de-coupling caps example pp15-16

unintended side effects

opamp_circuits_C_GARRETT/Makefile

@@ -1,6 +1,6 @@
 
 
-PNG_DIA = circuit1_dag.png mvampcircuit.png pd.png invamp.png
+PNG_DIA = circuit1_dag.png mvampcircuit.png pd.png invamp.png shared_component.png
 
 
 

opamp_circuits_C_GARRETT/opamps.tex

@@ -44,7 +44,7 @@ Function $fm$ applied to a component returns its failure modes.
 \section{Non-Inverting OPAMP}
 Consider a non inverting op-amp designed to amplify
 a small positive voltage (typical use would be a thermocouple amplifier
-taking a range from 0 to 25mV and amplifiying it to the range of an ADC approx 0 to 4 volts).
+taking a range from 0 to 25mV and amplifiying it to the useful range of an ADC, approx 0 to 4 volts).
  
  
 \begin{figure}[h+]
@@ -56,20 +56,21 @@ taking a range from 0 to 25mV and amplifiying it to the range of an ADC approx 0
 \end{figure}
 
 We can begin by looking for functional groups. 
-The resistors would together to perform a fairly common function in electronics, that of the potential divider.
+The resistors $ R1, R2 $  perform a fairly common function in electronics, that of the potential divider.
-So our first functional group is $\{ R1, R2 \}$. 
+So we can examine  $\{ R1, R2 \}$  as a {\fg}. 
 
 
 \subsection{The Resistor in terms of failure modes}
 
-We can now take the failure modes for the resistors (OPEN and SHORT EN298).
+We can now determine how the resistors can fail.
+According to GAS standard EN298 the failure modes to consider for resistors are OPEN and SHORT.
 
 
-We can express the fialure modes of a component using the function $fm$, thus for the resistor,  $ fm(R) = \{ OPEN, SHORT \}$.
+We can express the failure modes of a component using the function $fm$, thus for the resistor,  $ fm(R) = \{ OPEN, SHORT \}$.
 
 
-We have two resistors in this circuit and therefore four component failure modes to consider for the potential divider,
+We have two resistors in this circuit and therefore four component failure modes to consider for the potential divider.
-we can now examine what effect each of these failures will have on the {\fg} (the potential divider see figure~\ref{fig:pdcircuit}).
+We can now examine what effect each of these failures will have on the {\fg}.
 
 
 \subsection{Analysing a potential divider in terms of failure modes}
@@ -123,7 +124,7 @@ We can collect symptoms from the analysis and cretae a derived component
 to represent the non-inverting amplifier $NI\_AMP$.
 We now have can express the failure mode behaviour of this type of amplifier thus:
 
-$$ fm(NI\_AMP) = \{  N\_INVAMP_{lowpass}, N\_INVAMP_{high}, N\_INVAMP_{low} \}.$$
+$$ fm(NI\_AMP) = \{  {lowpass}, {high}, {low} \}.$$
 
 
 
@@ -141,12 +142,16 @@ $$ fm(NI\_AMP) = \{  N\_INVAMP_{lowpass}, N\_INVAMP_{high}, N\_INVAMP_{low} \}.$
 This configuration is interesting from methodology perspective.
 There are two ways in which we can tackle this.
 One is to do this in two stages, by considing the gain resistors to be a potential divider
-and then combining the potential divider with the OPAMP failure mode model.
+and then combining it with the OPAMP failure mode model.
 The other way is to place all three components in a {\fg}.
+Both approaches are followed in the next two sub-sections.
 
 \subsection{Inverting OPAMP using a Potential Divider {\dc}}
 
 Re-using the $PD$ - potential divider works only if the input voltage is negative.
+We want if possible to have detectable errors, HIGH and LOW are better than OUTOFRANGE.
+If we can refine the operational states of the fungional group, we can obtain clearer
+symptoms.
 If we consider the input will only be positive, we can invert the potential divider.
 
 \begin{table}[h+]
@@ -167,9 +172,9 @@ We can now form a {\fg} from the OPAMP and the $INVPD$
 
 This gives the same results as the analysis from figure~\ref{fig:invampanalysis}.
 The differences are the root causes or component failure modes that
-lead to the symptoms.
+lead to the symptoms (i.e. the symptoms are the same but causation tree will be different).
 
