%%% Appendix for detailed workings out from CH5 \chapter{Detailed FMMD analyses} \section{Bubba Oscillator FMMD analyses} For clarity the detailed workings of the FMMD analysis stages in many of the examples in chapter 5 have been moved here for reference. \subsection{PHS45 Detailed Analysis} \label{detail:PHS45} \begin{table}[h+] \caption{PhaseShift: Failure Mode Effects Analysis: Single Faults} % title of Table \label{tbl:firstorderlp} \begin{tabular}{|| l | c | l ||} \hline % \textbf{Failure Scenario} & & \textbf{First Order} & & \textbf{Symptom} \\ % & & \textbf{Low Pass Filter} & & \\ \textbf{Failure} & \textbf{$PHS45$ } & \textbf{Derived Component} \\ \textbf{cause} & \textbf{Effect} & \textbf{Failure Mode} \\ \hline FS1: R SHORT & 0 degree's of phase shift & $0\_phaseshift$ \\ % 90 degree's of phase shift & & $90\_phaseshift$ FS2: R OPEN & No Signal & $nosignal$ \\ \hline FS3: C SHORT & Grounded,No Signal & $nosignal$ \\ FS4: C OPEN & 0 degree's of phase shift & $0\_phaseshift$ \\ \hline \hline \end{tabular} \end{table} % PHS45 \subsection{Bubba Oscillator: One Large Functional Group: Detailed Analysis} \label{detail:BUBOSC1} \begin{table}[h+] \caption{Bubba Oscillator: Failure Mode Effects Analysis: One Large Functional Group} % title of Table \label{tbl:bubbalargefg} \begin{tabular}{|| l | l | c | c | l ||} \hline % \textbf{Failure Scenario} & & \textbf{Bubba} & & \textbf{Symptom} \\ % & & \textbf{Oscillator} & & \\ \textbf{Failure} & & \textbf{$BubbaOscillator$ } & & \textbf{Derived Component} \\ \textbf{cause} & & \textbf{Effect} & & \textbf{Failure Mode} \\ \hline FS1: $PHS45_1$ $0\_phaseshift$ & & osc frequency high & & $HI_{fosc}$ \\ FS2: $PHS45_1$ $no\_signal$ & & signal lost & & $NO_{osc}$ \\ \hline % FS3: $PHS45_1$ $90\_phaseshift$ & & osc frequency low & & $LO_{fosc}$ \\ \hline FS3: $NIBUFF_1$ $L_{up}$ & & output high No Oscillation & & $NO_{osc}$ \\ FS4: $NIBUFF_1$ $L_{dn}$ & & output low No Oscillation & & $NO_{osc}$ \\ FS5: $NIBUFF_1$ $N_{oop}$ & & output low No Oscillation & & $NO_{osc}$ \\ FS6: $NIBUFF_1$ $L_{slew}$ & & signal lost & & $NO_{osc}$ \\ \hline FS7: $PHS45_2$ $0\_phaseshift$ & & osc frequency high & & $HI_{fosc}$ \\ FS8: $PHS45_2$ $no\_signal$ & & signal lost & & $NO_{osc}$ \\ %FS10: $PHS45_2$ $90\_phaseshift$ & & osc frequency low & & $LO_{fosc}$ \\ \hline FS9: $NIBUFF_2$ $L_{up}$ & & output high No Oscillation & & $NO_{osc}$ \\ FS10: $NIBUFF_2$ $L_{dn}$ & & output low No Oscillation & & $NO_{osc}$ \\ FS11: $NIBUFF_2$ $N_{oop}$ & & output low No Oscillation & & $NO_{osc}$ \\ FS12: $NIBUFF_2$ $L_{slew}$ & & signal lost & & $NO_{osc}$ \\ \hline FS13: $PHS45_3$ $0\_phaseshift$ & & osc frequency high & & $HI_{fosc}$ \\ FS14: $PHS45_3$ $no\_signal$ & & signal lost & & $NO_{osc}$ \\ \hline % FS17: $PHS45_3$ $90\_phaseshift$ & & osc frequency low & & $LO_{fosc}$ \\ \hline FS15: $NIBUFF_3$ $L_{up}$ & & output high No Oscillation & & $NO_{osc}$ \\ FS16: $NIBUFF_3$ $L_{dn}$ & & output low No Oscillation & & $NO_{osc}$ \\ FS17: $NIBUFF_3$ $N_{oop}$ & & output low No Oscillation & & $NO_{osc}$ \\ FS18: $NIBUFF_3$ $L_{slew}$ & & signal lost & & $NO_{osc}$ \\ \hline FS19: $PHS45_4$ $0\_phaseshift$ & & osc frequency high & & $HI_{fosc}$ \\ FS20: $PHS45_4$ $no\_signal$ & & signal lost & & $NO_{osc}$ \\ \hline % FS24: $PHS45_4$ $90\_phaseshift$ & & osc frequency low & & $LO_{fosc}$ \\ \hline FS21: $INVAMP$ $OUTOFRANGE$ & & signal lost & & $NO_{osc}$ \\ FS22: $INVAMP$ $ZEROOUTPUT$ & & signal lost & & $NO_{osc}$ \\ FS23: $INVAMP$ $NOGAIN$ & & signal lost & & $NO_{osc}$ \\ FS24: $INVAMP$ $LOWPASS$ & & signal lost & & $NO_{osc}$ \\ \hline % FS1: $CAP_{10nF}$ $OPEN$ & & osc frequency low & & $LO_{fosc}$ \\ \hline % FS1: $CAP_{10nF}$ $SHORT$ & & osc frequency low & & $LO_{fosc}$ \\ \hline \hline \end{tabular} \end{table} Collecting symptoms from table~\ref{tbl:bubbalargefg} we can show that for single failure modes, applying $fm$ to the bubba oscillator returns three failure modes, % $$ fm(BubbaOscillator) = \{ NO_{osc}, HI_{fosc}\} . $$ %, LO_{fosc} \} . $$ \subsection{BUFF45: Detailed Analysis} \label{detail:BUFF45} \begin{table}[h+] \caption{BUFF45: Failure Mode Effects Analysis} % title of Table \label{tbl:buff45} \begin{tabular}{|| l | l | c | c | l ||} \hline %\textbf{Failure Scenario} & & \textbf{BUFF45} & & \textbf{Symptom} \\ % & & & & \\ \textbf{Failure} & & \textbf{$BUFF45$ } & & \textbf{Derived Component} \\ \textbf{cause} & & \textbf{Effect} & & \textbf{Failure Mode} \\ \hline FS1: $PHS45_1$ $0\_phaseshift$ & & phase shift low & & $0\_phaseshift$ \\ FS2: $PHS45_1$ $no\_signal$ & & signal lost & & $NO_{signal}$ \\ \hline %FS3: $PHS45_1$ $90\_phaseshift$ & & phase shift high & & $90\_phaseshift$ \\ \hline FS3: $NIBUFF_1$ $L_{up}$ & & output high & & $NO_{signal}$ \\ FS4: $NIBUFF_1$ $L_{dn}$ & & output low & & $NO_{signal}$ \\ FS5: $NIBUFF_1$ $N_{oop}$ & & output low & & $NO_{signal}$ \\ FS6: $NIBUFF_1$ $L_{slew}$ & & signal lost & & $NO_{signal}$ \\ \hline \hline \end{tabular} \end{table} collecting symptoms from table~\ref{tbl:buff45}, we can create a derived component $BUFF45$ which has the following failure modes: $$ fm (BUFF45) = \{ 0\_phaseshift, NO\_signal .\} % 90\_phaseshift, $$ % \subsection{PHS135BUFFERED: Failure Mode Effects Analysis} % title of Table \label{detail:PHS135BUFFERED} \begin{table}[h+] \caption{PHS135BUFFERED: Failure Mode Effects Analysis} % title of Table \label{tbl:phs135buffered} \begin{tabular}{|| l | l | c | c | l ||} \hline %\textbf{Failure Scenario} & & \textbf{PHS135 Buffered} & & \textbf{Symptom} \\ % & & & & \\ \textbf{Failure} & & \textbf{$PHS135BUFFERED$ } & & \textbf{Derived Component} \\ \textbf{cause} & & \textbf{Effect} & & \textbf{Failure