250 lines
9.6 KiB
TeX
250 lines
9.6 KiB
TeX
\documentclass[a4paper,10pt]{article}
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\usepackage[utf8x]{inputenc}
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\usepackage{graphicx}
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\usepackage{fancyhdr}
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\usepackage{lastpage}
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\clubpenalty=300
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\widowpenalty=300
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%
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% Make the revision and doc number macro's then they are defined in one place
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\newcommand{\rev}{PA5}
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\newcommand{\etcdoc}{ HR222975 }
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\newcommand{\wlc}{{Water~Level~Controller~Unit}}
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\newcommand{\ft}{{\em 4 $\rightarrow$ 20mA } }
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\newcommand{\tds}{TDS Daughterboard}
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\newcommand{\oc}{$^{o}{C}$}
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\newcommand{\adctw}{{${\mathcal{ADC}}_{12}$}}
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\newcommand{\adcten}{{${\mathcal{ADC}}_{10}$}}
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\newcommand{\ohms}[1]{\ensuremath{#1\Omega}}
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\title{TDS Daughter Board Design Notes \\ \etcdoc revision \rev}
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\author{R.P. Clark}
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\begin{document}
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\pagenumbering{roman}
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\pagestyle{fancy}
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\maketitle
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\lhead{}
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\chead{\textbf{ETC6211: Total Dissolved Solids Daughterboard}}
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\rhead{}
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\rfoot{\thepage}
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\cfoot{}
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\lfoot{\textbf{\small ETC Document Number: \etcdoc Revision: \rev}}
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\maketitle
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\begin{abstract}
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The PT100, or platinum wire \ohms{100} sensor is
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a wisely used industrial temperature sensor that is
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are slowly replacing the use of thermocouples in many
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industrial applications below 600\oc, due to high accuracy\cite{aoe}.
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This chapter looks at the most common configuration, the
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four wire circuit, and analyses it from an FMEA perspective twice.
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Once considering single faults (cardinality constrained powerset of 1) and then again, considering the
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possibility of double simultaneous faults (cardinality constrained powerset of 2).
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The analysis is performed using Propositional Logic
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diagrasms to aid in the reasoning process, which takes
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the failure modes of the components, and produces a
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failure mode model for the circuit as a whole.
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Thus after the analysis the PT100 temperature sensing circuit, may be veiwed
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from an FMEA persepective as a component itsself, with a set of know failure modes.
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\end{abstract}
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\section{Overview of PT100 four wire circuit}
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The PT100 four wire circuit consists of teo resistors supplying
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a current to a third, the thermistor or PT100. By measuring volatges
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from sections of this circuit forming potential dividers, we can determine the
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current resistance of the platinum wire sensor. The resistance
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of this is directly related to temperature, and may be determined by
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look-up tables or a suitable polynomial expression.
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\subsection{Accuracy despite variable resistance in cables}
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For electronic and accuracy reasons the four wire circiut is used
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because of resistance in the cables. Resitance from the supply
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causes a slight voltage
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drop in the supply to the PT100. As no significant current
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is carried by the two `sense' lines the resistance back to the ADC
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causes only a negligible voltage drop. The current flowing though the
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whole circuit can be measured on the PCB by reading a third
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sense voltage from one of the load resistors. Knowing the current flowing
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through the circuit
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and knowing the voltage drop over the PT100, we can calculate its
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resistance by ohms law $V=I.R$, $R=\frac{I}{V}$.
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Thus a little loss of supply current due to resistance in the cables
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does not impinge on accuracy.
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The resistance to temperature conversion is achieved
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through the published PT100 tables\cite{eurothermtables}.
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\section{Safety case for 4 wire circuit}
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This sub-section looks at the behaviour of the PT100 four wire circuit
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for the effects of component failures.
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All components have a set of known `failure modes'.
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In other words we know that a given component can fail in several distict ways.
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Studies have been published which list common component types
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and their sets of failure modes, often with MTTF statistics \cite{mil1991}.
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Thus for each component, an analysis is made for each of it failure modes,
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with respect to its effect on the
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circuit. Each one of these scenarios is termed a `test case'.
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The resultant circuit behaviour for each of these test cases is noted.
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The worst case for this type of
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analysis would be a fault that we cannot detect.
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Where this occurs a circuit re-design is probably the only sensible course of action.
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\subsection{Single Fault FMEA Analysis of PT100 Four wire circuit}
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\label{fmea}
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Looking at this circuit, it simply consists of three resistors.
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Resistors according to the DOD Electronic component fault handbook
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1991, fail by either going OPEN or SHORT circuit \cite{mil1991}.
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%Should wires become disconnected these will have the same effect as
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%given resistors going open.
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For the purpose of his analyis;
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$R_{1}$ is the \ohms{2k2} from 5V to the thermistor,
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$R_p$ is the PT100 thermistor and $R_{2}$ connects the thermistor to ground.
