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LaTeX Error: Environment abstract undefined. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.4 \begin{abstract} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + + +! LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.5 T + he PT100, or platinum wire \ohms{100} sensor is +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + +Missing character: There is no T in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no P in font nullfont! +Missing character: There is no T in font nullfont! +Missing character: There is no 1 in font nullfont! +Missing character: There is no 0 in font nullfont! +Missing character: There is no 0 in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no w in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +! Undefined control sequence. +l.5 The PT100, or platinum wire \ohms + {100} sensor is +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no 1 in font nullfont! +Missing character: There is no 0 in font nullfont! +Missing character: There is no 0 in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no w in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no y in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no w in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no y in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no y in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no b in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no w in font nullfont! +Missing character: There is no 6 in font nullfont! +Missing character: There is no 0 in font nullfont! +Missing character: There is no 0 in font nullfont! +! Undefined control sequence. +l.8 industrial applications below 600\oc + , due to high accuracy\cite{aoe}. +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no , in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no y in font nullfont! +Missing character: There is no [ in font nullfont! +\citation{aoe} +! Undefined control sequence. + ...: Citation `\@citeb ' on page \thepage + \space undefined\on@line . +l.8 ...elow 600\oc, due to high accuracy\cite{aoe} + . +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + + +LaTeX Warning: Citation `aoe' on page undefined on input line 8. + +Missing character: There is no ] in font nullfont! +Missing character: There is no . in font nullfont! + +Overfull \hbox (20.0pt too wide) in paragraph at lines 5--9 +[] + [] + + +Overfull \hbox (5.43053pt too wide) in paragraph at lines 5--9 +[] + [] + + +! LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.10 T + his chapter looks at the most common configuration, the +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + +Missing character: There is no T in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no k in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no t in font nullfont! 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+Missing character: There is no s in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no 2 in font nullfont! +Missing character: There is no ) in font nullfont! +Missing character: There is no . in font nullfont! + +Overfull \hbox (20.0pt too wide) in paragraph at lines 10--14 +[] + [] + + +! LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.15 T + he analysis is performed using Propositional Logic +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + +Missing character: There is no T in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no y in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no o in font nullfont! 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LaTeX Error: \begin{document} ended by \end{abstract}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.22 \end{abstract} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + + +! LaTeX Error: Environment figure undefined. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.25 \begin{figure} + [h] +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + + +! LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.25 \begin{figure}[ + h] +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + +Missing character: There is no [ in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no ] in font nullfont! +! 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LaTeX Error: \caption outside float. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.29 \caption + {PT100 four wire circuit} +You're in trouble here. 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LaTeX Error: \begin{document} ended by \end{figure}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.31 \end{figure} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + + +Overfull \hbox (20.0pt too wide) in paragraph at lines 25--32 +[] + [] + +! Undefined control sequence. +l.34 \section + {Overview of PT100 four wire circuit} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + + +! LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.34 \section{O + verview of PT100 four wire circuit} +You're in trouble here. 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LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.36 T + he PT100 four wire circuit consists of teo resistors supplying +You're in trouble here. 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LaTeX Error: Environment figure undefined. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.44 \begin{figure} + [h] +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + + +! LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.44 \begin{figure}[ + h] +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + +Missing character: There is no [ in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no ] in font nullfont! +! Undefined control sequence. +l.46 \includegraphics + [width=150pt,bb=0 0 273 483,keepaspectratio=true]{./pt... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). 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LaTeX Error: \caption outside float. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.48 \caption + {PT100 expected voltage range} +You're in trouble here. 