Need to check the Bubba OSC. Chris said the 90_degree
symptom of the PHS45 was actually 0_degrees. So that ripples through. And then do the SUMJ, mix it with the opamp
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Robin Clark
parent
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commit
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@ -1,6 +1,6 @@
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PNG_DIA = cfg2.png cfg.png compco2.png compco3.png compco.png component.png componentpl.png fmmd_uml2.png fmmd_uml.png partitioncfm.png master_uml.png top_down_de_comp.png dc1.png dc2.png eulerfmmd.png
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PNG_DIA = cfg2.png cfg.png compco2.png compco3.png compco.png component.png componentpl.png fmmd_uml2.png fmmd_uml.png partitioncfm.png master_uml.png top_down_de_comp.png dc1.png dc2.png eulerfmmd.png
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%.png:%.dia
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@ -830,6 +830,7 @@ as {\fcs} in table~\ref{tbl:ampfmea1}.
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%
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%
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%
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\label{sec:invamp}
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%
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\begin{figure}[h+]
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\centering
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@ -1476,11 +1477,11 @@ that it inherits a set of failure modes.
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%We thus have a `new' component, %or system building block, but
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%with a known and traceable
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%fault behaviour.
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A {\fg} must comprise of two or more components, and the UML diagram shows this
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with the two to many relationship.
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A {\fg} must comprise of at least one component, and the UML diagram shows this
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with the one to many relationship.
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Under exceptional circumstances a component may need to be a member of more than
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one {\fg} (this is looked at in section~\ref{sec:sideeffects}). The relationship between
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the {\fg} and component is therefore $ \star \leftrightarrow 2..\star$.
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the {\fg} and component is therefore $ \star \leftrightarrow 1..\star$.
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%
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A {\fg} will only be associated with one {\dc} and is given a one to one relationship in the UML diagram.
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%
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@ -5,7 +5,7 @@ PNG_DIA = blockdiagramcircuit2.png bubba_oscillator_block_diagram.png circuit1
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poss1finalbubba.png poss2finalbubba.png pt100.png pt100_doublef.png pt100_singlef.png \
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pt100_tc.png pt100_tc_sp.png shared_component.png stat_single.png three_tree.png \
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tree_abstraction_levels.png vrange.png sigma_delta_block.png ftcontext.png ct1.png hd.png \
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sigdel1.png sdadc.png
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sigdel1.png sdadc.png bubba_euler_1.png bubba_euler_2.png
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BIN
submission_thesis/CH5_Examples/bubba_euler_1.dia
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BIN
submission_thesis/CH5_Examples/bubba_euler_1.dia
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BIN
submission_thesis/CH5_Examples/bubba_euler_2.dia
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BIN
submission_thesis/CH5_Examples/bubba_euler_2.dia
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Binary file not shown.
@ -7,7 +7,16 @@
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%
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% * OPERATIONAL STATE (perhaps a self test on an ADC where it is set to output and driven high and low and read)
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% to do: 23SEP2012
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%
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% 90_degrees is an incorrect failure mode in bubba and must be purged
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%
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% summing junction in sigma delta is not a valid fg, prob have to include
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% the op-amp....
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%
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% very annoying to have to pull out the comparison complexity.
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% makes the comparisons between approaches have less meaning.
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% have to discuss this.
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\label{sec:chap5}
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@ -25,15 +34,18 @@ we are conforming to for our particular project).
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This is followed by several example FMMD analyses,
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the first analysing a common configuration of
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the inverting amplifier (see section~\ref{sec:invamp}) using
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an op-amp and two resistors, which demonstrates how the potential divider from section~\ref{subsec:potdiv}
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~\ref{sec:chap4}
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can be re-used. %, but with provisos.
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an op-amp and two resistors, which demonstrates how the re-use of the potential divider from section~\ref{subsec:potdiv}.
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The inverting amplifier is analysed again, but this time with different
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{\fgs}. The two approaches, i.e. choice of membership for {\fgs}, are then discussed.
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%~\ref{sec:chap4}
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%can be re-used. %, but with provisos.
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%
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%The first
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%(see section~\ref{sec:diffamp})
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Section~\ref{sec:diffamp} analyses a circuit where two op-amps are used
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to create a differencing amplifier.