- $$ fm(NI\_AMP) = \{  N\_INVAMP_{lowpass}, N\_INVAMP_{high}, N\_INVAMP_{low} \}.$$
+ $$ fm(NI\_AMP) = \{  {lowpass}, {high}, {low} \}.$$
 
 
 \subsection{Inverting OPAMP using three components}
@@ -177,7 +182,9 @@ lead to the symptoms.
 We can use this for a more general case, because we can examine the 
 effects on the circuit for each operational case (i.e. input +ve
 or input -ve). Because symptom collection is defined as surjective (from component failure modes 
-to symptoms) we cannot have a component failure mode that maps to two different symptoms !
+to symptoms) we cannot have a component failure mode that maps to two different symptoms (within a functional group).
+Note that here we have a more general symptom $ OUT OF RANGE $ which could mean either
+$HIGH$ or $LOW$ output.
 
 
 
@@ -222,8 +229,7 @@ Could further refine this if MTTF stats available for each component failure.
 
 If the input voltage can be negative the potential divider
 becomes reversed in polarity.
-This means that was essentially get an either situation with the error detection.
+This means that detecting which failure mode has occurred from knowing the symptom, has become a more difficult task.
-
 
 \clearpage
 \section{Op-Amp circuit 1}
@@ -348,7 +354,7 @@ Here it is more intuitive to model the resistors not as a potential divider, but
 %get a high or low reading if R3 or R4 fail.
 
 \begin{table}[ht]
-\caption{Differencing Amplifier $D\_AMP$: Failure Mode Effects Analysis: Single Faults} % title of Table
+\caption{Second Amplifier $SEC\_AMP$: Failure Mode Effects Analysis: Single Faults} % title of Table
 \centering % used for centering table
 \begin{tabular}{||l|c|c|l|l||}
 \hline \hline
@@ -376,10 +382,10 @@ Here it is more intuitive to model the resistors not as a potential divider, but
 
 Collecting the symptoms we can see that this amplifier fails
 in 4 ways $\{ AMPHigh, AMPLow,  LowPass, AMPIncorrectOutput\}$.
-We can now create a derived component, $D\_AMP$, to represent it.
+We can now create a derived component, $SEC\_AMP$, to represent it.
 
  
-$$ fm(D\_AMP) = \{ AMPHigh, AMPLow, LowPass, AMPIncorrectOutput \} $$
+$$ fm(SEC\_AMP) = \{ AMPHigh, AMPLow, LowPass, AMPIncorrectOutput \} $$
  
 
 
@@ -390,7 +396,7 @@ $$ fm(D\_AMP) = \{ AMPHigh, AMPLow, LowPass, AMPIncorrectOutput \} $$
 \subsection{Modelling the circuit}
 
 For the final stage of this we can create a functional group consisting of
-two derived components of the type $NI\_AMP$ and $D\_AMP$.
+two derived components of the type $NI\_AMP$ and $SEC\_AMP$.
 
 
 
@@ -407,11 +413,11 @@ two derived components of the type $NI\_AMP$ and $D\_AMP$.
  TC1: $NI\_AMP$ AMPHigh        &  opamp 2 driven high          &      & DiffAMPLow \\ 
  TC2: $NI\_AMP$  AMPLow        &  opamp 2 fdriven low          &      &  DiffAMPHigh \\  
  TC3: $NI\_AMP$ LowPass        &  opamp 2 driven with lag      &      &  DiffAMP\_LP \\  \hline 
- TC4: $D\_AMP$ AMPHigh        &  Diff amplifier high           &      &   DiffAMPHigh\\  
+ TC4: $SEC\_AMP$ AMPHigh        &  Diff amplifier high           &      &   DiffAMPHigh\\  
- TC5: $D\_AMP$ AMPLow         &  Diff amplifier low            &      &  DiffAMPLow \\  
+ TC5: $SEC\_AMP$ AMPLow         &  Diff amplifier low            &      &  DiffAMPLow \\  
- TC6: $D\_AMP$ LowPass        &  Diff amplifier lag/lowpass    &      &  DiffAMP\_LP \\ \hline 
+ TC6: $SEC\_AMP$ LowPass        &  Diff amplifier lag/lowpass    &      &  DiffAMP\_LP \\ \hline 
- TC7: $D\_AMP$ IncorrectOutput &  Output voltage               &      &  DiffAMPIncorrect \\  
+ TC7: $SEC\_AMP$ IncorrectOutput &  Output voltage               &      &  DiffAMPIncorrect \\  
- TC7: $D\_AMP$                 & $ \neg (V2 - V1) $ &      &   \\ \hline
+ TC7: $SEC\_AMP$                 & $ \neg (V2 - V1) $ &      &   \\ \hline
 \hline
 \end{tabular} 
 \label{ampfmea}
@@ -432,7 +438,7 @@ of the failure modes and derived components.
 Using this we can trace any top level fault back to 
 a component failure mode that could have caused it.
 In fact we can re-construct an FTA diagram from the information in this graph.
-We merely have to choose a top level event and work down using or gates.
+We merely have to choose a top level event and work down using $XOR$ gates.
 
