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Robin Clark 2011-06-06 08:34:20 +01:00
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invopamp/invopamp.tex
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@ -9,28 +9,32 @@ configuration %, with the opamp and gain resistors
using the FMMD using the FMMD
methodology. methodology.
% %
It has five base components, four resistors %two resistors programming gain, two programming a reference, or virtual ground voltage The circuit under analysis has five `base components', four resistors % two resistors programming gain, two programming a reference, or virtual ground voltage
and one op-amp. and one op-amp.
%
Two resistors are used as a current balance/virtual ground to program the gain Two resistors are used as a current balance/virtual ground to program the gain
of the amplifier, and another pair to set the reference or virtual ground voltage. of the amplifier and another pair to set the reference or virtual ground voltage.
We consider two of the resistors as a functional group, a potential divider We consider the resistors setting the reference voltage as a functional group, a potential divider. %.$PD$.
where their function is to operate as a virtual ground voltage reference. %where their function is to operate as a virtual ground voltage reference.
The gain resistors work with the op-amp to determine the gain characteristics. The gain resistors work with the op-amp to determine the gain characteristics, and therefore the two gain resistors and the op-amp
form a second functional group.% $GAMP$.
% %
The base component error modes of the The base component failure modes
components are used to model the amplifier from are used to model each functional group %the amplifier from
a failure mode perspective. from a failure mode perspective.
% %
We determine the failure symptoms of the potential divider and We determine the failure symptoms from each of these {\fgs} and
consider this as a derived component. create {\dcs} to represent them.
We can have a {\dc} represetnting the potential~divider and another representing the gain stage.
We can now create a functional group representing the inverting amplifier, We can now create a functional group representing the inverting amplifier,
by bringing the failure modes from the potential divider and by bringing the {\dcs} %
the op-amp with its gain programming resistors into a functional group. $PD$ and $GMAP$
together to form a higher level functional group .
% %
This can be analysed and a derived component to represent the inverting This can be analysed and a derived component, %$INVAMP$
amplifier determined. created, to represent the failure mode behaviour of the inverting
amplifier.
} }
\section{Introduction} \section{Introduction}
} }
@ -40,28 +44,30 @@ configuration %, with the opamp and gain resistors
using the FMMD using the FMMD
methodology. methodology.
% %
It has five base components, four resistors % two resistors programming gain, two programming a reference, or virtual ground voltage The circuit under analysis has five 'base components', four resistors % two resistors programming gain, two programming a reference, or virtual ground voltage
and one op-amp. and one op-amp.
%
Two resistors are used as a current balance/virtual ground to program the gain Two resistors are used as a current balance/virtual ground to program the gain
of the amplifier, and another pair to set the reference or virtual ground voltage. of the amplifier and another pair to set the reference or virtual ground voltage.
We consider two of the resistors as a functional group, a potential divider We consider the resistors setting the reference voltage as a functional group, a potential divider $PD$.
where their function is to operate as a virtual ground voltage reference. This chapter re-uses the $PD$ derived component from \ref{lab:nonivopamp}.
The gain resistors work with the op-amp to determine the gain characteristics. %where their function is to operate as a virtual ground voltage reference.
The gain resistors work with the op-amp to determine the gain characteristics, and therefore the two gain resistors and the op-amp
form a second functional group $GAMP$.
% %
The base component error modes of the The base component error modes of the
components are used to model the amplifier from components are used to model each functional group %the amplifier from
a failure mode perspective. from a failure mode perspective.
% %
We determine the failure symptoms of the potential divider and We determine the failure symptoms from each of these {\fgs} and
consider this as a derived component. create {\dcs} to represent them.
We can now create a functional group representing the inverting amplifier, We can now create a functional group representing the inverting amplifier,
by bringing the failure modes from the potential divider and by bringing the {\dcs} $PD$ and $GMAP$ together to form a higher level functional group .
the op-amp with its gain programming resistors into a functional group.
% %
This can be analysed and a derived component to represent the inverting This can be analysed and a derived component, $INVAMP$ created, to represent the inverting
amplifier determined. amplifier determined.
\section{Introduction: The non-inverting amplifier} \section{Introduction: The non-inverting amplifier}
} }
@ -80,18 +86,17 @@ A standard non inverting op amp (from ``The Art of Electronics'' ~\cite{aoe}[pp
The function of the resistors in this circuit is to set the amplifier gain. The voltage gain of this circuit ($G_v$)
They operate as a current balance/virtual ground and program the minus input on the op-amp defined by $ G_v = -\frac{R4}{R3} $.
to balance them against the positive input, giving the voltage gain ($G_v$)
defined by $ G_v = 1 + \frac{R2}{R1} $ at the output.