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LaTeX Error: \begin{document} ended by \end{figure}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.50 \end{figure} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + + +Overfull \hbox (20.0pt too wide) in paragraph at lines 44--51 +[] + [] + + +! LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.55 T + he voltage ranges we expect from from this three stage potential divider +You're in trouble here. 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Undefined control sequence. + ...nce `fig:pt100vrange' on page \thepage + \space undefined\on@line . +l.56 are shown in figure \ref{fig:pt100vrange} + . Note that there is +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). 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Undefined control sequence. +l.59 \subsection + {Accuracy despite variable resistance in cables} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + + +! LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.59 \subsection{A + ccuracy despite variable resistance in cables} +You're in trouble here. 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LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.61 F + or electronic and accuracy reasons the four wire circiut is used +You're in trouble here. 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Undefined control sequence. + ...: Citation `\@citeb ' on page \thepage + \space undefined\on@line . +l.75 ...blished PT100 tables\cite{eurothermtables} + . +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + + +LaTeX Warning: Citation `eurothermtables' on page undefined on input line 75. + +Missing character: There is no ] in font nullfont! +Missing character: There is no . in font nullfont! + +Overfull \hbox (20.0pt too wide) in paragraph at lines 61--76 +[] + [] + + +Overfull \hbox (18.61107pt too wide) in paragraph at lines 61--76 +\OML/cmm/m/it/10 V \OT1/cmr/m/n/10 = + [] + + +Overfull \hbox (15.62848pt too wide) in paragraph at lines 61--76 +\OML/cmm/m/it/10 I:R$ + [] + + +Overfull \hbox (18.22566pt too wide) in paragraph at lines 61--76 +\OML/cmm/m/it/10 R \OT1/cmr/m/n/10 = + [] + + +Overfull \hbox (8.84447pt too wide) in paragraph at lines 61--76 +[]$ + [] + + +Overfull \hbox (5.43053pt too wide) in paragraph at lines 61--76 +[] + [] + +! Undefined control sequence. +l.77 \section + {Safety case for 4 wire circuit} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + + +! LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.77 \section{S + afety case for 4 wire circuit} +You're in trouble here. 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LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.79 T + his sub-section looks at the behaviour of the PT100 four wire circuit +You're in trouble here. 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Undefined control sequence. + ...: Citation `\@citeb ' on page \thepage + \space undefined\on@line . +l.84 ... often with MTTF statistics \cite{mil1991} + . +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). 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Undefined control sequence. +l.95 \subsection + {Single Fault FMEA Analysis of PT100 Four wire circuit} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + + +! LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.95 \subsection{S + ingle Fault FMEA Analysis of PT100 Four wire circuit} +You're in trouble here. 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Undefined control sequence. +l.143 \subsection + {Range and PT100 Calculations} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + + +! LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.143 \subsection{R + ange and PT100 Calculations} +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + +Missing character: There is no R in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no P in font nullfont! +Missing character: There is no T in font nullfont! +Missing character: There is no 1 in font nullfont! +Missing character: There is no 0 in font nullfont! +Missing character: There is no 0 in font nullfont! +Missing character: There is no C in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no P in font nullfont! +Missing character: There is no T in font nullfont! +Missing character: There is no 1 in font nullfont! +Missing character: There is no 0 in font nullfont! +Missing character: There is no 0 in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no 1 in font nullfont! +Missing character: There is no 0 in font nullfont! +Missing character: There is no 0 in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no 0 in font nullfont! +! Undefined control sequence. +l.146 have a resistance of ohms{100} at 0 \oc + \cite{eurothermtables}. +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no [ in font nullfont! +\citation{eurothermtables} +! Undefined control sequence. + ...: Citation `\@citeb ' on page \thepage + \space undefined\on@line . +l.146 ...hms{100} at 0 \oc \cite{eurothermtables} + . +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + + +LaTeX Warning: Citation `eurothermtables' on page undefined on input line 146. + + +Missing character: There is no ] in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no A in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no b in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no ` in font nullfont! +Missing character: There is no w in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no b in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no x in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no ' in font nullfont! +Missing character: There is no w in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no b in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no - in font nullfont! +Missing character: There is no 1 in font nullfont! +Missing character: There is no 0 in font nullfont! +Missing character: There is no 0 in font nullfont! +! Undefined control sequence. +l.147 ...cted range' was considered to be {-100\oc + } to {300\oc}. +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no t in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no 3 in font nullfont! +Missing character: There is no 0 in font