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old_thesis/opamp_circuits_C_GARRETT/opamps.tex
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@ -73,9 +73,12 @@ oversimplifies the task of failure mode analysis, and makes the process arbitrar
Fortunately most real-world designs take a modular approach. In Electronics
for instance, commonly used configurations of parts are used to create
amplifiers, filters, potential dividers etc.
It is therefore natural to collect parts to form functional groups.
%It is therefore natural to collect parts to form functional groups.
It is common design practise in electronics, to use collections of parts in specific configurations
to form well defined and known building blocks.
These commonly used configurations of parts, or {\fgs}, will
also have failure mode behaviour. We can take a {\fg} and determine its symptoms of failure.
also have a specific failure mode behaviour.
We can take a {\fg} and determine its symptoms of failure.
When we have done this we can treat this as a component in its own right.
If we terms `parts' as base~components and components we have determined
from functional groups as derived components, we can modularise the FMEA task.
@ -135,7 +138,9 @@ When we have determined the symptoms, we can
create a {\dc} (called say AMP1) which has a {\em known set of failure modes} (i.e. its symptoms).
We can now treat $AMP1$ as a pre-analysed, higher level component.
The amplifier is an abstract concept, in terms of the components.
The components brought together in a specific way make it an amplifier !
To a make an `amplifier' we have to connect a a group of components
in a specific configuration. This specific configuration corresponds to
a {\fg}. Our use of it as a building block corresponds to a {\dc}.
%What this means is the `fault~symptoms' of the module have been derived.
@ -185,7 +190,7 @@ fm : \mathcal{C} \rightarrow \mathcal{P}\mathcal{F}.
This is defined by, where $c$ is a component and $F$ is a set of failure modes,
$ fm ( c ) = F. $
We can use the variable name $FG$ to represent a {\fg}. A {\fg} is a collection
We can use the variable name $\FG$ to represent a {\fg}. A {\fg} is a collection
of components.
%We thus define $FG$ as a set of chosen components defining
%a {\fg}; all functional groups
@ -295,53 +300,7 @@ Idea stage on this section
\clearpage
Two areas that cannot be automated. Choosing {\fgs} and the analysis/symptom collection process itself.
\section{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 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.
A possible 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.
This does not break the modularity of the FMMD technique, because, as {\irl}
one component failure may affect more than one sub-system.
It does uncover a weakness in the FMMD methodology though.
It could be very easy to miss the side effect and include
the component causing the side effect into the wrong {\fg}, or only one germane {\fg}.
\pagebreak[3]
\subsection{{\fgs} Sharing components and Hierarchy}
With electronics we need to follow the signal path to make sense of failure modes
@ -622,6 +581,56 @@ $$
%
% can I say that ?
\section{Problems in choosing membership of functional groups}
\subsection{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 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]
\subsubsection{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.
A possible 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.
This does not break the modularity of the FMMD technique, because, as {\irl}
one component failure may affect more than one sub-system.
It does uncover a weakness in the FMMD methodology though.
It could be very easy to miss the side effect and include
the component causing the side effect into the wrong {\fg}, or only one germane {\fg}.
\section{Double Simultaneous Failures}
@ -724,10 +733,10 @@ For Functional Group 2 (FG2), let us map:
FS6 & \mapsto & S5
\end{eqnarray*}
This AUTOMATIC check can reveal WHEN double checking no longer necessary
in the hierarchy to cover dub sum !!!!! YESSSS
%This AUTOMATIC check can reveal WHEN double checking no longer necessary
%in the hierarchy to cover dub sum !!!!! YESSSS
\section{Non-Inverting OPAMP}
\section{Example Analysis: 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 useful range of an ADC, approx 0 to 4 volts).
@ -776,7 +785,7 @@ We can now examine what effect each of these failures will have on the {\fg} (se
\begin{table}[h+]
\caption{Potential Divider: Sinlge failure analysis}
\caption{Potential Divider: Single failure analysis}
\begin{tabular}{|| l | l | c | c | l ||} \hline
\textbf{Failure Scenario} & & \textbf{Pot Div Effect} & & \textbf{Symptom} \\
\hline
@ -842,6 +851,7 @@ With this two stage analysis we have a comparison complexity (see equation~\ref{
$4.(2-1)=4$ for the potential divider and $6.(2-1)=6$, giving a total of $10$ for the $NIAMP$.
