diff --git a/burner/Makefile b/burner/Makefile new file mode 100644 index 0000000..b86b046 --- /dev/null +++ b/burner/Makefile @@ -0,0 +1,17 @@ + +# +# Make the propositional logic diagram a paper +# + + +paper: paper.tex burner_paper.tex + #latex paper.tex + #dvipdf paper pdflatex cannot use eps ffs + pdflatex paper.tex + okular paper.pdf + + +# Remove the need for referncing graphics in subdirectories +# +burner_paper.tex: burner.tex + cat burner.tex | sed 's/burner\///' > paper.tex diff --git a/burner/burner.tex b/burner/burner.tex new file mode 100644 index 0000000..e083aa4 --- /dev/null +++ b/burner/burner.tex @@ -0,0 +1,63 @@ +% +% Make the revision and doc number macro's then they are defined in one place + +\begin{abstract} +things can get very abstract +\end{abstract} + + +\section{Overview of A Burner Controller : Safety Perspective} + +\section{Background to the Industrial Burner Safety Analysis Problem} + +An industrial burner is a good example of a safety critical system. +It has the potential for devistating explosions due to boiler overpressure, low water, or +ignition of an explosive mixture, and, because of the large amounts of fuel used, +is also a fire hazard. Industrial boilers are often left running unattended +for long periods of time (typically days). + +To add to these problems +Operators are often under pressure to keep them running. A boiler supplying +heat to a large greenhouse complex could ruin crops +should it go off-line. Similarly a production line relying on heat or steam +can be very expensive in production down-time should it fail. +This places extra responsibility on the burner controller. + + +These are common place and account for a very large proportion of the enery usage +in the world today (find and ref stats) +Industrial burners are common enough to have different specific standards +written for the fuel types they use \ref{EN298} \ref{EN230} \ref{EN12067}. + +A modern industrial burner has mechanical, electronic and software +elements, that are all safety critical. That is to say +unhandled failures could create dangerous faults. + +A more detailed description of industrial burner controllers +is dealt with in chapter~\ref{burnercontroller}. + + +Systems such as industrial burners have been partially automated for some time. +A mechanical cam arrangement controls the flow of air and fuel for the range of +firing rate (output of the boiler). + +These mechanical systems could suffer failures (such as a mechanical linkage beoming +detached) and could then operate in a potentially dangerous state. + +More modern burner controllers use a safety critical computer controlling +motors to operate the fuel and air mixture and to control the safety +valves. + +In working in the industrial burner industry and submitting product for +North American and European safety approval, it was apparent that +formal techniques could be applied to aspects of the ciruit design. +Some safety critical circuitry would be subjected to thought experiments, where +the actions of one or more components failing would be examined. +As a simple example a milli-volt input could become disconnected. +A milli-volt input is typically amplified so that its range matches that +of the A->D converter that you are reading. were this signal source to become disconnected +the systems would see a floating, amplified signal. +A high impedance safety resistor can be added to the circuit, +to pull the signal high (or out of nornal range) upon disconnection. +The system then knows that a fault has occurred and will not use +that sensor reading (see \ref{fig:millivolt}). \ No newline at end of file diff --git a/burner/burner.tex~ b/burner/burner.tex~ new file mode 100644 index 0000000..7c6088f --- /dev/null +++ b/burner/burner.tex~ @@ -0,0 +1,9 @@ +% +% Make the revision and doc number macro's then they are defined in one place + +\begin{abstract} + +\end{abstract} + + +\section{Overview of A Burner Controller : Safety Perspective} diff --git a/burner/mybib.bib b/burner/mybib.bib new file mode 100644 index 0000000..150c845 --- /dev/null +++ b/burner/mybib.bib @@ -0,0 +1,404 @@ +% +% +% $Id: mybib.bib,v 1.5 2008/12/18 17:05:23 robin Exp $ +% +% + +@TechReport{db, + author = {R Clark, D Legge}, + title = {ETC6000 Daughterboard Design notes}, + institution = {ETC HR221850}, + year = {2004}, + key = {}, + OPTtype = {}, + OPTnumber = {}, + OPTaddress = {}, + OPTmonth = {}, + OPTnote = {}, + OPTannote = {}, + OPTurl = {}, + OPTdoi = {}, + issn = {HR221850}, + OPTlocalfile = {}, + OPTabstract = {}, +} + +@TechReport{mil1991, + author = {U.S. Department of Defence}, + title = {Reliability Prediction of Electronic Equipment}, + institution = {DOD}, + year = {1991}, + key = {MIL-HDBK-217F}, + OPTtype = {}, + OPTnumber = {}, + OPTaddress = {}, + OPTmonth = {}, + OPTnote = {}, + OPTannote = {}, + OPTurl = {}, + OPTdoi = {}, + OPTissn = {}, + OPTlocalfile = {}, + OPTabstract = {}, +} + +@Manual{tlp181, + title = {TLP 181 Datasheet}, + key = {TOSHIBA Photocoupler GaAs Ired & Photo−Transistor}, + author = {Toshiba inc.}, + OPTorganization = {}, + %address = {http://www.toshiba.com/taec/components2/Datasheet\_Sync//206/4191.pdf}, + OPTedition = {}, + OPTmonth = {}, + year = {2009}, +OPTnote = {}, + OPTannote = {}, + OPTurl = {}, + OPTdoi = {}, +OPTissn = {}, + OPTlocalfile = {}, + OPTabstract = {}, +} + + + + +@Manual{pic18f2523, + title = {PIC18F2523 Datasheet}, + OPTkey = {}, + author = {Microchip inc}, + OPTorganization = {}, + address = {http://ww1.microchip.com/downloads/en/DeviceDoc/39755c.pdf}, + OPTedition = {}, + OPTmonth = {}, + year = {2009}, + OPTnote = {}, + OPTannote = {}, + OPTurl = {}, + OPTdoi = {}, + OPTissn = {}, + OPTlocalfile = {}, + OPTabstract = {}, +} + + +@Book{wt, + title = {Water Treatment Essentials for Boiler Plant Operation}, + publisher = {Mc Graw Hill ISBN 0-07-048291-5}, + year = {1997}, + author = {Robert G Nunn}, + ALTALTeditor = {}, + OPTkey = {}, + OPTvolume = {}, + OPTnumber = {}, + OPTseries = {}, + OPTaddress = {}, + OPTedition = {}, + OPTmonth = {}, + OPTnote = {}, + OPTannote = {}, + OPTurl = {}, + OPTdoi = {}, + OPTissn = {ISBN 0-07-048291-5}, + OPTlocalfile = {}, + OPTabstracts = {}, +} + +@TechReport{pcbAI222562, + author = {C Talmay}, + title = {Circuit Schematic TDS Daughterboard AI222562}, + institution = {ETC}, + year = {2010}, + OPTkey = {}, + OPTtype = {}, + OPTnumber = {AI222562}, + OPTaddress = {}, + OPTmonth = {}, + OPTnote = {}, + OPTannote = {}, + OPTurl = {}, + OPTdoi = {}, + OPTissn = {}, + OPTlocalfile = {}, + OPTabstract = {}, +} + +@TechReport{spiraxsarco, + author = {Spirax Sarco}, + title = {http://www.spiraxsarco.com/resources/steam-engineering-tutorials.asp}, + institution = {Spirax Sarco}, + year = {2010}, + OPTkey = {}, + OPTtype = {}, + OPTnumber = {}, + OPTaddress = {}, + OPTmonth = {}, + OPTnote = {}, + OPTannote = {}, + OPTurl = {}, + OPTdoi = {}, + OPTissn = {}, + OPTlocalfile = {}, + OPTabstract = {}, +} + +@Book{aoe, + title = {The Art of Electronics}, + publisher = {Cambridge}, + year = {1989}, + author = {Paul Horowitz, Winfield Hill}, + %author = {}, + OPTkey = {}, + OPTvolume = {}, + OPTnumber = {}, + OPTseries = {}, + OPTaddress = {}, + OPTedition = {2nd}, + OPTmonth = {}, + OPTnote = {}, + OPTannote = {}, + OPTurl = {}, + OPTdoi = {}, + OPTissn = {ISBN 0-521-37095-7}, + OPTlocalfile = {}, + OPTabstracts = {}, +} + +@TechReport{eurothermtables, + author = {}, + title = {Thermocouple Emf TABLES and PLATINUM 100 RESISTANCE THERMOMETER TABLES}, + institution = {Eurotherm}, + year = {1973}, + OPTkey = {}, + OPTtype = {}, + OPTnumber = {}, + OPTaddress = {}, + OPTmonth = {June}, + OPTnote = {Bulletin TT-1}, + OPTannote = {}, + OPTurl = {}, + OPTdoi = {}, + OPTissn = {}, + OPTlocalfile = {}, + OPTabstract = {}, +} + +@MISC{iso639-1, + title = "ISO 639-1: Code for the Representation of Names of Languages", + author = "International Standardization Organization", + howpublished = "http://www.loc.gov/standards/iso639-2/criteria1.html" + year = "1998" +} + +@MISC{nano-x, + title = "The nano-X windowing system", + author = "Greg Haerr", + howpublished = "http://www.microwindows.org/" + year = "2003" +} + + + + +@MISC{X11, + title = "The XFree86 Project, Inc", + author = "Open Source", + howpublished = "http://www.xfree86.org/" + year = "1992" +} + + +http://www.xfree86.org/ + +@MISC{iso639-2, + title = "ISO 639-2: Code for the Representation of Names of Languages", + author = "International Standardization Organization", + howpublished = "http://www.loc.gov/standards/iso639-2/criteria1.html" + year = "1998" +} + + +@misc{ touchscreenprod, + author = "M. Thirsk", + title = "Touchscreen Production Procedure : HR~222165", + howpublished = "Internal ETC Document", + year = "2008" }; + + +@misc{ touchscreensoftware, + author = "ETC Software Dept.", + title = "Touchscreen Software released to Production : HR~222162", + howpublished = "Internal ETC Software (medium: 2 MMC cards)", + year = "2008" }; + +@misc{ touchscreengui, + author = "D.J. Legge, R.P.Clark", + title = "Touchscreen GUI Design Document : HR~222163", + howpublished = "Internal ETC Document", + year = "2008" }; + + +@misc{ gumstix, + author = "Gumstix Inc", + title = "Gumstix Home Page", + howpublished = "WEB http://www.gumstix.com/", + year = "2008" }; + + +@misc{ fltk, + author = "FLTK open Source Developers", + title = "Fast Light Toolkit", + howpublished = "WEB http://www.fltk.org/", + year = "2008" }; + + +@Book{ldd, +author = {Jonathon Corbet}, +ALTeditor = {Alessandro Rubini}, +ALTeditor = {Greg Kroah-Hartman}, +title = {Linux Device Drivers}, +publisher = {O'Reilly ISBN 0-596-00590-3}, +year = {1998}, +OPTkey = {ISBN 0-596-00590-3}, +OPTvolume = {}, +OPTnumber = {}, +OPTseries = {linux}, +OPTaddress = {}, +OPTedition = {3rd}, +OPTmonth = {}, +OPTnote = {}, +OPTannote = {}, +OPTurl = {www.oreilly.com}, +OPTdoi = {}, +OPTissn = {}, +OPTlocalfile = {}, +OPTabstract = {} +}; + + +@Book{bash, +author = {Carl Albing}, +title = {Bash Cookbook}, +publisher = {O'Reilly ISBN 0-596-52678-4}, +year = {2007}, +OPTkey = {ISBN 0-596-52678-4}, +OPTvolume = {}, +OPTnumber = {}, +OPTseries = {unix/linux}, +OPTaddress = {}, +OPTedition = {}, +OPTmonth = {}, +OPTnote = {}, +OPTannote = {}, +OPTurl = {www.oreilly.com}, +OPTdoi = {}, +OPTissn = {}, +OPTlocalfile = {}, +OPTabstract = {} +}; + +@Book{sedawk, +author = {Dale Dougherty, Arnold Robbins}, +title = {Sed and Awk}, +publisher = {O'Reilly ISBN 1-56592-225-5}, +year = {1997}, +OPTkey = {ISBN 1-56592-225-5}, +OPTvolume = {}, +OPTnumber = {}, +OPTseries = {unix/linux}, +OPTaddress = {}, +OPTedition = {}, +OPTmonth = {}, +OPTnote = {}, +OPTannote = {}, +OPTurl = {www.oreilly.com}, +OPTdoi = {}, +OPTissn = {}, +OPTlocalfile = {}, +OPTabstract = {} +}; + +@Book{bels, +author = {Karim Yaghmour}, +title = {Building Embedded LINUX systems}, +publisher = {O'Reilly ISBN ISBN 0-596-00222-X}, +year = {2003}, +OPTkey = {ISBN 0-596-00222-X}, +OPTvolume = {}, +OPTnumber = {}, +OPTseries = {linux}, +OPTaddress = {}, +OPTedition = {3rd}, +OPTmonth = {}, +OPTnote = {}, +OPTannote = {}, +OPTurl = {www.oreilly.com}, +OPTdoi = {}, +OPTissn = {}, +OPTlocalfile = {}, +OPTabstract = {} +}; + +@Book{can, +author = {Olaf Pfeiffer}, +ALTeditor = {Andrew Ayre}, +ALTeditor = {Christian Keydel}, +title = {Embedded networking with CAN and CANopen}, +publisher = {RTC ISBN 0-929392-78-7}, +year = {2003}, +OPTkey = { }, +OPTvolume = {}, +OPTnumber = {}, +OPTseries = {Embedded Systems}, +OPTaddress = {}, +OPTedition = {1st}, +OPTmonth = {}, +OPTnote = {}, +OPTannote = {}, +OPTurl = {www.rtcbooks.com}, +OPTdoi = {}, +OPTissn = {}, +OPTlocalfile = {}, +OPTabstract = {} +}; + +@Article{article, +author = {dd}, +title = {dd}, +journal = {dd}, +year = {2008}, +OPTkey = {}, +OPTvolume = {}, +OPTnumber = {}, +OPTpages = {1,2}, +OPTmonth = {JAN}, +OPTnote = {}, +OPTannote = {}, +OPTurl = {}, +OPTdoi = {}, +OPTissn = {}, +OPTlocalfile = {}, +OPTabstract = {} +}; + +@Book{sqlite, +author = {Micheal Owens}, +title = {The definitive guide to SQLite}, +publisher = {Apres ISBN 1-59059-673-0}, +year = {2006}, +OPTkey = {}, +OPTvolume = {}, +OPTnumber = {}, +OPTseries = {Databases/SQLite}, +OPTaddress = {}, +OPTedition = {}, +OPTmonth = {}, +OPTnote = {}, +OPTannote = {}, +OPTurl = {}, +OPTdoi = {}, +OPTissn = {}, +OPTlocalfile = {}, +OPTabstract = {} +}; + diff --git a/burner/papaer.tex b/burner/papaer.tex new file mode 100644 index 0000000..36dd25e --- /dev/null +++ b/burner/papaer.tex @@ -0,0 +1,2 @@ +:e paper.tex + diff --git a/burner/paper.aux b/burner/paper.aux new file mode 100644 index 0000000..f27c7f2 --- /dev/null +++ b/burner/paper.aux @@ -0,0 +1,53 @@ +\relax +\citation{aoe} +\@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces PT100 four wire circuit}}{1}} +\newlabel{fig:pt100}{{1}{1}} +\@writefile{toc}{\contentsline {section}{\numberline {1}Overview of PT100 four wire circuit}{1}} +\@writefile{toc}{\contentsline {subsection}{\numberline {1.1}Accuracy despite variable \\ resistance in cables}{1}} +\citation{eurothermtables} +\citation{mil1991} +\citation{mil1991} +\@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces PT100 expected voltage ranges}}{2}} +\newlabel{fig:pt100vrange}{{2}{2}} +\@writefile{toc}{\contentsline {subsection}{\numberline {1.2}Calculating Temperature from \\ the sense line voltages}{2}} +\@writefile{toc}{\contentsline {section}{\numberline {2}Safety case for 4 wire circuit}{2}} +\citation{aoe} +\citation{eurothermtables} +\citation{eurothermtables} +\@writefile{toc}{\contentsline {subsection}{\numberline {2.1}Single Fault FMEA Analysis \\ of PT100 Four wire circuit}{3}} +\newlabel{fmea}{{2.1}{3}} +\@writefile{lot}{\contentsline {table}{\numberline {1}{\ignorespaces PT100 FMEA Single Faults}}{3}} +\newlabel{ptfmea}{{1}{3}} +\@writefile{toc}{\contentsline {subsection}{\numberline {2.2}Range and PT100 Calculations}{3}} +\newlabel{pt100temp}{{2.2}{3}} +\@writefile{lot}{\contentsline {table}{\numberline {2}{\ignorespaces PT100 Maximum and Minimum