nullfont! +Missing character: There is no 0 in font nullfont! +! Undefined control sequence. +l.147 ...was considered to be {-100\oc} to {300\oc + }. +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no . in font nullfont! +Missing character: There is no A in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no E in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no P in font nullfont! +Missing character: There is no T in font nullfont! +Missing character: There is no 1 in font nullfont! +Missing character: There is no 0 in font nullfont! +Missing character: There is no 0 in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no b in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no [ in font nullfont! +\citation{eurothermtables} +! Undefined control sequence. + ...: Citation `\@citeb ' on page \thepage + \space undefined\on@line . +l.149 tables \cite{eurothermtables} + , this corresponded to the resistances \o... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + + +LaTeX Warning: Citation `eurothermtables' on page undefined on input line 149. + + +Missing character: There is no ] in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +! Undefined control sequence. +l.149 ...his corresponded to the resistances \ohms + {60.28} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no 6 in font nullfont! +Missing character: There is no 0 in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no 2 in font nullfont! +Missing character: There is no 8 in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no d in font nullfont! +! Undefined control sequence. +l.150 and \ohms + {212.02} respectively. From this the potential divider circui... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no 2 in font nullfont! +Missing character: There is no 1 in font nullfont! +Missing character: There is no 2 in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no 0 in font nullfont! +Missing character: There is no 2 in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no y in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no F in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no b in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no y in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no x in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no b in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no T in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no b in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no b in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no y in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no P in font nullfont! +Missing character: There is no T in font nullfont! +Missing character: There is no 1 in font nullfont! +Missing character: There is no 0 in font nullfont! +Missing character: There is no 0 in font nullfont! +Missing character: There is no F in font nullfont! +Missing character: There is no M in font nullfont! +Missing character: There is no E in font nullfont! +Missing character: There is no A in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no y in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +! Undefined control sequence. + ...ing: Reference `fmea' on page \thepage + \space undefined\on@line . +l.153 PT100 FMEA analysis in section \ref{fmea} + . +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + + +LaTeX Warning: Reference `fmea' on page undefined on input line 153. + +Missing character: There is no . in font nullfont! + +Overfull \hbox (20.0pt too wide) in paragraph at lines 143--154 +[] + [] + + +Overfull \hbox (5.43053pt too wide) in paragraph at lines 143--154 +[] + [] + + +Overfull \hbox (5.43053pt too wide) in paragraph at lines 143--154 +[] + [] + + +Overfull \hbox (10.86105pt too wide) in paragraph at lines 143--154 +[] + [] + + +! LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.155 A + s the PT100 forms a potential divider with the \ohms{2k2} load resis... + +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + +Missing character: There is no A in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no P in font nullfont! +Missing character: There is no T in font nullfont! +Missing character: There is no 1 in font nullfont! +Missing character: There is no 0 in font nullfont! +Missing character: There is no 0 in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no w in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no e in font nullfont! +! Undefined control sequence. +l.155 ... forms a potential divider with the \ohms + {2k2} load resistors, +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no 2 in font nullfont! +Missing character: There is no k in font nullfont! +Missing character: There is no 2 in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no w in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no b in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no : in font nullfont! + +Overfull \hbox (20.0pt too wide) in paragraph at lines 155--157 +[] + [] + + +! LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.158 $ + $ highreading = 5V.\frac{2k2+pt100}{2k2+2k2+pt100} $$ +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + + +Overfull \hbox (20.0pt too wide) in paragraph at lines 158--158 +[] + [] + + +Overfull \hbox (163.63742pt too wide) detected at line 158 +\OML/cmm/m/it/10 highreading \OT1/cmr/m/n/10 = 5\OML/cmm/m/it/10 V:[] + [] + + +Overfull \hbox (158.99672pt too wide) detected at line 159 +\OML/cmm/m/it/10 lowreading \OT1/cmr/m/n/10 = 5\OML/cmm/m/it/10 V:[] + [] + + +! LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.161 T + o convert these to twelve bit ADC (\adctw) counts: +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + +Missing character: There is no T in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no w in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no b in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no A in font nullfont! +Missing character: There is no D in font nullfont! +Missing character: There is no C in font nullfont! +Missing character: There is no ( in font nullfont! +! Undefined control sequence. +l.161 To convert these to twelve bit ADC (\adctw + ) counts: +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no ) in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no : in font nullfont! + +Overfull \hbox (20.0pt too wide) in paragraph at lines 161--162 +[] + [] + + +! LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.163 $ + $ highreading = 2^{12}.