+
+
+\begin{figure}[h]
+ \centering
+ \includegraphics[width=200pt,keepaspectratio=true]{./noninvopamp/noninvampa.png}
+ % noninvampa.jpg: 436x720 pixel, 72dpi, 15.38x25.40 cm, bb=0 0 436 720
+ \caption{Non Inverting Amplifier Derived Component}
+ \label{fig:noninvampa}
+\end{figure}
+
+
+%failure mode contours).
+\clearpage
+\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

noninvopamp/paper.tex

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+
+\documentclass[a4paper,10pt]{article}
+\usepackage{graphicx}
+\usepackage{fancyhdr}
+\usepackage{tikz}
+\usetikzlibrary{shapes,snakes}
+\usepackage{amsfonts,amsmath,amsthm}
+\input{../style}
+\usepackage{ifthen}
+\usepackage{lastpage}
+
+\newboolean{paper}
+\setboolean{paper}{true} % boolvar=true or false
+
+
+%\newtheorem{definition}{Definition:}
+
+\begin{document}
+\pagestyle{fancy}
+\fancyhf{}
+%\renewcommand{\chaptermark}[1]{\markboth{ \emph{#1}}{}}
+\fancyhead[LO]{}
+\fancyhead[RE]{\leftmark}
+%\fancyfoot[LE,RO]{\thepage}
+\cfoot{Page \thepage\ of \pageref{LastPage}}
+\rfoot{\today}
+\lhead{Two stage FMMD analysis of a non inverting op-amp}
+
+%\outerhead{{\small\bf Developing a rigorous bottom-up modular static failure mode modelling methodology}}
+%\innerfoot{{\small\bf R.P. Clark } }   
+                                              % numbers at outer edges
+\pagenumbering{arabic}                        % Arabic page numbers hereafter
+\author{R.P.Clark}
+\title{Two stage FMMD analysis of a non inverting op-amp}
+\maketitle 
+\input{noninvopamp_paper}
+
+\bibliographystyle{plain}
+\bibliography{../vmgbibliography,../mybib}
+
+\today
+\end{document}

thesis.tex

@@ -139,6 +139,10 @@
 \typeout{ ---------------- pt100}
 \input{pt100/pt100}
 
+\chapter{FMMD functional~groups to \\derived component example : Non Inverting Op-AMP}
+\typeout{ ---------------- non inv op amp}
+\input{noninvopamp/noninvopamp}
+
 \chapter{FMMD functional~group to \\derived component example: `ON/OFF' Switch}
 \typeout{ ---------------- switch1}
 %\input{switch1/switch1}