From 926d55412bb224c6acbcfe45ffc0a805ebb5e23e Mon Sep 17 00:00:00 2001
From: Robin Clark <robin48gx@gmail.com>
Date: Fri, 15 Apr 2011 17:01:16 +0100
Subject: [PATCH] home edit,

---
 noninvopamp/dc1.dia         | Bin 2571 -> 2559 bytes
 noninvopamp/noninvopamp.tex | 156 ++++++++++++++++++++++++------------
 noninvopamp/op1.dia         | Bin 1240 -> 1430 bytes
 3 files changed, 104 insertions(+), 52 deletions(-)

diff --git a/noninvopamp/dc1.dia b/noninvopamp/dc1.dia
index e19b6176f4592cd76bbb05fd7364100b942fb0ed..ac098b33ce4778e713d2b27fac5380313e151e85 100644
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diff --git a/noninvopamp/noninvopamp.tex b/noninvopamp/noninvopamp.tex
index 4e946d3..62f4e14 100644
--- a/noninvopamp/noninvopamp.tex
+++ b/noninvopamp/noninvopamp.tex
@@ -5,33 +5,59 @@
 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.
-
+where their function 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.
+consider these as failure modes of a new derived component.
 
-We can now create a functional group representing the amplifier,
+We can now create a functional group representing the non-inverting 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
+%
+This can be analysed and a derived component to represent the non inverting
 amplifier determined.
 }
+\section{Introduction}
 }
 {
+This chapter 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.\section{Introduction}
+
+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 their function 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 new derived component.
+
+We can create a functional group representing the non-inverting 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: The non-inverting amplifier}
 }
 
-\section{Introduction}
+
 
 A standard non inverting  op amp (from ``The Art of Electronics'' ~\cite{aoe}[pp.234]) is shown in figure \ref{fig:noninvamp}.
 
@@ -45,20 +71,25 @@ A standard non inverting  op amp (from ``The Art of Electronics'' ~\cite{aoe}[pp
 
 
 
-The functional of the resistors in this circuit is to set the amplifier gain.
+The function 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.
 
+A functional group, is an ideally small in number collection of components, 
+that interact to provide
+a function or task within a system.
 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,.
+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 $\{R2\_OPEN, R2\_SHORT\}$.
 
+\clearpage
 \section{Failure Mode Analysis of the Potential Divider}
 
-Modelling this as a functional group, we can draw a circle to represent each failure mode
+Modelling this as a functional group, we can draw a simple closed curve
+to represent each failure mode, taken from the components R1 and R2,
 in the potential divider, shown in figure \ref{fig:fg1}.
 
 
@@ -72,11 +103,14 @@ in the potential divider, shown in figure \ref{fig:fg1}.
 
 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}).
+%Each failure mode scenario we look at will be given a test case number,
+%which is represented on the diagram, with an asterisk marking 
+%which failure modes is modelling (see figure \ref{fig:fg1a}).
+Each labelled asterisk in the diagram represents a failure mode scenario.
+The failure mode scenarios are given test case numbers, and an example to clarify this follows
+in table~\ref{pdfmea}.
 
-\begin{figure}[h]
+\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
@@ -106,13 +140,14 @@ which failure modes is is modelling (see figure \ref{fig:fg1a}).
 
 
 We can now collect the symptoms of failure. From the four base component failure modes, we now
-have two symptoms, $LowPD, HighPD$. 
+have two symptoms, where the potential divider will give an incorrect low voltage (which we can term $LowPD$)
+or an incorrect high voltage (which we can term $HighPD$). 
 
 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]
+\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
@@ -120,13 +155,15 @@ the test cases and naming them (see figure \ref{fig:fg1b}).
  \label{fig:fg1b}
 \end{figure}
 
+%\clearpage
+
 We can now make a `derived component' to represent this potential divider.
-This {\dc} will have two failure failure modes.
+This {\dc} will have two 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]
+\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
@@ -134,29 +171,24 @@ We can use the symbol $\bowtie$ to represent taking the analysed
  \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.
+Because the derived component is defined by its failure modes and 
+the functional group used to derive it, we can use it
+as a building block for other {\fgs} in the same way as we used the resistors $R1$ and $R2$.
+
+\clearpage
 
 \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
+FMD-91~\cite{fmd91}[3-116] an op amp may have the following 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]
+
+\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
@@ -164,12 +196,23 @@ and the component potential divider into a new functional group.
  \label{fig:op1}
 \end{figure}
 
+%\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 \textbf{opamp}
+and the component potential divider into a new functional group.
+
+
 
 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]
+\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
@@ -177,24 +220,19 @@ from the potential divider {\dc} to analyse represented by figure~\ref{fig:fgamp
  \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]
+\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
+ % fgampa.jpg: 430x330 pixel, 72dpi, 15.17x11.64 cm, bb=0 0 430 330 hno
  \caption{Amplifier Functional Group with Test Cases}
- \label{fig:fgampa.jpg}
+ \label{fig:fgampa}
 \end{figure}
 
-
+\clearpage
 
 \begin{table}[ht]
 \caption{Non Inverting Amplifier: Failure Mode Effects Analysis: Single Faults} % title of Table
@@ -218,14 +256,13 @@ regions) see figure~\ref{fig:fgampa}.
 \label{ampfmea}
 \end{table}
 
-For this amplifier configuration we have three failure modes, $AMPHigh, AMPLow, LowPass$ see figure~\ref{fig:fgampb}.
+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}.
+We can now derive a `component' to represent this amplifier configuration (see figure ~\ref{fig:noninvampa}).
 
 
 
-\begin{figure}[h]
+\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
@@ -236,9 +273,24 @@ and use it it to model higher level functional groups see figure~\ref{fig:noninv
 
 %failure mode contours).
 \clearpage
-\vspace{60pt}
-$$ \int_{0\-}^{\infty}  f(t).e^{-s.t}.dt  \; | \; s \in \mathcal{C}$$
-\today
+\section{Conclusion}
 
- $$\frac{-b\pm\sqrt{ {b^2-4ac}}}{2a}$$
-\today
+We now have a derived component that represents the failure modes of a non-inverting 
+op-amp based amplifier. We can now use this to model higher level designs, where we have systems
+that use this type of amplifier.
+If failure mode/reliability statistics were required these could be derived 
+from the model, as each failure mode of the  derived component
+is traceable to one or more base component failure mode causes, for which established 
+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
diff --git a/noninvopamp/op1.dia b/noninvopamp/op1.dia
index 62792f9a8443f1ff1511b132bbf9af5202ca79d5..055c1b5298fbd7286c4037523a19ca56006cb451 100644
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