Sigma delta CC figures written into table

submission_thesis/CH5_Examples/copy.tex

@@ -1709,7 +1709,7 @@ $$ fm (DL2AL) = \{ LOW, HIGH,  LOW\_{SLEW}  \} $$
 % This is a single component as a {\fg}, and we can state
 % $$ fm (DCM) = \{ HIGH, LOW, NOOP \} $$
 
-The digital element of the {\sd}, is the one bit memory, or D type flip flop. This
+The digital element of the {\sd}, is a `one~bit~memory', or D type flip flop. This
 buffers the feedback result and provides the output bit stream.
 We create a {\fg} from the CLOCK and IC4 to model this digital buffer.
 
@@ -1866,7 +1866,7 @@ We now show the   final {\dc} hierarchy in figure~\ref{fig:eulersdfinal}.
 The \sd example, shows that FMMD can be applied to mixed digital and analogue circuitry.
 
 
-\clearpage
+%\clearpage
 \section{Pt100 Analysis: FMMD and Double Failure Mode Analysis}
 \label{sec:Pt100}
 {

submission_thesis/CH6_Evaluation/copy.tex

@@ -126,7 +126,7 @@ with additional indexing when appropriate.
 \paragraph{Defining a function that returns failure modes given a component.}
 The function $fm$ has a component as its domain and the components failure modes, $fms$, as its range. % (see equation~\ref{eqn:fm}).
 Where $\mathcal{F}$ is the set of all failures, 
-$$ fm: \mathcal{C} \rightarrow \mathcal{F}$$.
+$$ fm: \mathcal{C} \rightarrow \mathcal{F}.$$
 We can represent the number of potential failure modes of a component $c$, to be  $ | fm(c) | .$
 
 \paragraph{Indexing components with the group $G$.}
@@ -146,7 +146,7 @@ Where $\mathcal{G}$ represents the set of all {\fgs}, and $ \mathbb{Z}^{+} $, $C
 %
 %and, where n is the number of components in the system/{\fg},   
 and $|fm(c_i)|$ is the number of failure modes
-in component ${c_i}$, is given by
+in component ${c_i}$, comparison complexity, $CC$ is given by
 
 \begin{equation}
 \label{eqn:CC}
@@ -369,14 +369,15 @@ $$
 %\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 
+All the FMMD examples in chapters \ref{sec:chap5} 
+and \ref{sec:chap6} showed a marked reduction in comparison 
 complexity compared to the RFMEA worst case figures. 
+To calculate RFMEA Comparison complexity equation~\ref{eqn:CC} is used.
 %
-
 %
 Complexity comparison vs. RFMEA for the first three examples
 are presented in table~\ref{tbl:firstcc}.
-
+%
 %\usepackage{multirow}
 \begin{table}
  \label{tbl:firstcc}
@@ -550,33 +551,39 @@ by more than  a factor of ten.
 \multicolumn{3}{ |c| }{{\sd} FMMD Hierarchy: section~\ref{sec:sigmadelta}} \\ \hline
 %\multirow{3}{*} {Inverting Amplifier Two stage FMMD Hierarchy: section~\ref{sec:invamp}}  & & \\
 \hline
-1 &              & 4        & 2 \\
-1 & INVAMP              & 16        & 3 \\
-0 & NIBUFF              & 0        & 4 \\
-%
-% final one has 8 components 3* NIBUFF +  1 * INVAMP + 4 * PHS45
-%                    (8-1) * ( (3*4) + (1*16) +    (4 *  4) )
-2 & {\sd}              & 308      & 2 \\
-%                                 NIBUFF  PHS45
-% 8 components so LEVEL 2 (8-1) \times ( (3*4) +  (4*2) + 3 ) + LEVEL 0 16 for the INVAMP
-2 & Total for {\sd}: &   328 (FMMD)  &   \\  
-%                               R&C     OPAMPS
-% 14 components so 13 \times ( (10*2)   (4*4) )
-0 & Total for {\sd}: &  468  (RFMEA) &   \\
 
-  \hline
+1 & SUMJINT & 30 & 4 \\
+0 & HISB    & 0  & 4 \\
+2 & BISJ    & 8  & 2 \\ \hline
+
+1 & DIGBUF  & 2 & 4 \\
+1 & PD      & 4 & 2 \\
+2 & DL2AL   & 6 & 3 \\
+3 & FFB     & 5 & 2 \\ \hline 
+%                  
+2 & {\sd}              & 4      & 2 \\ \hline
+%                               
+%  
+2 & Total for {\sd}: &   55 (FMMD)  &   \\  
+%                               R&C     OPAMPS
+% 14 components so (10-1) * 
+0 & Total for {\sd}: &  225  (RFMEA) &   \\
+
+  \hline \hline
 
 \end{tabular}
-\caption{Complexity Comparison figures for the Bubba Oscillator FMMD example (see section~\ref{sec:bubba}).}
+\caption{Complexity Comparison figures for the {\sd} FMMD example (see section~\ref{sec:sigmadelta}).}
 \end{table}
-
+%
+The complexity figures for this mixed analogue to digital circuit are not adversely affected by the digital to
+analogue level interfacing circuitry. This is where the modular approach aids understanding and analysis.
+When following this circuit through in a traditional way, we have to follow signal paths that
+are level shifted, adding to the complication of analysing it for failures.
 
 % \subsection{Exponential squared to Exponential}
 % 
 % can I say that ?
-
+%
-
-
 \section{Unitary State Component Failure Mode sets}
 \label{sec:unitarystate}
 \paragraph{Design Decision/Constraint}

submission_thesis/appendixes/detailed_analysis.tex

@@ -204,10 +204,10 @@ $$
      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   &  &    $NO_{signal}$           \\  
+     FS3: $INVAMP$  $L_{up}$      &  &  output high   &  &    $NO_{signal}$        \\  
-     FS4: $INVAMP$  $L_{dn}$      &  &  output low   &  &     $NO_{signal}$              \\       
+     FS4: $INVAMP$  $L_{dn}$      &  &  output low   &  &     $NO_{signal}$        \\       
-     FS5: $INVAMP$  $N_{oop}$     &  &  output low   &  &     $NO_{signal}$                \\  
+     FS5: $INVAMP$  $N_{oop}$     &  &  output low   &  &     $NO_{signal}$        \\  
-     FS6: $INVAMP$  $L_{slew}$    &  &  signal lost                &  &   $NO_{signal}$          \\  \hline 
+     FS6: $INVAMP$  $L_{slew}$    &  &  signal lost  &  &   $NO_{signal}$          \\  \hline 
 
 \hline