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Re-use of the potential divider model is discussed in the context of this circuit,
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Building on the two approaches section~\ref{sec:invamp}, re-use of the potential divider {\dc}
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is discussed in the context of this circuit,
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where its re-use is appropriate in the first stage and
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not in the second.
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%
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@ -48,6 +60,7 @@ Section~\ref{sec:sigmadelta} shows FMMD analysing the sigma delta analogue to di
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analogue and digital signals.
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%
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% Moving Pt100 to metrics
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%
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%Sections~\ref{sec:Pt100}~and~\ref{sec:Pt100d} demonstrate both statistical
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%failure mode classification % analysis for top level events traced back to {\bc} failure modes
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%and the analysis of double simultaneous failure modes.
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@ -222,13 +235,14 @@ as shown below.
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\item Shorted 3.9\% $\mapsto$ SHORT
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\item Lead damage 1.9\% $\mapsto$ OPEN.
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\end{itemize}
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%
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The main causes of drift are overloading of components.
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This is borne out in in the FMD-91~\cite{fmd91}[232] entry for a resistor network where the failure
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modes do not include drift.
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%
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If we can ensure that our resistors will not be exposed to overload conditions, the
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probability of drift (sometimes called parameter change) occurring
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is significantly reduced, enough for some standards to exclude it~\cite{en298}.
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is significantly reduced, enough for some standards to exclude it~\cite{en298}~\cite{en230}.
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\paragraph{Resistor failure modes according to EN298.}
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@ -554,121 +568,7 @@ component {\fms} in FMEA or FMMD and require interpretation.
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% is shown as a `$\derivec$' symbol.
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%
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%
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%
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% \section{Example Analysis: Non-Inverting OPAMP}
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% \label{sec:noninvamp}
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% Consider a non inverting op-amp designed to amplify
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% a small positive voltage (typical use would be a thermocouple amplifier
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% taking a range from 0 to 25mV and amplifying it to the useful range of an ADC, approx 0 to 4 volts).
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%
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%
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% \begin{figure}[h+]
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% \centering
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% \includegraphics[width=100pt]{CH5_Examples/mvampcircuit.png}
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% % mvampcircuit.png: 243x143 pixel, 72dpi, 8.57x5.04 cm, bb=0 0 243 143
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% \label{fig:mvampcircuit}
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% \caption{positive mV amplifier circuit}
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% \end{figure}
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%
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% We can begin by looking for functional groups.
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% The resistors $ R1, R2 $ perform a fairly common function in electronics, that of the potential divider.
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% So we can examine $\{ R1, R2 \}$ as a {\fg}.
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%
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%
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% \subsection{The Resistor in terms of failure modes}
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%
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% We can now determine how the resistors can fail.
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% We consider the {\fms} for resistors to be OPEN and SHORT (see section~\ref{ros}).
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% %, i.e.
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% %$ fm(R) = \{ OPEN, SHORT \} . $
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%
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% We can express the failure modes of a component using the function $fm$, thus for the resistor, $ fm(R) = \{ OPEN, SHORT \}$.
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%
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%
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% We have two resistors in this circuit and therefore four component failure modes to consider for the potential divider.
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% We can now examine what effect each of these failures will have on the {\fg} (see table~\ref{tbl:pd}).
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%
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%
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% \subsection{Analysing a potential divider in terms of failure modes}
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%
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%
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% \label{potdivfmmd}
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%
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%
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%
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% \begin{figure}[h+]
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% \centering
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% \includegraphics[width=100pt,keepaspectratio=true]{CH5_Examples/pd.png}
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% % pd.png: 361x241 pixel, 72dpi, 12.74x8.50 cm, bb=0 0 361 241
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% \label{fig:pdcircuit}
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% \caption{Potential Divider Circuit}
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% \end{figure}
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%
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%
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% \begin{table}[h+]
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% \caption{Potential Divider: Single failure analysis}
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% \begin{tabular}{|| l | l | c | c | l ||} \hline
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% \textbf{Failure Scenario} & & \textbf{Pot Div Effect} & & \textbf{Symptom} \\
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% \hline
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% FS1: R1 SHORT & & $LOW$ & & $PDLow$ \\
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% FS2: R1 OPEN & & $HIGH$ & & $PDHigh$ \\ \hline
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% FS3: R2 SHORT & & $HIGH$ & & $PDHigh$ \\
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% FS4: R2 OPEN & & $LOW$ & & $PDLow$ \\ \hline
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% \hline
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% \end{tabular}
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% \label{tbl:pd}
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% \end{table}
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%
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% We can now create a {\dc} for the potential divider, $PD$.
