robin/Robin_PHD
1
0
Fork 0
Code Issues Pull Requests Actions Packages Projects Releases Wiki Activity

typos mainly

Browse Source
This commit is contained in:
Robin 2010-06-25 20:17:52 +01:00
parent 3e63538142
commit da7ee04b17
1 changed files with 15 additions and 15 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

30
pt100/pt100.tex
View File

@ -40,8 +40,8 @@ diagrams to assist the reasoning process.
This chapter describes taking This chapter describes taking
the failure modes of the components, analysing the circuit using FMEA the failure modes of the components, analysing the circuit using FMEA
and producing a failure mode model for the circuit as a whole. and producing a failure mode model for the circuit as a whole.
Thus after the analysis the PT100 temperature sensing circuit, may be veiwed Thus after the analysis the PT100 temperature sensing circuit, may be viewed
from an FMEA persepective as a component itself, with a set of known failure modes. from an FMEA perspective as a component itself, with a set of known failure modes.
} }
\begin{figure}[h] \begin{figure}[h]
@ -57,7 +57,7 @@ from an FMEA persepective as a component itself, with a set of known failure mod
The PT100 four wire circuit uses two wires to supply small electrical current, The PT100 four wire circuit uses two wires to supply small electrical current,
and returns two sense volages by the other two. and returns two sense volages by the other two.
By measuring volatges By measuring voltages
from sections of this circuit forming potential dividers, we can determine the from sections of this circuit forming potential dividers, we can determine the
resistance of the platinum wire sensor. The resistance resistance of the platinum wire sensor. The resistance
of this is directly related to temperature, and may be determined by of this is directly related to temperature, and may be determined by
@ -79,16 +79,16 @@ through the circuit to obtain accurate temperature readings}
are shown in figure \ref{fig:pt100vrange}. Note that there is are shown in figure \ref{fig:pt100vrange}. Note that there is
an expected range for each reading, for a given temperature span. an expected range for each reading, for a given temperature span.
Note that the low reading goes down as temperature increases, and the higher reading goes up. Note that the low reading goes down as temperature increases, and the higher reading goes up.
For this reason the low reading will be reffered to as {\em sense-} For this reason the low reading will be referred to as {\em sense-}
and the higher as {\em sense+}. and the higher as {\em sense+}.
\subsection{Accuracy despite variable \\ resistance in cables} \subsection{Accuracy despite variable \\ resistance in cables}
For electronic and accuracy reasons a four wire circuit is preffered For electronic and accuracy reasons a four wire circuit is preferred
because of resistance in the cables. Resistance from the supply because of resistance in the cables. Resistance from the supply
causes a slight voltage causes a slight voltage
drop in the supply to the PT100. As no significant current drop in the supply to the PT100. As no significant current
is carried by the two `sense' lines the resistance back to the ADC is carried by the two `sense' lines, the resistance back to the ADC
causes only a negligible voltage drop, and thus the four wire causes only a negligible voltage drop, and thus the four wire
configuration is more accurate\footnote{The increased accuracy is because the voltage measured, is the voltage across configuration is more accurate\footnote{The increased accuracy is because the voltage measured, is the voltage across
the thermistor and not the voltage across the thermistor and current supply wire resistance.}. the thermistor and not the voltage across the thermistor and current supply wire resistance.}.
@ -100,7 +100,7 @@ whole circuit can be measured on the PCB by reading a third
sense voltage from one of the load resistors. Knowing the current flowing sense voltage from one of the load resistors. Knowing the current flowing
through the circuit through the circuit
and knowing the voltage drop over the PT100, we can calculate its and knowing the voltage drop over the PT100, we can calculate its
resistance by ohms law $V=I.R$, $R=\frac{V}{I}$. resistance by Ohms law $V=I.R$, $R=\frac{V}{I}$.
Thus a little loss of supply current due to resistance in the cables Thus a little loss of supply current due to resistance in the cables
does not impinge on accuracy. does not impinge on accuracy.
The resistance to temperature conversion is achieved The resistance to temperature conversion is achieved
@ -131,7 +131,7 @@ All components have a set of known `failure modes'.
In other words we know that a given component can fail in several distinct ways. In other words we know that a given component can fail in several distinct ways.