\frac{2k2+pt100}{2k2+2k2+pt100} $$ +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + + +Overfull \hbox (20.0pt too wide) in paragraph at lines 163--163 +[] + [] + + +Overfull \hbox (165.7208pt too wide) detected at line 163 +\OML/cmm/m/it/10 highreading \OT1/cmr/m/n/10 = 2[]\OML/cmm/m/it/10 :[] + [] + + +Overfull \hbox (161.0801pt too wide) detected at line 164 +\OML/cmm/m/it/10 lowreading \OT1/cmr/m/n/10 = 2[]\OML/cmm/m/it/10 :[] + [] + + +! LaTeX Error: Environment table undefined. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.167 \begin{table} + [ht] +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + + +! LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.167 \begin{table}[ + ht] +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + +Missing character: There is no [ in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no ] in font nullfont! + +! LaTeX Error: \caption outside float. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.168 \caption + {PT100 Maximum and Minimum Values} % title of Table +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + +Missing character: There is no P in font nullfont! +Missing character: There is no T in font nullfont! +Missing character: There is no 1 in font nullfont! +Missing character: There is no 0 in font nullfont! +Missing character: There is no 0 in font nullfont! +Missing character: There is no M in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no x in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no M in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no V in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no - in font nullfont! +Missing character: There is no 1 in font nullfont! +Missing character: There is no 0 in font nullfont! +Missing character: There is no 0 in font nullfont! +! Undefined control sequence. +l.175 {-100 \oc + } & {\ohms{68.28}} & 2.46V & 2.53V & Bounda... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Undefined control sequence. +l.175 {-100 \oc} & {\ohms + {68.28}} & 2.46V & 2.53V & Bounda... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no 6 in font nullfont! +Missing character: There is no 8 in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no 2 in font nullfont! +Missing character: There is no 8 in font nullfont! +Missing character: There is no 2 in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no 4 in font nullfont! +Missing character: There is no 6 in font nullfont! +Missing character: There is no V in font nullfont! +Missing character: There is no 2 in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no 5 in font nullfont! +Missing character: There is no 3 in font nullfont! +Missing character: There is no V in font nullfont! +Missing character: There is no B in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no y in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no 2 in font nullfont! +Missing character: There is no 0 in font nullfont! +Missing character: There is no 1 in font nullfont! +Missing character: There is no 7 in font nullfont! +! Undefined control sequence. +l.176 & & 2017\adctw + & 2079\adctw & out ... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no 2 in font nullfont! +Missing character: There is no 0 in font nullfont! +Missing character: There is no 7 in font nullfont! +Missing character: There is no 9 in font nullfont! +! Undefined control sequence. +l.176 ... & 2017\adctw & 2079\adctw + & out of range LOW \\ ... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no o in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no L in font nullfont! +Missing character: There is no O in font nullfont! +Missing character: There is no W in font nullfont! +Missing character: There is no 0 in font nullfont! +! Undefined control sequence. +l.177 {0 \oc + } & {\ohms{100}} & 2.44V & 2.56V & Mid R... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Undefined control sequence. +l.177 {0 \oc} & {\ohms + {100}} & 2.44V & 2.56V & Mid R... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no 1 in font nullfont! +Missing character: There is no 0 in font nullfont! +Missing character: There is no 0 in font nullfont! +Missing character: There is no 2 in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no 4 in font nullfont! +Missing character: There is no 4 in font nullfont! +Missing character: There is no V in font nullfont! +Missing character: There is no 2 in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no 5 in font nullfont! +Missing character: There is no 6 in font nullfont! +Missing character: There is no V in font nullfont! +Missing character: There is no M in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no R in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no 2 in font nullfont! +Missing character: There is no 0 in font nullfont! +Missing character: There is no 0 in font nullfont! +Missing character: There is no 2 in font nullfont! +! Undefined control sequence. +l.178 & & 2002\adctw + & 2094\adctw & ... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no 2 in font nullfont! +Missing character: There is no 0 in font nullfont! +Missing character: There is no 9 in font nullfont! +Missing character: There is no 4 in font nullfont! +! Undefined control sequence. +l.178 ... & 2002\adctw & 2094\adctw + & \\ \hline +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no + in font nullfont! +Missing character: There is no 3 in font nullfont! +Missing character: There is no 0 in font nullfont! +Missing character: There is no 0 in font nullfont! +! Undefined control sequence. +l.179 {+300 \oc + } & {\ohms{212.02}} & 2.38V & 2.62V & Boun... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Undefined control sequence. +l.179 {+300 \oc} & {\ohms + {212.02}} & 2.38V & 2.62V & Boun... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no 2 in font nullfont! +Missing character: There is no 1 in font nullfont! +Missing character: There is no 2 in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no 0 in font nullfont! +Missing character: There is no 2 in font nullfont! +Missing character: There is no 2 in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no 3 in font nullfont! +Missing character: There is no 8 in font nullfont! +Missing character: There is no V in font nullfont! +Missing character: There is no 2 in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no 6 in font nullfont! +Missing character: There is no 2 in font nullfont! +Missing character: There is no V in font nullfont! +Missing character: There is no B in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no y in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no 1 in font nullfont! +Missing character: There is no 9 in font nullfont! +Missing character: There is no 5 in font nullfont! +Missing character: There is no 4 in font nullfont! +! Undefined control sequence. +l.180 & & 1954\adctw + & 2142\adctw & out... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no 2 in font nullfont! +Missing character: There is no 1 in font nullfont! +Missing character: There is no 4 in font nullfont! +Missing character: There is no 2 in font nullfont! +! Undefined control sequence. +l.180 ... & 1954\adctw & 2142\adctw + & out of range HIGH \... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no o in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no H in font nullfont! +Missing character: There is no I in font nullfont! +Missing character: There is no G in font nullfont! +Missing character: There is no H in font nullfont! + +! LaTeX Error: \begin{document} ended by \end{table}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.184 \end{table} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + + +Overfull \hbox (20.0pt too wide) in paragraph at lines 167--185 +[] + [] + + +Overfull \hbox (273.6625pt too wide) in paragraph at lines 167--185 +[] + [] + + +! LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.186 T + able \ref{ptbounds} gives ranges that determine correct operation. In... + +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + +Missing character: There is no T in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no b in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +! Undefined control sequence. + ... Reference `ptbounds' on page \thepage + \space undefined\on@line . +l.186 Table \ref{ptbounds} + gives ranges that determine correct operation. In... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + + +LaTeX Warning: Reference `ptbounds' on page undefined on input line 186. + +Missing character: There is no g in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no I in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no b in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no w in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no y in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no ( in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no f in font nullfont! 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+ +Overfull \hbox (20.0pt too wide) in paragraph at lines 186--189 +[] + [] + + +Overfull \hbox (10.86105pt too wide) in paragraph at lines 186--189 +[] + [] + +! Undefined control sequence. +l.190 \subsection + {Proof of Out of Range Values for Failures} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + + +! LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.190 \subsection{P + roof of Out of Range Values for Failures} +You're in trouble here. 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Undefined control sequence. +l.196 \subsubsection + { Voltages $R_1$ SHORT } +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + + +! LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.196 \subsubsection{ V + oltages $R_1$ SHORT } +You're in trouble here. 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Undefined control sequence. +l.202 ... high end of the temperature range 300\oc + . +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no . in font nullfont! + +Overfull \hbox (80.99788pt too wide) detected at line 203 +\OML/cmm/m/it/10 highreading \OT1/cmr/m/n/10 = 5\OML/cmm/m/it/10 V + [] + + +Overfull \hbox (181.778pt too wide) detected at line 204 +\OML/cmm/m/it/10 lowreading \OT1/cmr/m/n/10 = 5\OML/cmm/m/it/10 V:[] \OT1/cmr/m +/n/10 = 4\OML/cmm/m/it/10 :\OT1/cmr/m/n/10 56\OML/cmm/m/it/10 V + [] + + +! LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.206 T + hus with $R_1$ shorted both readingare outside the +You're in trouble here. 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Undefined control sequence. + ... Reference `ptbounds' on page \thepage + \space undefined\on@line . +l.207 proscribed range in table \ref{ptbounds} + . +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + + +LaTeX Warning: Reference `ptbounds' on page undefined on input line 207. + +Missing character: There is no . in font nullfont! + +Overfull \hbox (20.0pt too wide) in paragraph at lines 206--208 +[] + [] + + +Overfull \hbox (12.07903pt too wide) in paragraph at lines 206--208 +\OML/cmm/m/it/10 R[]$ + [] + + +Overfull \hbox (10.86105pt too wide) in paragraph at lines 206--208 +[] + [] + +! Undefined control sequence. +l.209 \subsubsection + { Voltages $R_1$ OPEN } +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + + +! LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.209 \subsubsection{ V + oltages $R_1$ OPEN } +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + +Missing character: There is no V in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no O in font nullfont! +Missing character: There is no P in font nullfont! +Missing character: There is no E in font nullfont! +Missing character: There is no N in font nullfont! + +Overfull \hbox (20.0pt too wide) in paragraph at lines 209--210 +[] + [] + + +Overfull \hbox (12.07903pt too wide) in paragraph at lines 209--210 +\OML/cmm/m/it/10 R[]$ + [] + + +! LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.211 I + n this case the 5V rail is disconnected. All voltages read are 0V, and +You're in trouble here. 