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%
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% $$ fm(PD) = \{ PDLow, PDHigh \}$$
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%
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% %Let us now consider the op-amp. According to
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% %FMD-91~\cite{fmd91}[3-116] an op-amp may have the following failure modes:
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% %latchup(12.5\%), latchdown(6\%), nooperation(31.3\%), lowslewrate(50\%).
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%
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%
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% \subsection{Analysing the non-inverting amplifier in terms of failure modes}
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%
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% From section~\ref{sec:opamp_fms}
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% $$ fm(OPAMP) = \{L\_{up}, L\_{dn}, Noop, L\_slew \} $$
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%
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%
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% We can now form a {\fg} with $PD$ and $OPAMP$.
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%
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% \begin{figure}
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% \centering
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% \includegraphics[width=300pt]{CH5_Examples/non_inv_amp_fmea.png}
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% % non_inv_amp_fmea.png: 964x492 pixel, 96dpi, 25.50x13.02 cm, bb=0 0 723 369
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% \label{fig:invampanalysis}
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% \end{figure}
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%
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%
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%
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%
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% \begin{table}[h+]
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% \caption{NIAMP: Single failure analysis}
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% \begin{tabular}{|| l | l | c | c | l ||} \hline
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% \textbf{Failure Scenario} & & \textbf{Non In Amp Effect} & & \textbf{Symptom} \\
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% \hline
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% FS1: PD HIGH & & $LOW$ & & $Low$ \\
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% FS2: PD LOW & & $HIGH$ & & $High$ \\ \hline
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% FS3: OPAMP $L_{UP}$ & & $HIGH$ & & $High$ \\
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% FS4: OPAMP $L_{DOWN}$ & & $LOW$ & & $Low$ \\
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% FS5: OPAMP $Noop$ & & $LOW$ & & $Low$ \\
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% FS5: OPAMP $Low slew$ & & $LOW$ & & $Lowpass$ \\ \hline
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%
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% \hline
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% \end{tabular}
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% \label{tbl:pd}
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% \end{table}
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%
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% We can collect symptoms from the analysis and create a derived component
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% to represent the non-inverting amplifier $NI\_AMP$.
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% We can now express the failure mode behaviour of this type of amplifier thus:
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%
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% $$ fm(NIAMP) = \{ {lowpass}, {high}, {low} \}.$$
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%
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%
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%
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\clearpage
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@ -1591,7 +1491,7 @@ determine {\dcs}.
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This has been analysed in section~\ref{sec:invamp}.
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The inverting amplifier, as a {\dc}, has the following failure modes:
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$$ fm(INVAMP) = \{ HIGH, LOW, LOW PASS \}. $$
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$$ fm(INVAMP) = \{ AMP\_High, AMP\_Low, LowPass \}. $$ % \{ HIGH, LOW, LOW PASS \}. $$
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% METRICS and has a CC of 10.
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@ -1612,7 +1512,8 @@ Our functional group for the phase shifter consists of a resistor and a capacito
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\textbf{Failure Scenario} & & \textbf{First Order} & & \textbf{Symptom} \\
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& & \textbf{Low Pass Filter} & & \\
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\hline
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FS1: R SHORT & & 90 degree's of phase shift & & $90\_phaseshift$ \\ \hline
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FS1: R SHORT & & 0 degree's of phase shift & & $0\_phaseshift$ \\ \hline
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% 90 degree's of phase shift & & $90\_phaseshift$ \\ \hline
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FS2: R OPEN & & No Signal & & $nosignal$ \\ \hline
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FS3: C SHORT & & Grounded,No Signal & & $nosignal$ \\ \hline
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FS4: C OPEN & & 0 degree's of phase shift & & $0\_phaseshift$ \\ \hline
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@ -1624,10 +1525,10 @@ Our functional group for the phase shifter consists of a resistor and a capacito
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% PHS45
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$$ fm (G_0) = \{ 90\_phaseshift, nosignal, 0\_phaseshift \} $$
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$$ CC(G_0) = 4.1 = 4 $$
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$$ fm (G_0) = \{ nosignal, 0\_phaseshift \} $$
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%$$ CC(G_0) = 4 \times 1 = 4 $$
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%23SEP2012
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\subsection{Non Inverting Buffer: NIBUFF.}
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The non-inverting buffer functional group, is comprised of one component, an op-amp.