Mode} \\ \hline FS1: $PHS45_1$ $0\_phaseshift$ & & phase shift low & & $90\_phaseshift$ \\ FS2: $PHS45_1$ $no\_signal$ & & signal lost & & $NO_{signal}$ \\ \hline %FS3: $PHS45_1$ $90\_phaseshift$ & & phase shift high & & $180\_phaseshift$ \\ \hline FS3: $PHS45_2$ $0\_phaseshift$ & & phase shift low & & $90\_phaseshift$ \\ FS4: $PHS45_2$ $no\_signal$ & & signal lost & & $NO_{signal}$ \\ \hline % FS6: $PHS45_2$ $90\_phaseshift$ & & phase shift high & & $180\_phaseshift$ \\ \hline FS5: $PHS45_3$ $0\_phaseshift$ & & phase shift low & & $90\_phaseshift$ \\ FS6: $PHS45_3$ $no\_signal$ & & signal lost & & $NO_{signal}$ \\ \hline % FS9: $PHS45_3$ $90\_phaseshift$ & & phase shift high & & $180\_phaseshift$ \\ \hline \hline \end{tabular} \end{table} % % Collecting symptoms from table~\ref{tbl:phs135buffered}, we can create a derived component $PHS135BUFFERED$ which has the following failure modes: $$ fm (PHS135BUFFERED) = \{ 90\_phaseshift, NO\_signal .\} % 180\_phaseshift, $$ % \subsection{PHS225AMP: Failure Mode Effects Analysis} % title of Table \label{detail:PHS225AMP} \begin{table}[h+] \caption{PHS225AMP: Failure Mode Effects Analysis} % title of Table \label{tbl:phs225amp} \begin{tabular}{|| l | l | c | c | l ||} \hline %\textbf{Failure Scenario} & & \textbf{PHS225AMP} & & \textbf{Symptom} \\ % & & \textbf{Oscillator} & & \\ \textbf{Failure} & & \textbf{$PHS225AMP$ } & & \textbf{Derived Component} \\ \textbf{cause} & & \textbf{Effect} & & \textbf{Failure Mode} \\ \hline FS1: $PHS45_1$ $0\_phaseshift$ & & phase shift low & & $180\_phaseshift$ \\ FS2: $PHS45_1$ $no\_signal$ & & signal lost & & $NO_{signal}$ \\ \hline % FS3: $PHS45_1$ $90\_phaseshift$ & & phase shift high & & $270\_phaseshift$ \\ \hline FS3: $INVAMP$ $L_{up}$ & & output high & & $NO_{signal}$ \\ FS4: $INVAMP$ $L_{dn}$ & & output low & & $NO_{signal}$ \\ FS5: $INVAMP$ $N_{oop}$ & & output low & & $NO_{signal}$ \\ FS6: $INVAMP$ $L_{slew}$ & & signal lost & & $NO_{signal}$ \\ \hline \hline \end{tabular} \end{table} % Applying FMMD we create a derived component $PHS225AMP$ which has the following failure modes: $$ fm (PHS225AMP) = \{ 180\_phaseshift, NO\_signal .\} % 270\_phaseshift, $$ \subsection{BUBBAOSC: Failure Mode Effects Analysis} % title of Table \label{detail:BUBBAOSC} \begin{table}[h+] \caption{BUBBAOSC: Failure Mode Effects Analysis} % title of Table \label{tbl:bubba2} \begin{tabular}{|| l | l | c | c | l ||} \hline %\textbf{Failure Scenario} & & \textbf{BUBBAOSC} & & \textbf{Symptom} \\ % & & & & \\ \textbf{Failure} & & \textbf{$BUBBAOSC$ } & & \textbf{Derived Component} \\ \textbf{cause} & & \textbf{Effect} & & \textbf{Failure Mode} \\ \hline %FS1: $PHS135BUFFERED$ $180\_phaseshift$ & & phase shift high & & $LO_{fosc}$ \\ FS1: $PHS135BUFFERED$ $no\_signal$ & & signal lost & & $NO_{osc}$ \\ FS2: $PHS135BUFFERED$ $90\_phaseshift$ & & phase shift low & & $HI_{osc}$ \\ \hline % FS4: $PHS225AMP$ $270\_phaseshift$ & & phase shift high & & $LO_{fosc}$ \\ FS4: $PHS225AMP$ $180\_phaseshift$ & & phase shift low & & $HI_{osc}$ \\ FS5: $PHS225AMP$ $NO\_signal$ & & lost signal & & $NO_{signal}$ \\ \hline \hline \end{tabular} \end{table} % Collecting symptoms from table~\ref{tbl:bubba2}, we can create a derived component $BUBBAOSC$ which has the following failure modes: $$ fm (BUBBAOSC) = \{ HI_{osc}, NO\_signal .\} % LO_{fosc}, $$ \clearpage \section{Sigma Delta Detailed FMMD Analyses} \subsection{FMMD Analysis of Summing Junction Integrator: SUMJINT} \label{detail:SUMJINT} \begin{table}[h+] \center \caption{Summing Junction Integrator($SUMJINT$): Failure Mode Effects Analysis} % title of Table \label{tbl:sumjint} \begin{tabular}{|| l | l | c | c | l ||} \hline %\textbf{Failure Scenario} & & \textbf{failure result} & & \textbf{Symptom} \\ % & & & & \\ \textbf{Failure} & & \textbf{$SUMJINT$ } & & \textbf{Derived Component} \\ \textbf{cause} & & \textbf{Effect} & & \textbf{Failure Mode} \\ \hline\hline FS1: $R1$ $OPEN$ & & $V_{in}$ dominates input & & $V_{in} DOM$ \\ FS2: $R1$ $SHORT$ & & $V_{fb}$ dominates input & & $V_{fb} DOM$ \\ \hline FS3: $R2$ $OPEN$ & & $V_{fb}$ dominates input & & $V_{fb} DOM$ \\ FS4: $R2$ $SHORT$ & & $V_{in}$ dominates input & & $V_{in} DOM$ \\ \hline FS5: $IC1$ $HIGH$ & & output perm. high & & HIGH \\ FS6: $IC1$ $LOW$ & & output perm. low & & LOW \\ \hline FS7: $IC1$ $NOOP$ & & no current to drive C1 & & NO\_INTEGRATION \\ FS8: $IC1$ $LOW\_SLEW$ & & signal delay to C1 & & NO\_INTEGRATION \\ \hline FS9: $C1$ $OPEN$ & & no capacitance & & NO\_INTEGRATION \\ FS10: $C1$ $SHORT$ & & no capacitance & & NO\_INTEGRATION \\ \hline % \hline % FS1: $IC2$ $HIGH$ & & output perm. high & & HIGH \\ % FS2: $IC2$ $LOW$ & & output perm. low & & LOW \\ \hline % FS3: $IC2$ $NOOP$ & & no current drive & & LOW \\ % FS4: $IC2$ $LOW\_SLEW$ & & delayed signal & & LOW\_SLEW \\ \hline % \hline \hline \end{tabular} \end{table} Collecting the {\dc} failure modes of $SUMJINT$ we obtain $$\{ V_{in} DOM, V_{fb} DOM, NO\_INTEGRATION, HIGH, LOW \} .$$ \subsection{FMMD Analysis of High Impedance Signal Buffer : HISB} \label{detail:HISB} \begin{table}[h+] \center % \center \caption{ High Impedance Signal Buffer : Failure Mode Effects Analysis} % title of Table \begin{tabular}{|| l | l | c | c | l ||} \hline %\textbf{Failure Scenario} & & \textbf{failure result} & & \textbf{Symptom} \\ % & & & & \\ \textbf{Failure} & & \textbf{$HISB$ } & & \textbf{Derived Component} \\ \textbf{cause} & & \textbf{Effect} & & \textbf{Failure Mode} \\ \hline\hline FS1: $IC2$ $HIGH$ & & output perm. high & & HIGH \\ FS2: $IC2$ $LOW$ & & output perm. low & & LOW \\ FS3: $IC2$ $NOOP$ & & no current to output & & $NOOP$ \\ FS4: $IC2$ $LOW\_SLEW$ & & delay signal & & $LOW\_{SLEW}$ \\ \hline \end{tabular} \end{table} % \hline \subsection{FMMD Analysis of Digital level to analogue level converter : DL2AL} \label{detail:DL2AL} \begin{table}[h+] \center \caption{$PD , IC3$ Digital level to analogue level converter: Failure Mode Effects Analysis} % title of Table \label{tbl:DS2AS} \begin{tabular}{|| l | l | c | c | l ||} \hline %\textbf{Failure Scenario} & & \textbf{failure result } & & \textbf{Symptom} \\ % & & & & \\ % & & & & \\ \textbf{Failure} & & \textbf{$DS2AL$ } & & \textbf{Derived Component} \\ \textbf{cause} & & \textbf{Effect} & & \textbf{Failure Mode} \\ \hline \hline FS1: $PD $ $HIGH$ & & output perm. low & & LOW \\ FS2: $PD $ $LOW$ & & output perm. low & & HIGH \\ \hline \hline FS3: $IC3$ $HIGH$ & & output perm. high & & HIGH \\ FS4: $IC3$ $LOW$ & & output perm. low & & LOW \\ FS5: $IC3$ $NOOP$ & & no current drive & & LOW \\ FS6: $IC3$ $LOW\_{SLEW}$ & & delayed signal & & $LOW\_{SLEW}$ \\ \hline \hline \end{tabular} \end{table} We collect the symptoms of failure $\{ LOW, HIGH, LOW\_{SLEW} \}$. \subsection{FMMD Analysis of Digital level to analogue level converter : DL2AL} \label{detail:DIGBUF} \begin{table}[h+] \center \caption{$ IC4, CLOCK $ Digital Buffer: Failure Mode Effects Analysis} % title of Table \label{tbl:digbuf} \begin{tabular}{|| l | l | c | c | l ||} \hline %\textbf{Failure Scenario} & & \textbf{failure result } & & \textbf{Symptom} \\ % & & & & \\ % & & & & \\ \textbf{Failure} & & \textbf{$DIGBUF$ } & & \textbf{Derived Component} \\ \textbf{cause} & & \textbf{Effect} & & \textbf{Failure Mode} \\ %$$ fm ( CD4013B) = \{ HIGH, LOW, NOOP \} $$ \hline \hline FS1: $CLOCK$ $STOPPED$ & & buffer stopped & & STOPPED \\ \hline FS2: $IC4$ $HIGH$ & & buffer stopped & & STOPPED \\ FS3: $IC4$ $LOW$ & & buffer stopped & & STOPPED \\ FS4: $IC4$ $NOOP$ & & no current drive & & LOW \\ \hline \hline \hline \end{tabular} \end{table} We collect the symptoms of failure $\{ LOW, STOPPED \}$. \subsection{FMMD Analysis of buffered integrating summing junction : BISJ} \label{detail:BISJ} \begin{table}[h+] \caption{ $HISB , SUMJINT$ buffered integrating summing junction($BISJ$): Failure Mode Effects Analysis} % title of Table \label{tbl:BISJ} \begin{tabular}{|| l | l | c | c | l ||} \hline % \textbf{Failure Scenario} & & \textbf{failure result } & & \textbf{Symptom} \\ % & & & & \\ % & & & & \\ \textbf{Failure} & & \textbf{$BISJ$ } & & \textbf{Derived Component} \\ \textbf{cause} & & \textbf{Effect} & & \textbf{Failure Mode} \\ \hline \hline FS1: $SUMJINT$ $V_{in} DOM$ & & output integral of $V_{in}$ & & $OUTPUT STUCK$ \\ FS2: $SUMJINT$ $V_{fb} DOM$ & & output integral of $V_{fb}$ & & $OUTPUT STUCK$ \\ % $$ fm(SUMJUINT^1_0) = \{ V_{in} DOM, V_{fb} DOM, NO\_INTEGRATION, HIGH, LOW \} .