lunchtime

opamp_circuits_C_GARRETT/Makefile

@@ -1,6 +1,6 @@
 
 
-PNG_DIA = circuit1_dag.png
+PNG_DIA = circuit1_dag.png mvampcircuit.png pd.png invamp.png
 
 
 

opamp_circuits_C_GARRETT/opamps.tex

@@ -10,6 +10,17 @@
 \usepackage{algorithm}
 \usepackage{algorithmic}
 \usepackage{lastpage}
+
+\newcommand{\fg}{\em functional~group}
+\newcommand{\fgs}{\em functional~groups}
+\newcommand{\dc}{\em derived~component}
+\newcommand{\dcs}{\em derived~components}
+\newcommand{\bc}{\em base~component}
+\newcommand{\bcs}{\em base~components}
+\newcommand{\irl}{in~real~life}
+
+
+
 %\usepackage{glossary}
 %opening
 \title{Example OPAMP circuits}
@@ -31,12 +42,101 @@ Function $fm$ applied to a component returns its failure modes.
 
 
 
-\section{Non Inverting OPAMP}
+\section{Non-Inverting OPAMP}
 Consider a non inverting op-amp designed to amplify
 a small positive voltage, typical use would be a thermocouple.
  
  
+\begin{figure}[h+]
+ \centering
+ \includegraphics[width=100pt]{./mvampcircuit.png}
+ % mvampcircuit.png: 243x143 pixel, 72dpi, 8.57x5.04 cm, bb=0 0 243 143
+ \label{fig:mvampcircuit}
+ \caption{positive mV amplifier circuit}
+\end{figure}
+
+We can begin by looking for functional groups. 
+The resistors would together to perform a fairly common function in electronics, that of the potential divider.
+So our first functional group is $\{ R1, R2 \}$. 
+
+
+\subsection{The Resistor in terms of failure modes}
+
+We can now take the failure modes for the resistors (OPEN and SHORT EN298).
+
+
+We can express the fialure modes of a component using the function $fm$, thus for the resistor,  $ fm(R) = \{ OPEN, SHORT \}$.
+
+
+We have two resistors in this circuit and therefore four component failure modes to consider for the potential divider,
+we can now examine what effect each of these failures will have on the {\fg} (the potential divider see figure~\ref{fig:pdcircuit}).
+
+
+\subsection{Analysing a potential divider in terms of failure modes}
+
+\begin{figure}[h+]
+ \centering
+ \includegraphics[width=100pt,keepaspectratio=true]{./pd.png}
+ % pd.png: 361x241 pixel, 72dpi, 12.74x8.50 cm, bb=0 0 361 241
+ \label{fig:pdcircuit}
+ \caption{Potential Divider Circuit}
+\end{figure}
+ 
+
+\begin{table}[h+]
+\begin{tabular}{|| l | l | c | c | l ||} \hline
+ \textbf{Failure Scenario} & &  \textbf{Pot Div Effect}  &   & \textbf{Symptom}          \\ 
+               \hline
+     FS1: R1 SHORT    &  &  $LOW$   &  &  $PDLow$              \\ \hline
+     FS2: R1 OPEN     &  &  $HIGH$  &  &  $PDHigh$             \\ \hline
+     FS3: R2 SHORT    &  &  $HIGH$  &  &  $PDHigh$             \\ \hline
+     FS4: R2 OPEN     &  &  $LOW$   &  &  $PDLow$              \\ \hline
+\hline
+\end{tabular}
+\end{table}
+
+We can now create a {\dc} for the potential divider, $PD$.
+
+ $$ fm(PD) = \{ PDLow, PDHigh \}$$
+
+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\%).
+
+
+\subsection{Analysing the non-inverting amplifier in terms of failure modes}
+
+$$ fm(OPAMP) = \{L\_{up}, L\_{dn}, Noop, L\_slew \} $$
+
+
+We can now form a {\fg} with $PD$ and $OPAMP$.
+
+\begin{figure}
+ \centering
+ \includegraphics[width=300pt]{./non_inv_amp_fmea.png}
+ % non_inv_amp_fmea.png: 964x492 pixel, 96dpi, 25.50x13.02 cm, bb=0 0 723 369
+\end{figure}
+
+
+We can collect symptoms from the analysis and cretae a derived component 
+to represent the non-inverting amplifier $NI\_AMP$.
+We now have can express the failure mode behaviour of this type of amplifier thus:
+
+$$ fm(NI\_AMP) = \{  N\_INVAMP_{lowpass}, N\_INVAMP_{high}, N\_INVAMP_{low} \}.$$
+
+
+
+
 \section{Inverting OPAMP}
+
+\begin{figure}[h]
+ \centering
+ \includegraphics[width=200pt]{./invamp.png}
+ % invamp.png: 378x207 pixel, 72dpi, 13.34x7.30 cm, bb=0 0 378 207
+ \caption{Inverting Amplifier Configuration}
+ \label{fig:invamp}
+\end{figure}
+
 This configuration is interesting from methodology perspective.
 There are two ways in which we can tackle this.
 One is to do this in two stages, by considing the gain resistors to be a potential divider
@@ -47,6 +147,8 @@ The other way is to place all three components in a {\fg}.
  
 \subsection{Inverting OPAMP using three components}
 
+\subsection{Comparison between the two approaches}
+
 
 \clearpage
 \section{Op-Amp circuit 1}