295 lines
11 KiB
TeX
295 lines
11 KiB
TeX
%
|
|
% Make the revision and doc number macro's then they are defined in one place
|
|
|
|
\begin{abstract}
|
|
The PT100, or platinum wire \ohms{100} sensor is
|
|
a wisely used industrial temperature sensor that is
|
|
are slowly replacing the use of thermocouples in many
|
|
industrial applications below 600\oc, due to high accuracy\cite{aoe}.
|
|
|
|
This chapter looks at the most common configuration, the
|
|
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
|
|
possibility of double simultaneous faults (cardinality constrained powerset of 2).
|
|
|
|
The analysis is performed using Propositional Logic
|
|
diagrasms to aid in the reasoning process, which takes
|
|
the failure modes of the components, and produces a
|
|
failure mode model for the circuit as a whole.
|
|
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.
|
|
|
|
\end{abstract}
|
|
|
|
|
|
\begin{figure}[h]
|
|
\centering
|
|
\includegraphics[width=400pt,bb=0 0 714 180,keepaspectratio=true]{./pt100/pt100.jpg}
|
|
% pt100.jpg: 714x180 pixel, 72dpi, 25.19x6.35 cm, bb=0 0 714 180
|
|
\caption{PT100 four wire circuit}
|
|
\label{fig:pt100}
|
|
\end{figure}
|
|
|
|
|
|
\section{Overview of PT100 four wire circuit}
|
|
|
|
The PT100 four wire circuit consists of teo resistors supplying
|
|
a current to a third, the thermistor or PT100. By measuring volatges
|
|
from sections of this circuit forming potential dividers, we can determine the
|
|
current resistance of the platinum wire sensor. The resistance
|
|
of this is directly related to temperature, and may be determined by
|
|
look-up tables or a suitable polynomial expression.
|
|
|
|
\subsection{Accuracy despite variable resistance in cables}
|
|
|
|
For electronic and accuracy reasons the four wire circiut is used
|
|
because of resistance in the cables. Resitance from the supply
|
|
causes a slight voltage
|
|
drop in the supply to the PT100. As no significant current
|
|
is carried by the two `sense' lines the resistance back to the ADC
|
|
causes only a negligible voltage drop. The current flowing though the
|
|
whole circuit can be measured on the PCB by reading a third
|
|
sense voltage from one of the load resistors. Knowing the current flowing
|
|
through the circuit
|
|
and knowing the voltage drop over the PT100, we can calculate its
|
|
resistance by ohms law $V=I.R$, $R=\frac{I}{V}$.
|
|
Thus a little loss of supply current due to resistance in the cables
|
|
does not impinge on accuracy.
|
|
The resistance to temperature conversion is achieved
|
|
through the published PT100 tables\cite{eurothermtables}.
|
|
|
|
\section{Safety case for 4 wire circuit}
|
|
|
|
This sub-section looks at the behaviour of the PT100 four wire circuit
|
|
for the effects of component failures.
|
|
All components have a set of known `failure modes'.
|
|
In other words we know that a given component can fail in several distict ways.
|
|
Studies have been published which list common component types
|
|
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,
|
|
with respect to its effect on the
|
|
circuit. Each one of these scenarios is termed a `test case'.
|
|
The resultant circuit behaviour for each of these test cases is noted.
|
|
The worst case for this type of
|
|
analysis would be a fault that we cannot detect.
|
|
Where this occurs a circuit re-design is probably the only sensible course of action.
|
|
|
|
\subsection{Single Fault FMEA Analysis of PT100 Four wire circuit}
|
|
|
|
\label{fmea}
|
|
Looking at this circuit, it simply consists of three resistors.
|
|
Resistors according to the DOD Electronic component fault handbook
|
|
1991, fail by either going OPEN or SHORT circuit \cite{mil1991}.
|
|
%Should wires become disconnected these will have the same effect as
|
|
%given resistors going open.
|
|
For the purpose of his analyis;
|
|
$R_{1}$ is the \ohms{2k2} from 5V to the thermistor,
|
|
$R_p$ is the PT100 thermistor and $R_{2}$ connects the thermistor to ground.
|
|
|
|
\begin{table}[ht]
|
|
\caption{PT100 FMEA Single Faults} % title of Table
|
|
\centering % used for centering table
|
|
\begin{tabular}{||l|c|c|l|l||}
|
|
\hline \hline
|
|
\textbf{Test} & \textbf{Result} & \textbf{Result } & \textbf{General} \\
|
|
\textbf{Case} & \textbf{sense +} & \textbf{sense -} & \textbf{Symtom Description} \\
|
|
% R & wire & res + & res - & description
|
|
\hline
|
|
\hline
|
|
$R_1$ SHORT & High & - & Value Out of Range Value \\ \hline
|
|
$R_1$ OPEN & Low & Low & Both values out of range \\ \hline
|
|
\hline
|
|
$R_p$ SHORT & Low & High & Both values out of range \\ \hline
|
|
$R_p$ OPEN & High & Low & Both values out of range \\ \hline
|
|
\hline
|
|
$R_2$ SHORT & - & Low & Value Out of Range Value \\
|
|
$R_2$ OPEN & High & High & Both values out of range \\ \hline
|
|
\hline
|
|
\end{tabular}
|
|
\label{ptfmea}
|
|
\end{table}
|
|
|
|
From table \ref{ptfmea} it can be seen that any component failure in the circuit
|
|
will cause a common symptom, that of one or more of the values being out of range.
