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Robin Clark 2013-09-18 08:57:39 +01:00
parent 9bec687779
commit 2f17ed2ec8
2 changed files with 17 additions and 11 deletions
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3
submission_thesis/CH2_FMEA/copy.tex
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@ -429,8 +429,11 @@ investigations.
\fmmdglossOPAMP \fmmdglossOPAMP
The symptom for this is given as a low slew rate. The symptom for this is given as a low slew rate.
% %
Slew rate for a circuit/component is the rate at which it changes an output voltage level (i.e. $\frac{\delta V}{\delta t} $).
%
This means that the op-amp will not react quickly to changes on its input terminals. This means that the op-amp will not react quickly to changes on its input terminals.
% %
%
This is a failure symptom that may not be of concern in a slow responding system like an This is a failure symptom that may not be of concern in a slow responding system like an
instrumentation amplifier. However, where higher frequencies are being processed, instrumentation amplifier. However, where higher frequencies are being processed,
a signal may be lost entirely. a signal may be lost entirely.

25
submission_thesis/CH5_Examples/copy.tex
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@ -78,9 +78,7 @@ A valid range for the output value of this circuit is assumed.
%and voltages higher than a given threshold considered as HIGH. %and voltages higher than a given threshold considered as HIGH.
% %
Because the amplifier inverts and the input is guaranteed positive any Because the amplifier inverts and the input is guaranteed positive any
output voltage above or equal to zero would be erroneous. output voltage above or equal to zero would be erroneous i.e. an `$AMP_{HIGH}$' failure symptom.
%
This would be an `$AMP_{HIGH}$' failure symptom.
% %
A threshold would be determined for an `$AMP_{LOW}$' failure symptom (i.e. the output voltage more negative than expected). % error given the expected input range. A threshold would be determined for an `$AMP_{LOW}$' failure symptom (i.e. the output voltage more negative than expected). % error given the expected input range.
% %
@ -183,7 +181,8 @@ The final stage of analysis for this amplifier, is made by
by forming a {\fg} with the OpAmp and the new {\dc} $IPD$. by forming a {\fg} with the OpAmp and the new {\dc} $IPD$.
% %
\begin{table}[h+] \begin{table}[h+]
\caption{Inverting Amplifier: Single failure analysis using the $PD$ {\dc}} \centering
\caption{Inverting Amplifier: Single failure analysis using the $IPD$ {\dc}}
\begin{tabular}{|| l | l | c | c | l ||} \hline \begin{tabular}{|| l | l | c | c | l ||} \hline
%\textbf{Failure Scenario} & & \textbf{Inverted Amp Effect} & & \textbf{Symptom} \\ \hline %\textbf{Failure Scenario} & & \textbf{Inverted Amp Effect} & & \textbf{Symptom} \\ \hline
\textbf{Failure} & & \textbf{Inverted Amp. Effect} & & \textbf{Symptom} \\ \textbf{Failure} & & \textbf{Inverted Amp. Effect} & & \textbf{Symptom} \\
@ -460,7 +459,10 @@ This means R3 R4 is not a fixed potential divider, with R4 being on the positive
% %
It could be at either polarity. % (i.e. the other way around R4 could be the negative side). It could be at either polarity. % (i.e. the other way around R4 could be the negative side).
% %
Here it is more intuitive to model the resistors not as a potential divider, but individually. Here, even though R3 and R4 are used as a potential divider,
it could be either inverted or non-inverted according to the voltages on the inputs.
Therefore the resistors cannot modelled as a potential divider, but must be placed in the {\fg}
with the OpAmp and analysed.
%This means we are either going to %This means we are either going to
%get a high or low reading if R3 or R4 fail. %get a high or low reading if R3 or R4 fail.
