completed analysis of BUBBA from bth perspectives.
Needs tidying up (somewhat).
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@ -843,8 +843,8 @@ We could at this point bring all the {\dcs} together into one large functional
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group (see figure~\ref{fig:poss1finalbubba})
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or we could try to merge smaller stages.
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The capactior and 180 degree inverting amplifier, form a {\fg}
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providing an amplified 225 degree phase shift, which we can call $PHS225AMP$.
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A PHS45 {\dc} and an inverting amplifier (which always gives $180^{\circ}$ phase shift), form a {\fg}
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providing an amplified $225^{\circ}$ phase shift, which we can call $PHS225AMP$.
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%
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We could also merge the $NIBUFF$ and $PHS45$
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{\dcs} into a {\fg} and the resultant derived component from this we could call a $BUFF45$,
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@ -855,6 +855,15 @@ and then merge $PHS135BUFFERED$ and $PHS225AMP$ in a final stage (see figure~\r
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\subsection{FMMD Analysis using one large functional group}
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\begin{figure}[h+]
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\centering
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\includegraphics[width=300pt,keepaspectratio=true]{./poss1finalbubba.png}
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% largeosc.png: 916x390 pixel, 72dpi, 32.31x13.76 cm, bb=0 0 916 390
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\caption{Bubba Oscillator: One final large functional group.}
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\label{fig:poss1finalbubba}
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\end{figure}
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\begin{table}[h+]
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\caption{Bubba Oscillator: Failure Mode Effects Analysis: One Large Functional Group} % title of Table
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\label{tbl:bubbalargefg}
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@ -865,42 +874,42 @@ and then merge $PHS135BUFFERED$ and $PHS225AMP$ in a final stage (see figure~\r
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\hline
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FS1: $PHS45_1$ $90\_phaseshift$ & & osc frequency high & & $HI_{fosc}$ \\
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FS1: $PHS45_1$ $no\_signal$ & & signal lost & & $NO_{osc}$ \\
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FS1: $PHS45_1$ $0\_phaseshift$ & & osc frequency low & & $LO_{fosc}$ \\ \hline
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FS1: $PHS45_1$ $0\_phaseshift$ & & osc frequency high & & $HI_{fosc}$ \\
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FS2: $PHS45_1$ $no\_signal$ & & signal lost & & $NO_{osc}$ \\
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FS3: $PHS45_1$ $90\_phaseshift$ & & osc frequency low & & $LO_{fosc}$ \\ \hline
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FS1: $NIBUFF_1$ $L_{up}$ & & output high No Oscillation & & $NO_{osc}$ \\
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FS1: $NIBUFF_1$ $L_{dn}$ & & output low No Oscillation & & $NO_{osc}$ \\
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FS1: $NIBUFF_1$ $N_{oop}$ & & output low No Oscillation & & $NO_{osc}$ \\
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FS1: $NIBUFF_1$ $L_{slew}$ & & signal lost & & $NO_{osc}$ \\ \hline
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FS4: $NIBUFF_1$ $L_{up}$ & & output high No Oscillation & & $NO_{osc}$ \\
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FS5: $NIBUFF_1$ $L_{dn}$ & & output low No Oscillation & & $NO_{osc}$ \\
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FS6: $NIBUFF_1$ $N_{oop}$ & & output low No Oscillation & & $NO_{osc}$ \\
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FS7: $NIBUFF_1$ $L_{slew}$ & & signal lost & & $NO_{osc}$ \\ \hline
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FS1: $PHS45_2$ $90\_phaseshift$ & & osc frequency high & & $HI_{fosc}$ \\
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FS1: $PHS45_2$ $no\_signal$ & & signal lost & & $NO_{osc}$ \\
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FS1: $PHS45_2$ $0\_phaseshift$ & & osc frequency low & & $LO_{fosc}$ \\ \hline
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FS8: $PHS45_2$ $0\_phaseshift$ & & osc frequency high & & $HI_{fosc}$ \\
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FS9: $PHS45_2$ $no\_signal$ & & signal lost & & $NO_{osc}$ \\
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FS10: $PHS45_2$ $90\_phaseshift$ & & osc frequency low & & $LO_{fosc}$ \\ \hline
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FS1: $NIBUFF_2$ $L_{up}$ & & output high No Oscillation & & $NO_{osc}$ \\
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FS1: $NIBUFF_2$ $L_{dn}$ & & output low No Oscillation & & $NO_{osc}$ \\
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FS1: $NIBUFF_2$ $N_{oop}$ & & output low No Oscillation & & $NO_{osc}$ \\
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FS1: $NIBUFF_2$ $L_{slew}$ & & signal lost & & $NO_{osc}$ \\ \hline
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FS11: $NIBUFF_2$ $L_{up}$ & & output high No Oscillation & & $NO_{osc}$ \\
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FS12: $NIBUFF_2$ $L_{dn}$ & & output low No Oscillation & & $NO_{osc}$ \\
