From eab783bdb275c8d3c41d0fe1437d4b2436bdff30 Mon Sep 17 00:00:00 2001 From: Robin Clark Date: Fri, 6 Jan 2012 17:51:58 +0000 Subject: [PATCH] OK now need to do working out for the final two stages --- opamp_circuits_C_GARRETT/opamps.tex | 38 +++++++++++++++++++++++------ thesis.tex | 2 +- 2 files changed, 32 insertions(+), 8 deletions(-) diff --git a/opamp_circuits_C_GARRETT/opamps.tex b/opamp_circuits_C_GARRETT/opamps.tex index 5ab2391..8d613b8 100644 --- a/opamp_circuits_C_GARRETT/opamps.tex +++ b/opamp_circuits_C_GARRETT/opamps.tex @@ -35,6 +35,11 @@ Not a document to be proof read. Proof of analysis concept. Function $fm$ applied to a component returns its failure modes. + + +The circuits specified are not typical saftey critical circuitry which usually +has both redundancy and self~checking and/or diagnostic features build in. +These are examples of the FMMD methodology being applied to some standard electronic circuits. \end{abstract} \maketitle \tableofcontents @@ -457,7 +462,7 @@ We merely have to choose a top level event and work down using $XOR$ gates. This circuit performs poorly from a safety point of view. Its failure modes could be indistinguishable from valid readings (especially -wihen it becomes a V2 follower). +when it becomes a V2 follower). \begin{figure}[h] \centering @@ -773,10 +778,20 @@ This circuit is described in the Analog Applications Journal~\cite{bubba}. The circuit uses four 45 degree phase shifts, and an inverting amplifier to provide gain and the final 180 degrees of phase shift (making a total of 360 degrees of phase shift). -We identifiy three functional groups, the inverting amplifer (analysed in section~\ref{fig:invamp}), -a 45 degree phase shifter (a {$10k\Omega$} resistor and a $10nF$ capacitor) and a noninverting buffer +From a fault finding perspective this circuit is less than ideal. +The signal path is circular (its a positive feedback circuit) and most failures would simply cause the output to stop oscillating. +However, FMMD is a bottom -up analysis methodology and we can therefore still identify +{\fgs} and apply analysis from a failure mode perspective. + +If we were to analyse this circuit without modularisation, we have 14 components with +($4.4 +10.2 = 36$) failure modes . Applying equation~\ref{eqnrd2} gives a complexity comparison figure of $13.36=468$. +The reduce the complexity required to analyse this circuit we apply FMMD and start by determining {\fgs}. + + +We identify three types functional groups, an inverting amplifier (analysed in section~\ref{fig:invamp}), +a 45 degree phase shifter (a {$10k\Omega$} resistor and a $10nF$ capacitor) and a non-inverting buffer amplifier. We can name these $INVAMP$, $PHS45$ and $NIBUFF$ respectively. -We can use these {\fgs} to describe the circuit in block diagram form, as in figure ~\ref{fig:bubbablock}. +We can use these {\fgs} to describe the circuit in block diagram form, see figure ~\ref{fig:bubbablock}. \begin{figure}[h] \centering @@ -838,7 +853,7 @@ $$ fm(NIBUFF) = fm(OPAMP) = \{L\_{up}, L\_{dn}, Noop, L\_slew \} $$ % describe what we are doing, a buffered 45 degree phase shift element -\subsection{Bringing the functional Groups Together: The `Bubba' Oscillator.} +\subsection{Bringing the functional Groups Together: FMMD model of the `Bubba' Oscillator.} We could at this point bring all the {\dcs} together into one large functional group (see figure~\ref{fig:poss1finalbubba}) @@ -848,7 +863,9 @@ The capactior and 180 degree inverting amplifier, form a {\fg} providing an amplified 225 degree phase shift, which we can call $PHS225AMP$. % We could also merge the $NIBUFF$ and $PHS45$ -{\dcs} into a {\fg} and the resulant derived component from this we could call a $BUFF45$, and then with those three, form a $PHS135BUFFERED$ functional group -- with the remaining $PHS45$ and the $INVAMP$ in a second group $PHS225AMP$, +{\dcs} into a {\fg} and the resulant derived component from this we could call a $BUFF45$, +and then with those three, form a $PHS135BUFFERED$ +functional group---with the remaining $PHS45$ and the $INVAMP$ (re-used from section~\ref{sec:invamp})in a second group $PHS225AMP$--- and then merge $PHS135BUFFERED$ and $PHS225AMP$ in a final stage (see figure~\ref{fig:poss2finalbubba}) @@ -1239,7 +1256,14 @@ in component ${c_i}$, is given by \end{equation} This can be simplified if we can determine the total number of failure modes in the system $K$, (i.e. $ K = \sum_{n=1}^{|G|} {|fm(c_n)|}$); -equation~\ref{eqn:CC} becomes $$ CC(\FG) = K.(|\FG|-1).$$ +equation~\ref{eqn:CC} becomes + +%$$ +\begin{equation} +\label{eqn:rd2} + CC(\FG) = K.(|\FG|-1). +\end{equation} +%$$ %Equation~\ref{eqn:rd} can also be expressed as % % \begin{equation} diff --git a/thesis.tex b/thesis.tex index 6c0d9b2..85f7a5e 100644 --- a/thesis.tex +++ b/thesis.tex @@ -5,7 +5,7 @@ \usepackage{tikz} \usetikzlibrary{shapes,snakes} \usetikzlibrary{shapes.gates.logic.US,trees,positioning,arrows} -\usepackage{subfigure} +%\usepackage{subfigure} \usepackage{amsfonts,amsmath,amsthm} \usepackage{algorithm} \usepackage{algorithmic}