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@ -1654,17 +1555,25 @@ Initially we use the first identified {\fgs} to create our model without further
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\subsection{FMMD Analysis using initially identified functional groups}
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Our functional group for this analysis can be expressed thus:
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$$ G^1_0 = PHS45^1_1, NIBUFF^0_1, PHS45^1_2, NIBUFF^0_2, PHS45^1_3, NIBUFF^0_3 PHS45^1_4, INVAMP^1_0 \} .$$
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or in Euler diagram format as in figure~\ref{fig:bubbaeuler1}.
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$$ G^1_0 = \{ PHS45^1_1, NIBUFF^0_1, PHS45^1_2, NIBUFF^0_2, PHS45^1_3, NIBUFF^0_3 PHS45^1_4, INVAMP^1_0 \} ,$$
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\begin{figure}[h+]
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% HTR 23SEP2012 \begin{figure}[h+]
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% HTR 23SEP2012 \centering
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% HTR 23SEP2012 \includegraphics[width=300pt,keepaspectratio=true]{CH5_Examples/poss1finalbubba.png}
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% HTR 23SEP2012 % largeosc.png: 916x390 pixel, 72dpi, 32.31x13.76 cm, bb=0 0 916 390
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% HTR 23SEP2012 \caption{Bubba Oscillator: One large functional group using the initial functional groups to model oscillator.}
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% HTR 23SEP2012 \label{fig:poss1finalbubba}
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% HTR 23SEP2012 \end{figure}
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\begin{figure}[h]
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\centering
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\includegraphics[width=300pt,keepaspectratio=true]{CH5_Examples/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 large functional group using the initial functional groups to model oscillator.}
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\label{fig:poss1finalbubba}
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\includegraphics[width=400pt]{./CH5_Examples/bubba_euler_1.png}
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% bubba_euler_1.png: 946x404 pixel, 72dpi, 33.37x14.25 cm, bb=0 0 946 404
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\caption{Euler diagram showing the hierarchy of the initial FMMD analysis performed on the Bubba Oscillator circuit.}
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\label{fig:bubbaeuler1}
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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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@ -1677,40 +1586,40 @@ $$ G^1_0 = PHS45^1_1, NIBUFF^0_1, PHS45^1_2, NIBUFF^0_2, PHS45^1_3, NIBUFF^0_3 P
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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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% FS3: $PHS45_1$ $90\_phaseshift$ & & osc frequency low & & $LO_{fosc}$ \\ \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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FS3: $NIBUFF_1$ $L_{up}$ & & output high No Oscillation & & $NO_{osc}$ \\
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FS4: $NIBUFF_1$ $L_{dn}$ & & output low No Oscillation & & $NO_{osc}$ \\
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FS5: $NIBUFF_1$ $N_{oop}$ & & output low No Oscillation & & $NO_{osc}$ \\
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FS6: $NIBUFF_1$ $L_{slew}$ & & signal lost & & $NO_{osc}$ \\ \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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FS7: $PHS45_2$ $0\_phaseshift$ & & osc frequency high & & $HI_{fosc}$ \\
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FS8: $PHS45_2$ $no\_signal$ & & signal lost & & $NO_{osc}$ \\
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%FS10: $PHS45_2$ $90\_phaseshift$ & & osc frequency low & & $LO_{fosc}$ \\ \hline