\section{Potential Divider - OP-AMP Virtual ground reference}
A functional group, is an ideally small in number collection of components, A functional group, is an ideally small in number collection of components,
that interact to provide that interact to provide
a function or task within a system. a function or task within a system.
As the resistors work to provide a specific function, that of a current balance/virtual ground, As the resistors work to provide a specific function, that of a potential divider to program a given voltage,
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] Using the EN298 specification for resistor failure ~\cite{en298}[App.A]
we can assign failure modes of $OPEN$ and $SHORT$ to the resistors. we can assign failure modes of $OPEN$ and $SHORT$ to the resistors.
@ -120,7 +125,7 @@ We can now represent a resistor in terms of its failure modes as a directed acyc
} }
{ {
} }
Thus $R1$ has failure modes $\{R1\_OPEN, R1\_SHORT\}$ and $R2$ has failure modes $\{R2\_OPEN, R2\_SHORT\}$. Thus for the potential~divider stage $R1$ has failure modes $\{R1\_OPEN, R1\_SHORT\}$ and $R2$ has failure modes $\{R2\_OPEN, R2\_SHORT\}$.
%\clearpage %\clearpage
@ -130,14 +135,14 @@ Thus $R1$ has failure modes $\{R1\_OPEN, R1\_SHORT\}$ and $R2$ has failure modes
{ {
Modelling this as a functional group, we can draw a simple closed curve 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, to represent each failure mode, taken from the components R1 and R2,
in the current balance/virtual ground, shown in figure \ref{fig:fg1}. in the potential divider, shown in figure \ref{fig:fg1}.
% \begin{figure}[h] \begin{figure}[h]
% \centering \centering
% \includegraphics[width=200pt,keepaspectratio=true]{./invopamp/fg1.png} \includegraphics[width=200pt,keepaspectratio=true]{./invopamp/fg1.png}
% % fg1.jpg: 430x271 pixel, 72dpi, 15.17x9.56 cm, bb=0 0 430 271 % fg1.jpg: 430x271 pixel, 72dpi, 15.17x9.56 cm, bb=0 0 430 271
% \caption{current balance/virtual ground `functional group' failure modes} \caption{potential divider failure modes}
% \label{fig:fg1} \label{fig:fg1}
% \end{figure} \end{figure}
} }
{ {
} }
@ -146,7 +151,7 @@ in the current balance/virtual ground, shown in figure \ref{fig:fg1}.
{ {
Modelling this as a functional group, we can draw this as a directed graph Modelling this as a functional group, we can draw this as a directed graph
failure modes, taken from the components R1 and R2, failure modes, taken from the components R1 and R2,
in the current balance/virtual ground, shown in figure \ref{fig:fg1dag}. in the potential divider, shown in figure \ref{fig:fg1dag}.
\begin{figure} \begin{figure}
\centering \centering
\begin{tikzpicture}[shorten >=1pt,->,draw=black!50, node distance=\layersep] \begin{tikzpicture}[shorten >=1pt,->,draw=black!50, node distance=\layersep]
@ -193,7 +198,7 @@ in the current balance/virtual ground, shown in figure \ref{fig:fg1dag}.
} }
We can now look at each of these base component failure modes, We can now look at each of these base component failure modes,
and determine how they will affect the operation of the current balance/virtual ground. and determine how they will affect the operation of the potential divider.
%Each failure mode scenario we look at will be given a test case number, %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 is represented on the diagram, with an asterisk marking
%which failure modes is modelling (see figure \ref{fig:fg1a}). %which failure modes is modelling (see figure \ref{fig:fg1a}).
@ -204,13 +209,13 @@ 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 The failure mode scenarios are given test case numbers, and an example to clarify this follows
in table~\ref{pdfmea}. in table~\ref{pdfmea}.
% \begin{figure}[h+] \begin{figure}[h+]
% \centering \centering
% \includegraphics[width=200pt,keepaspectratio=true]{./invopamp/fg1a.png} \includegraphics[width=200pt,keepaspectratio=true]{./invopamp/fg1a.png}
% % fg1a.jpg: 430x271 pixel, 72dpi, 15.17x9.56 cm, bb=0 0 430 271 % fg1a.jpg: 430x271 pixel, 72dpi, 15.17x9.56 cm, bb=0 0 430 271
% \caption{current balance/virtual ground with test cases} \caption{potential divider with test cases}
% \label{fig:fg1a} \label{fig:fg1a}
% \end{figure} \end{figure}
} }
{ {
} }
@ -222,10 +227,10 @@ For this example we can look at single failure modes only.
For each failure mode in our {\fg} `potential~divider' For each failure mode in our {\fg} `potential~divider'
we can assign a test case number (see table \ref{pdfmea}). we can assign a test case number (see table \ref{pdfmea}).