Values}}{4}} +\newlabel{ptbounds}{{2}{4}} +\@writefile{toc}{\contentsline {section}{\numberline {3}Single Fault FMEA Analysis \\ of PT100 Four wire circuit}{4}} +\@writefile{toc}{\contentsline {subsection}{\numberline {3.1}Single Fault Modes as PLD}{4}} +\@writefile{lof}{\contentsline {figure}{\numberline {3}{\ignorespaces PT100 Component Failure Modes}}{4}} +\newlabel{fig:pt100_tc}{{3}{4}} +\@writefile{lof}{\contentsline {figure}{\numberline {4}{\ignorespaces Voltage Divider}}{5}} +\newlabel{fig:vd}{{4}{5}} +\newlabel{eqn:vd}{{1}{5}} +\@writefile{toc}{\contentsline {subsection}{\numberline {3.2}Proof of Out of Range \\ Values for Failures}{5}} +\newlabel{pt110range}{{3.2}{5}} +\@writefile{toc}{\contentsline {subsubsection}{\numberline {3.2.1} TC1 : Voltages $R_1$ SHORT }{5}} +\@writefile{toc}{\contentsline {subsubsection}{\numberline {3.2.2} TC2 : Voltages $R_1$ OPEN }{5}} +\@writefile{toc}{\contentsline {subsubsection}{\numberline {3.2.3} TC 3 : Voltages $R_2$ SHORT }{5}} +\@writefile{toc}{\contentsline {subsubsection}{\numberline {3.2.4} TC : 4 Voltages $R_2$ OPEN }{6}} +\@writefile{toc}{\contentsline {subsubsection}{\numberline {3.2.5} TC 5 : Voltages $R_3$ SHORT }{6}} +\@writefile{toc}{\contentsline {subsubsection}{\numberline {3.2.6} TC 6 : Voltages $R_3$ OPEN }{6}} +\@writefile{toc}{\contentsline {subsection}{\numberline {3.3}Summary of Analysis}{6}} +\@writefile{lof}{\contentsline {figure}{\numberline {5}{\ignorespaces PT100 Component Failure Modes}}{7}} +\newlabel{fig:pt100_tc_sp}{{5}{7}} +\@writefile{lof}{\contentsline {figure}{\numberline {6}{\ignorespaces PT100 Circuit Failure Modes : From Single Faults Analysis}}{7}} +\newlabel{fig:pt100_singlef}{{6}{7}} +\citation{mil1991} +\@writefile{toc}{\contentsline {subsection}{\numberline {3.4}Mean Time to Failure}{8}} +\@writefile{lot}{\contentsline {table}{\numberline {3}{\ignorespaces PT100 FMEA Single // Fault Statistics}}{8}} +\newlabel{tab:stat_single}{{3}{8}} 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Clark } } + % numbers at outer edges +\pagenumbering{arabic} % Arabic page numbers hereafter +\author{R.P.Clark} +\title{PT100 FMMD analysis} +\maketitle +\input{pt100_paper} + +\bibliographystyle{plain} +\bibliography{vmgbibliography,mybib} + +\today +\end{document} diff --git a/burner/pt100.dia~ b/burner/pt100.dia~ new file mode 100644 index 0000000..fda9b8d Binary files /dev/null and b/burner/pt100.dia~ differ diff --git a/burner/pt100.log b/burner/pt100.log new file mode 100644 index 0000000..2468ba9 --- /dev/null +++ b/burner/pt100.log @@ -0,0 +1,12452 @@ +This is pdfTeXk, Version 3.141592-1.40.3 (Web2C 7.5.6) (format=pdflatex 2010.2.1) 22 MAR 2010 21:03 +entering extended mode + %&-line parsing enabled. +**pt100.tex +(./pt100.tex +LaTeX2e <2005/12/01> +Babel and hyphenation patterns for english, usenglishmax, dumylang, noh +yphenation, loaded. + +! 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'). 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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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+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 a 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 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 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! 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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.23 \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.26 \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.26 \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.28 \includegraphics + [width=400pt,bb=0 0 714 180,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.30 \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.32 \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 26--33 +[] + [] + +! Undefined control sequence. +l.35 \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.35 \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.37 T + he PT100 four wire circuit consists of two 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.45 \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.45 \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.47 \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.49 \caption + {PT100 expected voltage ranges} +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.51 \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 45--52 +[] + [] + + +! LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.56 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.57 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.63 \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.63 \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.65 F + or electronic and accuracy reasons a four wire circuit is preffered +You're in trouble here. 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Undefined control sequence. + ...: Citation `\@citeb ' on page \thepage + \space undefined\on@line . +l.84 ...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 84. + +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 75--85 +[] + [] + + +Overfull \hbox (18.61107pt too wide) in paragraph at lines 75--85 +\OML/cmm/m/it/10 V \OT1/cmr/m/n/10 = + [] + + +Overfull \hbox (15.62848pt too wide) in paragraph at lines 75--85 +\OML/cmm/m/it/10 I:R$ + [] + + +Overfull \hbox (18.22566pt too wide) in paragraph at lines 75--85 +\OML/cmm/m/it/10 R \OT1/cmr/m/n/10 = + [] + + +Overfull \hbox (8.84447pt too wide) in paragraph at lines 75--85 +[]$ + [] + + +Overfull \hbox (5.43053pt too wide) in paragraph at lines 75--85 +[] + [] + +! Undefined control sequence. +l.86 \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.86 \section{S + afety case for 4 wire circuit} +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + +Missing character: There is no S in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no f 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 y 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 s 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 o in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no 4 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! +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! + +Overfull \hbox (20.0pt too wide) in paragraph at lines 86--87 +[] + [] + + +! LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.88 T + his sub-section looks at the behaviour of the PT100 four wire circuit +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 s in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no b 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 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! +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! 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Undefined control sequence. + ...: Citation `\@citeb ' on page \thepage + \space undefined\on@line . +l.93 ... 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'). Otherwise just continue, +and I'll forget about whatever was undefined. + + +LaTeX Warning: Citation `mil1991' on page undefined on input line 93. + +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 u 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 o 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 c in font nullfont! +Missing character: There is no h 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 m in font nullfont! +Missing character: There is no p in font nullfont! 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Undefined control sequence. +l.113 $R_{1}$ is the \ohms + {2k2} from 5V to the thermistor, +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: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.116 W + e can define the terms `High Fault' and `Low Fault' here, with refere... + +You're in trouble here. 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Undefined control sequence. + ...nce `fig:pt100vrange' on page \thepage + \space undefined\on@line . +l.117 \ref{fig:pt100vrange} + . Should we get a reading outside the safe green ... +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: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.122 T + he Table \ref{ptfmea} plays through the scenarios of each of the resi... + +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 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! +! 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Undefined control sequence. +l.124 The range 0\oc + to 300\oc will be analysed using potential divider equa... +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.124 The range 0\oc to 300\oc + will be analysed using potential divider equa... +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 w in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no l 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 u 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 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 e in font nullfont! +Missing character: There is no q in font nullfont! +Missing character: There is no u 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 t in font nullfont! +Missing character: There is no o 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 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 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 l 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 i 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 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. + ... Reference `ptbounds' on page \thepage + \space undefined\on@line . +l.125 ... voltage limits in section \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 125. + +Missing character: There is no . in font nullfont! + +Overfull \hbox (20.0pt too wide) in paragraph at lines 122--126 +[] + [] + + +Overfull \hbox (10.86105pt too wide) in paragraph at lines 122--126 +[] + [] + + +Overfull \hbox (10.86105pt too wide) in paragraph at lines 122--126 +[] + [] + + +! LaTeX Error: Environment table undefined. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.127 \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.127 \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.128 \caption + {PT100 FMEA Single Faults} % 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 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 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 F in font nullfont! +Missing character: There is no a 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 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 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 F in font nullfont! +Missing character: There is no a 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 - 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 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 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 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 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 F in font nullfont! +Missing character: There is no a 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 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 F in font nullfont! +Missing character: There is no a 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 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 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 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 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 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 F in font nullfont! +Missing character: There is no a 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 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 F in font nullfont! +Missing character: There is no a 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 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 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 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 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 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 F in font nullfont! +Missing character: There is no a 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 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 F in font nullfont! +Missing character: There is no a 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 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 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 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 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 - 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 F in font nullfont! +Missing character: There is no a 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 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 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 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 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 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 F in font nullfont! +Missing character: There is no a 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 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 F in font nullfont! +Missing character: There is no a 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 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 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 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! + +! LaTeX Error: \begin{document} ended by \end{table}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.148 \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 127--149 +[] + [] + + +Overfull \hbox (202.02669pt too wide) in paragraph at lines 127--149 +[] + [] + + +! LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.150 F + rom table \ref{ptfmea} it can be seen that any component failure in t... + +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + +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 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. + ...g: Reference `ptfmea' on page \thepage + \space undefined\on@line . +l.150 From table \ref{ptfmea} + it can be seen that any component failure in t... +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 `ptfmea' on page undefined on input line 150. + +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 e 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 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 a in font nullfont! +Missing character: There is no n in font nullfont! 