From bb2fce91a9a5e3d843cefff3d7a709d39670c96f Mon Sep 17 00:00:00 2001 From: Robin Clark Date: Sat, 2 Feb 2013 15:27:04 +0000 Subject: [PATCH] Comparison complexity results. Very good for Bubba Oscillator --- mybib.bib | 17 +++ related_papers_books/LM358_CD00000464.pdf | Bin 0 -> 780705 bytes submission_thesis/CH5_Examples/copy.tex | 43 ++++-- submission_thesis/CH6_Evaluation/copy.tex | 155 ++++++++++++++++++---- 4 files changed, 177 insertions(+), 38 deletions(-) create mode 100644 related_papers_books/LM358_CD00000464.pdf diff --git a/mybib.bib b/mybib.bib index babef95..29b5aa8 100644 --- a/mybib.bib +++ b/mybib.bib @@ -924,6 +924,23 @@ strength of materials, the causes of boiler explosions", year = "2000" } +@Manual{lm358, + title = {Datasheet: Low-Power dual operation amplifiers LM158,LM258,LM358: Doc ID 2163 Rev 10}, + key = {Doc ID 2163 Rev 10}, + author = {ST Microelecronics.}, + OPTorganization = {}, + address = {http://www.st.com/}, + OPTedition = {}, + OPTmonth = {}, + year = {2012}, +OPTnote = {}, + OPTannote = {}, + OPTurl = {}, + OPTdoi = {}, +OPTissn = {}, + OPTlocalfile = {}, + OPTabstract = {}, +} @Manual{tlp181, title = {TLP 181 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za$&v%bdjKa70?d@dovI|gLe+0^*-p*!1^1Yv`4|}0I)d)!wWn%w59_s065J!V1p1l z0tGfamq!8dLdT&%Z3UGZXof@kbs)hc!D1)~q0pKb?DwEyISn4vU{K!#QZtw@2J(gT zlthH~Pr>V=MA-8{UkVoUz~i93DqzqASWH2|dz%DM>Vo%ysA~Ub4~+n_c4)m%0BI-8 z@8ZE8BUCp)3jpTZsqH4H?t%su8sc++-V8KJg{#}S}Cb3ij5 zmJ@C;sD_iMhg%xOz%mc zXoAiK8%VIZB)ILUo}(^R&w?jJFq)oi$-B>u~?iv*$$1d1r0tNihxJk zlN@jgazrxLo64PNLrat@|Y mj~B>jfET&JUuaNptOFb__VJ^gJ^&knpcZ2l72T_+%KCpMPFVv0 literal 0 HcmV?d00001 diff --git a/submission_thesis/CH5_Examples/copy.tex b/submission_thesis/CH5_Examples/copy.tex index 7b4b553..841feec 100644 --- a/submission_thesis/CH5_Examples/copy.tex +++ b/submission_thesis/CH5_Examples/copy.tex @@ -901,10 +901,10 @@ when it becomes a V2 follower). The {\fm} $DiffAMPIncorrect$ may seem like a vague {\fm}---however, this {\fm} is impossible to detect in this circuit--- in fault finding terminology~\cite{garrett}~\cite{maikowski} this {\fm} is said to be unobservable, and in EN61508~\cite{en61508} -terminology is called an undetectable fault. +terminology is an `undetectable~fault'. % Were this failure to have safety implications, this FMMD analysis will have revealed -the un-observability and would likely prompt re-design of this +this un-observability condition; this would likely prompt re-design of this circuit. A typical way to solve an un-observability such as this is to periodically switch in test signals in place of the input signal. %\footnote{A typical way to solve an un-observability such as this is @@ -1211,9 +1211,19 @@ could be easily detected; the failure symptom $FilterIncorrect$ may be less obs This example shows the analysis of a linear signal path circuit with three easily identifiable {\fgs} and re-use of the Sallen-Key {\dc}. -\clearpage + + + + + + +\clearpage +% +% BUBBAOSC +% + \section{Quad Op-Amp Oscillator} \label{sec:bubba} @@ -1221,7 +1231,7 @@ This example shows the analysis of a linear signal path circuit with three easil \centering \includegraphics[width=200pt]{CH5_Examples/circuit3003.png} % circuit3003.png: 503x326 pixel, 72dpi, 17.74x11.50 cm, bb=0 0 503 326 -\caption{Circuit 3} +\caption{Circuit diagram for the Quad Op-Amp `Bubba' Oscillator} \label{fig:circuit3} \end{figure} @@ -1233,8 +1243,8 @@ The circuit