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Robin_PHD/submission_thesis/appendixes/detailed_analysis.tex
Robin Clark c63022bc93 Made a chapter 5 and a half, well 6 
software.tex in CH5.

Next sort out the conclusions to the bullet points at the start
of CH% and make a closed loop software and hardware example
for the new software.tex chapter....
2012-11-17 21:03:02 +00:00

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%%% 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\}$$
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