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Undefined control sequence. + ...eference `pt100range' on page \thepage + \space undefined\on@line . +l.153 ...ase are found in section \ref{pt100range} + +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 `pt100range' on page undefined on input line 153. + +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. + ...Reference `pt100temp' on page \thepage + \space undefined\on@line . +l.154 and \ref{pt100temp} + . +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 `pt100temp' on page undefined on input line 154. + +Missing character: There is no . in font nullfont! + +Overfull \hbox (20.0pt too wide) in paragraph at lines 150--155 +[] + [] + + +Overfull \hbox (10.86105pt too wide) in paragraph at lines 150--155 +[] + [] + + +Overfull \hbox (10.86105pt too wide) in paragraph at lines 150--155 +[] + [] + + +Overfull \hbox (10.86105pt too wide) in paragraph at lines 150--155 +[] + [] + + +Underfull \vbox (badness 10000) has occurred while \output is active [] + + + +! LaTeX Error: The font size command \normalsize is not defined: + there is probably something wrong with the class file. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.178 + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + +[1{/var/lib/texmf/fonts/map/pdftex/updmap/pdftex.map} +! Undefined control sequence. + \newlabel{fig:pt100}{{}{\thepage + }} +l.178 + +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. + +\newlabel{fig:pt100}{{}{}} +! Undefined control sequence. + \newlabel{fig:pt100vrange}{{}{\thepage + }} +l.178 + +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. + +\newlabel{fig:pt100vrange}{{}{}} +! Undefined control sequence. + \newlabel{fmea}{{}{\thepage + }} +l.178 + +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. + +\newlabel{fmea}{{}{}} +! Undefined control sequence. + \newlabel{ptfmea}{{}{\thepage + }} +l.178 + +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. + +\newlabel{ptfmea}{{}{}} +] + +! LaTeX Error: Environment figure undefined. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.180 \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.180 \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.182 \includegraphics + [width=100pt,bb=0 0 183 170,keepaspectratio=true]{./p... +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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Missing $ inserted. + + $ +l.182 ...70,keepaspectratio=true]{./pt100/voltage_ + divider.png} +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Extra }, or forgotten $. +l.182 ...tratio=true]{./pt100/voltage_divider.png} + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + + +! LaTeX Error: \caption outside float. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.184 \caption + {Voltage Divider} +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + + +! LaTeX Error: \begin{document} ended by \end{figure}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.186 \end{figure} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + +! Missing $ inserted. + + $ +l.186 \end{figure} + +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +! Missing } inserted. + + } +l.186 \end{figure} + +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + + +Overfull \hbox (20.0pt too wide) in paragraph at lines 180--188 +[] + [] + + +Overfull \hbox (119.86273pt too wide) in paragraph at lines 180--188 +[]\OML/cmm/m/it/10 ivider:png[][]$ + [] + + +! LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.189 \begin{equation} + +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 189--189 +[] + [] + + +Overfull \hbox (87.9519pt too wide) detected at line 192 +[]\OML/cmm/m/it/10 V[] \OT1/cmr/m/n/10 = \OML/cmm/m/it/10 V[]:[] + [] + +! Undefined control sequence. +l.195 \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.195 \subsection{R + ange and PT100 Calculations} +You're in trouble here. 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Undefined control sequence. +l.198 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.198 ...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'). 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Undefined control sequence. +l.199 ...xpected range' was considered to be {0\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.199 ...e' was considered to be {0\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'). 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Undefined control sequence. + ...: Citation `\@citeb ' on page \thepage + \space undefined\on@line . +l.202 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 202. + + +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.202 ...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.203 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! 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+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.206 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 206. + +Missing character: There is no . in font nullfont! + +Overfull \hbox (20.0pt too wide) in paragraph at lines 195--207 +[] + [] + + +Overfull \hbox (5.43053pt too wide) in paragraph at lines 195--207 +[] + [] + + +Overfull \hbox (5.43053pt too wide) in paragraph at lines 195--207 +[] + [] + + +Overfull \hbox (10.86105pt too wide) in paragraph at lines 195--207 +[] + [] + + +! LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.208 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.208 ... 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 208--210 +[] + [] + + +! LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.212 $ + $ 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 212--212 +[] + [] + + +Overfull \hbox (163.63742pt too wide) detected at line 212 +\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 213 +\OML/cmm/m/it/10 lowreading \OT1/cmr/m/n/10 = 5\OML/cmm/m/it/10 V:[] + [] + +Missing character: There is no S 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 y 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 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 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 n 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 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 s 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 m in font nullfont! 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+Missing character: There is no s 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 i 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 d in font nullfont! +Missing character: There is no . in font nullfont! + +! LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.219 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.219 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 219--220 +[] + [] + + +! LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.221 $ + $ 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 221--221 +[] + [] + + +Overfull \hbox (165.7208pt too wide) detected at line 221 +\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 222 +\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.225 \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.225 \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.226 \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 0 in font nullfont! +! Undefined control sequence. +l.235 {0 \oc + } & {\ohms{100}} & 2.44V & 2.56V & Bound... +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.235 {0 \oc} & {\ohms + {100}} & 2.44V & 2.56V & Bound... +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 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 0 in font nullfont! +Missing character: There is no 2 in font nullfont! +! Undefined control sequence. +l.236 & & 2002\adctw + & 2094\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 9 in font nullfont! +Missing character: There is no 4 in font nullfont! +! Undefined control sequence. +l.236 ... & 2002\adctw & 2094\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 + 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.237 {+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.237 {+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.238 & & 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.238 ... & 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.242 \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 225--243 +[] + [] + + +Overfull \hbox (273.6625pt too wide) in paragraph at lines 225--243 +[] + [] + + +! LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.244 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.244 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 244. + +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! 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+ +Overfull \hbox (20.0pt too wide) in paragraph at lines 244--247 +[] + [] + + +Overfull \hbox (10.86105pt too wide) in paragraph at lines 244--247 +[] + [] + +! Undefined control sequence. +l.291 \section + {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.291 \section{S + ingle Fault FMEA Analysis of PT100 Four wire circuit} +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + +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 F in font nullfont! +Missing character: There is no a 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 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 o in font nullfont! +Missing character: There is no f 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 u 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 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 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! + +Overfull \hbox (20.0pt too wide) in paragraph at lines 291--292 +[] + [] + +! Undefined control sequence. +l.293 \subsection + {Single Fault Modes as PLD} +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.293 \subsection{S + ingle Fault Modes as PLD} +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + +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 F in font nullfont! +Missing character: There is no a 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 M in font nullfont! +Missing character: There is no o 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 a 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 L in font nullfont! +Missing character: There is no D in font nullfont! + +Overfull \hbox (20.0pt too wide) in paragraph at lines 293--294 +[] + [] + + +! LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.295 T + he component~failure~modes in table \ref{ptfmea} can be represented a... + +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 c 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 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 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 f in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no i 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 r 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 o 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 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. + ...g: Reference `ptfmea' on page \thepage + \space undefined\on@line . +l.295 ...onent~failure~modes in table \ref{ptfmea} + can be represented as con... +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 `ptfmea' on page undefined on input line 295. + +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 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 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 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 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 t 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 r 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 n 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 L in font nullfont! +Missing character: There is no D 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 a in font nullfont! +Missing character: There is no g 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 m in font nullfont! +Missing character: There is no . 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 c 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 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 c 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 e 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 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 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 f in font nullfont! +Missing character: There is no f 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 s 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 c 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 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 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 f in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no i 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 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 a 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 b 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 c 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 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 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 f in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no i 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 r 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 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 p 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 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 y 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 l 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 e in font nullfont! +Missing character: There is no l 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 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 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 i in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no k in font nullfont! +Missing character: There is no . in font nullfont! + +Overfull \hbox (20.0pt too wide) in paragraph at lines 295--298 +[] + [] + + +Overfull \hbox (10.86105pt too wide) in paragraph at lines 295--298 +[] + [] + + +! LaTeX Error: Environment figure undefined. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.300 \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.300 \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.302 \includegraphics + [width=400pt,bb=0 0 518 365,keepaspectratio=true]{./p... +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 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 t in font nullfont! +Missing character: There is no h 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 0 in font nullfont! +Missing character: There is no 0 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 , in font nullfont! +Missing character: There is no b in font nullfont! +Missing character: There is no b 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 0 in font nullfont! +Missing character: There is no 5 in font nullfont! +Missing character: There is no 1 in font nullfont! +Missing character: There is no 8 in font nullfont! +Missing character: There is no 3 in font nullfont! +Missing character: There is no 6 in font nullfont! +Missing character: There is no 5 in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no k 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 p 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 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 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 = 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 u 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 . in font nullfont! +Missing character: There is no / 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 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 $ inserted. + + $ +l.302 ... 365,keepaspectratio=true]{./pt100/pt100_ + tc.jpg} +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Extra }, or forgotten $. +l.302 ...epaspectratio=true]{./pt100/pt100_tc.jpg} + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + + +! LaTeX Error: \caption outside float. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.304 \caption + {PT100 Component Failure Modes} +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + + +! LaTeX Error: \begin{document} ended by \end{figure}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.306 \end{figure} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + +! Missing $ inserted. + + $ +l.306 \end{figure} + +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +! Missing } inserted. + + } +l.306 \end{figure} + +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + + +Overfull \hbox (20.0pt too wide) in paragraph at lines 300--307 +[] + [] + + +Overfull \hbox (172.24731pt too wide) in paragraph at lines 300--307 +[]\OML/cmm/m/it/10 c:jpg[][]$ + [] + + +! LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.308 T + his circuit supplies two results, sense+ and sense- voltage readings. +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 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 s 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 l in font nullfont! +Missing character: There is no i 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 w 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 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 , 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 e 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 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 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 e in font nullfont! +Missing character: There is no - 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 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 . 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 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 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 i 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 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 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 i in font nullfont! +Missing character: There is no d 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 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 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 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 , 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 k in font nullfont! +Missing character: There is no n 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 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 u in font nullfont! +Missing character: There is no r 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 i 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 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 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 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 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 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 e in font nullfont! +Missing character: There is no x in font nullfont! +Missing character: There is no a 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 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 0 in font nullfont! +! Undefined control sequence. +l.310 ...empperature range for this example ({0\oc + } .. {300\oc}) we can calc... +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 . 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.310 ...range for this example ({0\oc} .. {300\oc + }) we can calculate +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 w 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 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 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 i in font nullfont! +Missing character: There is no d 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 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 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 b 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 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 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 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 d 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 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 e in font nullfont! +Missing character: There is no q in font nullfont! +Missing character: There is no u 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! +! Undefined control sequence. + ...g: Reference `eqn:vd' on page \thepage + \space undefined\on@line . +l.311 ...ard voltage divider equation \ref{eqn:vd} + +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 `eqn:vd' on page undefined on input line 311. + +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 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 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 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 i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no . in font nullfont! + +Overfull \hbox (20.0pt too wide) in paragraph at lines 308--313 +[] + [] + + +Overfull \hbox (10.86105pt too wide) in paragraph at lines 308--313 +[] + [] + +! Undefined control sequence. +l.316 \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.316 \subsection{P + roof of Out of Range Values for Failures} +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 r 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 f 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 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 V in font nullfont! 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Undefined control sequence. +l.322 \subsubsection + { TC1 : 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.322 \subsubsection{ T + C1 : Voltages $R_1$ SHORT } +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 C in font nullfont! +Missing character: There is no 1 in font nullfont! +Missing character: There is no : 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 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 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 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 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.323 With pt100 at 0\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. + + +Overfull \hbox (20.0pt too wide) in paragraph at lines 322--324 +[] + [] + + +Overfull \hbox (12.07903pt too wide) in paragraph at lines 322--324 +\OML/cmm/m/it/10 R[]$ + [] + + +Overfull \hbox (80.99788pt too wide) detected at line 324 +\OML/cmm/m/it/10 highreading \OT1/cmr/m/n/10 = 5\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 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! 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Undefined control sequence. +l.328 ... 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 329 +\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 330 +\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.332 T + hus with $R_1$ 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.333 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 333. + +Missing character: There is no . in font nullfont! + +Overfull \hbox (20.0pt too wide) in paragraph at lines 332--334 +[] + [] + + +Overfull \hbox (12.07903pt too wide) in paragraph at lines 332--334 +\OML/cmm/m/it/10 R[]$ + [] + + +Overfull \hbox (10.86105pt too wide) in paragraph at lines 332--334 +[] + [] + +! Undefined control sequence. +l.335 \subsubsection + { TC2 : 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.335 \subsubsection{ T + C2 : Voltages $R_1$ OPEN } +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + +Missing character: There is no T in font nullfont! +Missing character: There is no C 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 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 335--336 +[] + [] + + +Overfull \hbox (12.07903pt too wide) in paragraph at lines 335--336 +\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.337 I + n this case the 5V rail is disconnected. All voltages read are 0V, and +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + +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 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 a 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 h in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no 5 in font nullfont! +Missing character: There is no V 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 i in font nullfont! 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Undefined control sequence. + ... Reference `ptbounds' on page \thepage + \space undefined\on@line . +l.339 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 339. + +Missing character: There is no . in font nullfont! + +Overfull \hbox (20.0pt too wide) in paragraph at lines 337--340 +[] + [] + + +Overfull \hbox (10.86105pt too wide) in paragraph at lines 337--340 +[] + [] + +! Undefined control sequence. +l.342 \subsubsection + { TC 4 : 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.342 \subsubsection{ T + C 4 : Voltages $R_2$ SHORT } +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + +Missing character: There is no T in font nullfont! +Missing character: There is no C in font nullfont! +Missing character: There is no 4 in font nullfont! +Missing character: There is no : 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 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 342--343 +[] + [] + + +Overfull \hbox (12.07903pt too wide) in paragraph at lines 342--343 +\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.344 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 344--345 +[] + [] + + +Overfull \hbox (76.35718pt too wide) detected at line 345 +\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.349 ... 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 350 +\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 351 +\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.353 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.354 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 354. + +Missing character: There is no . in font nullfont! + +Overfull \hbox (20.0pt too wide) in paragraph at lines 353--355 +[] + [] + + +Overfull \hbox (12.07903pt too wide) in paragraph at lines 353--355 +\OML/cmm/m/it/10 R[]$ + [] + + +Overfull \hbox (10.86105pt too wide) in paragraph at lines 353--355 +[] + [] + +! Undefined control sequence. +l.356 \subsubsection + { TC : 5 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'). 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.356 \subsubsection{ T + C : 5 Voltages $R_2$ OPEN } +You're in trouble here. 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Undefined control sequence. +l.361 \subsubsection + { TC 5 : Voltages $R_3$ 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.361 \subsubsection{ T + C 5 : Voltages $R_3$ SHORT } +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.370 $ + $ 5V.\frac{2k2*0.99}{2k2*1.01+2k2*0.99} = 2.475V $$ +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + + +Overfull \hbox (20.0pt too wide) in paragraph at lines 370--370 +[] + [] + + +Overfull \hbox (158.44156pt too wide) detected at line 370 +\OT1/cmr/m/n/10 5\OML/cmm/m/it/10 V:[] \OT1/cmr/m/n/10 = 2\OML/cmm/m/it/10 :\OT +1/cmr/m/n/10 475\OML/cmm/m/it/10 V + [] + + +! LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.372 $ + $ 5V.\frac{2k2*1.01}{2k2*1.01+2k2*0.99} = 2.525V $$ +You're in trouble here. 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+ +Overfull \hbox (20.0pt too wide) in paragraph at lines 374--376 +[] + [] + +! Undefined control sequence. +l.377 \subsubsection + { TC 6 : Voltages $R_3$ 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.377 \subsubsection{ T + C 6 : Voltages $R_3$ OPEN } +You're in trouble here. 