|
|
Temperature range calculations and detailed calculations
|
|
on the effects of each test case are found in section \ref{pt100range}
|
|
and \ref{pt100temp}. So by defining an acceptable measurement/temperature range, and ensuring the
|
|
values are always within these bounds we can be confident that none of the
|
|
resistors in this circuit has failed.
|
|
|
|
|
|
\subsection{Single Fault Modes as PLD}
|
|
|
|
% Place in PLD diagram
|
|
|
|
\subsection{Range and PT100 Calculations}
|
|
\label{pt100temp}
|
|
PT100 resistors are designed to
|
|
have a resistance of ohms{100} at 0 \oc \cite{eurothermtables}.
|
|
A suitable `wider than to be expected range' was considered to be {-100\oc} to {300\oc}.
|
|
According to the Eurotherm PT100
|
|
tables \cite{eurothermtables}, this corresponded to the resistances \ohms{60.28}
|
|
and \ohms{212.02} respectively. From this the potential divider circuit can be
|
|
analysed and the maximum and minimum acceptable voltages determined.
|
|
These can be used as bounds results to apply the findings from the
|
|
PT100 FMEA analysis in section \ref{fmea}.
|
|
|
|
As the PT100 forms a potential divider with the \ohms{2k2} load resistors,
|
|
the upper and lower readings can be calculated thus:
|
|
|
|
$$ highreading = 5V.\frac{2k2+pt100}{2k2+2k2+pt100} $$
|
|
$$ lowreading = 5V.\frac{2k2}{2k2+2k2+pt100} $$
|
|
|
|
To convert these to twelve bit ADC (\adctw) counts:
|
|
|
|
$$ highreading = 2^{12}.\frac{2k2+pt100}{2k2+2k2+pt100} $$
|
|
$$ lowreading = 2^{12}.\frac{2k2}{2k2+2k2+pt100} $$
|
|
|
|
|
|
\begin{table}[ht]
|
|
\caption{PT100 Maximum and Minimum Values} % title of Table
|
|
\centering % used for centering table
|
|
\begin{tabular}{||c|c|c|l|l||}
|
|
\hline \hline
|
|
\textbf{Temperature} & \textbf{PT100 resistance} &
|
|
\textbf{Lower} & \textbf{Higher} & \textbf{Description} \\
|
|
\hline
|
|
{-100 \oc} & {\ohms{68.28}} & 2.46V & 2.53V & Boundary of \\
|
|
& & 2017\adctw & 2079\adctw & out of range LOW \\ \hline
|
|
{0 \oc} & {\ohms{100}} & 2.44V & 2.56V & Mid Range \\
|
|
& & 2002\adctw & 2094\adctw & \\ \hline
|
|
{+300 \oc} & {\ohms{212.02}} & 2.38V & 2.62V & Boundary of \\
|
|
& & 1954\adctw & 2142\adctw & out of range HIGH \\ \hline
|
|
\hline
|
|
\end{tabular}
|
|
\label{ptbounds}
|
|
\end{table}
|
|
|
|
Table \ref{ptbounds} gives ranges that determine correct operation. In fact it can be shown that
|
|
for any single error (short or opening of any resistor) this bounds check
|
|
will detect it.
|
|
|
|
\subsection{Proof of Out of Range Values for Failures}
|
|
\label{pt110range}
|
|
Using the temperature ranges defined above we can compare the voltages
|
|
we would get from the resistor failures to prove that they are
|
|
`out of range'. There are six cases and each will be examined in turn.
|
|
|
|
\subsubsection{ Voltages $R_1$ SHORT }
|
|
With pt100 at -100\oc
|
|
$$ highreading = 5V $$
|
|
Since the highreading or sense+ is directly connected to the 5V rail,
|
|
both temperature readings will be 5V..
|
|
$$ lowreading = 5V.\frac{2k2}{2k2+68\Omega} = 4.85V$$
|
|
With pt100 at the high end of the temperature range 300\oc.
|
|
$$ highreading = 5V $$
|
|
$$ lowreading = 5V.\frac{2k2}{2k2+212.02\Omega} = 4.56V$$
|
|
|
|
Thus with $R_1$ shorted both readingare outside the
|
|
proscribed range in table \ref{ptbounds}.