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\begin{table}[ht]
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\caption{PT100 FMEA Single Faults} % title of Table
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\centering % used for centering table
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\begin{tabular}{||l|c|c|l|l||}
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\hline \hline
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\textbf{Test} & \textbf{Result} & \textbf{Result } & \textbf{General} \\
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\textbf{Case} & \textbf{sense +} & \textbf{sense -} & \textbf{Symtom Description} \\
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% R & wire & res + & res - & description
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\hline
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\hline
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$R_1$ SHORT & High & - & Value Out of Range Value \\ \hline
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$R_1$ OPEN & Low & Low & Both values out of range \\ \hline
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\hline
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$R_p$ SHORT & Low & High & Both values out of range \\ \hline
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$R_p$ OPEN & High & Low & Both values out of range \\ \hline
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\hline
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$R_2$ SHORT & - & Low & Value Out of Range Value \\
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$R_2$ OPEN & High & High & Both values out of range \\ \hline
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\hline
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\end{tabular}
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\label{ptfmea}
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\end{table}
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From table \ref{ptfmea} it can be seen that any component failure in the circuit
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will cause a common symptom, that of one or more of the values being out of range.
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So by defining an acceptable measurement/temperature range, and ensuring the
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values are always within these bounds we can be confident that none of the
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resistors in this circuit has failed.
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\subsection{Single Fault Modes as PLD}
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% Place in PLD diagram
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\subsection{Range and PT100 Calculations}
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PT100 resistors are designed to
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have a resistance of ohms{100} at 0 \oc \cite{eurothermtables}.
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A suitable `wider than to be expected range' was considered to be {-100\oc} to {300\oc}.
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According to the Eurotherm PT100
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tables \cite{eurothermtables}, this corresponded to the resistances \ohms{60.28}
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and \ohms{212.02} respectively. From this the potential divider circuit can be
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analysed and the maximum and minimum acceptable voltages determined.
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These can be used as bounds results to apply the findings from the
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PT100 FMEA analysis in section \ref{fmea}.
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As the PT100 forms a potential divider with the \ohms{2k2} load resistors,
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the upper and lower readings can be calculated thus:
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$$ highreading = 5V.\frac{2k2+pt100}{2k2+2k2+pt100} $$
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$$ lowreading = 5V.\frac{2k2}{2k2+2k2+pt100} $$
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To convert these to twelve bit ADC (\adctw) counts:
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$$ highreading = 2^{12}.\frac{2k2+pt100}{2k2+2k2+pt100} $$
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$$ lowreading = 2^{12}.\frac{2k2}{2k2+2k2+pt100} $$
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\begin{table}[ht]
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\caption{PT100 Maximum and Minimum Values} % title of Table
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\centering % used for centering table
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\begin{tabular}{||c|c|c|l|l||}
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\hline \hline
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\textbf{Temperature} & \textbf{PT100 resistance} &
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\textbf{Lower} & \textbf{Higher} & \textbf{Description} \\
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\hline
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{-100 \oc} & {\ohms{68.28}} & 2.46V & 2.53V & Boundary of \\
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& & 2017\adctw & 2079\adctw & out of range LOW \\ \hline
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{0 \oc} & {\ohms{100}} & 2.44V & 2.56V & Mid Range \\
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& & 2002\adctw & 2094\adctw & \\ \hline
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{+300 \oc} & {\ohms{212.02}} & 2.38V & 2.62V & Boundary of \\
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& & 1954\adctw & 2142\adctw & out of range HIGH \\ \hline
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\hline
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\end{tabular}
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\label{ptbounds}
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\end{table}
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Table \ref{ptbounds} gives ranges that determine correct operation. In fact it can be shown that
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for any single error (short or opening of any resistor) this bounds check
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will detect it.
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%\vbox{
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%\subsubsection{Calculating Bounds: High Value : HP48 RPL}
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%
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%
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%HP RPL calculator program to take pt100 resistance
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%and convert to voltage and {\adctw} values.
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%
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%\begin{verbatim}
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%<< -> p
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% <<
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% p 2200 + 2200 2200 + p + / 5 * DUP 5
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% / 4096 *
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% >>
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%>>
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%\end{verbatim}
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%}
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%
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%\vbox{
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%\subsubsection{Calculating Bounds: LOW Value : HP48 RPL}
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%
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%
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%HP RPL calculator program to take pt100 resistance
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%and convert to voltage and {\adctw} values.
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%
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%\begin{verbatim}
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%<< -> p
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% <<
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% p 2200 2200 p 2200 + + / 5 * DUP 5
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% / 4096 *
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% >>
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%>>
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%\end{verbatim}
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%}
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%
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%\subsection{Implementation of Four Wire Circuit}
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%
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%A standard 4 wire PT100\cite[pp 992]{aoe} circuit is read by
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%ports on the 12 bit ADC of the PIC18F2523\cite{pic18f2523}.
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%Three readings are taken. A reading to confirm the voltage level
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%over $R_2$ is taken,
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%from which the current can be determined.
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%The two sense lines then give the voltage over the PT100 thermistor.
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%As we know the current flowing through it we can determine the
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%resistance.
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%
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%After verification (PT100 voltages/readings in range etc) the temperature
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%value is determined by interpolation via the PT100 tables \cite{eurothermtables}.
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%First order low pass filtering is then applied to smooth the value.
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%\section{Water Level Readings - \ft Inputs}
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%\label{wl}
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%After h/w revision 0.4, water level sensor \ft connections are wired to the TDS daughterboard,
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%but are passed to the main unit via a multiplexer, and connect to the
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%14 pin harwin (to PIN 13 of JP1 \cite{pcbAI222562}).
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%
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%The safety critical \ft water~level readings are thus handled in the \wlc.
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%
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\subsection{Single Fault FMEA Analysis of PT100 Four wire circuit}
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typeset in {\Huge \LaTeX} \today
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