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Undefined control sequence. +l.382 \subsection + {Summary of Analysis} +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.382 \subsection{S + ummary of Analysis} +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.384 A + ll six test cases have been analysed and the results agree with the h... + +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.397 \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.397 \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.399 \includegraphics + [width=400pt,bb=0 0 518 365,keepaspectratio=true]{./p... +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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Missing $ inserted. + + $ +l.399 ... 365,keepaspectratio=true]{./pt100/pt100_ + tc_sp.jpg} +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Extra }, or forgotten $. +l.399 ...spectratio=true]{./pt100/pt100_tc_sp.jpg} + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + + +! LaTeX Error: \caption outside float. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.401 \caption + {PT100 Component Failure Modes} +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + + +! LaTeX Error: \begin{document} ended by \end{figure}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.403 \end{figure} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + +! Missing $ inserted. + + $ +l.403 \end{figure} + +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +! Missing } inserted. + + } +l.403 \end{figure} + +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + + +Overfull \hbox (20.0pt too wide) in paragraph at lines 397--404 +[] + [] + + +Overfull \hbox (181.55289pt too wide) in paragraph at lines 397--404 +[]\OML/cmm/m/it/10 c[]p:jpg[][]$ + [] + + +! LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.406 T + he PT100 circuit can now be treated as a component in its own right, ... + +You're in trouble here. 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Undefined control sequence. + ...e `fig:pt100_singlef' on page \thepage + \space undefined\on@line . +l.407 ... a PLD see figure \ref{fig:pt100_singlef} + . +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 `fig:pt100_singlef' on page undefined on input line 4 +07. + +Missing character: There is no . in font nullfont! + +Overfull \hbox (20.0pt too wide) in paragraph at lines 406--408 +[] + [] + + +Overfull \hbox (8.63884pt too wide) in paragraph at lines 406--408 +\OT1/cmr/bx/n/10 O[][] + [] + + +Overfull \hbox (10.86105pt too wide) in paragraph at lines 406--408 +[] + [] + + +! LaTeX Error: Environment figure undefined. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.409 \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.409 \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.411 \includegraphics + [width=100pt,bb=0 0 167 194,keepaspectratio=true]{./p... +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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Missing $ inserted. + + $ +l.411 ... 194,keepaspectratio=true]{./pt100/pt100_ + singlef.jpg} +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Extra }, or forgotten $. +l.411 ...ectratio=true]{./pt100/pt100_singlef.jpg} + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + + +! LaTeX Error: \caption outside float. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.413 \caption + {PT100 Circuit Failure Modes : From Single Faults Analysis} +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + + +! LaTeX Error: \begin{document} ended by \end{figure}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.415 \end{figure} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + +! Missing $ inserted. + + $ +l.415 \end{figure} + +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +! Missing } inserted. + + } +l.415 \end{figure} + +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + + +Overfull \hbox (20.0pt too wide) in paragraph at lines 409--416 +[] + [] + + +Overfull \hbox (312.11783pt too wide) in paragraph at lines 409--416 +[]\OML/cmm/m/it/10 inglef:jpg[][]$ + [] + + +! LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.423 T + he PT100 analysis presents a simple result for single faults. +You're in trouble here. 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Undefined control sequence. +l.428 \subsection + {Statistical MTTF for the PT100 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.428 \subsection{S + tatistical MTTF for the PT100 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.430 M + il1991\cite{mil1991} gives a mean time to failure for a fixed film re... + +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + +Missing character: There is no M in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no l 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 9 in font nullfont! +Missing character: There is no 1 in font nullfont! +Missing character: There is no [ in font nullfont! +\citation{mil1991} +! Undefined control sequence. + ...: Citation `\@citeb ' on page \thepage + \space undefined\on@line . +l.430 Mil1991\cite{mil1991} + gives a mean time to failure for a fixed film re... +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: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.434 1 + 3.8 failure per billion hours of operation. +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.437 R + AC \cite{rac} states that a resistor will fail 9/10 OPEN and 1/10 SHORT. + +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 C in font nullfont! +Missing character: There is no [ in font nullfont! +\citation{rac} +! Undefined control sequence. + ...: Citation `\@citeb ' on page \thepage + \space undefined\on@line . +l.437 RAC \cite{rac} + states that a resistor will fail 9/10 OPEN and 1/10 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'). 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LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.441 M + ILL 1991 gives Thermisitors, bead $$0.21 15 1.0 1000$$ +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.444 A + gain we can apply the RAC division of resistor errors. +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.446 W + e can now see the six error types and see a statistical +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.450 T + he next analysis phase looks at how the circuit will behave under dou... + +You're in trouble here. 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Undefined control sequence. +l.454 \section + { PT100 Double Simultaneous Fault Analysis} +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.454 \section{ P + T100 Double Simultaneous Fault Analysis} +You're in trouble here. 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LaTeX Error: Environment table undefined. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.481 \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.481 \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.482 \caption + {PT100 FMEA Single Fault Statistics} % 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 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 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 F in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no u in font nullfont! 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LaTeX Error: \begin{document} ended by \end{table}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.502 \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 481--503 +[] + [] + + +Overfull \hbox (230.26279pt too wide) in paragraph at lines 481--503 +[] + [] + + +! LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.505 T + he ciruit overall has a MTTF of (13.8*2 + 3150) 3177.6 +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.510 I + nterestingly though we can now look at the results of our analysis +You're in trouble here. 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Emergency stop. +<*> pt100.tex + +*** (job aborted, no legal \end found) + + +Here is how much of TeX's memory you used: + 34 strings out of 95086 + 430 string characters out of 1183256 + 53034 words of memory out of 1500000 + 3302 multiletter control sequences out of 10000+50000 + 4294 words of font info for 16 fonts, out of 1200000 for 2000 + 28 hyphenation exceptions out of 8191 + 20i,7n,26p,127b,154s stack positions out of 5000i,500n,6000p,200000b,5000s +! ==> Fatal error occurred, no output PDF file produced! diff --git a/burner/pt100.tex.25MAR2010 b/burner/pt100.tex.25MAR2010 new file mode 100644 index 0000000..7a00e98 --- /dev/null +++ b/burner/pt100.tex.25MAR2010 @@ -0,0 +1,526 @@ +% +% 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 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. + +\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 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 +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 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, 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 +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} +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, +$R_3$ 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 +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 hypothesises an error condition in the readings. +The range 0\oc to 300\oc will be analysed using potential divider equations to +determine out of range voltage limits in section \ref{ptbounds}. + +\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 +$R_3$ 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 +\hline +\end{tabular} +\label{ptfmea} +\end{table} + +From table \ref{ptfmea} it can be seen that any component failure in the circuit +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}. + + +\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} + + +\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 {0\oc} to {300\oc} +for a given application. +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: + + +$$ highreading = 5V.\frac{2k2+pt100}{2k2+2k2+pt100} $$ +$$ lowreading = 5V.\frac{2k2}{2k2+2k2+pt100} $$ +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: + +$$ highreading = 2^{12}.\frac{2k2+pt100}{2k2+2k2+pt100} $$ +$$ lowreading = 2^{12}.\frac{2k2}{2k2+2k2+pt100} $$ + + +\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 & Boundary of \\ + & & 2002\adctw & 2094\adctw & out of range LOW \\ \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. + +%\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 vo + +\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. + +% OK we can look at stats here. +% the probabilities of the faults occurring in failures per billion hours +% of operation. +\subsection{Statistical MTTF for the PT100 circuit} + +Mil1991\cite{mil1991} gives a mean time to failure for a fixed film resistor +at up to 60oC at a low stress (current) level as +$$0.00092 . 1.0 . 15 . 1.0 . 1000$$ + +13.8 failure per billion hours of operation. + + +RAC \cite{rac} states that a resistor will fail 9/10 OPEN and 1/10 SHORT. +So 13.8 - 1.38 OPEN +1.38 SHORT + +MILL 1991 gives Thermisitors, bead $$0.21 15 1.0 1000$$ +3150 failures per billion hours of operation. + +Again we can apply the RAC division of resistor errors. + +We can now see the six error types and see a statistical +prediction of which will occur. We can also +determine the reliability of the circuit as a whole. + +The next analysis phase looks at how the circuit will behave under double simultaneous failure +conditions. + + + +% typeset in {\Huge \LaTeX} \today + +% +%\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 & Boundary of \\ +% & & 2002\adctw & 2094\adctw & out of range LOW \\ \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} +% + + + +\begin{table}[ht] +\caption{PT100 FMEA Single Fault Statistics} % title of Table +\centering % used for centering table +\begin{tabular}{||l|c|c|l|c||} +\hline \hline + \textbf{Test} & \textbf{Result} & \textbf{Result } & \textbf{MTTF} \\ + \textbf{Case} & \textbf{sense +} & \textbf{sense -} & \textbf{per $10^9$ hours of operation} \\ +% R & wire & res + & res - & description +\hline +\hline + $R_1$ SHORT & High Fault & - & 12.42 \\ \hline +$R_1$ OPEN & Low Fault & Low Fault & 1.38 \\ \hline + \hline +$R_3$ SHORT & Low Fault & High Fault & 2835 \\ \hline + $R_3$ OPEN & High Fault & Low Fault & 315 \\ \hline +\hline +$R_2$ SHORT & - & Low Fault & 12.42 \\ + $R_2$ OPEN & High Fault & High Fault & 1.38 \\ \hline +\hline +\end{tabular} +\label{pt100_single_stats} +\end{table} + + +The ciruit overall has a MTTF of (13.8*2 + 3150) 3177.6 +Failure in Time FIT\footnote{FIT values are measured as failures per billion ($10^9$) hours of operation}. +This gives an individual pt100 circuit of this type an MTTF of around 39 years. + +Interestingly though we can now look at the results of our analysis +as a probablistic tree see figure \ref{fig:stat_single}. We can see the overall +reliability of the circuit +and we can see the most likely fault (the thermisitor going OPEN circuit). +The circuit is 8 times more likely to fail in this way than in any other. +Were we to need a more reliable temperature sensor this would probably +be the component area we would scrutinise first. + +\begin{figure}[h] + \centering + \includegraphics[width=400pt,bb=0 0 856 328,keepaspectratio=true]{./stat_single.jpg} + % stat_single.jpg: 856x328 pixel, 72dpi, 30.20x11.57 cm, bb=0 0 856 328 + \caption{Probablistic Tree} + \label{fig:stat_single} +\end{figure} + +\clearpage + +\section{ PT100 Double Simultaneous Fault Analysis} diff --git a/burner/pt100.tex.backup b/burner/pt100.tex.backup new file mode 100644 index 0000000..9ba3923 --- /dev/null +++ b/burner/pt100.tex.backup @@ -0,0 +1,412 @@ +% +% 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 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. + +\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 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 +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 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, 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 +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} +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. + +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. + +\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} + + +\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 {0\oc} to {300\oc} +for a given application. +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 & Boundary of \\ + & & 2002\adctw & 2094\adctw & out of range LOW \\ \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. + +%\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 vo + +\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. + + + +\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} + +%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/burner/pt100.tex~ b/burner/pt100.tex~ new file mode 100644 index 0000000..4451784 --- /dev/null +++ b/burner/pt100.tex~ @@ -0,0 +1,516 @@ +% +% 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 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. + +\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 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 +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 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, 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 +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} +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, +$R_3$ 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 +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 hypothesises an error condition in the readings. +The range 0\oc to 300\oc will be analysed using potential divider equations to +determine out of range voltage limits in section \ref{ptbounds}. + +\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 +$R_3$ 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 +\hline +\end{tabular} +\label{ptfmea} +\end{table} + +From table \ref{ptfmea} it can be seen that any component failure in the circuit +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}. + + +\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} + + +\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 {0\oc} to {300\oc} +for a given application. +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: + + +$$ highreading = 5V.\frac{2k2+pt100}{2k2+2k2+pt100} $$ +$$ lowreading = 5V.\frac{2k2}{2k2+2k2+pt100} $$ +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: + +$$ highreading = 2^{12}.\frac{2k2+pt100}{2k2+2k2+pt100} $$ +$$ lowreading = 2^{12}.\frac{2k2}{2k2+2k2+pt100} $$ + + +\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 & Boundary of \\ + & & 2002\adctw & 2094\adctw & out of range LOW \\ \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. + +%\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 vo + +\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. + +% OK we can look at stats here. +% the probabilities of the faults occurring in failures per billion hours +% of operation. +\subsection{Statistical MTTF for the PT100 circuit} + +Mil1991\cite{mil1991} gives a mean time to failure for a fixed film resistor +at up to 60oC at a low stress (current) level as +$$0.00092 . 1.0 . 15 . 1.0 . 1000$$ + +13.8 failure per billion hours of operation. + + +RAC \cite{rac} states that a resistor will fail 9/10 OPEN and 1/10 SHORT. +So 13.8 - 1.38 OPEN +1.38 SHORT + +MILL 1991 gives Thermisitors, bead $$0.21 15 1.0 1000$$ +3150 failures per billion hours of operation. + +Again we can apply the RAC division of resistor errors. + +We can now see the six error types and see a statistical +prediction of which will occur. We can also +determine the reliability of the circuit as a whole. + +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 + +% +%\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 & Boundary of \\ +% & & 2002\adctw & 2094\adctw & out of range LOW \\ \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} +% + + + +\begin{table}[ht] +\caption{PT100 FMEA Single Fault Statistics} % title of Table +\centering % used for centering table +\begin{tabular}{||l|c|c|l|c||} +\hline \hline + \textbf{Test} & \textbf{Result} & \textbf{Result } & \textbf{MTTF} \\ + \textbf{Case} & \textbf{sense +} & \textbf{sense -} & \textbf{per $10^9$ hours of operation} \\ +% R & wire & res + & res - & description +\hline +\hline + $R_1$ SHORT & High Fault & - & 12.42 \\ \hline +$R_1$ OPEN & Low Fault & Low Fault & 1.38 \\ \hline + \hline +$R_3$ SHORT & Low Fault & High Fault & 2835 \\ \hline + $R_3$ OPEN & High Fault & Low Fault & 315 \\ \hline +\hline +$R_2$ SHORT & - & Low Fault & 12.42 \\ + $R_2$ OPEN & High Fault & High Fault & 1.38 \\ \hline +\hline +\end{tabular} +\label{pt100_single_stats} +\end{table} + + +The ciruit overall has a MTTF of (13.8*2 + 3150) 3177.6 +per billion ($10^9$) hours of operation. +This gives an individual circuit a MTTF of around 39 years. + + +Interestingly though we can now look at the results of our analysis +as a probablistioc tree. We can see the overall reliability of the circuit +and we can see the most likely fault (the thermisitor going OPEN circuit). +The circuit is 8 times more likely to fail in this way than in any other. +Were we to need a more reliable temperature sensor this would probably +be the component area we would scrutinise first. + diff --git a/burner/pt100_paper.tex b/burner/pt100_paper.tex new file mode 100644 index 0000000..8c29335 --- /dev/null +++ b/burner/pt100_paper.tex @@ -0,0 +1,434 @@ +% +% 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 widely used industrial temperature sensor that is +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 faults (cardinality constrained powerset of 2). + +The analysis is performed using Propositional Logic +diagrams 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 itself, with a set of known failure modes. + +\end{abstract} + + +\begin{figure}[h] + \centering + \includegraphics[width=400pt,bb=0 0 714 180,keepaspectratio=true]{./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 uses two wires to supply small electrical current, +and returns two sense volages by the other two. +By measuring volatges +from sections of this circuit forming potential dividers, we can determine the +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]{./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 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 a four wire circuit is preffered +because of resistance in the cables. Resistance 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, 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 +and knowing the voltage drop over the PT100, we can calculate its +resistance by ohms law $V=I.R$, $R=\frac{V}{I}$. +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 distinct 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} +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 this analyis; +$R_{1}$ is the \ohms{2k2} from 5V to the thermistor, +$R_3$ is the PT100 thermistor and $R_{2}$ connects the thermistor to ground. + +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'. + +Table \ref{ptfmea} plays through the scenarios of each of the resistors failing +in both SHORT and OPEN failure modes, and hypothesises an error condition in the readings. +The range {0\oc} to {300\oc} will be analysed using potential divider equations to +determine out of range voltage limits in section \ref{ptbounds}. + +\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 +$R_3$ 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 +\hline +\end{tabular} +\label{ptfmea} +\end{table} + +From table \ref{ptfmea} it can be seen that any component failure in the circuit +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}. + + + +\subsection{Range and PT100 Calculations} +\label{pt100temp} +PT100 resistors are designed to +have a resistance of \ohms{100} at {0\oc} \cite{aoe},\cite{eurothermtables}. +A suitable `wider than to be expected range' was considered to be {0\oc} to {300\oc} +for a given application. +According to the Eurotherm PT100 +tables \cite{eurothermtables}, this corresponded to the resistances \ohms{100} +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: + + +$$ highreading = 5V.\frac{2k2+pt100}{2k2+2k2+pt100} $$ +$$ lowreading = 5V.\frac{2k2}{2k2+2k2+pt100} $$ +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: + +$$ highreading = 2^{12}.\frac{2k2+pt100}{2k2+2k2+pt100} $$ +$$ lowreading = 2^{12}.\frac{2k2}{2k2+2k2+pt100} $$ + + +\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 & Boundary of \\ + & & 2002\adctw & 2094\adctw & out of range LOW \\ \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. + + +\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, is defined by the contours that enclose +it. The test cases here deal with single faults only +and are thus enclosed by one contour each. + + +\begin{figure}[h] + \centering + \includegraphics[width=400pt,bb=0 0 518 365,keepaspectratio=true]{./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 temperature range for this example ({0\oc} .. {300\oc}) we can calculate +valid voltage reading ranges by using the standard voltage divider equation \ref{eqn:vd} +for the circuit shown in figure \ref{fig:vd}. + + +\begin{figure}[h] + \centering + \includegraphics[width=100pt,bb=0 0 183 170,keepaspectratio=true]{./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} + + + +\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.. +$$ lowreading = 5V.\frac{2k2}{2k2+100\Omega} = 4.78V$$ +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 3 : Voltages $R_2$ SHORT } + +With pt100 at 0\oc +$$ lowreading = 0V $$ +Since the lowreading or sense- is directly connected to the 0V rail, +both temperature readings will be 0V. +$$ lowreading = 5V.\frac{100\Omega}{2k2+100\Omega} = 0.218V$$ +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 readings are outside the +proscribed range in table \ref{ptbounds}. + +\subsubsection{ TC : 4 Voltages $R_2$ OPEN } +Here there is no potential divider operating and both sense lines +will read 5V, outside of the proscribed 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_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_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) ??? +\clearpage +\subsection{Mean Time to Failure} + +Using the MIL1991\cite{mil1991} specifications for resistor and thermistor +failure statistics we calculate the reliability of this circuit. +MIL1991 gives MTTF for a wide range of common components. +It does not specify how the components will fail (in this case OPEN or SHORT). {Some standards, notably EN298 only consider resistors failing in OPEN mode}. +FMD-97 Gives 27\% OPEN and 3\% SHORTED, for resistors under certain electrical and environmental stresses. This example +compromises and uses a 90:10 ratio, for resistor failure. +Thus for this example resistors are expevcted to fail OPEN in 90\% of cases and SHORTED +in the other 10\%. + +A standard fixed film resistor, for use in a benign environment, non military spec at +temperatures up to 60\oc is given a probability of 13.8 failures per billion ($10^9$) +hours of operation. This figure is referred to as a FIT\footnote{FIT values are measured as the number of failures per billion hours of operation, (roughly 1.1 Million years). The smaller the FIT number the more reliable the fault~mode}, Failure in time. + +A thermistor, bead type, non military spec is given a FIT of 3150. + +Using the RIAC finding we can draw up the following table (table \ref{tab:stat_single}), +showing the FIT values for all faults considered. + + + +\begin{table}[h+] +\caption{PT100 FMEA Single // Fault Statistics} % title of Table +\centering % used for centering table +\begin{tabular}{||l|c|c|l|l||} +\hline \hline + \textbf{Test} & \textbf{Result} & \textbf{Result } & \textbf{MTTF} \\ + \textbf{Case} & \textbf{sense +} & \textbf{sense -} & \textbf{per $10^9$ hours of operation} \\ +% R & wire & res + & res - & description +\hline +\hline +TC:1 $R_1$ SHORT & High Fault & - & 12.42 \\ \hline +TC:2 $R_1$ OPEN & Low Fault & Low Fault & 1.38 \\ \hline + \hline +TC:3 $R_3$ SHORT & Low Fault & High Fault & 2835 \\ \hline +TC:4 $R_3$ OPEN & High Fault & Low Fault & 315 \\ \hline +\hline +TC:5 $R_2$ SHORT & - & Low Fault & 12.42 \\ +TC:6 $R_2$ OPEN & High Fault & High Fault & 1.38 \\ \hline +\hline +\end{tabular} +\label{tab:stat_single} +\end{table} + +The FIT for the circuit as a whole is the sum of MTTF values for all the +test cases. The PT100 circuit here has a FIT of 3177.6. This is a MTTF of +about 360 years per circuit. + +A Probablistic tree can now be drawn, with a FIT value for the PT100 +circuit and FIT values for all the component fault modes that it was calculated from. +We can see from this that that the most likely fault is the thermistor going OPEN. +This circuit is 8 times more likely to fail in this way than in any other. +Were we to need a more reliable temperature sensor this would probably +be the fault~mode we would scrutinise first. + + +\begin{figure}[h+] + \centering + \includegraphics[width=400pt,bb=0 0 856 327,keepaspectratio=true]{./stat_single.jpg} + % stat_single.jpg: 856x327 pixel, 72dpi, 30.20x11.54 cm, bb=0 0 856 327 + \caption{Probablistic Fault Tree : PT100 Single Faults} + \label{fig:stat_single} +\end{figure} + + +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. + +\clearpage +\section{ PT100 Double Simultaneous \\ Fault Analysis} + +% typeset in {\Huge \LaTeX} \today + diff --git a/burner/stat_single.dia~ b/burner/stat_single.dia~ new file mode 100644 index 0000000..e4edbcb Binary files /dev/null and b/burner/stat_single.dia~ differ diff --git a/burner/vrange.dia~ b/burner/vrange.dia~ new file mode 100644 index 0000000..e129adb Binary files /dev/null and b/burner/vrange.dia~ differ diff --git a/component_failure_modes_definition/component_failure_modes_definition.tex b/component_failure_modes_definition/component_failure_modes_definition.tex index 233d823..660885f 100644 --- a/component_failure_modes_definition/component_failure_modes_definition.tex +++ b/component_failure_modes_definition/component_failure_modes_definition.tex @@ -1,6 +1,6 @@ \abstract{ This chapter defines what is meant by the terms -components, component fault modess and `unitary~state' component fault modes. +components, component fault modes and `unitary~state' component fault modes. Mathematical constraints and definitions are made using set theory. } @@ -12,15 +12,28 @@ For most common electrical and mechanical components, the failure modes for a given type of part can be obtained from standard literature\cite{mil1991} \cite{mech}. %The failure modes for a given component $K$ form a set $F$. -An important factor in defining a failure mode is that they +An important factor in defining a set of failure modes is that they should be as clearly defined as possible. % It should not be possible for instance for a component to have two or more failure modes active at once. -Should this be the case, the failure modes have not been clearly analysed. -The combination could be represented by a new failure mode, or -the component should be re-analysed. A set of failure modes where only one fault mode + +Having a set of failure modes where $N$ modes could be active simultaneously +would mean having to consider $2^N$ failure mode scenarios. +% +Should a component be analysed and simultaneous failure mode cases exit, +the combinations could be represented by a new failure modes, or +the component should be considered from a fresh perspective, +perhaps considering it as several smaller components +within one package. + +\begin{definition} +A set of failure modes where only one fault mode can be active at a time is termed a `unitary~state' failure mode set. +This is termed the $U$ set thoughout this study. +This corresponds to the `mutually exclusive' definition in +probability theory\cite{probandstat}. +\end{definition} We can define a function $FM()$ to take a given component $K$ and return its set of failure modes $F$. @@ -38,61 +51,29 @@ A component with simple ``unitary~state'' failure modes is the electrical resist Electrical resistors can fail by going OPEN or SHORTED. However they cannot fail with both conditions active. The conditions -OPEN and SHORT are mutually exlusive. +OPEN and SHORT are mutually exclusive. Because of this the failure mode set $F=FM(R)$ is `unitary~state'. -%A more complex component, say a micro controller could have several -%faults active. It could for instance have a broken I/O output -%and an unstable ADC input. Here the faults cannot be considered `unitary~state'. - -% A set of failure modes, where only one or no failure modes -% are active is termed an `unitary~state' failure mode set. This -% will be donoted as set $A$. -% -To define `unitary~state' using set theory we can define a function -`active'. -The function $active(f)$ deontes that the failure mode $f$ (where $f$ is an element of $F$) is currently active. - -Thus for the set $F$ to exist in $U$ the following condition must be true. - -\begin{equation} -\label{unitarystate_def} - F \in U | f \in F \wedge active(f) \wedge f1 \in F \wedge f1 \neq f \wedge \neg active(f1) -\end{equation} - -As an example the resistor $R$ -has two failure modes $R_{open}$ and $R_{shorted}$. - -$$ FM(R) = F = \{ R_{open}, R_{shorted} \} $$ - -Applying equation \ref{`unitarystate'_definition} to a resistor -for both fault modes - - $$ active(R_{short}) | R_{short} \in F \wedge R_{open} \in F \wedge R_{open} \neq R_{short} \wedge \neg active(R_{open}) $$ - $$ active(R_{open}) | R_{open} \in F \wedge R_{short} \in F \wedge R_{short} \neq R_{open} \wedge \neg active(R_{short}) $$ - -For the case of the resistor with only two failure modes the results above, being true, -show that the failure modes for a resistor of $ F = \{ R_{open}, R_{shorted} \} $ are `unitary~state' -component failure modes. - -Thus - $$ FM(R) = \{ R_{open}, R_{shorted} \} \in U $$ -A general case can be stated by taking equation \ref{unitary_state_def} and making it a function thus. +Thus + +$$ R_{SHORTED} \cap R_{OPEN} = \emptyset $$ -\begin{equation} -\label{`unitarystate'_def} - UnitaryState(F) = \forall f \in F | active(f) \wedge f1 \in F \wedge f1 \neq f \wedge \neg active(f1) -\end{equation} - -%Which can be written - -%$$ UnitaryState(FM(K)) $$ +We can make this a general case by taking a set $C$ representing a collection +of component failure modes, +We can now state that +$$ c1 \cap c2 \neq \emptyset | c1 \neq c2 \wedge c1,c2 \in C \wedge C \not\in U $$ -% should this be a paragraph in Symptom Abstraction ???? +That is to say that if it is impossible that any pair of failure modes can be active at the same time +the failure mode set is not unitary~state and does not exist in the family of sets $U$ + Note where that are more than two failure~modes, by banning pairs from happening at the same time + we have banned larger combinations as well +%$$ c1 \cap c2 \eq \emptyset | c1 \neq c2 \wedge c1,c2 \in C \wedge C \in U $$ +%Thus if the failure~modes are pairwaise mutually exclusive they qualify for inclusion into the +%unitary~state set family. diff --git a/introduction/introduction.tex b/introduction/introduction.tex index 756b8dd..245bf25 100644 --- a/introduction/introduction.tex +++ b/introduction/introduction.tex @@ -21,12 +21,21 @@ This changed the target for the study slightly to encompass these domains in a c I completed an MSc in Software engineering in 2004 at Brighton university while working for an Engineering firm as a software Engineer. The firm make industrial burner controllers. -iIndustrial Burners are potentially very dangerous industrail plant. -They are subject to stringent safety regulations and any product controlling them -must conform to specific `EN' standards. This involved not only writing software and designing hardware in compliance, -but also stages of formal certification testing. The certification testing had to be performed by -`competent body' recognised under European law. A significant part -of this process was `static testing'. This involved looking at the design of the products, +Industrial Burners are potentially very dangerous industrial plant. +They are generally left running unattended for long periods. +They are subject to stringent safety regulations and +must conform to specific `EN' standards. + +One cannot merely comply with the standards. + +The product must be `certified' by an independent +and +`competent body' recognised under European law. +The cerification involved stress testing with repeated operation cycles, +within a range of temperatures. Electrical stress testing with high voltage interference, and +power supply voltage surges and dips. Electro static discharge testing, and +EMC (Electro Magnetic Compatibility). A significant part +of this process however, was `static testing'. This involved looking at the design of the products, from the perspective of components failing, and the effect on safety this would have. Some of the static testing involved checking that the germane `EN' standards had been complied with. Failure Mode Effects Analysis (FMEA) was also applied. This involved @@ -36,9 +45,19 @@ answer was required, or a counter proposal to change the design to cope with the comonent failure eventuality. FMEA was time consuming, and being directed by experts undoubtly ironed out many potential safety faults before the product saw light of day. However it was quickly apparent that only a small proportion -of copmponent~failure modes was considered. Also there was no formaliswm. +of copmponent~failure modes was considered. Also there was no formalism. The component~failure~modes investigated were not analysed within any rigourous framework. + +\subsection{ Blanket Risk Reduction Approach } + +The suite of tests applied for a certified product amount to a `blanket' approach. +That is to say that by applying Electrical, repeated operations, and environmental +stress testing it is hoped that the majority of latent faults are discovered. +The FMEA, or static sections, only look at the most obviously safety critical +aspects, and a small minority of the total component base for a product. + +Systememic faults, or mistakes will often by-pass this testing. \subsection{Possibility of applying mathematical techniques to FMEA} @@ -66,23 +85,25 @@ obviously impractical. \subsection{General description of a Safety Critical System} A safety critical system is one in which lives may depend upon it or -it has the potential to become dangerous. -(/usr/share/texmf-texlive/tex/latex/amsmath/amstext.sty) +it has the potential to become dangerous\cite{sccs}. +%(/usr/share/texmf-texlive/tex/latex/amsmath/amstext.sty) An industrial burner is typical of plant that is potentially dangerous. An incorrect air/fuel mixture can be explosive. Medical electronics for automatically dispensing drugs or maintaining life support are examples of systems that lives depend upon. -\subsection{Two approaches : Probablistic, and Compnent fault tolerant} +\subsection{Two approaches : Probablistic, and Deterministic} There are two main philosophies applied to safety critical systems certification. -\paragraph{Statistical safety Measures} -One is a general number of acceptable failure per hour of operation. +\paragraph{Probablistic safety Measures} +One is a general number of acceptable failures per hour\footnote{The common metric is Failure in Time (FIT) values - failures per ${10}^{9}$ +hours of operation} of operation or +a given statistical failure on demand. This is the probablistic approach and is embodied in the european standard EN61508 \cite{EN61508}. -\paragraph{Prescriptive safety Measures} +\paragraph{Deterministic safety Measures} The second philosophy, applied to application specific standards, is to investigate components ior sub-systems in the critical safety path and to look at component failure modes and ensure that they cannot cause dangerous faults. @@ -114,67 +135,36 @@ reference chapter dealing speciifically with this but given a quick overview. \subsubsection{Overview of current testing and certification} ref chapter speciifically on this but give an overview now -\section{Background to the Industrial Burner Safety Analysis Problem} - -An industrial burner is a good example of a safety critical system. -It has the potential for devistating explosions due to boiler overpressure, or -ignition of an explosive mixture, and, because of the large amounts of fuel used, -is also a fire hazard. Also Industrial boilers are often left running unattended -for long periods of time (typically days). - -To add to these problems -Operators are often under pressure to keep them running. An boiler supplying -heat to a large greenhouse complex could ruin crops -should it go off-line. Similarly a production line relying on heat or steam -can be very expensive in production down-time should it fail. -This places extra responsibility on the burner controller. - - -These are common place and account for a very large proportion of the enery usage -in the world today (find and ref stats) -Industrial burners are common enough to have different specific standards -written for the fuel types they use \ref{EN298} \ref{EN230} \ref{EN12067}. - A modern industrial burner has mechanical, electronic and software elements, that are all safety critical. That is to say unhandled failures could create dangerous faults. -To add to these problems -Operators are often under pressure to keep them running. An boiler supplying -heat to a large greenhouse complex could ruin crops -should it go off-line. Similarly a production line relying on heat or steam -can be very expensive in production down-time should it fail. -This places extra responsibility on the burner controller. - - -These are common place and account for a very large proportion of the enery usage -in the world today (find and ref stats) -Industrial burners are common enough to have different specific standards -written for the fuel types they usei \ref{EN298} \ref{EN230} \ref{EN12067}. - -A modern industrial burner has mechanical, electronic and software -elements, that are all safety critical. That is to say -unhandled failures could create dangerous faults. - -A more detailed description of industrial burner controllers -is dealt with in chapter~\ref{burnercontroller}. - -\subsection{Mechanical components} -describe the mechanical parts - gas valves damper s -electronic and software -give a diagram of how it all fits A -together with a -\subsection{electronic Components} - -\subsection{Software/Firmware Components} - - -\subsection{A high level Fault Hierarchy for an Industrial Burner} - -This section shows the component level, leading up higher and higher in the abstraction level -to the software levels and finally a top level abstract level. If the system has been -designed correctly no `undetected faults' should be present here. +%To add to these problems +%Operators are often under pressure to keep them running. An boiler supplying +%heat to a large greenhouse complex could ruin crops +%should it go off-line. Similarly a production line relying on heat or steam +%can be very expensive in production down-time should it fail. +%This places extra responsibility on the burner controller. +% +% +% This needs to become a chapter +%\subsection{Mechanical components} +%describe the mechanical parts - gas valves damper s +%electronic and software +%give a diagram of how it all fits A +%together with a +%\subsection{electronic Components} +% +%\subsection{Software/Firmware Components} +% +% +%\subsection{A high level Fault Hierarchy for an Industrial Burner} +% +%This section shows the component level, leading up higher and higher in the abstraction level +%to the software levels and finally a top level abstract level. If the system has been +%designed correctly no `undetected faults' should be present here. +% \section{An Outline of the FMMD Technique} The methodology takes a bottom up approach to @@ -182,8 +172,10 @@ the design of an integrated system. Each component is assigned