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FS13: $NIBUFF_2$ $N_{oop}$ & & output low No Oscillation & & $NO_{osc}$ \\
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FS14: $NIBUFF_2$ $L_{slew}$ & & signal lost & & $NO_{osc}$ \\ \hline
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FS1: $PHS45_3$ $90\_phaseshift$ & & osc frequency high & & $HI_{fosc}$ \\
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FS1: $PHS45_3$ $no\_signal$ & & signal lost & & $NO_{osc}$ \\
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FS1: $PHS45_3$ $0\_phaseshift$ & & osc frequency low & & $LO_{fosc}$ \\ \hline
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FS15: $PHS45_3$ $0\_phaseshift$ & & osc frequency high & & $HI_{fosc}$ \\
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FS16: $PHS45_3$ $no\_signal$ & & signal lost & & $NO_{osc}$ \\
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FS17: $PHS45_3$ $90\_phaseshift$ & & osc frequency low & & $LO_{fosc}$ \\ \hline
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FS1: $NIBUFF_3$ $L_{up}$ & & output high No Oscillation & & $NO_{osc}$ \\
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FS1: $NIBUFF_3$ $L_{dn}$ & & output low No Oscillation & & $NO_{osc}$ \\
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FS1: $NIBUFF_3$ $N_{oop}$ & & output low No Oscillation & & $NO_{osc}$ \\
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FS1: $NIBUFF_3$ $L_{slew}$ & & signal lost & & $NO_{osc}$ \\ \hline
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FS18: $NIBUFF_3$ $L_{up}$ & & output high No Oscillation & & $NO_{osc}$ \\
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FS19: $NIBUFF_3$ $L_{dn}$ & & output low No Oscillation & & $NO_{osc}$ \\
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FS20: $NIBUFF_3$ $N_{oop}$ & & output low No Oscillation & & $NO_{osc}$ \\
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FS21: $NIBUFF_3$ $L_{slew}$ & & signal lost & & $NO_{osc}$ \\ \hline
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FS1: $PHS45_4$ $90\_phaseshift$ & & osc frequency high & & $HI_{fosc}$ \\
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FS1: $PHS45_4$ $no\_signal$ & & signal lost & & $NO_{osc}$ \\
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FS1: $PHS45_4$ $0\_phaseshift$ & & osc frequency low & & $LO_{fosc}$ \\ \hline
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FS22: $PHS45_4$ $0\_phaseshift$ & & osc frequency high & & $HI_{fosc}$ \\
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FS23: $PHS45_4$ $no\_signal$ & & signal lost & & $NO_{osc}$ \\
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FS24: $PHS45_4$ $90\_phaseshift$ & & osc frequency low & & $LO_{fosc}$ \\ \hline
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FS1: $INVAMP$ $OUTOFRANGE$ & & signal lost & & $NO_{osc}$ \\
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FS1: $INVAMP$ $ZEROOUTPUT$ & & signal lost & & $NO_{osc}$ \\
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FS1: $INVAMP$ $NOGAIN$ & & signal lost & & $NO_{osc}$ \\
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FS1: $INVAMP$ $LOWPASS$ & & signal lost & & $NO_{osc}$ \\ \hline
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FS25: $INVAMP$ $OUTOFRANGE$ & & signal lost & & $NO_{osc}$ \\
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FS26: $INVAMP$ $ZEROOUTPUT$ & & signal lost & & $NO_{osc}$ \\
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FS27: $INVAMP$ $NOGAIN$ & & signal lost & & $NO_{osc}$ \\
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FS28: $INVAMP$ $LOWPASS$ & & signal lost & & $NO_{osc}$ \\ \hline
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% FS1: $CAP_{10nF}$ $OPEN$ & & osc frequency low & & $LO_{fosc}$ \\ \hline
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@ -917,38 +926,166 @@ returns three failure modes,
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$$ fm(BubbaOscillator) = \{ NO_{osc}, HI_{fosc}, LO_{fosc} \} . $$
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\begin{figure}[h]
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\centering
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\includegraphics[width=300pt,keepaspectratio=true]{./poss1finalbubba.png}
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% largeosc.png: 916x390 pixel, 72dpi, 32.31x13.76 cm, bb=0 0 916 390
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\caption{Bubba Oscillator: One final large functional group.}
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\label{fig:poss1finalbubba}
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\end{figure}
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\subsection{FMMD Analysis using smaller functional groups}
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\begin{figure}[h+]
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\centering
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\includegraphics[width=300pt,keepaspectratio=true]{./poss2finalbubba.png}
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% largeosc.png: 916x390 pixel, 72dpi, 32.31x13.76 cm, bb=0 0 916 390
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\caption{Bubba Oscillator: Smaller Functional Groups, One more FMMD hierarchy stage.}
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\label{fig:poss2finalbubba}
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\end{figure}
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We can take a more modular approach by creating two intermediate functional groups, a buffered $45^{\circ}$ phase shifter (BUFF45)
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we can combine three $BUFF45$'s to make
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a $135^{\circ}$ buffer phase shifter (PHS135BUFFERED).