@ -661,6 +663,7 @@ The first order low pass filter is analysed in table~\ref{tbl:firstorderlpass}.\
\begin{table}[h+] \begin{table}[h+]
\centering
\caption{FirstOrderLP: Failure Mode Effects Analysis: Single Faults} % title of Table \caption{FirstOrderLP: Failure Mode Effects Analysis: Single Faults} % title of Table
\label{tbl:firstorderlpass} \label{tbl:firstorderlpass}
@ -821,7 +824,7 @@ and these are marked on the circuit schematic in figure~\ref{fig:circuit2002_FIV
\label{fig:circuit2002_FIVEPOLE} \label{fig:circuit2002_FIVEPOLE}
\end{figure} \end{figure}
% %
\pagebreak[4] %\pagebreak[4]
% %
So the final {\fg} will consist of the derived components $\{ LP1, SKLP_1, SKLP_2 \}$. So the final {\fg} will consist of the derived components $\{ LP1, SKLP_1, SKLP_2 \}$.
% %
@ -1214,7 +1217,7 @@ increases the potential for re-use. % of pre-analysed {\dcs}.
% %
A finer grained model---with potentially more hierarchy stages---also means that A finer grained model---with potentially more hierarchy stages---also means that
%more work, or %more work, or
more reasoning stages have been used in the analysis. more reasoning stages, i.e. FMMD analysis stages with their associated analysis reports, have been used in the analysis.
% HTR The more we can modularise, the more we decimate the $O(N^2)$ effect % HTR The more we can modularise, the more we decimate the $O(N^2)$ effect
% HTR of complexity comparison. % HTR of complexity comparison.
% %
@ -1227,7 +1230,7 @@ However, it involves a large reasoning distance, the final stage
having 24 failure modes to consider against each of the other seven {\dcs}. having 24 failure modes to consider against each of the other seven {\dcs}.
A finer grained approach produces more potentially re-usable {\dcs} and A finer grained approach produces more potentially re-usable {\dcs} and
involves several stages with lower reasoning distances. involves several stages with lower reasoning distances.
The lower reasoning distances, or complexity comparision figures are given in the metrics chapter~\ref{sec:chap7} The lower reasoning distances, or complexity comparison figures are given in the metrics chapter~\ref{sec:chap7}
at section~\ref{sec:bubbaCC}. at section~\ref{sec:bubbaCC}.
These show that the finer grained models also benefit from lower reasoning distances for the failure mode model. These show that the finer grained models also benefit from lower reasoning distances for the failure mode model.
@ -1731,7 +1734,7 @@ expected voltages for failure mode and temperature reading purposes.
\begin{equation} \begin{equation}
\label{eqn:vd} \label{eqn:vd}
V_{out} = V_{in}.\frac{Z2}{Z2+Z1} V_{out} = V_{in}.\frac{Z_2}{Z_2+Z_1}
\end{equation} \end{equation}
\subsection{Safety case for 4 wire circuit: Detailed calculations} \subsection{Safety case for 4 wire circuit: Detailed calculations}
@ -1843,8 +1846,8 @@ As the voltage over $R_3$ is relative (a design feature to eliminate resistance
the current can be calculated by reading the current can be calculated by reading
the voltage over the known resistor the voltage over the known resistor
$R2$.\footnote{To calculate the resistance of the Pt100 we need the current flowing though it. $R2$.\footnote{To calculate the resistance of the Pt100 we need the current flowing though it.
This can be determined via Ohms law applied to $R_2$, $V=IR$, $I=\frac{V}{R_2}$, This can be determined via Ohms law applied to $R_2$, $V=I R_2$, $I=\frac{V}{R_2}$,
and then using $I$, with $I$, $R_{3} = \frac{V_{R3}}{I}$.} and then using $I$, $R_{3} = \frac{V_{R3}}{I}$.}
As these calculations are performed by Ohms law, which is linear, the accuracy of the reading As these calculations are performed by Ohms law, which is linear, the accuracy of the reading
will be determined by the accuracy of $R_2$ and $R_{3}$. will be determined by the accuracy of $R_2$ and $R_{3}$.
%It is reasonable to %It is reasonable to