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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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FS9: $NIBUFF_2$ $L_{up}$ & & output high No Oscillation & & $NO_{osc}$ \\
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FS10: $NIBUFF_2$ $L_{dn}$ & & output low No Oscillation & & $NO_{osc}$ \\
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FS11: $NIBUFF_2$ $N_{oop}$ & & output low No Oscillation & & $NO_{osc}$ \\
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FS12: $NIBUFF_2$ $L_{slew}$ & & signal lost & & $NO_{osc}$ \\ \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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FS13: $PHS45_3$ $0\_phaseshift$ & & osc frequency high & & $HI_{fosc}$ \\
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FS14: $PHS45_3$ $no\_signal$ & & signal lost & & $NO_{osc}$ \\
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% FS17: $PHS45_3$ $90\_phaseshift$ & & osc frequency low & & $LO_{fosc}$ \\ \hline
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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 & & $NO_{osc}$ \\
|
||||
FS21: $NIBUFF_3$ $L_{slew}$ & & signal lost & & $NO_{osc}$ \\ \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
|
||||
|
||||
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
|
||||
FS19: $PHS45_4$ $0\_phaseshift$ & & osc frequency high & & $HI_{fosc}$ \\
|
||||
FS20: $PHS45_4$ $no\_signal$ & & signal lost & & $NO_{osc}$ \\
|
||||
% FS24: $PHS45_4$ $90\_phaseshift$ & & osc frequency low & & $LO_{fosc}$ \\ \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
|
||||
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
|
||||
@ -1724,23 +1633,25 @@ $$ G^1_0 = PHS45^1_1, NIBUFF^0_1, PHS45^1_2, NIBUFF^0_2, PHS45^1_3, NIBUFF^0_3 P
|
||||
Collecting symptoms from table~\ref{tbl:bubbalargefg} we can show that for single failure modes, applying $fm$ to the bubba oscillator
|
||||
returns three failure modes,
|
||||
|
||||
$$ fm(BubbaOscillator) = \{ NO_{osc}, HI_{fosc}, LO_{fosc} \} . $$
|
||||
$$ fm(BubbaOscillator) = \{ NO_{osc}, HI_{fosc}\} . $$ %, LO_{fosc} \} . $$
|
||||
|
||||
For the final stage of this FMMD model, we can calculate the complexity using equation~\ref{eqn:rd2}.
|
||||
$$ CC = 28.8 = 224$$
|
||||
%For the final stage of this FMMD model, we can calculate the complexity using equation~\ref{eqn:rd2}.
|
||||
%$$ CC = 28 \times 8 = 224$$
|
||||
|
||||
To obtain the total comparison complexity ($TCC$), we need to add the complexity from the
|
||||
{\dcs} that $BubbaOscillator$ was built from.
|
||||
%To obtain the total comparison complexity ($TCC$), we need to add the complexity from the
|
||||
%{\dcs} that $BubbaOscillator$ was built from.
|
||||
|
||||
$$ TCC = 28.8 + 4.4 + 4.0 + 10 = 250$$
|
||||
%$$ TCC = 28 \times 8 + 4 \times 4 + 4 \times 0 + 10 = 250$$
|
||||
|
||||
%As we have re-used the analysis for BUFF45 we could even reasonably remove
|
||||
%$3.4=12$ from this result, because the results from $BUFF45$ have been used four times.
|
||||
Traditional FMEA would have lead us to a much higher comparison complexity
|
||||
of $468$ failure modes to check against components.
|
||||
However, the analysis here appears top-heavy; we should be able to refine the model more
|
||||
and break this down into smaller functional groups, by allowing more stages of hierarchy and hopefully
|
||||
this should lead a further reduction in the complexity comparison figure.
|
||||
%$3 \times 4=12$ from this result, because the results from $BUFF45$ have been used four times.
|
||||
%Traditional FMEA would have lead us to a much higher comparison complexity
|
||||
%of $468$ failure modes to check against components.
|
||||
%However,
|
||||
The analysis here appears top-heavy; we should be able to refine the model more
|
||||
and break this down into smaller functional groups, by allowing more stages of hierarchy.
|
||||
%and hopefully
|
||||
%this should lead a further reduction in the complexity comparison figure.
|
||||
By decreasing the size of the modules with further refinement,
|
||||
we may also discover new derived components that may be of use for other analyses in the future.