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We can combine a $PHS45$ and a $NIBUFF$ to create
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and an amplifying $225^{\circ}$ phase shifter (PHS225AMP).
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By combining PHS225AMP and PHS135BUFFERED we can create a more modularised hierarchical
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model of the bubba oscillator.
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The proposed hierarchy is shown in figure~\ref{fig:poss2finalbubba}.
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BUFF45 will comprise of a $PHS45$ {\dc} and a $NIBUFF$.
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\begin{table}[h+]
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\caption{Bubba Oscillator: Failure Mode Effects Analysis: Smaller Functional Groups, one more stage of hierarchy} % title of Table
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\label{tbl:bubbalargefg}
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\caption{BUFF45: Failure Mode Effects Analysis} % title of Table
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\label{tbl:buff45}
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\begin{tabular}{|| l | l | c | c | l ||} \hline
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\textbf{Failure Scenario} & & \textbf{Bubba} & & \textbf{Symptom} \\
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& & \textbf{Oscillator} & & \\
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\textbf{Failure Scenario} & & \textbf{BUFF45} & & \textbf{Symptom} \\
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& & & & \\
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\hline
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FS1: $PHS45_1$ $0\_phaseshift$ & & phase shift low & & $0\_phaseshift$ \\
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FS2: $PHS45_1$ $no\_signal$ & & signal lost & & $NO_{signal}$ \\
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FS3: $PHS45_1$ $90\_phaseshift$ & & phase shift high & & $90\_phaseshift$ \\ \hline
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FS4: $NIBUFF_1$ $L_{up}$ & & output high & & $NO_{signal}$ \\
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FS5: $NIBUFF_1$ $L_{dn}$ & & output low & & $NO_{signal}$ \\
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FS6: $NIBUFF_1$ $N_{oop}$ & & output low & & $NO_{signal}$ \\
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FS7: $NIBUFF_1$ $L_{slew}$ & & signal lost & & $NO_{signal}$ \\ \hline
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\hline
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\end{tabular}
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\end{table}
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\begin{figure}[h]
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\centering
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\includegraphics[width=300pt,keepaspectratio=true]{./poss2finalbubba.png}
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% largeosc.png: 916x390 pixel, 72dpi, 32.31x13.76 cm, bb=0 0 916 390
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\caption{Bubba Oscillator: Smaller Functional Groups, One more FMMD hierarchy stage.}
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\label{fig:poss1finalbubba}
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\end{figure}
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Collecting symptoms from table~\ref{tbl:buff45}, we can create a derived component $BUFF45$ which has the following failure modes:
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$$
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fm (BUFF45) = \{ 90\_phaseshift, 0\_phaseshift, NO\_signal .\}
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$$
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We can now combine three $BUFF45$ {\dcs} and create a $PHS135BUFFERED$ {\dc}.