Studies have been published which list common component types Studies have been published which list common component types
and their sets of failure modes, often with MTTF statistics \cite{mil1991}. and their sets of failure modes, often with MTTF statistics \cite{mil1991}.
Thus for each component, an analysis is made for each of it failure modes, Thus for each component, an analysis is made for each of its failure modes,
with respect to its effect on the with respect to its effect on the
circuit. Each one of these scenarios is termed a `test case'. circuit. Each one of these scenarios is termed a `test case'.
The resultant circuit behaviour for each of these test cases is noted. The resultant circuit behaviour for each of these test cases is noted.
@ -269,7 +269,7 @@ and are thus enclosed by one contour each.
\end{figure} \end{figure}
%ating input Fault %ating input Fault
This circuit supplies two results, sense+ and sense- voltage readings. This circuit supplies two results, the {\em sense+} and {\em sense-} voltage readings.
To establish the valid voltage ranges for these, and knowing our To establish the valid voltage ranges for these, and knowing our
valid temperature range for this example ({0\oc} .. {300\oc}) we can calculate valid temperature range for this example ({0\oc} .. {300\oc}) we can calculate
valid voltage reading ranges by using the standard voltage divider equation \ref{eqn:vd} valid voltage reading ranges by using the standard voltage divider equation \ref{eqn:vd}
@ -308,7 +308,7 @@ With pt100 at the high end of the temperature range 300\oc.
$$ highreading = 5V $$ $$ highreading = 5V $$
$$ lowreading = 5V.\frac{2k2}{2k2+212.02\Omega} = 4.56V$$ $$ lowreading = 5V.\frac{2k2}{2k2+212.02\Omega} = 4.56V$$
Thus with $R_1$ shorted both readingare outside the Thus with $R_1$ shorted both readings are outside the
proscribed range in table \ref{ptbounds}. proscribed range in table \ref{ptbounds}.
\subsubsection{ TC 2 : Voltages $R_1$ OPEN } \subsubsection{ TC 2 : Voltages $R_1$ OPEN }
@ -461,9 +461,9 @@ give the following failures in ${10}^6$ hours:
While MIL-HDBK-217F gives MTTF for a wide range of common components, While MIL-HDBK-217F gives MTTF for a wide range of common components,
it does not specify how the components will fail (in this case OPEN or SHORT). {Some standards, notably EN298 only consider resistors failing in OPEN mode}. it does not specify how the components will fail (in this case OPEN or SHORT). {Some standards, notably EN298 only consider resistors failing in OPEN mode}.
FMD-97 Gives 27\% OPEN and 3\% SHORTED, for resistors under certain electrical and environmental stresses. This example FMD-97 gives 27\% OPEN and 3\% SHORTED, for resistors under certain electrical and environmental stresses. This example
compromises and uses a 90:10 ratio, for resistor failure. compromises and uses a 90:10 ratio, for resistor failure.
Thus for this example resistors are expevcted to fail OPEN in 90\% of cases and SHORTED Thus for this example resistors are expected to fail OPEN in 90\% of cases and SHORTED
in the other 10\%. in the other 10\%.
A standard fixed film resistor, for use in a benign environment, non military spec at A standard fixed film resistor, for use in a benign environment, non military spec at
temperatures up to 60\oc is given a probability of 13.8 failures per billion ($10^9$) temperatures up to 60\oc is given a probability of 13.8 failures per billion ($10^9$)
@ -566,9 +566,9 @@ conditions.
In this section we examine the failure mode behaviour for all single In this section we examine the failure mode behaviour for all single
faults and double simultaneous faults. faults and double simultaneous faults.
This corresponds to the cardinality contstrained powerset of This corresponds to the cardinality constrained powerset of
the failure modes in the functional group. the failure modes in the functional group.
All the single faults have already be proved in the last section. All the single faults have already been proved in the last section.
For the next set of test cases, let us again hypothesise For the next set of test cases, let us again hypothesise
the failure modes, and then examine each one in detail with the failure modes, and then examine each one in detail with
potential divider equation proofs. potential divider equation proofs.
@ -678,7 +678,7 @@ in the pt100 circuit. The next task is to investigate
these test cases in more detail to prove the failure mode hypothese set out in table \ref{tab:ptfmea2}. these test cases in more detail to prove the failure mode hypothese set out in table \ref{tab:ptfmea2}.
\subsection{Proof of Double Faults Hypothese } \subsection{Proof of Double Faults Hypothesis }
\subsubsection{ TC 7 : Voltages $R_1$ OPEN $R_2$ OPEN } \subsubsection{ TC 7 : Voltages $R_1$ OPEN $R_2$ OPEN }
\label{pt100:bothfloating} \label{pt100:bothfloating}