|
|
|
|
\subsubsection{ Voltages $R_1$ OPEN }
|
|
|
|
In this case the 5V rail is disconnected. All voltages read are 0V, and
|
|
therefore both readings are outside the
|
|
proscribed range in table \ref{ptbounds}.
|
|
|
|
\subsubsection{ Voltages $R_p$ SHORT }
|
|
|
|
Here the potential divider is simply between
|
|
the two 2k2 load resistors. Thus it will read a nominal;
|
|
2.5V.
|
|
|
|
Assuming the load resistors are
|
|
precision components, and then taking an absolute worst case of 1\% either way.
|
|
|
|
$$ 5V.\frac{2k2*0.99}{2k2*1.01+2k2*0.99} = 2.475V $$
|
|
|
|
$$ 5V.\frac{2k2*1.01}{2k2*1.01+2k2*0.99} = 2.525V $$
|
|
|
|
These readings both lie outside the proscribed range.
|
|
Also the sense+ and sense- readings would have the same value.
|
|
|
|
\subsubsection{ Voltages $R_p$ OPEN }
|
|
|
|
Here the potential divider is broken. The sense- will read 0V and the sense+ will
|
|
read 5V. Both readings are outside the proscribed range.
|
|
|
|
\subsubsection{ Voltages $R_2$ SHORT }
|
|
|
|
With pt100 at -100\oc
|
|
$$ lowreading = 0V $$
|
|
Since the lowreading or sense- is directly connected to the 0V rail,
|
|
both temperature readings will be 0V.
|
|
$$ lowreading = 5V.\frac{68\Omega}{2k2+68\Omega} = 0.15V$$
|
|
With pt100 at the high end of the temperature range 300\oc.
|
|
$$ highreading = 5V $$
|
|
$$ lowreading = 5V.\frac{212.02\Omega}{2k2+212.02\Omega} = 0.44V$$
|
|
|
|
Thus with $R_2$ shorted both readingare outside the
|
|
proscribed range in table \ref{ptbounds}.
|
|
\subsubsection{ Voltages $R_2$ OPEN }
|
|
Here there is no potential divider operating and both sense lines
|
|
will read 5V, outside of the proscibed range.
|
|
|
|
%\vbox{
|
|
%\subsubsection{Calculating Bounds: High Value : HP48 RPL}
|
|
%
|
|
%
|
|
%HP RPL calculator program to take pt100 resistance
|
|
%and convert to voltage and {\adctw} values.
|
|
%
|
|
%\begin{verbatim}
|
|
%<< -> p
|
|
% <<
|
|
% p 2200 + 2200 2200 + p + / 5 * DUP 5
|
|
% / 4096 *
|
|
% >>
|
|
%>>
|
|
%\end{verbatim}
|
|
%}
|
|
%
|
|
%\vbox{
|
|
%\subsubsection{Calculating Bounds: LOW Value : HP48 RPL}
|
|
%
|
|
%
|
|
%HP RPL calculator program to take pt100 resistance
|
|
%and convert to voltage and {\adctw} values.
|
|
%
|
|
%\begin{verbatim}
|
|
%<< -> p
|
|
% <<
|
|
% p 2200 2200 p 2200 + + / 5 * DUP 5
|
|
% / 4096 *
|
|
% >>
|
|
%>>
|
|
%\end{verbatim}
|
|
%}
|
|
%
|
|
%\subsection{Implementation of Four Wire Circuit}
|
|
%
|
|
%A standard 4 wire PT100\cite[pp 992]{aoe} circuit is read by
|
|
%ports on the 12 bit ADC of the PIC18F2523\cite{pic18f2523}.
|
|
%Three readings are taken. A reading to confirm the voltage level
|
|
%over $R_2$ is taken,
|
|
%from which the current can be determined.
|
|
%The two sense lines then give the voltage over the PT100 thermistor.
|
|
%As we know the current flowing through it we can determine the
|
|
%resistance.
|
|
%
|
|
%After verification (PT100 voltages/readings in range etc) the temperature
|
|
%value is determined by interpolation via the PT100 tables \cite{eurothermtables}.
|
|
%First order low pass filtering is then applied to smooth the value.
|
|
%\section{Water Level Readings - \ft Inputs}
|
|
%\label{wl}
|
|
%After h/w revision 0.4, water level sensor \ft connections are wired to the TDS daughterboard,
|
|
%but are passed to the main unit via a multiplexer, and connect to the
|
|
%14 pin harwin (to PIN 13 of JP1 \cite{pcbAI222562}).
|
|
%
|
|
%The safety critical \ft water~level readings are thus handled in the \wlc.
|
|
%
|
|
|
|
\subsection{Single Fault FMEA Analysis of PT100 Four wire circuit}
|
|
typeset in {\Huge \LaTeX} \today
|
|
|