From 488d4082ecfda85163c91e018278a9171e625841 Mon Sep 17 00:00:00 2001 From: Robin Clark Date: Sat, 21 Jan 2012 14:07:54 +0000 Subject: [PATCH] completed analysis of BUBBA from bth perspectives. Needs tidying up (somewhat). --- .../opamp_circuits_C_GARRETT/opamps.tex | 243 ++++++++++++++---- 1 file changed, 190 insertions(+), 53 deletions(-) diff --git a/old_thesis/opamp_circuits_C_GARRETT/opamps.tex b/old_thesis/opamp_circuits_C_GARRETT/opamps.tex index a93bf05..d54633d 100644 --- a/old_thesis/opamp_circuits_C_GARRETT/opamps.tex +++ b/old_thesis/opamp_circuits_C_GARRETT/opamps.tex @@ -843,8 +843,8 @@ We could at this point bring all the {\dcs} together into one large functional group (see figure~\ref{fig:poss1finalbubba}) or we could try to merge smaller stages. -The capactior and 180 degree inverting amplifier, form a {\fg} -providing an amplified 225 degree phase shift, which we can call $PHS225AMP$. +A PHS45 {\dc} and an inverting amplifier (which always gives $180^{\circ}$ phase shift), form a {\fg} +providing an amplified $225^{\circ}$ phase shift, which we can call $PHS225AMP$. % We could also merge the $NIBUFF$ and $PHS45$ {\dcs} into a {\fg} and the resultant derived component from this we could call a $BUFF45$, @@ -855,6 +855,15 @@ and then merge $PHS135BUFFERED$ and $PHS225AMP$ in a final stage (see figure~\r \subsection{FMMD Analysis using one large functional group} +\begin{figure}[h+] + \centering + \includegraphics[width=300pt,keepaspectratio=true]{./poss1finalbubba.png} + % largeosc.png: 916x390 pixel, 72dpi, 32.31x13.76 cm, bb=0 0 916 390 + \caption{Bubba Oscillator: One final large functional group.} + \label{fig:poss1finalbubba} +\end{figure} + + \begin{table}[h+] \caption{Bubba Oscillator: Failure Mode Effects Analysis: One Large Functional Group} % title of Table \label{tbl:bubbalargefg} @@ -865,42 +874,42 @@ and then merge $PHS135BUFFERED$ and $PHS225AMP$ in a final stage (see figure~\r \hline - FS1: $PHS45_1$ $90\_phaseshift$ & & osc frequency high & & $HI_{fosc}$ \\ - FS1: $PHS45_1$ $no\_signal$ & & signal lost & & $NO_{osc}$ \\ - FS1: $PHS45_1$ $0\_phaseshift$ & & osc frequency low & & $LO_{fosc}$ \\ \hline + FS1: $PHS45_1$ $0\_phaseshift$ & & osc frequency high & & $HI_{fosc}$ \\ + FS2: $PHS45_1$ $no\_signal$ & & signal lost & & $NO_{osc}$ \\ + FS3: $PHS45_1$ $90\_phaseshift$ & & osc frequency low & & $LO_{fosc}$ \\ \hline - FS1: $NIBUFF_1$ $L_{up}$ & & output high No Oscillation & & $NO_{osc}$ \\ - FS1: $NIBUFF_1$ $L_{dn}$ & & output low No Oscillation & & $NO_{osc}$ \\ - FS1: $NIBUFF_1$ $N_{oop}$ & & output low No Oscillation & & $NO_{osc}$ \\ - FS1: $NIBUFF_1$ $L_{slew}$ & & signal lost & & $NO_{osc}$ \\ \hline + FS4: $NIBUFF_1$ $L_{up}$ & & output high No Oscillation & & $NO_{osc}$ \\ + FS5: $NIBUFF_1$ $L_{dn}$ & & output low No Oscillation & & $NO_{osc}$ \\ + FS6: $NIBUFF_1$ $N_{oop}$ & & output low No Oscillation & & $NO_{osc}$ \\ + FS7: $NIBUFF_1$ $L_{slew}$ & & signal lost & & $NO_{osc}$ \\ \hline - FS1: $PHS45_2$ $90\_phaseshift$ & & osc frequency high & & $HI_{fosc}$ \\ - FS1: $PHS45_2$ $no\_signal$ & & signal lost & & $NO_{osc}$ \\ - FS1: $PHS45_2$ $0\_phaseshift$ & & osc frequency low & & $LO_{fosc}$ \\ \hline + FS8: $PHS45_2$ $0\_phaseshift$ & & osc frequency high & & $HI_{fosc}$ \\ + FS9: $PHS45_2$ $no\_signal$ & & signal lost & & $NO_{osc}$ \\ + FS10: $PHS45_2$ $90\_phaseshift$ & & osc frequency low & & $LO_{fosc}$ \\ \hline - FS1: $NIBUFF_2$ $L_{up}$ & & output high No Oscillation & & $NO_{osc}$ \\ - FS1: $NIBUFF_2$ $L_{dn}$ & & output low No Oscillation & & $NO_{osc}$ \\ - FS1: $NIBUFF_2$ $N_{oop}$ & & output low No Oscillation & & $NO_{osc}$ \\ - FS1: $NIBUFF_2$ $L_{slew}$ & & signal lost & & $NO_{osc}$ \\ \hline + FS11: $NIBUFF_2$ $L_{up}$ & & output high No Oscillation & & $NO_{osc}$ \\ + FS12: $NIBUFF_2$ $L_{dn}$ & & output low No Oscillation & & $NO_{osc}$ \\ + FS13: $NIBUFF_2$ $N_{oop}$ & & output low No Oscillation & & $NO_{osc}$ \\ + FS14: $NIBUFF_2$ $L_{slew}$ & & signal lost & & $NO_{osc}$ \\ \hline - FS1: $PHS45_3$ $90\_phaseshift$ & & osc frequency high & & $HI_{fosc}$ \\ - FS1: $PHS45_3$ $no\_signal$ & & signal lost & & $NO_{osc}$ \\ - FS1: $PHS45_3$ $0\_phaseshift$ & & osc frequency low & & $LO_{fosc}$ \\ \hline + FS15: $PHS45_3$ $0\_phaseshift$ & & osc frequency high & & $HI_{fosc}$ \\ + FS16: $PHS45_3$ $no\_signal$ & & signal lost & & $NO_{osc}$ \\ + FS17: $PHS45_3$ $90\_phaseshift$ & & osc frequency low & & $LO_{fosc}$ \\ \hline - FS1: $NIBUFF_3$ $L_{up}$ & & output high No Oscillation & & $NO_{osc}$ \\ - FS1: $NIBUFF_3$ $L_{dn}$ & & output low No Oscillation & & $NO_{osc}$ \\ - FS1: $NIBUFF_3$ $N_{oop}$ & & output low No Oscillation & & $NO_{osc}$ \\ - FS1: $NIBUFF_3$ $L_{slew}$ & & signal lost & & $NO_{osc}$ \\ \hline + FS18: $NIBUFF_3$ $L_{up}$ & & output high No Oscillation & & $NO_{osc}$ \\ + FS19: $NIBUFF_3$ $L_{dn}$ & & output low No Oscillation & & $NO_{osc}$ \\ + FS20: $NIBUFF_3$ $N_{oop}$ & & output low No Oscillation & & $NO_{osc}$ \\ + FS21: $NIBUFF_3$ $L_{slew}$ & & signal lost & & $NO_{osc}$ \\ \hline - FS1: $PHS45_4$ $90\_phaseshift$ & & osc frequency high & & $HI_{fosc}$ \\ - FS1: $PHS45_4$ $no\_signal$ & & signal lost & & $NO_{osc}$ \\ - FS1: $PHS45_4$ $0\_phaseshift$ & & osc frequency low & & $LO_{fosc}$ \\ \hline + FS22: $PHS45_4$ $0\_phaseshift$ & & osc frequency high & & $HI_{fosc}$ \\ + FS23: $PHS45_4$ $no\_signal$ & & signal lost & & $NO_{osc}$ \\ + FS24: $PHS45_4$ $90\_phaseshift$ & & osc frequency low & & $LO_{fosc}$ \\ \hline - FS1: $INVAMP$ $OUTOFRANGE$ & & signal lost & & $NO_{osc}$ \\ - FS1: $INVAMP$ $ZEROOUTPUT$ & & signal lost & & $NO_{osc}$ \\ - FS1: $INVAMP$ $NOGAIN$ & & signal lost & & $NO_{osc}$ \\ - FS1: $INVAMP$ $LOWPASS$ & & signal lost & & $NO_{osc}$ \\ \hline + FS25: $INVAMP$ $OUTOFRANGE$ & & signal lost & & $NO_{osc}$ \\ + FS26: $INVAMP$ $ZEROOUTPUT$ & & signal lost & & $NO_{osc}$ \\ + FS27: $INVAMP$ $NOGAIN$ & & signal lost & & $NO_{osc}$ \\ + FS28: $INVAMP$ $LOWPASS$ & & signal lost & & $NO_{osc}$ \\ \hline % FS1: $CAP_{10nF}$ $OPEN$ & & osc frequency low & & $LO_{fosc}$ \\ \hline @@ -917,39 +926,167 @@ returns three failure modes, $$ fm(BubbaOscillator) = \{ NO_{osc}, HI_{fosc}, LO_{fosc} \} . $$ -\begin{figure}[h] - \centering - \includegraphics[width=300pt,keepaspectratio=true]{./poss1finalbubba.png} - % largeosc.png: 916x390 pixel, 72dpi, 32.31x13.76 cm, bb=0 0 916 390 - \caption{Bubba Oscillator: One final large functional group.