|
||||
|
||||
@ -1748,20 +1659,27 @@ we may also discover new derived components that may be of use for other analyse
|
||||
|
||||
\clearpage
|
||||
|
||||
\subsection{FMMD Analysis using more hierarchical stages}
|
||||
\subsection{FMMD Analysis of Bubba Oscillator using more hierarchical stages}
|
||||
|
||||
The example above---from the initial {\fgs}---used one very large functional group to model the circuit.
|
||||
This mean a quite large comparison complexity for this final stage.
|
||||
%This mean a quite large comparison complexity for this final stage.
|
||||
We should be able to determine smaller {\fgs} and refine the model further.
|
||||
|
||||
\begin{figure}[h+]
|
||||
\centering
|
||||
\includegraphics[width=300pt,keepaspectratio=true]{CH5_Examples/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:poss2finalbubba}
|
||||
\end{figure}
|
||||
% HTR 23SEP2012 \begin{figure}[h+]
|
||||
% HTR 23SEP2012 \centering
|
||||
% HTR 23SEP2012 \includegraphics[width=300pt,keepaspectratio=true]{CH5_Examples/poss2finalbubba.png}
|
||||
% HTR 23SEP2012 % largeosc.png: 916x390 pixel, 72dpi, 32.31x13.76 cm, bb=0 0 916 390
|
||||
% HTR 23SEP2012 \caption{Bubba Oscillator: Smaller Functional Groups, One more FMMD hierarchy stage.}
|
||||
% HTR 23SEP2012 \label{fig:poss2finalbubba}
|
||||
% HTR 23SEP2012 \end{figure}
|
||||
|
||||
\begin{figure}[h]
|
||||
\centering
|
||||
\includegraphics[width=400pt]{./CH5_Examples/bubba_euler_2.png}
|
||||
% bubba_euler_2.png: 1241x617 pixel, 72dpi, 43.78x21.77 cm, bb=0 0 1241 617
|
||||
\caption{Euler diagram showing functional groupings for the Bubba oscillator using a more de-composed approach.}
|
||||
\label{fig:bubbaeuler2}
|
||||
\end{figure}
|
||||
|
||||
%
|
||||
We take the $NIBUFF$ and $PHS45$
|
||||
@ -1771,7 +1689,8 @@ and with those three, form a $PHS135BUFFERED$
|
||||
functional group.
|
||||
$PHS135BUFFERED$ is a {\dc} representing an actively buffered $135^{\circ}$ phase shifter.
|
||||
|
||||
A PHS45 {\dc} and an inverting amplifier\footnote{Inverting amplifiers always apply a $180^{\circ}$ phase shift.}, form a {\fg}
|
||||
A PHS45 {\dc} and an inverting amplifier\footnote{Inverting amplifiers always apply a $180^{\circ}$ phase shift.},
|
||||
form a {\fg}
|
||||
providing an amplified $225^{\circ}$ phase shift, which we can call $PHS225AMP$.
|
||||
|
||||
%---with the remaining $PHS45$ and the $INVAMP$ (re-used from section~\ref{sec:invamp})in a second group $PHS225AMP$---
|
||||
@ -1801,12 +1720,12 @@ Finally we can merge $PHS135BUFFERED$ and $PHS225AMP$ in a final stage (see fig
|
||||
\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
|
||||
%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
|
||||
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
|
||||
@ -1817,10 +1736,10 @@ Finally we can merge $PHS135BUFFERED$ and $PHS225AMP$ in a final stage (see fig
|
||||
|
||||
Collecting symptoms from table~\ref{tbl:buff45}, we can create a derived component $BUFF45$ which has the following failure modes:
|
||||
$$
|
||||
fm (BUFF45) = \{ 90\_phaseshift, 0\_phaseshift, NO\_signal .\}
|
||||
fm (BUFF45) = \{ 0\_phaseshift, NO\_signal .\} % 90\_phaseshift,
|
||||
$$
|
||||
|
||||
$$ CC(BUFF45) = 7.1 = 7 $$
|
||||
%$$ CC(BUFF45) = 7 \times 1 = 7 $$
|
||||
|
||||
We can now combine three $BUFF45$ {\dcs} and create a $PHS135BUFFERED$ {\dc}.