Each test case is analysed to determine the `symptom' Each test case is analysed to determine the `symptom'
on the current balance/virtual grounds' operation. For instance on the potential diverders operation. For instance
were the resistor $R_1$ to go open, the circuit would not be grounded and the were the resistor $R_1$ to go open, the circuit would not be grounded and the
voltage output from it would be the +ve supply rail. voltage output from it would be the +ve supply rail.
This would mean the symptom of the failed current balance/virtual ground, would be that it This would mean the symptom of the failed potential divider, would be that it
gives an output high voltage reading. We can now consider the {\fg} gives an output high voltage reading. We can now consider the {\fg}
as a component in its own right, and its symptoms as its failure modes. as a component in its own right, and its symptoms as its failure modes.
@ -371,17 +376,61 @@ as a building block for other {\fgs} in the same way as we used the resistors $R
\clearpage \clearpage
\section{Failure Mode Analysis of the OP-AMP} \section{Failure Mode Analysis of the OP-AMP Gain Section}
Let use now consider the op-amp. According to Let use now consider the op-amp. According to
FMD-91~\cite{fmd91}[3-116] an op amp may have the following 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\%). latchup(12.5\%), latchdown(6\%), nooperation(31.3\%), lowslewrate(50\%).
The op-amp gain section use resistors $R4$ and $R3$ to determine the amount of negative gain.
Each of the reistors have two failure modes $SHORT$ and $OPEN$.
For our gain stage amplifier section, we have a {\fg} comprising
the opamp, R3 and R4.
\paragraph{Functional group context}
We have to consider the context the amplifier is used it to determine its failure mode symptoms.
If this were to be a instrumentaion amplifier, the low slew failure mode may not be a problem at all
but could affect an audio amplifier by introducing low-pass filtering.
TC2, TC1 and TC7, where there is no gain or ref voltage is output, could be very bad for an instrumentation amplifier
because the oputput may be in a valid reading range for the application.
For the purpose of example we shall consider this amplifier to be an instumentation
amplifier.
\begin{table}[ht]
\caption{Inverting Amplifier Gain Stage: 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: $R3_{OPEN}$ & Ref V. Output & & \\
TC2: $R3_{SHORT}$ & High Gain & & OUT\_OF\_RANGE \\ \hline
TC3: $R4_{OPEN}$ & High Gain & & OUT\_OF\_RANGE \\
TC4: $R4_{SHORT}$ & No Gain & & \\ \hline
TC5: $OPAMP$ LatchUP & High Output +Ve & & OUT\_OF\_RANGE \\
TC6: $OPAMP$ LatchDown & Low Output -Ve & & OUT\_OF\_RANGE \\ \hline
TC7: $OPAMP$ No Operation & Low Output -Ve & & OUT\_OF\_RANGE \\
TC8: $OPAMP$ Low Slew & Low pass filter & & \\ \hline
%TC7: $R_2$ OPEN & LOW & & LowPD \\ \hline
\hline
\end{tabular}
\label{ampfmea}
\end{table}
\ifthenelse {\boolean{pld}} \ifthenelse {\boolean{pld}}
{ {
We can represent these failure modes on a diagram (see figure~\ref{fig:op1}). We can represent these failure modes of this {\fg} on a diagram (see figure~\ref{fig:op1}).
\begin{figure}[h+] \begin{figure}[h+]
\centering \centering
\includegraphics[width=200pt,keepaspectratio=true]{./invopamp/op1.png} \includegraphics[width=200pt,keepaspectratio=true]{./invopamp/op1.png}
@ -395,7 +444,7 @@ We can represent these failure modes on a diagram (see figure~\ref{fig:op1}).
\ifthenelse {\boolean{dag}} \ifthenelse {\boolean{dag}}
{ {
We can represent these failure modes on a DAG (see figure~\ref{fig:op1dag}). We can represent the failure modes of this {\fg} on a DAG (see figure~\ref{fig:op1dag}).
\begin{figure} \begin{figure}
\centering \centering
\begin{tikzpicture}[shorten >=1pt,->,draw=black!50, node distance=\layersep] \begin{tikzpicture}[shorten >=1pt,->,draw=black!50, node distance=\layersep]
@ -413,11 +462,30 @@ We can represent these failure modes on a DAG (see figure~\ref{fig:op1dag}).