implements an oscillator using four 45 degree phase shifts, and an i gain and the final 180 degrees of phase shift (making a total of 360). % degrees of phase shift). The circuit provides two outputs with a quadrature phase relationship. % -From a fault finding perspective this circuit cannot be decomposed -because the whole circuit is enclosed within a feedback loop, +From a fault finding perspective this circuit cannot be decomposed, +as the whole circuit is enclosed within a feedback loop, hence a fault anywhere in the loop is likely to affect all stages. % However, this is not a problem for FMMD, as {\fgs} are readily identifiable. @@ -1314,7 +1324,7 @@ Initially we use the first identified {\fgs} to create our model without further \subsection{FMMD Analysis using initially identified functional groups} - +\label{sec:bubba1} Our {\fg} for this analysis can be expressed thus: % %$$ 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 \} ,$$ @@ -1368,7 +1378,7 @@ we may also discover new derived components that may be of use for other analyse \clearpage \subsection{FMMD Analysis of Bubba Oscillator using a finer grained modular approach (i.e. more hierarchical stages)} - +\label{sec:bubba2} The example above---from the initial {\fgs}---used one very large functional group to model the circuit. %This mean a quite large comparison complexity for this final stage. We should be able to determine smaller {\fgs} and refine the model further. @@ -1415,6 +1425,10 @@ A PHS45 {\dc} and an inverting amplifier\footnote{Inverting amplifiers apply a form a {\fg} providing an amplified $225^{\circ}$ phase shift, analysed in table~\ref{tbl:phs225amp} resulting in the {\dc} $PHS225AMP$. +Applying FMMD we create a derived component $PHS225AMP$ which has the following failure modes: +$$ +fm (PHS225AMP) = \{ 180\_phaseshift, NO\_signal .\} % 270\_phaseshift, +$$ % %---with the remaining $PHS45$ and the $INVAMP$ (re-used from section~\ref{sec:invamp})in a second group $PHS225AMP$--- Finally we form a final {\fg} with $PHS135BUFFERED$ and $PHS225AMP$. @@ -1485,9 +1499,12 @@ $$ % 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. +%It has %also +This more de-composed approach has +given us five {\dcs}, building blocks, which could % +be re-used in other projects. +%potentially be re-used for similar circuitry +%to analyse in the future. % % \subsection{Comparing both approaches} @@ -1512,6 +1529,8 @@ However, it involves a large reasoning distance, the final stage having 24 failure modes to consider against each of the other seven {\dcs}. A finer grained approach produces more potentially re-usable {\dcs} and involves several stages with lower reasoning distances. +The lower reasoning distances, or complexity comparision figures are given in the metrics chapter~\ref{sec:chap7} +at section~\ref{sec:bubbaCC}. @@ -1552,7 +1571,7 @@ The following example is used to demonstrate FMMD analysis of a mixed analogue a \paragraph{How the circuit works.} -A detailed description of \sd may be found in~\cite{mixedsignaldsp}[pp.69-80]. +A detailed description of {\sd} may be found in~\cite{mixedsignaldsp}[pp.69-80]. The diagram in~\ref{fig:sigmadeltablock} shows the signal path used by this configuration for a \sd. % diff --git a/submission_thesis/CH6_Evaluation/copy.tex b/submission_thesis/CH6_Evaluation/copy.tex index 69d7354..4589f84 100644 --- a/submission_thesis/CH6_Evaluation/copy.tex +++ b/submission_thesis/CH6_Evaluation/copy.tex @@ -365,6 +365,8 @@ $$ \sum_{n=0}^{3} {3}^{n}.3.3.