copied from non-inv but have done into/abstract
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Robin Clark
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invopamp/Makefile
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27
invopamp/Makefile
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DIA_IMAGES = dc1.png fg1b.png fgampa.png fgamp.png opamp.png fg1a.png fg1.png fgampb.png op1.png
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#
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#
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#
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%.png : %.dia
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dia $< -e $@
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echo source $< target $@
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#graphics: $(DIA_IMAGES)
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paper: paper.tex invopamp_paper.tex $(DIA_IMAGES)
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#latex paper.tex
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#dvipdf paper pdflatex cannot use eps ffs
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pdflatex paper.tex
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cp paper.pdf invopamp_paper.pdf
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okular invopamp_paper.pdf
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# Remove the need for referncing graphics in subdirectories
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#
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invopamp_paper.tex: invopamp.tex paper.tex
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cat invopamp.tex | sed 's/invopamp\///' > invopamp_paper.tex
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bib:
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bibtex paper
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@ -8,25 +8,27 @@ This paper analyses an inverting op-amp
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configuration, with the opamp and gain resistors using the FMMD
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methodology.
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%
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It has three base components, two resistors
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It has five base components, ifour resistors %two resistors programming gain, two programming a reference, or virtual ground voltage
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and one op-amp.
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The two resistors are used as a current balance/virtual ground to program the gain
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of the amplifier. We consider the two resistors as a functional group
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where their function is to operate as a current balance/virtual ground.
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Two resistors are used as a current balance/virtual ground to program the gain
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of the amplifier, and another pair to set the reference or virtual ground voltage.
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We consider two of the resistors as a functional group, a potential divider
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where their function is to operate as a virtual ground volatge reference.
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The gain resistors work with the op-amp to determeine the gain characteristics.
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%
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The base component error modes of the
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resistors are used to model the current balance/virtual ground from
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components are used to model the amplifier from
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a failure mode perspective.
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%
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We determine the failure symptoms of the current balance/virtual ground and
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consider these as failure modes of a new derived component.
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We determine the failure symptoms of the potential divider and
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consider this as a derived component.
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We can now create a functional group representing the non-inverting amplifier,
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by bringing the failure modes from the current balance/virtual ground and
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the op-amp into a functional group.
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We can now create a functional group representing the inverting amplifier,
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by bringing the failure modes from the potential divider and
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the op-amp with its gain programming resistors into a functional group.
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%
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This can be analysed and a derived component to represent the non inverting
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This can be analysed and a derived component to represent the inverting
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amplifier determined.
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}
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\section{Introduction}
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@ -36,25 +38,27 @@ This chapter analyses an inverting op-amp
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configuration, with the opamp and gain resistors using the FMMD
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methodology.
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%
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It has three base components, two resistors
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and one op-amp.\section{Introduction}
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It has five base components, ifour resistors %two resistors programming gain, two programming a reference, or virtual ground voltage
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and one op-amp.
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The two resistors are used as a current balance/virtual ground to program the gain
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of the amplifier. We consider the two resistors as a functional group
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where their function is to operate as a current balance/virtual ground.
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Two resistors are used as a current balance/virtual ground to program the gain
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of the amplifier, and another pair to set the reference or virtual ground voltage.
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We consider two of the resistors as a functional group, a potential divider
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where their function is to operate as a virtual ground volatge reference.
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The gain resistors work with the op-amp to determeine the gain characteristics.
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%
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The base component error modes of the
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resistors are used to model the current balance/virtual ground from
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components are used to model the amplifier from
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a failure mode perspective.
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%
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We determine the failure symptoms of the current balance/virtual ground and
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consider these as failure modes of a new derived component.
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We determine the failure symptoms of the potential divider and
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consider this as a derived component.
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We can create a functional group representing the non-inverting amplifier,
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by bringing the failure modes from the current balance/virtual ground and
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the op-amp into a functional group.
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We can now create a functional group representing the inverting amplifier,
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by bringing the failure modes from the potential divider and
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the op-amp with its gain programming resistors into a functional group.
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%
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This can now be analysed and a derived component to represent the non inverting
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This can be analysed and a derived component to represent the inverting
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amplifier determined.
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\section{Introduction: The non-inverting amplifier}
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}
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@ -64,13 +68,13 @@ amplifier determined.
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A standard non inverting op amp (from ``The Art of Electronics'' ~\cite{aoe}[pp.234]) is shown in figure \ref{fig:noninvamp}.
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\begin{figure}[h]
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\centering
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\includegraphics[width=200pt,keepaspectratio=true]{./invopamp/noninv.png}
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% noninv.jpg: 341x186 pixel, 72dpi, 12.03x6.56 cm, bb=0 0 341 186
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\caption{Standard non inverting amplifier configuration}
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\label{fig:noninvamp}
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\end{figure}
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% \begin{figure}[h]
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% \centering
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% \includegraphics[width=200pt,keepaspectratio=true]{./invopamp/noninv.png}
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% % noninv.jpg: 341x186 pixel, 72dpi, 12.03x6.56 cm, bb=0 0 341 186
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% \caption{Standard non inverting amplifier configuration}
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% \label{fig:noninvamp}
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% \end{figure}
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@ -125,13 +129,13 @@ Thus $R1$ has failure modes $\{R1\_OPEN, R1\_SHORT\}$ and $R2$ has failure modes
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Modelling this as a functional group, we can draw a simple closed curve
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to represent each failure mode, taken from the components R1 and R2,
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in the current balance/virtual ground, shown in figure \ref{fig:fg1}.