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\begin{table}[h+]
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\caption{PHS135BUFFERED: Failure Mode Effects Analysis} % title of Table
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\label{tbl:phs135buffered}
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\begin{tabular}{|| l | l | c | c | l ||} \hline
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\textbf{Failure Scenario} & & \textbf{PHS135 Buffered} & & \textbf{Symptom} \\
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& & & & \\
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\hline
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FS1: $PHS45_1$ $0\_phaseshift$ & & phase shift low & & $90\_phaseshift$ \\
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FS2: $PHS45_1$ $no\_signal$ & & signal lost & & $NO_{signal}$ \\
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FS3: $PHS45_1$ $90\_phaseshift$ & & phase shift high & & $180\_phaseshift$ \\ \hline
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FS4: $PHS45_2$ $0\_phaseshift$ & & phase shift low & & $90\_phaseshift$ \\
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FS5: $PHS45_2$ $no\_signal$ & & signal lost & & $NO_{signal}$ \\
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FS6: $PHS45_2$ $90\_phaseshift$ & & phase shift high & & $180\_phaseshift$ \\ \hline
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FS7: $PHS45_3$ $0\_phaseshift$ & & phase shift low & & $90\_phaseshift$ \\
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FS8: $PHS45_3$ $no\_signal$ & & signal lost & & $NO_{signal}$ \\
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FS9: $PHS45_3$ $90\_phaseshift$ & & phase shift high & & $180\_phaseshift$ \\ \hline
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\hline
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\end{tabular}
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\end{table}
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Collecting symptoms from table~\ref{tbl:phs135buffered}, we can create a derived component $PHS135BUFFERED$ which has the following failure modes:
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$$
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fm (PHS135BUFFERED) = \{ 90\_phaseshift, 180\_phaseshift, NO\_signal .\}
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$$
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The $PHS225AMP$ consists of a $PHS45$ and an $INVAMP$ (which provides $180^{\circ}$ of phase shift).
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\begin{table}[h+]
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\caption{PHS225AMP: Failure Mode Effects Analysis} % title of Table
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\label{tbl:phs225amp}
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\begin{tabular}{|| l | l | c | c | l ||} \hline
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\textbf{Failure Scenario} & & \textbf{PHS225AMP} & & \textbf{Symptom} \\
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& & \textbf{Oscillator} & & \\
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\hline
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FS1: $PHS45_1$ $0\_phaseshift$ & & phase shift low & & $270\_phaseshift$ \\
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FS2: $PHS45_1$ $no\_signal$ & & signal lost & & $NO_{signal}$ \\
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FS3: $PHS45_1$ $90\_phaseshift$ & & phase shift high & & $180\_phaseshift$ \\ \hline
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FS4: $NIBUFF_1$ $L_{up}$ & & output high & & $NO_{signal}$ \\
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FS5: $NIBUFF_1$ $L_{dn}$ & & output low & & $NO_{signal}$ \\
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FS6: $NIBUFF_1$ $N_{oop}$ & & output low & & $NO_{signal}$ \\
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FS7: $NIBUFF_1$ $L_{slew}$ & & signal lost & & $NO_{signal}$ \\ \hline
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\hline
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\end{tabular}
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\end{table}
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Collecting symptoms from table~\ref{tbl:phs225amp}, we can create a derived component $PHS225AMP$ which has the following failure modes:
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$$
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fm (PHS225AMP) = \{ 270\_phaseshift, 180\_phaseshift, NO\_signal .\}
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$$
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The $PHS225AMP$ consists of a $PHS45$ and an $INVAMP$ (which provides $180^{\circ}$ of phase shift).
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To complete the analysis we now bring the derived components $PHS135BUFFERED$ and $PHS225AMP$ together
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and perform FMEA with these.
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\begin{table}[h+]
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\caption{BUBBAOSC: Failure Mode Effects Analysis} % title of Table
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\label{tbl:bubba2}
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\begin{tabular}{|| l | l | c | c | l ||} \hline
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\textbf{Failure Scenario} & & \textbf{BUBBAOSC} & & \textbf{Symptom} \\
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& & & & \\
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\hline
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FS1: $PHS135BUFFERED$ $180\_phaseshift$ & & phase shift high & & $LO_{fosc}$ \\
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FS2: $PHS135BUFFERED$ $no\_signal$ & & signal lost & & $NO_{osc}$ \\
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FS3: $PHS135BUFFERED$ $90\_phaseshift$ & & phase shift low & & $HI_{osc}$ \\ \hline
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FS4: $PHS225AMP$ $270\_phaseshift$ & & phase shift high & & $LO_{fosc}$ \\
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FS5: $PHS225AMP$ $180\_phaseshift$ & & phase shift low & & $HI_{osc}$ \\
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FS6: $PHS225AMP$ $NO\_signal$ & & lost signal & & $NO_{signal}$ \\ \hline
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\hline
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\end{tabular}
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\end{table}
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Collecting symptoms from table~\ref{tbl:bubba2}, we can create a derived component $BUBBAOSC$ which has the following failure modes:
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$$
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fm (BUBBAOSC) = \{ LO_{fosc}, HI_{osc}, NO\_signal .\}
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$$
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We could trace the DAGs here and ensure that both analysis strategies worked ok.....
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\subsection{Comparing both approaches}
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