diff --git a/invopamp/invopamp.tex b/invopamp/invopamp.tex index d68055c..e17642e 100644 --- a/invopamp/invopamp.tex +++ b/invopamp/invopamp.tex @@ -9,28 +9,32 @@ configuration %, with the opamp and gain resistors using the FMMD 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. - +% 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. -We consider two of the resistors as a functional group, a potential divider -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. +of the amplifier and another pair to set the reference or virtual ground voltage. +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. +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 -components are used to model the amplifier from -a failure mode perspective. +The base component failure modes +are used to model each functional group %the amplifier from +from a failure mode perspective. % -We determine the failure symptoms of the potential divider and -consider this as a derived component. +We determine the failure symptoms from each of these {\fgs} and +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, -by bringing the failure modes from the potential divider and -the op-amp with its gain programming resistors into a functional group. +by bringing the {\dcs} % +$PD$ and $GMAP$ +together to form a higher level functional group . % -This can be analysed and a derived component to represent the inverting -amplifier determined. +This can be analysed and a derived component, %$INVAMP$ +created, to represent the failure mode behaviour of the inverting +amplifier. } \section{Introduction} } @@ -40,28 +44,30 @@ configuration %, with the opamp and gain resistors using the FMMD 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. - +% 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. -We consider two of the resistors as a functional group, a potential divider -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. +of the amplifier and another pair to set the reference or virtual ground voltage. +We consider the resistors setting the reference voltage as a functional group, a potential divider $PD$. +This chapter re-uses the $PD$ derived component from \ref{lab:nonivopamp}. +%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 -components are used to model the amplifier from -a failure mode perspective. +components are used to model each functional group %the amplifier from +from a failure mode perspective. % -We determine the failure symptoms of the potential divider and -consider this as a derived component. +We determine the failure symptoms from each of these {\fgs} and +create {\dcs} to represent them. We can now create a functional group representing the inverting amplifier, -by bringing the failure modes from the potential divider and -the op-amp with its gain programming resistors into a functional group. +by bringing the {\dcs} $PD$ 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, $INVAMP$ created, to represent the inverting amplifier determined. + \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. -They operate as a current balance/virtual ground 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. +The voltage gain of this circuit ($G_v$) +defined by $ G_v = -\frac{R4}{R3} $. +\section{Potential Divider - OP-AMP Virtual ground reference} 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 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 $R2$. Using the EN298 specification for resistor failure ~\cite{en298}[App.A] 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 @@ -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 to represent each failure mode, taken from the components R1 and R2, -in the current balance/virtual ground, shown in figure \ref{fig:fg1}. -% \begin{figure}[h] -% \centering -% \includegraphics[width=200pt,keepaspectratio=true]{./invopamp/fg1.png} -% % fg1.jpg: 430x271 pixel, 72dpi, 15.17x9.56 cm, bb=0 0 430 271 -% \caption{current balance/virtual ground `functional group' failure modes} -% \label{fig:fg1} -% \end{figure} +in the potential divider, shown in figure \ref{fig:fg1}. +\begin{figure}[h] + \centering + \includegraphics[width=200pt,keepaspectratio=true]{./invopamp/fg1.png} + % fg1.jpg: 430x271 pixel, 72dpi, 15.17x9.56 cm, bb=0 0 430 271 + \caption{potential divider failure modes} + \label{fig:fg1} +\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 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} \centering \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, -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, %which is represented on the diagram, with an asterisk marking %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 in table~\ref{pdfmea}. -% \begin{figure}[h+] -% \centering -% \includegraphics[width=200pt,keepaspectratio=true]{./invopamp/fg1a.png} -% % fg1a.jpg: 430x271 pixel, 72dpi, 15.17x9.56 cm, bb=0 0 430 271 -% \caption{current balance/virtual ground with test cases} -% \label{fig:fg1a} -% \end{figure} +\begin{figure}[h+] + \centering + \includegraphics[width=200pt,keepaspectratio=true]{./invopamp/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} } { } @@ -222,10 +227,10 @@ For this example we can look at single failure modes only. For each failure mode in our {\fg} `potential~divider' we can assign a test case number (see table \ref{pdfmea}). 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 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} 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 -\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 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\%). +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}} { -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+] \centering \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}} { -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} \centering \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] (OPAMPLS) at (\layersep,-6) {lowslew}; + + + \path (OPAMP) edge (OPAMPLU); \path (OPAMP) edge (OPAMPLD); \path (OPAMP) edge (OPAMPNP); \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 of code \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 -\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 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}. Each of these failure modes will be given a test case for analysis, and this is represented in table \ref{ampfmea}. - } { } @@ -479,7 +546,7 @@ and this is represented in table \ref{ampfmea}. \clearpage \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 \begin{tabular}{||l|c|c|l|l||} \hline \hline @@ -488,12 +555,20 @@ and this is represented in table \ref{ampfmea}. % R & wire & res + & res - & description \hline \hline - TC1: $OPAMP$ LatchUP & Output High & & AMPHigh \\ - TC2: $OPAMP$ LatchDown & Output Low : Low gain& & 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 : Low Gain& & AMPLow \\ \hline +% TC1: $R3_{OPEN}$ & Output High & & AMPHigh \\ +% TC2: $R3_{SHORT}$ & Output Low : Low gain& & AMPLow \\ \hline +% +% TC3: $R4_{OPEN}$ LatchUP & Output High & & AMPHigh \\ +% TC4: $R4_{SHORT}$ LatchDown & 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 \hline \end{tabular} diff --git a/noninvopamp/noninvopamp.tex b/noninvopamp/noninvopamp.tex index 5cf4488..5b5d371 100644 --- a/noninvopamp/noninvopamp.tex +++ b/noninvopamp/noninvopamp.tex @@ -1,5 +1,5 @@ - +\label{lab:nonivopamp} \ifthenelse {\boolean{paper}} {