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Undefined control sequence. + ... Reference `ptbounds' on page \thepage + \space undefined\on@line . +l.213 proscribed range in table \ref{ptbounds} + . +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + + +LaTeX Warning: Reference `ptbounds' on page undefined on input line 213. + +Missing character: There is no . in font nullfont! + +Overfull \hbox (20.0pt too wide) in paragraph at lines 211--214 +[] + [] + + +Overfull \hbox (10.86105pt too wide) in paragraph at lines 211--214 +[] + [] + +! Undefined control sequence. +l.215 \subsubsection + { Voltages $R_p$ SHORT } +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + + +! LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.215 \subsubsection{ V + oltages $R_p$ SHORT } +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + +Missing character: There is no V in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no S in font nullfont! +Missing character: There is no H in font nullfont! +Missing character: There is no O in font nullfont! +Missing character: There is no R in font nullfont! +Missing character: There is no T in font nullfont! + +Overfull \hbox (20.0pt too wide) in paragraph at lines 215--216 +[] + [] + + +Overfull \hbox (12.21524pt too wide) in paragraph at lines 215--216 +\OML/cmm/m/it/10 R[]$ + [] + + +! LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.217 H + ere the potential divider is simply between +You're in trouble here. 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LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.221 A + ssuming the load resistors are +You're in trouble here. 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LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.224 $ + $ 5V.\frac{2k2*0.99}{2k2*1.01+2k2*0.99} = 2.475V $$ +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + + +Overfull \hbox (20.0pt too wide) in paragraph at lines 224--224 +[] + [] + + +Overfull \hbox (158.44156pt too wide) detected at line 224 +\OT1/cmr/m/n/10 5\OML/cmm/m/it/10 V:[] \OT1/cmr/m/n/10 = 2\OML/cmm/m/it/10 :\OT +1/cmr/m/n/10 475\OML/cmm/m/it/10 V + [] + + +! LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.226 $ + $ 5V.\frac{2k2*1.01}{2k2*1.01+2k2*0.99} = 2.525V $$ +You're in trouble here. 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+ +Overfull \hbox (20.0pt too wide) in paragraph at lines 228--230 +[] + [] + +! Undefined control sequence. +l.231 \subsubsection + { Voltages $R_p$ OPEN } +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + + +! LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.231 \subsubsection{ V + oltages $R_p$ OPEN } +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + +Missing character: There is no V in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no O in font nullfont! +Missing character: There is no P in font nullfont! +Missing character: There is no E in font nullfont! +Missing character: There is no N in font nullfont! + +Overfull \hbox (20.0pt too wide) in paragraph at lines 231--232 +[] + [] + + +Overfull \hbox (12.21524pt too wide) in paragraph at lines 231--232 +\OML/cmm/m/it/10 R[]$ + [] + + +! LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.233 H + ere the potential divider is broken. The sense- will read 0V and the ... + +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + +Missing character: There is no H in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no i in font nullfont! 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Undefined control sequence. +l.236 \subsubsection + { Voltages $R_2$ SHORT } +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + + +! LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.236 \subsubsection{ V + oltages $R_2$ SHORT } +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + +Missing character: There is no V in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no S in font nullfont! +Missing character: There is no H in font nullfont! +Missing character: There is no O in font nullfont! +Missing character: There is no R in font nullfont! +Missing character: There is no T in font nullfont! + +Overfull \hbox (20.0pt too wide) in paragraph at lines 236--237 +[] + [] + + +Overfull \hbox (12.07903pt too wide) in paragraph at lines 236--237 +\OML/cmm/m/it/10 R[]$ + [] + + +! LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.238 W + ith pt100 at -100\oc +You're in trouble here. 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If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + + +Overfull \hbox (20.0pt too wide) in paragraph at lines 238--239 +[] + [] + + +Overfull \hbox (76.35718pt too wide) detected at line 239 +\OML/cmm/m/it/10 lowreading \OT1/cmr/m/n/10 = 0\OML/cmm/m/it/10 V + [] + +Missing character: There is no S in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no w in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no a in font nullfont! 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Undefined control sequence. +l.243 ... high end of the temperature range 300\oc + . +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no . in font nullfont! + +Overfull \hbox (80.99788pt too wide) detected at line 244 +\OML/cmm/m/it/10 highreading \OT1/cmr/m/n/10 = 5\OML/cmm/m/it/10 V + [] + + +Overfull \hbox (181.778pt too wide) detected at line 245 +\OML/cmm/m/it/10 lowreading \OT1/cmr/m/n/10 = 5\OML/cmm/m/it/10 V:[] \OT1/cmr/m +/n/10 = 0\OML/cmm/m/it/10 :\OT1/cmr/m/n/10 44\OML/cmm/m/it/10 V + [] + + +! LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.247 T + hus with $R_2$ shorted both readingare outside the +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + +Missing character: There is no T in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no w in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no b in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no b in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no b in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +! Undefined control sequence. + ... Reference `ptbounds' on page \thepage + \space undefined\on@line . +l.248 proscribed range in table \ref{ptbounds} + . +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + + +LaTeX Warning: Reference `ptbounds' on page undefined on input line 248. + +Missing character: There is no . in font nullfont! +! Undefined control sequence. +l.249 \subsubsection + { Voltages $R_2$ OPEN } +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). 