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\begin{figure}[h]
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\centering
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\includegraphics[width=200pt,keepaspectratio=true]{./invopamp/fg1.png}
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% fg1.jpg: 430x271 pixel, 72dpi, 15.17x9.56 cm, bb=0 0 430 271
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\caption{current balance/virtual ground `functional group' failure modes}
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\label{fig:fg1}
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\end{figure}
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% \begin{figure}[h]
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% \centering
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% \includegraphics[width=200pt,keepaspectratio=true]{./invopamp/fg1.png}
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% % fg1.jpg: 430x271 pixel, 72dpi, 15.17x9.56 cm, bb=0 0 430 271
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% \caption{current balance/virtual ground `functional group' failure modes}
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% \label{fig:fg1}
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% \end{figure}
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}
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{
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}
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@ -198,13 +202,13 @@ Each labelled asterisk in the diagram represents a failure mode scenario.
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The failure mode scenarios are given test case numbers, and an example to clarify this follows
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in table~\ref{pdfmea}.
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\begin{figure}[h+]
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\centering
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\includegraphics[width=200pt,keepaspectratio=true]{./invopamp/fg1a.png}
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% fg1a.jpg: 430x271 pixel, 72dpi, 15.17x9.56 cm, bb=0 0 430 271
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\caption{current balance/virtual ground with test cases}
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\label{fig:fg1a}
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\end{figure}
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% \begin{figure}[h+]
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% \centering
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% \includegraphics[width=200pt,keepaspectratio=true]{./invopamp/fg1a.png}
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% % fg1a.jpg: 430x271 pixel, 72dpi, 15.17x9.56 cm, bb=0 0 430 271
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% \caption{current balance/virtual ground with test cases}
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% \label{fig:fg1a}
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% \end{figure}
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}
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{
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}
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@ -301,13 +305,13 @@ have two symptoms, where the current balance/virtual ground will give an incorre
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or an incorrect high voltage (which we can term $HighPD$).
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We can represent the collection of these symptoms by drawing connecting lines between
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the test cases and naming them (see figure \ref{fig:fg1b}).
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\begin{figure}[h+]
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\centering
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\includegraphics[width=200pt,keepaspectratio=true]{./invopamp/fg1b.png}
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% fg1b.jpg: 430x271 pixel, 72dpi, 15.17x9.56 cm, bb=0 0 430 271
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\caption{Collection of current balance/virtual ground failure mode symptoms}
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\label{fig:fg1b}
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\end{figure}
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% \begin{figure}[h+]
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% \centering
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% \includegraphics[width=200pt,keepaspectratio=true]{./invopamp/fg1b.png}
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% % fg1b.jpg: 430x271 pixel, 72dpi, 15.17x9.56 cm, bb=0 0 430 271
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% \caption{Collection of current balance/virtual ground failure mode symptoms}
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% \label{fig:fg1b}
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% \end{figure}
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%\clearpage
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We can now make a `derived component' to represent this current balance/virtual ground.
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@ -317,13 +321,13 @@ We can use the symbol $\bowtie$ to represent taking the analysed
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{\fg} and creating from it, a {\dc}.
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%We could represent it algebraically thus: $ \bowtie(PotDiv) =
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\begin{figure}[h+]
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\centering
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\includegraphics[width=200pt,keepaspectratio=true]{./invopamp/dc1.png}
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% dc1.jpg: 430x619 pixel, 72dpi, 15.17x21.84 cm, bb=0 0 430 619
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\caption{From functional group to derived component}
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\label{fig:dc1}
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\end{figure}
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% \begin{figure}[h+]
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% \centering
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% \includegraphics[width=200pt,keepaspectratio=true]{./invopamp/dc1.png}
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% % dc1.jpg: 430x619 pixel, 72dpi, 15.17x21.84 cm, bb=0 0 430 619
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% \caption{From functional group to derived component}
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% \label{fig:dc1}
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% \end{figure}
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}
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{
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}
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51
invopamp/paper.tex
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51
invopamp/paper.tex
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\documentclass[a4paper,10pt]{article}
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\usepackage{graphicx}
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\usepackage{fancyhdr}
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\usepackage{tikz}
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\usepackage{amsfonts,amsmath,amsthm}
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\usetikzlibrary{shapes.gates.logic.US,trees,positioning,arrows}
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\input{../style}
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\usepackage{ifthen}
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\usepackage{lastpage}
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\usetikzlibrary{shapes,snakes}
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\newboolean{paper}
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\setboolean{paper}{true} % boolvar=true or false
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\newboolean{pld}
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\setboolean{pld}{false} % boolvar=true or false : draw analysis using propositional logic diagrams
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\newboolean{dag}
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\setboolean{dag}{true} % boolvar=true or false : draw analysis using directed acylic graphs
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\def\layersep{2.5cm}
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%\newtheorem{definition}{Definition:}
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\begin{document}
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\pagestyle{fancy}
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\fancyhf{}
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%\renewcommand{\chaptermark}[1]{\markboth{ \emph{#1}}{}}
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\fancyhead[LO]{}
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\fancyhead[RE]{\leftmark}
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%\fancyfoot[LE,RO]{\thepage}
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\cfoot{Page \thepage\ of \pageref{LastPage}}
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\rfoot{\today}
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\lhead{Two stage FMMD analysis of an inverting op-amp configuration}
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%\outerhead{{\small\bf Developing a rigorous bottom-up modular static failure mode modelling methodology}}
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%\innerfoot{{\small\bf R.P. Clark } }
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% numbers at outer edges
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\pagenumbering{arabic} % Arabic page numbers hereafter
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\author{R.P.Clark}
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\title{Two stage FMMD analysis of a an inverting op-amp configuration}
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\maketitle
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\input{invopamp_paper}
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\bibliographystyle{plain}
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\bibliography{../vmgbibliography,../mybib}
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\today
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\end{document}
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