For this simple example, traditional flat/non-modular FMEA would have a CC of $(3-1).(4+2+2)=16$.
\clearpage
\section{Inverting OPAMP}
\label{sec:invamp}
@ -854,16 +864,16 @@ For this simple example, traditional flat/non-modular FMEA would have a CC of $(
\label{fig:invamp}
\end{figure}
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 considering the gain resistors to be a potential divider
%This configuration is interesting from methodology pers.
There are two obvious ways in which we can model this circuit:
One is to do this in two stages, by considering the gain resistors to be an inverted potential divider
and then combining it with the OPAMP failure mode model.
The other way is to place all three components in a {\fg}.
The second 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 cannot simply re-use the $PD$ from section~\ref{potdivfmmd}---that potential divider would only be valid if the input signal were 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 functional group, we can obtain clearer
symptoms.
@ -874,9 +884,9 @@ If we consider the input will only be positive, we can invert the potential divi
\begin{tabular}{|| l | l | c | c | l ||} \hline
\textbf{Failure Scenario} & & \textbf{Inverted Pot Div Effect} & & \textbf{Symptom} \\
\hline
FS1: R1 SHORT & & $HIGH$ & & $PDHigh$ \\ \hline
FS2: R1 OPEN & & $LOW$ & & $PDLow$ \\ \hline
FS3: R2 SHORT & & $LOW$ & & $PDLow$ \\ \hline
FS1: R1 SHORT & & $HIGH$ & & $PDHigh$ \\ \hline
FS2: R1 OPEN & & $LOW$ & & $PDLow$ \\ \hline
FS3: R2 SHORT & & $LOW$ & & $PDLow$ \\ \hline
FS4: R2 OPEN & & $HIGH$ & & $PDHigh$ \\ \hline
\hline
\end{tabular}
@ -892,8 +902,8 @@ We can now form a {\fg} from the OPAMP and the $INVPD$
\begin{tabular}{|| l | l | c | c | l ||} \hline
\textbf{Failure Scenario} & & \textbf{Inverted Amp Effect} & & \textbf{Symptom} \\ \hline
\hline
FS1: INVPD LOW & & NEGATIVE - input & & $ HIGH $ \\
FS2: INVPD HIGH & & Positive - input & & $ LOW $ \\
FS1: INVPD LOW & & NEGATIVE on -input & & $ HIGH $ \\
FS2: INVPD HIGH & & Positive on -input & & $ LOW $ \\
FS5: AMP L\_DN & & $ INVAMP_{low} $ & & $ LOW $ \\ \hline
@ -930,12 +940,12 @@ $HIGH$ or $LOW$ output.
\begin{table}[h+]
\caption{Inverting Amplifier: Single failure analysis}
\caption{Inverting Amplifier: Single failure analysis: 3 components}
\begin{tabular}{|| l | l | c | c | l ||} \hline
\textbf{Failure Scenario} & & \textbf{Inverted Amp Effect} & & \textbf{Symptom} \\ \hline
\hline
FS1: R1 SHORT +ve in & & NEGATIVE out of range & & $ OUT OF RANGE $ \\
FS1: R1 SHORT -ve in & & POSITIVE out of range & & $ OUT OF RANGE $ \\ \hline
FS1: R1 SHORT -ve in & & POSITIVE out of range & & $ OUT OF RANGE $ \\ \hline
FS2: R1 OPEN +ve in & & zero output & & $ ZERO OUTPUT $ \\
FS2: R1 OPEN -ve in & & zero output & & $ ZERO OUTPUT $ \\ \hline
@ -968,8 +978,8 @@ $$ fm(INVAMP) = \{ OUT OF RANGE, ZERO OUTPUT, NO GAIN, LOW PASS \} $$
%Could further refine this if MTTF stats available for each component failure.
\clearpage
\clearpage
\subsection{Comparison between the two approaches}
If the input voltage can be negative the potential divider