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Emergency stop. +<*> pt100.tex + +*** (job aborted, no legal \end found) + + +Here is how much of TeX's memory you used: + 25 strings out of 95086 + 326 string characters out of 1183256 + 53034 words of memory out of 1500000 + 3296 multiletter control sequences out of 10000+50000 + 3948 words of font info for 15 fonts, out of 1200000 for 2000 + 28 hyphenation exceptions out of 8191 + 20i,7n,26p,125b,150s stack positions out of 5000i,500n,6000p,200000b,5000s +! ==> Fatal error occurred, no output PDF file produced! diff --git a/pt100/pt100.tex b/pt100/pt100.tex index 48d9df0..d2b6749 100644 --- a/pt100/pt100.tex +++ b/pt100/pt100.tex @@ -13,9 +13,10 @@ Once considering single faults (cardinality constrained powerset of 1) and then 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. +diagrasms to assist the reasoning process. +This chapter describes taking +the failure modes of the components, analysing the circuit using FMEA +and producing 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. @@ -33,7 +34,7 @@ from an FMEA persepective as a component itsself, with a set of know failure mod \section{Overview of PT100 four wire circuit} -The PT100 four wire circuit consists of teo resistors supplying +The PT100 four wire circuit consists of two 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 @@ -61,12 +62,17 @@ and the higher as {\em sense+}. \subsection{Accuracy despite variable resistance in cables} -For electronic and accuracy reasons the four wire circiut is used +For electronic and accuracy reasons a four wire circuit is preffered 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 +causes only a negligible voltage drop, and thus the four wire +configuration is more accurate. + +\subsection{Calculating Temperature from the sense line voltages} + +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 @@ -98,14 +104,14 @@ Where this occurs a circuit re-design is probably the only sensible course of ac \subsection{Single Fault FMEA Analysis of PT100 Four wire circuit} \label{fmea} -Looking at this circuit, it simply consists of three resistors. +This circuit 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. +$R_3$ is the PT100 thermistor and $R_{2}$ connects the thermistor to ground. We can define the terms `High Fault' and `Low Fault' here, with reference to figure \ref{fig:pt100vrange}. Should we get a reading outside the safe green zone @@ -114,9 +120,10 @@ Should the reading be above its expected range this is a `High Fault' and if below a `Low Fault'. The Table \ref{ptfmea} plays through the scenarios of each of the resistors failing -in both SHORT and OPEN failure modes, and predicts 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 -to the out of range voltage limits in section \ref{ptbounds}. +determine out of range voltage limits in section \ref{ptbounds}. + \begin{table}[ht] \caption{PT100 FMEA Single Faults} % title of Table \centering % used for centering table @@ -130,8 +137,8 @@ to the out of range voltage limits in section \ref{ptbounds}. $R_1$ SHORT & High Fault & - & Value Out of Range Value \\ \hline $R_1$ OPEN & Low Fault & Low Fault & Both values out of range \\ \hline \hline -$R_p$ SHORT & Low Fault & High Fault & Both values out of range \\ \hline - $R_p$ OPEN & High Fault & Low Fault & Both values out of range \\ \hline +$R_3$ SHORT & Low Fault & High Fault & Both values out of range \\ \hline + $R_3$ OPEN & High Fault & Low Fault & Both values out of range \\ \hline \hline $R_2$ SHORT & - & Low Fault & Value Out of Range Value \\ $R_2$ OPEN & High Fault & High Fault & Both values out of range \\ \hline @@ -141,17 +148,49 @@ $R_2$ SHORT & - & Low Fault & Value Out of Range Value \\ \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. +should 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. +and \ref{pt100temp}. -\subsection{Single Fault Modes as PLD} +\pagebreak +% \subsection{Single Fault Modes as PLD} +% +% 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 +% caused by the component~failure is represented by an labelled asterisk. +% +% +% \begin{figure}[h] +% \centering +% \includegraphics[width=400pt,bb=0 0 518 365,keepaspectratio=true]{./pt100/pt100_tc.jpg} +% % pt100_tc.jpg: 518x365 pixel, 72dpi, 18.27x12.88 cm, bb=0 0 518 365 +% \caption{PT100 Component Failure Modes} +% \label{fig:pt100_tc} +% \end{figure} +% +% This circuit supplies two results, sense+ and sense- voltage readings. +% 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 voltage reading ranges by using the standard voltage divider equation \ref{eqn:vd} +% for the circuit shown in figure \ref{fig:vd}. + + +\begin{figure}[h] + \centering + \includegraphics[width=100pt,bb=0 0 183 170,keepaspectratio=true]{./pt100/voltage_divider.png} + % voltage_divider.png: 183x170 pixel, 72dpi, 6.46x6.00 cm, bb=0 0 183 170 + \caption{Voltage Divider} + \label{fig:vd} +\end{figure} +%The looking at figure \ref{fig:vd} the standard voltage divider formula (equation \ref{eqn:vd}) is used. + +\begin{equation} +\label{eqn:vd} + V_{out} = V_{in}.\frac{Z2}{Z2+Z1} +\end{equation} -% Place in PLD diagram \subsection{Range and PT100 Calculations} \label{pt100temp} @@ -169,8 +208,13 @@ 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: + $$ highreading = 5V.\frac{2k2+pt100}{2k2+2k2+pt100} $$ $$ lowreading = 5V.