(2) = 720 %\end{equation} $$ + +%\clearpage \subsection{Complexity Comparison applied to previous FMMD Examples} All the FMMD examples in chapters \ref{sec:chap5} and \ref{sec:chap6} showed a marked reduction in comparison @@ -372,14 +374,18 @@ complexity compared to the RFMEA worst case figures. % % -A table of complexity comparison vs. RFMEA is presented below. +Complexity comparison vs. RFMEA for the first three examples +are presented in table~\ref{tbl:firstcc}. %\usepackage{multirow} +\begin{table} + \label{tbl:firstcc} -\begin{tabular}{ |l|l|l| } +\begin{tabular}{ |c|l|l|c| } \hline -\textbf{Hierarchy} & \textbf{Analysis object} & \textbf{Complexity} \\ -\textbf{Level} & \textbf{Description} & \textbf{Comparison} \\ +\textbf{Hierarchy} & \textbf{Derived} & \textbf{Complexity} & $|fm(c)|$: \textbf{number} \\ +\textbf{Level} & \textbf{Component} & \textbf{Comparison} & \textbf{of derived} \\ + & & & \textbf{failure modes} \\ %\hline \hline %\multicolumn{3}{ |c| }{Complexity Comparison against RFMEA for examples in Chapter~\ref{sec:chap5}} \\ %\hline \hline @@ -391,37 +397,134 @@ A table of complexity comparison vs. RFMEA is presented below. \multicolumn{3}{ |c| }{Inverting Amplifier Two stage FMMD Hierarchy: section~\ref{sec:invamp}} \\ \hline %\multirow{3}{*} {Inverting Amplifier Two stage FMMD Hierarchy: section~\ref{sec:invamp}} & & \\ -0 & Potential Divider & 4 \\ -1 & PD + Opamp & 8 \\ - & Inverting Amplifier: & FMMD 10 \\ - & Inverting Amplifier: & RFMEA 16 \\ - \hline +\hline +0 & PD & 4 & 2 \\ +1 & INVAMP & 8 & 3 \\ +2 & Total for INVAMP: & 10 (FMMD) & \\ +0 & Total for INVAMP: & 16 (RFMEA) & \\ +% & $(3-1) \times (4 + 2 +2)$ & & \\ + \hline \hline \multicolumn{3}{ |c| } {Inverting Amplifier One stage FMMD Hierarchy: section~\ref{sec:invamp}} \\ \hline -0 & Resistors + Opamp & 16 \\ - & Inverting Amplifier: & FMMD 16 \\ - & Inverting Amplifier: & RFMEA 16 \\ +0 & INVAMP & 16 & 3 \\ +1 & Total for INVAMP: & 16 (FMMD) & \\ +0 & Total for INVAMP: & 16 (RFMEA) & \\ \hline - -\multicolumn{3}{ |c| } {Differencing Amplifier One stage FMMD Hierarchy: section~\ref{sec:invamp}} \\ \hline + \hline +\multicolumn{3}{ |c| } {Differencing Amplifier Three stage FMMD Hierarchy: section~\ref{sec:diffamp}} \\ \hline %\multirow{4}{*} {Differencing Amplifier FMMD Hierarchy: section~\ref{sec:diffamp}} & & \\ -2 & Non inv Amp reused (see section~\ref{sec:noninvamp}) & 10 \\ -0 & Inverting amplifier & 16 \\ - & Differencing Amplifier: & FMMD 26 \\ - & Differencing Amplifier: & RFMEA 80 \\ \hline +2 & NonInvAMP reused~\footnote{Reused analysed of NonInvAMP: see section~\ref{sec:invamp}.} & 10 & 3 \\ +0 & SEC\_AMP & 16 & 4 \\ +3 & DiffAMP & 7 & 4 \\ +3 & Total for DiffAMP & 33 (FMMD)& \\ +0 & Total for DiffAMP: & 80 (RFMEA) & \\ +% & Differencing Amplifier: & RFMEA 80-16 = 74 & \\ +% & & & \\ \hline + \hline +% \footnote{if we discount the comparison complexity for the pre-analysed INVAMP.}\hline - - - - -\hline \hline +\multicolumn{3}{ |c| } {Five Pole Sallen Key Low Pass Filter: Three stage FMMD Hierarchy: section~\ref{sec:fivepolelp}} \\ \hline +%\multirow{4}{*} {Differencing Amplifier FMMD Hierarchy: section~\ref{sec:diffamp}} & & \\ +0 & FirstOrderLP & 4 & 2 \\ +1 & LP1 & 10 & 4 \\ +2 & SKLP & 48 & 4 \\ +3 & FivePoleLP & 20 & 4 \\ +3 & Total for FivePoleLP & 82 (FMMD)& \\ +% & 20+48+10+4 & & \\ +0 & Total for FivePoleLP & 384 (RFMEA) & \\ +% & $(13-1) \times (3 \times 4 + 10 \times 2)$ & & \\ \hline +\hline + \end{tabular} - +\caption{Comparison Complexity figures for the first three examples in Chapter~\ref{sec:chap5}.