|
||||
|
||||
@ -1835,15 +1754,15 @@ We can now combine three $BUFF45$ {\dcs} and create a $PHS135BUFFERED$ {\dc}.
|
||||
\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
|
||||
%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
|
||||
FS3: $PHS45_2$ $0\_phaseshift$ & & phase shift low & & $90\_phaseshift$ \\
|
||||
FS4: $PHS45_2$ $no\_signal$ & & 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
|
||||
FS5: $PHS45_3$ $0\_phaseshift$ & & phase shift low & & $90\_phaseshift$ \\
|
||||
FS6: $PHS45_3$ $no\_signal$ & & signal lost & & $NO_{signal}$ \\
|
||||
% FS9: $PHS45_3$ $90\_phaseshift$ & & phase shift high & & $180\_phaseshift$ \\ \hline
|
||||
|
||||
|
||||
|
||||
@ -1855,11 +1774,11 @@ We can now combine three $BUFF45$ {\dcs} and create a $PHS135BUFFERED$ {\dc}.
|
||||
|
||||
Collecting symptoms from table~\ref{tbl:phs135buffered}, we can create a derived component $PHS135BUFFERED$ which has the following failure modes:
|
||||
$$
|
||||
fm (PHS135BUFFERED) = \{ 90\_phaseshift, 180\_phaseshift, NO\_signal .\}
|
||||
fm (PHS135BUFFERED) = \{ 90\_phaseshift, NO\_signal .\} % 180\_phaseshift,
|
||||
$$
|
||||
|
||||
|
||||
$$ CC (PHS135BUFFERED) = 3.2 = 6 $$
|
||||
%$$ CC (PHS135BUFFERED) = 3 \times 2 = 6 $$
|
||||
|
||||
|
||||
|
||||
@ -1873,14 +1792,14 @@ The $PHS225AMP$ consists of a $PHS45$ and an $INVAMP$ (which provides $180^{\cir
|
||||
\textbf{Failure Scenario} & & \textbf{PHS225AMP} & & \textbf{Symptom} \\
|
||||
& & \textbf{Oscillator} & & \\
|
||||
\hline
|
||||
FS1: $PHS45_1$ $0\_phaseshift$ & & phase shift low & & $270\_phaseshift$ \\
|
||||
FS1: $PHS45_1$ $0\_phaseshift$ & & phase shift low & & $180\_phaseshift$ \\
|
||||
FS2: $PHS45_1$ $no\_signal$ & & signal lost & & $NO_{signal}$ \\
|
||||
FS3: $PHS45_1$ $90\_phaseshift$ & & phase shift high & & $180\_phaseshift$ \\ \hline
|
||||
% FS3: $PHS45_1$ $90\_phaseshift$ & & phase shift high & & $270\_phaseshift$ \\ \hline
|
||||
|
||||
FS4: $INVAMP$ $L_{up}$ & & output high & & $NO_{signal}$ \\
|
||||
FS5: $INVAMP$ $L_{dn}$ & & output low & & $NO_{signal}$ \\
|
||||
FS6: $INVAMP$ $N_{oop}$ & & output low & & $NO_{signal}$ \\
|
||||
FS7: $INVAMP$ $L_{slew}$ & & signal lost & & $NO_{signal}$ \\ \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
|
||||
|
||||
@ -1889,10 +1808,10 @@ The $PHS225AMP$ consists of a $PHS45$ and an $INVAMP$ (which provides $180^{\cir
|
||||
|
||||
Collecting symptoms from table~\ref{tbl:phs225amp}, we can create a derived component $PHS225AMP$ which has the following failure modes:
|
||||
$$
|
||||
fm (PHS225AMP) = \{ 270\_phaseshift, 180\_phaseshift, NO\_signal .\}
|
||||
fm (PHS225AMP) = \{ 180\_phaseshift, NO\_signal .\} % 270\_phaseshift,
|
||||
$$
|
||||
|
||||
$$ CC(PHS225AMP) = 7.1 $$
|
||||
%$$ CC(PHS225AMP) = 7 \times 1 $$
|
||||
|
||||
The $PHS225AMP$ consists of a $PHS45$ and an $INVAMP$ (which provides $180^{\circ}$ of phase shift).