$$ FS3: $SUMJINT$ $NO\_INTEGRATION$ & & output stuck high or low & & $OUTPUT STUCK$ \\ FS4: $SUMJINT$ $HIGH$ & & output stuck high & & $OUTPUT STUCK$ \\ FS5: $SUMJINT$ $LOW$ & & output stuck low & & $OUTPUT STUCK$ \\ \hline %\hline FS6: $HISB$ $HIGH$ & & output perm. high & & $OUTPUT STUCK$ \\ FS7: $HISB$ $LOW$ & & output perm. low & & $OUTPUT STUCK$ \\ FS8: $HISB$ $ NO\_INTEGRATION$ & & no current drive & & $OUTPUT STUCK$ \\ FS9: $HISB$ $LOW\_SLEW$ & & delayed signal & & $REDUCED\_INTEGRATION$ \\ \hline \hline \end{tabular} \end{table} We now collect the symptoms of failure $\{ OUTPUT STUCK , REDUCED\_INTEGRATION \}$, and create a {\dc} called $BISJ$. \subsection{FMMD Analysis of flip flop buffered : FFB} \label{detail:FFB} \begin{table}[h+] \caption{ $DIGBUF,DL2AL$ flip flop buffered($FFB$): Failure Mode Effects Analysis} % title of Table \label{tbl:digbuf} \begin{tabular}{|| l | l | c | c | l ||} \hline %\textbf{Failure Scenario} & & \textbf{failure result } & & \textbf{Symptom} \\ % & & & & \\ % & & & & \\ \textbf{Failure} & & \textbf{$DIGBUF$ } & & \textbf{Derived Component} \\ \textbf{cause} & & \textbf{Effect} & & \textbf{Failure Mode} \\ \hline \hline FS1: $DIGBUF$ $STOPPED$ & & output stuck & & $OUTPUT STUCK$ \\ FS2: $DIGBUF$ $LOW$ & & output stuck low & & $OUTPUT STUCK$ \\ \hline %\hline FS3: $DL2AL$ $LOW$ & & output perm. high & & $OUTPUT STUCK$ \\ FS4: $DL2AL$ $HIGH$ & & output perm. low & & $OUTPUT STUCK$ \\ FS5: $DL2AL$ $LOW\_SLEW$ & & no current drive & & $LOW\_SLEW$ \\ \hline \hline \hline \end{tabular} \end{table} We now collect symptoms $\{OUTPUT STUCK, LOW\_SLEW\}$ and create a {\dc} %at the third level of symptom abstraction called $FFB$. \subsection{FMMD Analysis of \sd : SDADC} \label{detail:SDADC} \begin{table}[h+] \caption{ $FFB , BISJ $ \sd ($SDADC$): Failure Mode Effects Analysis} % title of Table \label{tbl:sdadc} \begin{tabular}{|| l | l | c | c | l ||} \hline %\textbf{Failure Scenario} & & \textbf{failure result } & & \textbf{Symptom} \\ % & & & & \\ % & & & & \\ \textbf{Failure} & & \textbf{$FFB$ } & & \textbf{Derived Component} \\ \textbf{cause} & & \textbf{Effect} & & \textbf{Failure Mode} \\ \hline \hline FS1: $FFB$ $OUTPUT STUCK$ & & value max high or low & & $OUTPUT\_OUT\_OF\_RANGE$ \\ FS2: $FFB$ $LOW\_SLEW$ & & values will appear larger & & $OUTPUT\_INCORRECT$ \\ % FS3: $IC4^0$ $NOOP$ & & output stuck low & & $OUTPUT STUCK$ \\ \hline %\hline FS3: $BISJ$ $OUTPUT STUCK$ & & value max high or low & & $OUTPUT\_OUT\_OF\_RANGE$ \\ FS4: $BISJ$ $REDUCED\_INTEGRATION$ & & values will appear larger & & $OUTPUT\_INCORRECT$ \\ \hline \hline \end{tabular} \end{table} %\clearpage We now collect the symptoms for the \sd $$ \; \{OUTPUT\_OUT\_OF\_RANGE, OUTPUT\_INCORRECT\}.$$ We can now create a {\dc} to represent the analogue to digital converter, $SDADC$. $$fm(SSDADC) = \{OUTPUT\_OUT\_OF\_RANGE, OUTPUT\_INCORRECT\}$$