} +\end{table} + % end table The complexity comparison figures for the example circuits in chapter~\ref{sec:chap5} show -that for increasing complexity the performance benefits from FMMD become apparent. +that for increasing complexity the performance benefits from FMMD are apparent. + + + +\clearpage +\subsection{Comparison Complexity for the Bubba Oscillator Example.} +The Bubba oscillator example (see section~\ref{sec:bubba}) was chosen because it had a circular +signal path. It was also analysed twice, once by +{na\"{\i}vely} using the first {\fgs} identified, and secondly be de-composing +the circuit further. +We use these two analyses to compare the effect on comparison complexity (see table~\ref{tbl:bubbacc}) with that of RFMEA. +% +\begin{table} + \label{tbl:bubbacc} + + +\begin{tabular}{ |c|l|l|c| } +\hline +\textbf{Hierarchy} & \textbf{Derived} & \textbf{Complexity} & $|fm(c)|$: \textbf{number} \\ +\textbf{Level} & \textbf{Component} & \textbf{Comparison} & \textbf{of derived} \\ + & & & \textbf{failure modes} \\ +%\hline \hline +%\multicolumn{3}{ |c| }{Complexity Comparison against RFMEA for examples in Chapter~\ref{sec:chap5}} \\ +%\hline \hline + + +%Goalkeeper & GK & Paul Robinson \\ \hline + +\hline + +\multicolumn{3}{ |c| }{Bubba Oscillator one stage ({na\"{\i}ve}) FMMD Hierarchy: section~\ref{sec:bubba1}} \\ \hline +%\multirow{3}{*} {Inverting Amplifier Two stage FMMD Hierarchy: section~\ref{sec:invamp}} & & \\ +\hline +1 & PHS45 & 4 & 2 \\ +1 & INVAMP & 16 & 3 \\ +0 & NIBUFF & 0 & 4 \\ +% +% NIBUFF PHS45 +% 8 components so LEVEL 2 (8-1) \times ( (3*4) + (4*2) + 3 ) + LEVEL 0 16 for the INVAMP +2 & Total for BUBBA: & 177 (FMMD) & \\ +% R&C OPAMPS +% 14 components so 13 \times ( (10*2) (4*4) ) +0 & Total for BUBBA: & 468 (RFMEA) & \\ +% & $(3-1) \times (4 + 2 +2)$ & & \\ + \hline \hline + +\multicolumn{3}{ |c| } {Inverting Amplifier Multiple stage FMMD Hierarchy: section~\ref{sec:bubba2}} \\ \hline +1 & PHS45 & 4 & 2 \\ +1 & INVAMP & 16 & 3 \\ +0 & NIBUFF & 0 & 4 \\ +2 & BUFF45 & 6 & 2 \\ +3 & PHS135BUFFERED & 4 & 2 \\ + + +2 & PHS225AMP & 5 & 2 \\ + +4 & BUBBA & 2 & 2 \\ +% +%Level 1: 16 + 4 == 20 +%Level 2: 6 + 5 == 11 +%Level 3: 4 == 4 +%Level 4: 2 == 2 +% +1 & Total for BUBBA: & 37 (FMMD) & \\ +0 & Total for BUBBA: & 468 (RFMEA) & \\ + \hline + + \hline + +\end{tabular} +\caption{Complexity Comparison figures for the Bubba Oscillator FMMD example (see section~\ref{sec:bubba}).} +\end{table} +% +The initial {na\"{\i}ve} FMMD analysis reduces the number of checks by over half, the more de-composed analysis +by more than a factor of ten. + + + +\subsection{Sigma delta Example: Comparison Complexity Results} + + +\label{sec:bubbaCC} % \subsection{Exponential squared to Exponential} % % can I say that ? @@ -430,7 +533,7 @@ that for increasing complexity the performance benefits from FMMD become apparen \section{Unitary State Component Failure Mode sets} \label{sec:unitarystate} -\paragraph{Design Descision/Constraint} +\paragraph{Design Decision/Constraint} An important factor in defining a set of failure modes is that they should represent the failure modes as simply and minimally as possible. It should not be possible, for instance, for