|
||||
|
||||
@ -1909,13 +1828,13 @@ and perform FMEA with these.
|
||||
\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
|
||||
%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 & & $LO_{fosc}$ \\
|
||||
FS5: $PHS225AMP$ $180\_phaseshift$ & & phase shift low & & $HI_{osc}$ \\
|
||||
FS6: $PHS225AMP$ $NO\_signal$ & & lost signal & & $NO_{signal}$ \\ \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
|
||||
@ -1926,33 +1845,36 @@ and perform FMEA with these.
|
||||
|
||||
Collecting symptoms from table~\ref{tbl:bubba2}, we can create a derived component $BUBBAOSC$ which has the following failure modes:
|
||||
$$
|
||||
fm (BUBBAOSC) = \{ LO_{fosc}, HI_{osc}, NO\_signal .\}
|
||||
fm (BUBBAOSC) = \{ HI_{osc}, NO\_signal .\} % LO_{fosc},
|
||||
$$
|
||||
|
||||
%We could trace the DAGs here and ensure that both analysis strategies worked ok.....
|
||||
|
||||
$$ CC(BUBBAOSC) = 6.(2-1) = 6 $$
|
||||
%$$ CC(BUBBAOSC) = 6 \times (2-1) = 6 $$
|
||||
|
||||
|
||||
We can now add the comparison complexities for all levels of the analysis represented in figure~\ref{fig:poss2finalbubba}.
|
||||
We have at the lowest level two $PHS45$ {\dcs} giving a CC of 8 and $INVAMP$ with a CC of 10, at the next level four $BUFF45$ {\dcs} giving $(4-1).7=21$,
|
||||
and penultimately $PHS135BUFFERED$ with 6 and $PHS225AMP$ with 7. The final top stage of the hierarchy, $BUBBAOSC$ has a CC of 6.
|
||||
Our total comparison complexity is $58$, this contrasts with $468$ for traditional `flat' FMEA,
|
||||
and $250$ for our first stage functional groups analysis.
|
||||
This has meant a drastic reduction in the number of failure-modes to check against components.
|
||||
It has also given us five {\dcs}, building blocks, which may be re-used for similar circuitry
|
||||
% We can now add the comparison complexities for all levels of the analysis represented in figure~\ref{fig:poss2finalbubba}.
|
||||
% We have at the lowest level two $PHS45$ {\dcs} giving a CC of 8 and $INVAMP$ with a CC of 10,
|
||||
% at the next level four $BUFF45$ {\dcs} giving $(4-1).7=21$,
|
||||
% and penultimately $PHS135BUFFERED$ with 6 and $PHS225AMP$ with 7.
|
||||
% The final top stage of the hierarchy, $BUBBAOSC$ has a CC of 6.
|
||||
% Our total comparison complexity is $58$, this contrasts with $468$ for traditional `flat' FMEA,
|
||||
% and $250$ for our first stage functional groups analysis.
|
||||
% This has meant a drastic reduction in the number of failure-modes to check against components.
|
||||
It has %also
|
||||
given us five {\dcs}, building blocks, which could potentially be re-used for similar circuitry
|
||||
to analyse in the future.
|
||||
|
||||
|
||||
\subsection{Comparing both approaches}
|
||||
|
||||
In general with large functional groups the comparison complexity
|
||||
is higher, by an order of $O(N^2)$.
|
||||
%In general with large functional groups the comparison complexity
|
||||
%is higher, by an order of $O(N^2)$.
|
||||
Smaller functional groups mean less by-hand checks are required.
|
||||
It also means a more finely grained model. This means that
|
||||
there are more {\dcs} and this increases the possibility of re-use.
|
||||
The more we can modularise, the more we decimate the $O(N^2)$ effect
|
||||
of complexity comparison.
|
||||
% HTR The more we can modularise, the more we decimate the $O(N^2)$ effect
|
||||
% HTR of complexity comparison.
|
||||
|
||||
|
||||
\section{Sigma Delta Analogue to Digital Converter.} %($\Sigma \Delta ADC$)}
|
||||
|
||||
Loading…
Reference in New Issue
Block a user