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pt100/pt100.tex
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@ -3,22 +3,22 @@
\begin{abstract} \begin{abstract}
The PT100, or platinum wire \ohms{100} sensor is The PT100, or platinum wire \ohms{100} sensor is
a wisely used industrial temperature sensor that is a widely used industrial temperature sensor that is
are slowly replacing the use of thermocouples in many slowly replacing the use of thermocouples in many
industrial applications below 600\oc, due to high accuracy\cite{aoe}. industrial applications below 600\oc, due to high accuracy\cite{aoe}.
This chapter looks at the most common configuration, the This chapter looks at the most common configuration, the
four wire circuit, and analyses it from an FMEA perspective twice. four wire circuit, and analyses it from an FMEA perspective twice.
Once considering single faults (cardinality constrained powerset of 1) and then again, considering the Once considering single faults (cardinality constrained powerset of 1) and then again, considering the
possibility of double simultaneous faults (cardinality constrained powerset of 2). possibility of double faults (cardinality constrained powerset of 2).
The analysis is performed using Propositional Logic The analysis is performed using Propositional Logic
diagrasms to assist the reasoning process. 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 veiwed
from an FMEA persepective as a component itsself, with a set of know failure modes. from an FMEA persepective as a component itself, with a set of known failure modes.
\end{abstract} \end{abstract}
@ -34,10 +34,11 @@ from an FMEA persepective as a component itsself, with a set of know failure mod
\section{Overview of PT100 four wire circuit} \section{Overview of PT100 four wire circuit}
The PT100 four wire circuit consists of two resistors supplying The PT100 four wire circuit consists supplies a test current vis two wires
a current to a third, the thermistor or PT100. By measuring volatges and returns two sense volages by the other two.
By measuring volatges
from sections of this circuit forming potential dividers, we can determine the from sections of this circuit forming potential dividers, we can determine the
current 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
look-up tables or a suitable polynomial expression. look-up tables or a suitable polynomial expression.
@ -53,9 +54,9 @@ look-up tables or a suitable polynomial expression.
The voltage ranges we expect from from this three stage potential divider The voltage ranges we expect from this three stage potential divider
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 reffered to as {\em sense-}
and the higher as {\em sense+}. and the higher as {\em sense+}.
@ -63,7 +64,7 @@ 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 preffered
because of resistance in the cables. Resitance 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
@ -77,7 +78,7 @@ 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 $V=I.R$, $R=\frac{I}{V}$. 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
@ -88,7 +89,7 @@ through the published PT100 tables\cite{eurothermtables}.
This sub-section looks at the behaviour of the PT100 four wire circuit This sub-section looks at the behaviour of the PT100 four wire circuit
for the effects of component failures. for the effects of component failures.
All components have a set of known `failure modes'. All components have a set of known `failure modes'.
In other words we know that a given component can fail in several distict 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 it failure modes,
@ -109,7 +110,7 @@ Resistors according to the DOD Electronic component fault handbook
1991, fail by either going OPEN or SHORT circuit \cite{mil1991}. 1991, fail by either going OPEN or SHORT circuit \cite{mil1991}.
%Should wires become disconnected these will have the same effect as %Should wires become disconnected these will have the same effect as
%given resistors going open. %given resistors going open.
For the purpose of his analyis; For the purpose of this analyis;
$R_{1}$ is the \ohms{2k2} from 5V to the thermistor, $R_{1}$ is the \ohms{2k2} from 5V to the thermistor,
$R_3$ is the PT100 thermistor and $R_{2}$ connects the thermistor to ground. $R_3$ is the PT100 thermistor and $R_{2}$ connects the thermistor to ground.
@ -119,9 +120,9 @@ in the diagram we can consider this a fault.
Should the reading be above its expected range this is a `High Fault' Should the reading be above its expected range this is a `High Fault'
and if below a `Low Fault'. and if below a `Low Fault'.
The Table \ref{ptfmea} plays through the scenarios of each of the resistors failing Table \ref{ptfmea} plays through the scenarios of each of the resistors failing
in both SHORT and OPEN failure modes, and hypothesises an error condition in the readings. in both SHORT and OPEN failure modes, and hypothesises an error condition in the readings.
The range 0\oc to 300\oc will be analysed using potential divider equations to The range {0\oc} to {300\oc} will be analysed using potential divider equations to
determine out of range voltage limits in section \ref{ptbounds}. determine out of range voltage limits in section \ref{ptbounds}.
\begin{table}[ht] \begin{table}[ht]
@ -195,7 +196,7 @@ and \ref{pt100temp}.