\frac{2k2}{2k2+2k2+pt100} $$ +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. To convert these to twelve bit ADC (\adctw) counts: @@ -201,69 +245,6 @@ Table \ref{ptbounds} gives ranges that determine correct operation. In fact it c 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 0\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} % @@ -305,22 +286,146 @@ will read 5V, outside of the proscibed range. %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. -% +%The two sense lines then give the vo -\subsection{Single Fault FMEA Analysis of PT100 Four wire circuit} -typeset in {\Huge \LaTeX} \today +\section{Single Fault FMEA Analysis of PT100 Four wire circuit} + +\subsection{Single Fault Modes as PLD} + +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 +caused by the component~failure is represented by an labelled asterisk. + + +\begin{figure}[h] + \centering + \includegraphics[width=400pt,bb=0 0 518 365,keepaspectratio=true]{./pt100/pt100_tc.jpg} + % pt100_tc.jpg: 518x365 pixel, 72dpi, 18.27x12.88 cm, bb=0 0 518 365 + \caption{PT100 Component Failure Modes} + \label{fig:pt100_tc} +\end{figure} + +This circuit supplies two results, sense+ and sense- voltage readings. +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 voltage reading ranges by using the standard voltage divider equation \ref{eqn:vd} +for the circuit shown in . + + + +\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 test cases and each will be examined in turn. + +\subsubsection{ TC1 : Voltages $R_1$ SHORT } +With pt100 at 0\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{ TC2 : 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{ TC 4 : 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{ TC : 5 Voltages $R_2$ OPEN } +Here there is no potential divider operating and both sense lines +will read 5V, outside of the proscibed range. + + +\subsubsection{ TC 5 : Voltages $R_3$ 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{ TC 6 : Voltages $R_3$ 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. + +\subsection{Summary of Analysis} + +All six test cases have been analysed and the results agree with the hypothesis +put in Table \ref{ptfmea}. The PLD diagram, can now be used to collect the +symptoms. In this case there is a common and easily detected symptom for all these single +resistor faults : Voltage out of range. + +A spider can be drawn on the PLD diagram to this effect. + +In practical use, 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. + + +\begin{figure}[h] + \centering + \includegraphics[width=400pt,bb=0 0 518 365,keepaspectratio=true]{./pt100/pt100_tc_sp.jpg} + % pt100_tc.jpg: 518x365 pixel, 72dpi, 18.27x12.88 cm, bb=0 0 518 365 + \caption{PT100 Component Failure Modes} + \label{fig:pt100_tc_sp} +\end{figure} + + +The PT100 circuit can now be treated as a component in its own right, and has one failure mode, +{\textbf OUT\_OF\_RANGE}. It can now be represnted as a PLD see figure \ref{fig:pt100_singlef}. + +\begin{figure}[h] + \centering + \includegraphics[width=100pt,bb=0 0 167 194,keepaspectratio=true]{./pt100/pt100_singlef.jpg} + % pt100_singlef.jpg: 167x194 pixel, 72dpi, 5.89x6.84 cm, bb=0 0 167 194 + \caption{PT100 Circuit Failure Modes : From Single Faults Analysis} + \label{fig:pt100_singlef} +\end{figure} + + + + +%Interestingly we can calculate the failure statistics for this circuit now. +%Mill 1991 gives resistor stats of ${10}^{11}$ times 6 (can we get special stats for pt100) ??? + +The PT100 analysis presents a simple result for single faults. +The next analysis phase looks at how the circuit will behave under double simultaneous failure +conditions. + + +\section{ PT100 Double Simultaneous Fault Analysis} + +% typeset in {\Huge \LaTeX} \today diff --git a/pt100/pt100.tex.backup b/pt100/pt100.tex.backup new file mode 100644 index 0000000..ace772c --- /dev/null +++ b/pt100/pt100.tex.backup @@ -0,0 +1,312 @@ +% +% 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. + + +\begin{figure}[h] + \centering + \includegraphics[width=150pt,bb=0 0 273 483,keepaspectratio=true]{./pt100/vrange.jpg} + % pt100.jpg: 714x180 pixel, 72dpi, 25.19x6.35 cm, bb=0 0 714 180 + \caption{PT100 expected voltage range} + \label{fig:pt100vrange} +\end{figure} + + + + +The voltage ranges we expect from from this three stage potential divider +are shown in figure \ref{fig:pt100vrange}. Note that there is +an expected range for each reading for a given temperature span. + +\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 + diff --git a/pt100/pt100.tex~ b/pt100/pt100.tex~ new file mode 100644 index 0000000..60786ba --- /dev/null +++ b/pt100/pt100.tex~ @@ -0,0 +1,325 @@ +% +% 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. + + +\begin{figure}[h] + \centering + \includegraphics[width=150pt,bb=0 0 273 483,keepaspectratio=true]{./pt100/vrange.jpg} + % pt100.jpg: 714x180 pixel, 72dpi, 25.19x6.35 cm, bb=0 0 714 180 + \caption{PT100 expected voltage ranges} + \label{fig:pt100vrange} +\end{figure} + + + + +The voltage ranges we expect from from this three stage potential divider +are shown in figure \ref{fig:pt100vrange}. Note that there is +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. +For this reason the low reading will be reffered to as {\em sense-} +and the higher as {\em sense+}. + +\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. + +We can define the terms `High Fault' and `Low Fault' here, with reference to figure +\ref{fig:pt100vrange}. Should we get a reading outside the safe green zone +in the diagram we can consider this a fault. +Should the reading be above its expected range this is a `High Fault' +and if below a `Low Fault'. + +The Table \ref{ptfmea} plays through the scenarios of each of the resistors failing +in both SHORT and OPEN failure modes, and predicts an error condition in the readings. +The range 0\oc to 300\oc will be analysed using potential divider equations to +to the out of range voltage limits in section \ref{ptbounds}. +\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 Fault & - & Value Out of Range Value \\ \hline +$R_1$ OPEN & Low Fault & Low Fault & Both values out of range \\ \hline + \hline +$R_p$ SHORT & Low Fault & High Fault & Both values out of range \\ \hline + $R_p$ OPEN & High Fault & Low Fault & Both values out of range \\ \hline +\hline +$R_2$ SHORT & - & Low Fault & Value Out of Range Value \\ + $R_2$ OPEN & High Fault & High Fault & 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 + diff --git a/pt100/pt100_singlef.dia 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