\node[failure] (OPAMPNP) at (\layersep,-4) {noop}; \node[failure] (OPAMPNP) at (\layersep,-4) {noop};
\node[failure] (OPAMPLS) at (\layersep,-6) {lowslew}; \node[failure] (OPAMPLS) at (\layersep,-6) {lowslew};
\path (OPAMP) edge (OPAMPLU); \path (OPAMP) edge (OPAMPLU);
\path (OPAMP) edge (OPAMPLD); \path (OPAMP) edge (OPAMPLD);
\path (OPAMP) edge (OPAMPNP); \path (OPAMP) edge (OPAMPNP);
\path (OPAMP) edge (OPAMPLS); \path (OPAMP) edge (OPAMPLS);
\node[component] (R3) at (0,-9) {$R3$};
\node[failure] (R3SHORT) at (\layersep,-8) {SHORT};
\node[failure] (R3OPEN) at (\layersep,-10) {OPEN};
\path (R3) edge (R3SHORT);
\path (R3) edge (R3OPEN);
\node[component] (R4) at (0,-14) {$R4$};
\node[failure] (R4SHORT) at (\layersep,-13) {SHORT};
\node[failure] (R4OPEN) at (\layersep,-15) {OPEN};
\path (R4) edge (R4SHORT);
\path (R4) edge (R4OPEN);
\end{tikzpicture} \end{tikzpicture}
% End of code % End of code
\caption{DAG representing failure modes of an Op-amp} \caption{DAG representing failure modes of an Op-amp}
@ -430,7 +498,7 @@ We can represent these failure modes on a DAG (see figure~\ref{fig:op1dag}).
%\clearpage %\clearpage
\section{Bringing the OP amp and the current balance/virtual ground together} \section{{\fg} forrmed from OP amp and the potential divider {\dcs}}
We can now consider bringing the OP amp and the current balance/virtual ground together to We can now consider bringing the OP amp and the current balance/virtual ground together to
model the non inverting amplifier. We have the failure modes of the functional group for the current balance/virtual ground, model the non inverting amplifier. We have the failure modes of the functional group for the current balance/virtual ground,
@ -471,7 +539,6 @@ We can now crate a {\fg} for the non-inverting amplifier
by bringing together the failure modes from \textbf{opamp} and \textbf{PD}. by bringing together the failure modes from \textbf{opamp} and \textbf{PD}.
Each of these failure modes will be given a test case for analysis, Each of these failure modes will be given a test case for analysis,
and this is represented in table \ref{ampfmea}. and this is represented in table \ref{ampfmea}.
} }
{ {
} }
@ -479,7 +546,7 @@ and this is represented in table \ref{ampfmea}.
\clearpage \clearpage
\begin{table}[ht] \begin{table}[ht]
\caption{Non Inverting Amplifier: Failure Mode Effects Analysis: Single Faults} % title of Table \caption{Inverting Amplifier: Failure Mode Effects Analysis: Single Faults} % title of Table
\centering % used for centering table \centering % used for centering table
\begin{tabular}{||l|c|c|l|l||} \begin{tabular}{||l|c|c|l|l||}
\hline \hline \hline \hline
@ -488,12 +555,20 @@ and this is represented in table \ref{ampfmea}.
% R & wire & res + & res - & description % R & wire & res + & res - & description
\hline \hline
\hline \hline
TC1: $OPAMP$ LatchUP & Output High & & AMPHigh \\ % TC1: $R3_{OPEN}$ & Output High & & AMPHigh \\
TC2: $OPAMP$ LatchDown & Output Low : Low gain& & AMPLow \\ \hline % TC2: $R3_{SHORT}$ & Output Low : Low gain& & AMPLow \\ \hline
TC3: $OPAMP$ No Operation & Output Low & & AMPLow \\ %
TC4: $OPAMP$ Low Slew & Low pass filtering & & LowPass \\ \hline % TC3: $R4_{OPEN}$ LatchUP & Output High & & AMPHigh \\
TC5: $PD$ LowPD & Output High & & AMPHigh \\ \hline % TC4: $R4_{SHORT}$ LatchDown & Output Low : Low gain& & AMPLow \\ \hline
TC6: $PD$ HighPD & Output Low : Low Gain& & AMPLow \\ \hline %
% TC5: $OPAMP$ LatchUP & Output High & & AMPHigh \\
% TC6: $OPAMP$ LatchDown & Output Low : Low gain& & AMPLow \\ \hline
% TC7: $OPAMP$ No Operation & Output Low & & AMPLow \\
% TC8: $OPAMP$ Low Slew & Low pass filtering & & LowPass \\ \hline
TC9: $PD$ LowPD & Output High & & AMPHigh \\
TC10: $PD$ HighPD & Output Low : Low Gain& & AMPLow \\ \hline
%TC7: $R_2$ OPEN & LOW & & LowPD \\ \hline %TC7: $R_2$ OPEN & LOW & & LowPD \\ \hline
\hline \hline
\end{tabular} \end{tabular}

2
noninvopamp/noninvopamp.tex
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@ -1,5 +1,5 @@
\label{lab:nonivopamp}
\ifthenelse {\boolean{paper}} \ifthenelse {\boolean{paper}}
{ {