\subsection{Range and PT100 Calculations} \subsection{Range and PT100 Calculations}
\label{pt100temp} \label{pt100temp}
PT100 resistors are designed to PT100 resistors are designed to
have a resistance of ohms{100} at 0 \oc \cite{eurothermtables}. have a resistance of \ohms{100} at 0 \oc \cite{eurothermtables}.
A suitable `wider than to be expected range' was considered to be {0\oc} to {300\oc} A suitable `wider than to be expected range' was considered to be {0\oc} to {300\oc}
for a given application. for a given application.
According to the Eurotherm PT100 According to the Eurotherm PT100
@ -293,8 +294,10 @@ will detect it.
\subsection{Single Fault Modes as PLD} \subsection{Single Fault Modes as PLD}
The component~failure~modes in table \ref{ptfmea} can be represented as contours The component~failure~modes in table \ref{ptfmea} can be represented as contours
on a PLD diagram. Each test case, or analysis into the effects of the component failure on a PLD diagram.
caused by the component~failure is represented by an labelled asterisk. Each test case, is defined by the contours that enclose
it. The test cases here deal with single faults only
and are thus enclosed by one contour each.
\begin{figure}[h] \begin{figure}[h]
@ -307,7 +310,7 @@ caused by the component~failure is represented by an labelled asterisk.
This circuit supplies two results, sense+ and sense- voltage readings. This circuit supplies two results, sense+ and 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 tempperature 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}
for the circuit shown in . for the circuit shown in .
@ -324,7 +327,7 @@ With pt100 at 0\oc
$$ highreading = 5V $$ $$ highreading = 5V $$
Since the highreading or sense+ is directly connected to the 5V rail, Since the highreading or sense+ is directly connected to the 5V rail,
both temperature readings will be 5V.. both temperature readings will be 5V..
$$ lowreading = 5V.\frac{2k2}{2k2+68\Omega} = 4.85V$$ $$ lowreading = 5V.\frac{2k2}{2k2+100\Omega} = 4.78V$$
With pt100 at the high end of the temperature range 300\oc. With pt100 at the high end of the temperature range 300\oc.
$$ highreading = 5V $$ $$ highreading = 5V $$
$$ lowreading = 5V.\frac{2k2}{2k2+212.02\Omega} = 4.56V$$ $$ lowreading = 5V.\frac{2k2}{2k2+212.02\Omega} = 4.56V$$
@ -339,13 +342,13 @@ therefore both readings are outside the
proscribed range in table \ref{ptbounds}. proscribed range in table \ref{ptbounds}.
\subsubsection{ TC 4 : Voltages $R_2$ SHORT } \subsubsection{ TC 3 : Voltages $R_2$ SHORT }
With pt100 at -100\oc With pt100 at 0\oc
$$ lowreading = 0V $$ $$ lowreading = 0V $$
Since the lowreading or sense- is directly connected to the 0V rail, Since the lowreading or sense- is directly connected to the 0V rail,
both temperature readings will be 0V. both temperature readings will be 0V.
$$ lowreading = 5V.\frac{68\Omega}{2k2+68\Omega} = 0.15V$$ $$ lowreading = 5V.\frac{100\Omega}{2k2+100\Omega} = 0.218V$$
With pt100 at the high end of the temperature range 300\oc. With pt100 at the high end of the temperature range 300\oc.
$$ highreading = 5V $$ $$ highreading = 5V $$
$$ lowreading = 5V.\frac{212.02\Omega}{2k2+212.02\Omega} = 0.44V$$ $$ lowreading = 5V.\frac{212.02\Omega}{2k2+212.02\Omega} = 0.44V$$
@ -353,9 +356,9 @@ $$ lowreading = 5V.\frac{212.02\Omega}{2k2+212.02\Omega} = 0.44V$$
Thus with $R_2$ shorted both readingare outside the Thus with $R_2$ shorted both readingare outside the
proscribed range in table \ref{ptbounds}. proscribed range in table \ref{ptbounds}.
\subsubsection{ TC : 5 Voltages $R_2$ OPEN } \subsubsection{ TC : 4 Voltages $R_2$ OPEN }
Here there is no potential divider operating and both sense lines Here there is no potential divider operating and both sense lines
will read 5V, outside of the proscibed range. will read 5V, outside of the proscribed range.
\subsubsection{ TC 5 : Voltages $R_3$ SHORT } \subsubsection{ TC 5 : Voltages $R_3$ SHORT }

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