 This circuit performs poorly from a safety point of view.
 Its failure modes could be indistinguishable from valid readings (especially
@@ -475,4 +481,76 @@ wihen it becomes a V2 follower).
 \clearpage
 \section{Standard Non-inverting OP AMP}
 
+
+\clearpage
+\section{Unintended Side Effects: A Problem for FMMD analysis}
+A problem with modularising according to functionality is that we can have component failures that would 
+intuitively be associated with one {\fg} that may cause unintended side effects in other
+{\fgs}.
+For instance were we to have a component that that on failing $SHORT$ could bring down 
+a voltage supply rail, this could have drastic consequences for other functional groups in the system we are examining.
+\pagebreak[3]
+\subsection{Example de-coupling capacitors in logic circuits}
+
+A good example of this are de-coupling capacitors, often used over the power supply pins of all chips in a digital logic circuit.
+Were any of these capacitors to fail $SHORT$ they could bring down the supply voltage to the other logic chips.
+
+
+To a power-supply, shorted capacitors on the supply rails are a potential source of the symptom, $SUPPLY\_SHORT$.
+In a logic chip/digital circuit {\fg} open capacitors are a potential source of symptoms caused by the failure mode $INTERFERENCE$.
+So we have a `symptom' of the power-supply, and a `failure~mode' of the logic chip to consider.
+
+The FMMD solution to this is to include the de-coupling capacitors
+in the power-supply {\fg}.
+% decision, could they be included in both places ????
+% I think so 
+
+
+Because the capacitor has two potential failure modes (EN298)
+this raises another issue for FMMD. A de-coupling capacitor going $OPEN$ might not be considered relevant to
+a power-supply module (but there might be additional noise on its output rails).
+But in {\fg} terms the power supply, now has a new symptom that of  $INTERFERENCE$.
+
+Some logic chips are more susceptible to  $INTERFERENCE$ than others.
+A logic chip with de-coupling capacitor failing, may operate correctly 
+but interfere with other chips in the circuit.
+
+There is no reason why the de-coupling capacitors could not be included {\em in the {\fg} they would intuitively be associated with as well}.
+This allows for the general principle of a component failure affecting more than one {\fg} in a circuit.
+This allows functional groups to share components where necessary.
+
+\pagebreak[3]
+\subsection{{\fgs} Sharing components and Hierarchy}
+
+With electronics we need to follow the signal path to make sense of failure modes
+effects on other parts of the circuit further down that path.
+%{\fgs} will naturally have to be in the position of starter 
+A power-supply is naturally first in a signal path (or failure reasoning path).
+That is to say, if the power-supply is faulty, its failure modes are likely to affect
+the {\fgs} that have to use it.
+
+This means that most electronic components should be placed higher in an FMMD
+hierarchy than the power-supply.
+A shorted de-coupling capactitor caused a `symptom' of the power-supply, 
+and an open de-coupling capactitor can be considered a `failure~mode' of the logic chip to consider.
+
+If components can be shared between functional groups, this means that components
+must be shareable between {\fgs} at different levels in the FMMD hierarchy.
+This hierarchy and an optionally shared de-coupling capacitor (with line highlighted in red and dashed)  are shown
+in figure~\ref{fig:shared_component}.
+
+\begin{figure}
+ \centering
+ \includegraphics[width=250pt,keepaspectratio=true]{./shared_component.png}
+ % shared_component.png: 729x670 pixel, 72dpi, 25.72x23.64 cm, bb=0 0 729 670
+ \caption{Optionally shared Component}
+ \label{fig:shared_component}
+\end{figure}
+
+\subsection{Hierarchy and structure}
+By having this structure, the logic circuit element, can accept failure modes from the 
+power-supply (for instance these might, for the sake of example  include: $NO\_POWER$, $LOW\_VOLTAGE$, $HIGH\_VOLTAGE$, $NOISE\_HF$, $NOISE\_LF$.
+Our logic circuit may be able to cope with $LOW\_VOLTAGE$ and $NOISE\_LF$, but react with a serious symptom to $NOISE\_HF$ say.
+But in order to process these failure modes it must be at a higher stage in the FMMD hierarchy.
+
 \end{document}