} - \label{fig:poss1finalbubba} -\end{figure} - \subsection{FMMD Analysis using smaller functional groups} -\begin{table}[h+] -\caption{Bubba Oscillator: Failure Mode Effects Analysis: Smaller Functional Groups, one more stage of hierarchy} % title of Table -\label{tbl:bubbalargefg} - -\begin{tabular}{|| l | l | c | c | l ||} \hline - \textbf{Failure Scenario} & & \textbf{Bubba} & & \textbf{Symptom} \\ - & & \textbf{Oscillator} & & \\ - \hline - -\hline - -\end{tabular} -\end{table} -\begin{figure}[h] +\begin{figure}[h+] \centering \includegraphics[width=300pt,keepaspectratio=true]{./poss2finalbubba.png} % largeosc.png: 916x390 pixel, 72dpi, 32.31x13.76 cm, bb=0 0 916 390 \caption{Bubba Oscillator: Smaller Functional Groups, One more FMMD hierarchy stage.} - \label{fig:poss1finalbubba} + \label{fig:poss2finalbubba} \end{figure} +We can take a more modular approach by creating two intermediate functional groups, a buffered $45^{\circ}$ phase shifter (BUFF45) +we can combine three $BUFF45$'s to make +a $135^{\circ}$ buffer phase shifter (PHS135BUFFERED). +We can combine a $PHS45$ and a $NIBUFF$ to create +and an amplifying $225^{\circ}$ phase shifter (PHS225AMP). +By combining PHS225AMP and PHS135BUFFERED we can create a more modularised hierarchical +model of the bubba oscillator. +The proposed hierarchy is shown in figure~\ref{fig:poss2finalbubba}. + +BUFF45 will comprise of a $PHS45$ {\dc} and a $NIBUFF$. + +\begin{table}[h+] +\caption{BUFF45: Failure Mode Effects Analysis} % title of Table +\label{tbl:buff45} + +\begin{tabular}{|| l | l | c | c | l ||} \hline + \textbf{Failure Scenario} & & \textbf{BUFF45} & & \textbf{Symptom} \\ + & & & & \\ + \hline + FS1: $PHS45_1$ $0\_phaseshift$ & & phase shift low & & $0\_phaseshift$ \\ + FS2: $PHS45_1$ $no\_signal$ & & signal lost & & $NO_{signal}$ \\ + FS3: $PHS45_1$ $90\_phaseshift$ & & phase shift high & & $90\_phaseshift$ \\ \hline + + FS4: $NIBUFF_1$ $L_{up}$ & & output high & & $NO_{signal}$ \\ + FS5: $NIBUFF_1$ $L_{dn}$ & & output low & & $NO_{signal}$ \\ + FS6: $NIBUFF_1$ $N_{oop}$ & & output low & & $NO_{signal}$ \\ + FS7: $NIBUFF_1$ $L_{slew}$ & & signal lost & & $NO_{signal}$ \\ \hline + + +\hline + +\end{tabular} +\end{table} + + +Collecting symptoms from table~\ref{tbl:buff45}, we can create a derived component $BUFF45$ which has the following failure modes: +$$ +fm (BUFF45) = \{ 90\_phaseshift, 0\_phaseshift, NO\_signal .\} +$$ + + +We can now combine three $BUFF45$ {\dcs} and create a $PHS135BUFFERED$ {\dc}. + + +\begin{table}[h+] +\caption{PHS135BUFFERED: Failure Mode Effects Analysis} % title of Table +\label{tbl:phs135buffered} + +\begin{tabular}{|| l | l | c | c | l ||} \hline + \textbf{Failure Scenario} & & \textbf{PHS135 Buffered} & & \textbf{Symptom} \\ + & & & & \\ + \hline + FS1: $PHS45_1$ $0\_phaseshift$ & & phase shift low & & $90\_phaseshift$ \\ + FS2: $PHS45_1$ $no\_signal$ & & signal lost & & $NO_{signal}$ \\ + FS3: $PHS45_1$ $90\_phaseshift$ & & phase shift high & & $180\_phaseshift$ \\ \hline + + FS4: $PHS45_2$ $0\_phaseshift$ & & phase shift low & & $90\_phaseshift$ \\ + FS5: $PHS45_2$ $no\_signal$ & & signal lost & & $NO_{signal}$ \\ + FS6: $PHS45_2$ $90\_phaseshift$ & & phase shift high & & $180\_phaseshift$ \\ \hline + + FS7: $PHS45_3$ $0\_phaseshift$ & & phase shift low & & $90\_phaseshift$ \\ + FS8: $PHS45_3$ $no\_signal$ & & signal lost & & $NO_{signal}$ \\ + FS9: $PHS45_3$ $90\_phaseshift$ & & phase shift high & & $180\_phaseshift$ \\ \hline + + + +\hline + +\end{tabular} +\end{table} + + +Collecting symptoms from table~\ref{tbl:phs135buffered}, we can create a derived component $PHS135BUFFERED$ which has the following failure modes: +$$ +fm (PHS135BUFFERED) = \{ 90\_phaseshift, 180\_phaseshift, NO\_signal .\} +$$ + + + + + +The $PHS225AMP$ consists of a $PHS45$ and an $INVAMP$ (which provides $180^{\circ}$ of phase shift). + +\begin{table}[h+] +\caption{PHS225AMP: Failure Mode Effects Analysis} % title of Table +\label{tbl:phs225amp} + +\begin{tabular}{|| l | l | c | c | l ||} \hline + \textbf{Failure Scenario} & & \textbf{PHS225AMP} & & \textbf{Symptom} \\ + & & \textbf{Oscillator} & & \\ + \hline + FS1: $PHS45_1$ $0\_phaseshift$ & & phase shift low & & $270\_phaseshift$ \\ + FS2: $PHS45_1$ $no\_signal$ & & signal lost & & $NO_{signal}$ \\ + FS3: $PHS45_1$ $90\_phaseshift$ & & phase shift high & & $180\_phaseshift$ \\ \hline + + FS4: $NIBUFF_1$ $L_{up}$ & & output high & & $NO_{signal}$ \\ + FS5: $NIBUFF_1$ $L_{dn}$ & & output low & & $NO_{signal}$ \\ + FS6: $NIBUFF_1$ $N_{oop}$ & & output low & & $NO_{signal}$ \\ + FS7: $NIBUFF_1$ $L_{slew}$ & & signal lost & & $NO_{signal}$ \\ \hline + +\hline + +\end{tabular} +\end{table} + +Collecting symptoms from table~\ref{tbl:phs225amp}, we can create a derived component $PHS225AMP$ which has the following failure modes: +$$ +fm (PHS225AMP) = \{ 270\_phaseshift, 180\_phaseshift, NO\_signal .\} +$$ + + +The $PHS225AMP$ consists of a $PHS45$ and an $INVAMP$ (which provides $180^{\circ}$ of phase shift). + + + +To complete the analysis we now bring the derived components $PHS135BUFFERED$ and $PHS225AMP$ together +and perform FMEA with these. + +\begin{table}[h+] +\caption{BUBBAOSC: Failure Mode Effects Analysis} % title of Table +\label{tbl:bubba2} + +\begin{tabular}{|| l | l | c | c | l ||} \hline + \textbf{Failure Scenario} & & \textbf{BUBBAOSC} & & \textbf{Symptom} \\ + & & & & \\ + \hline + FS1: $PHS135BUFFERED$ $180\_phaseshift$ & & phase shift high & & $LO_{fosc}$ \\ + FS2: $PHS135BUFFERED$ $no\_signal$ & & signal lost & & $NO_{osc}$ \\ + FS3: $PHS135BUFFERED$ $90\_phaseshift$ & & phase shift low & & $HI_{osc}$ \\ \hline + + FS4: $PHS225AMP$ $270\_phaseshift$ & & phase shift high & & $LO_{fosc}$ \\ + FS5: $PHS225AMP$ $180\_phaseshift$ & & phase shift low & & $HI_{osc}$ \\ + FS6: $PHS225AMP$ $NO\_signal$ & & lost signal & & $NO_{signal}$ \\ \hline + + +\hline + +\end{tabular} +\end{table} + + +Collecting symptoms from table~\ref{tbl:bubba2}, we can create a derived component $BUBBAOSC$ which has the following failure modes: +$$ +fm (BUBBAOSC) = \{ LO_{fosc}, HI_{osc}, NO\_signal .\} +$$ + +We could trace the DAGs here and ensure that both analysis strategies worked ok..... + + \subsection{Comparing both approaches}