a well defined set of failure modes. The components are formed into modules, or functional groups. These functional groups are analysed with respect to the failure modes of the -components. The `functional group' or module will have a set of derived -failure modes. The number of derived failure modes will be +components. The `functional group' or module will, after analysis, have a set of derived +failure modes. Thus we can now treat our `functional group' as a component in its own right, + with its own set of failure~modes. +The number of derived failure modes will be less than or equal to the sum of the failure modes of all its components. A `derived' set of failure modes, is at a higher abstraction level. derived modules may now be used as building blocks, to model the system at @@ -197,6 +189,7 @@ A formal description of this process is dealt with in Chapter \ref{fmmddefinitio %on simple control systems for maintaining temperature %and for industrial burners. It is hoped that a general mathematical %framework is created that can be applied to other fields of safety critical engineering. +\subsection{Automated Systems and Safety} Automated systems, as opposed to manual ones are now the norm in the home and in industry. @@ -238,30 +231,6 @@ corrections cannot be enough. It could also develop an internal fault, and must be able to cope with this. -Systems such as industrial burners have been partially automated for some time. -A mechanical cam arrangement controls the flow of air and fuel for the range of -firing rate (output of the boiler). - -These mechanical systems could suffer failures (such as a mechanical linkage beoming -detached) and could then operate in a potentially dangerous state. - -More modern burner controllers use a safety critical computer controlling -motors to operate the fuel and air mixture and to control the safety -valves. - -In working in the industrial burner industry and submitting product for -North American and European safety approval, it was apparent that -formal techniques could be applied to aspects of the ciruit design. -Some safety critical circuitry would be subjected to thought experiments, where -the actions of one or more components failing would be examined. -As a simple example a milli-volt input could become disconnected. -A milli-volt input is typically amplified so that its range matches that -of the A->D converter that you are reading. were this signal source to become disconnected -the systems would see a floating, amplified signal. -A high impedance safety resistor can be added to the circuit, -to pull the signal high (or out of nornal range) upon disconnection. -The system then knows that a fault has occurred and will not use -that sensor reading (see \ref{fig:millivolt}). @@ -389,6 +358,12 @@ The problem lay in a seal that had an operating temperature range. On the day of the launch the temperature of this seal was out of range. A bottom up safety approach would have revealed this as a fault. +The FTA in use by NASA and the US Nuclear regulatory commisssion +allows for enviromental considerations such as temperature\cite{NASA}\cite{NUK}. +But because of the top down nature of the FTA technique, the safety designer must be aware of +the environemtnal constraints of all component parts in order to use this correctly. +This element of FTA is discussed in \ref{surveysc} + \section{Problems with Natural Language} Written natural language desciptions can not only be ambiguous or easy to misinterpret, it @@ -427,6 +402,7 @@ temperature being the most typical. Very often what happens to the system outsid \section{Project Goals} \begin{itemize} +\item To create a Bottom up FMEA technique that is modular and permits a linked hierarchy to be build representing the fault behaviour of a system. \item To create a user friendly formal common visual notation to represent fault modes in Software, Electronic and Mechanical sub-systems. \item To formally define this visual language. diff --git a/standards/Makefile b/standards/Makefile new file mode 100644 index 0000000..4f0baf6 --- /dev/null +++ b/standards/Makefile @@ -0,0 +1,17 @@ + +# +# Make the propositional logic diagram a paper +# + + +paper: paper.tex standards_paper.tex + #latex paper.tex + #dvipdf paper pdflatex cannot use eps ffs + pdflatex paper.tex + okular paper.pdf + + +# Remove the need for referncing graphics in subdirectories +# +standards_paper.tex: standards.tex + cat standards.tex | sed 's/standards\///' > standards_paper.tex diff --git a/standards/paper.aux b/standards/paper.aux new file mode 100644 index 0000000..cf635bc --- /dev/null +++ b/standards/paper.aux @@ -0,0 +1,11 @@ +\relax +\bibstyle{plain} +\bibdata{vmgbibliography,mybib} +\@writefile{toc}{\contentsline {section}{\numberline {1}Introduction}{1}} +\@writefile{toc}{\contentsline {section}{\numberline {2}European Safety Standards Legal Framework}{1}} +\@writefile{toc}{\contentsline {section}{\numberline {3}North American Legal Framework}{1}} +\@writefile{toc}{\contentsline {section}{\numberline {4}Cross Referencing}{1}} +\@writefile{toc}{\contentsline {section}{\numberline {5}EN298}{1}} +\@writefile{toc}{\contentsline {section}{\numberline {6}UL1998}{1}} +\@writefile{toc}{\contentsline {section}{\numberline {7}EN230}{1}} +\@writefile{toc}{\contentsline {section}{\numberline {8}EN61508}{1}} diff --git a/standards/paper.log b/standards/paper.log new file mode 100644 index 0000000..2331d84 --- /dev/null +++ b/standards/paper.log @@ -0,0 +1,429 @@ +This is pdfTeXk, Version 3.141592-1.40.3 (Web2C 7.5.6) 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183820 words of memory out of 1500000 + 11159 multiletter control sequences out of 10000+50000 + 9805 words of font info for 37 fonts, out of 1200000 for 2000 + 28 hyphenation exceptions out of 8191 + 47i,6n,49p,350b,196s stack positions out of 5000i,500n,6000p,200000b,5000s + +Output written on paper.pdf (1 page, 42142 bytes). +PDF statistics: + 33 PDF objects out of 1000 (max. 8388607) + 0 named destinations out of 1000 (max. 131072) + 13 words of extra memory for PDF output out of 10000 (max. 10000000) + diff --git a/standards/paper.pdf b/standards/paper.pdf new file mode 100644 index 0000000..951aee0 Binary files /dev/null and b/standards/paper.pdf differ diff --git a/standards/paper.tex b/standards/paper.tex new file mode 100644 index 0000000..a649964 --- /dev/null +++ b/standards/paper.tex @@ -0,0 +1,27 @@ + +\documentclass[a4paper,10pt]{article} +\usepackage{graphicx} +\usepackage{fancyhdr} +\usepackage{tikz} +\usepackage{amsfonts,amsmath,amsthm} +\input{../style} + +%\newtheorem{definition}{Definition:} + +\begin{document} +\pagestyle{fancy} + +\outerhead{{\small\bf Safety Critical Standards Review}} +%\innerfoot{{\small\bf R.P. Clark } } + % numbers at outer edges +\pagenumbering{arabic} % Arabic page numbers hereafter +\author{R.P.Clark} +\title{Safety Critical Standards Review} +\maketitle +\input{standards_paper} + +\bibliographystyle{plain} +\bibliography{vmgbibliography,mybib} + +\today +\end{document} diff --git a/standards/pt100.tex b/standards/pt100.tex new file mode 100644 index 0000000..20feebb --- /dev/null +++ b/standards/pt100.tex @@ -0,0 +1,434 @@ +% +% 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 widely used industrial temperature sensor that is +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 faults (cardinality constrained powerset of 2). + +The analysis is performed using Propositional Logic +diagrams 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 itself, with a set of known 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 uses two wires to supply small electrical current, +and returns two sense volages by the other two. +By measuring volatges +from sections of this circuit forming potential dividers, we can determine the +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 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 a four wire circuit is preffered +because of resistance in the cables. Resistance 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, 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 +and knowing the voltage drop over the PT100, we can calculate its +resistance by ohms law $V=I.R$, $R=\frac{V}{I}$. +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 distinct 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} +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 this analyis; +$R_{1}$ is the \ohms{2k2} from 5V to the thermistor, +$R_3$ is the PT100 thermistor and $R_{2}$ connects the thermistor to ground. + +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'. + +Table \ref{ptfmea} plays through the scenarios of each of the resistors failing +in both SHORT and OPEN failure modes, and hypothesises an error condition in the readings. +The range {0\oc} to {300\oc} will be analysed using potential divider equations to +determine out of range voltage limits in section \ref{ptbounds}. + +\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 +$R_3$ 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 +\hline +\end{tabular} +\label{ptfmea} +\end{table} + +From table \ref{ptfmea} it can be seen that any component failure in the circuit +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}. + + + +\subsection{Range and PT100 Calculations} +\label{pt100temp} +PT100 resistors are designed to +have a resistance of \ohms{100} at {0\oc} \cite{aoe},\cite{eurothermtables}. +A suitable `wider than to be expected range' was considered to be {0\oc} to {300\oc} +for a given application. +According to the Eurotherm PT100 +tables \cite{eurothermtables}, this corresponded to the resistances \ohms{100} +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: + + +$$ highreading = 5V.\frac{2k2+pt100}{2k2+2k2+pt100} $$ +$$ lowreading = 5V.\frac{2k2}{2k2+2k2+pt100} $$ +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: + +$$ highreading = 2^{12}.\frac{2k2+pt100}{2k2+2k2+pt100} $$ +$$ lowreading = 2^{12}.\frac{2k2}{2k2+2k2+pt100} $$ + + +\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 & Boundary of \\ + & & 2002\adctw & 2094\adctw & out of range LOW \\ \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. + + +\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, is defined by the contours that enclose +it. The test cases here deal with single faults only +and are thus enclosed by one contour each. + + +\begin{figure}[h] + \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 temperature range for this example ({0\oc} .. {300\oc}) we can calculate +valid voltage reading ranges by using the standard voltage divider equation \ref{eqn:vd} +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} + + + +\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.. +$$ lowreading = 5V.\frac{2k2}{2k2+100\Omega} = 4.78V$$ +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 3 : Voltages $R_2$ SHORT } + +With pt100 at 0\oc +$$ lowreading = 0V $$ +Since the lowreading or sense- is directly connected to the 0V rail, +both temperature readings will be 0V. +$$ lowreading = 5V.\frac{100\Omega}{2k2+100\Omega} = 0.218V$$ +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 readings are outside the +proscribed range in table \ref{ptbounds}. + +\subsubsection{ TC : 4 Voltages $R_2$ OPEN } +Here there is no potential divider operating and both sense lines +will read 5V, outside of the proscribed 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) ??? +\clearpage +\subsection{Mean Time to Failure} + +Using the MIL1991\cite{mil1991} specifications for resistor and thermistor +failure statistics we calculate the reliability of this circuit. +MIL1991 gives MTTF for a wide range of common components. +It does not specify how the components will fail (in this case OPEN or SHORT). {Some standards, notably EN298 only consider resistors failing in OPEN mode}. +FMD-97 Gives 27\% OPEN and 3\% SHORTED, for resistors under certain electrical and environmental stresses. This example +compromises and uses a 90:10 ratio, for resistor failure. +Thus for this example resistors are expevcted to fail OPEN in 90\% of cases and SHORTED +in the other 10\%. + +A standard fixed film resistor, for use in a benign environment, non military spec at +temperatures up to 60\oc is given a probability of 13.8 failures per billion ($10^9$) +hours of operation. This figure is referred to as a FIT\footnote{FIT values are measured as the number of failures per billion hours of operation, (roughly 1.1 Million years). The smaller the FIT number the more reliable the fault~mode}, Failure in time. + +A thermistor, bead type, non military spec is given a FIT of 3150. + +Using the RIAC finding we can draw up the following table (table \ref{tab:stat_single}), +showing the FIT values for all faults considered. + + + +\begin{table}[h+] +\caption{PT100 FMEA Single // Fault Statistics} % title of Table +\centering % used for centering table +\begin{tabular}{||l|c|c|l|l||} +\hline \hline + \textbf{Test} & \textbf{Result} & \textbf{Result } & \textbf{MTTF} \\ + \textbf{Case} & \textbf{sense +} & \textbf{sense -} & \textbf{per $10^9$ hours of operation} \\ +% R & wire & res + & res - & description +\hline +\hline +TC:1 $R_1$ SHORT & High Fault & - & 12.42 \\ \hline +TC:2 $R_1$ OPEN & Low Fault & Low Fault & 1.38 \\ \hline + \hline +TC:3 $R_3$ SHORT & Low Fault & High Fault & 2835 \\ \hline +TC:4 $R_3$ OPEN & High Fault & Low Fault & 315 \\ \hline +\hline +TC:5 $R_2$ SHORT & - & Low Fault & 12.42 \\ +TC:6 $R_2$ OPEN & High Fault & High Fault & 1.38 \\ \hline +\hline +\end{tabular} +\label{tab:stat_single} +\end{table} + +The FIT for the circuit as a whole is the sum of MTTF values for all the +test cases. The PT100 circuit here has a FIT of 3177.6. This is a MTTF of +about 360 years per circuit. + +A Probablistic tree can now be drawn, with a FIT value for the PT100 +circuit and FIT values for all the component fault modes that it was calculated from. +We can see from this that that the most likely fault is the thermistor going OPEN. +This circuit is 8 times more likely to fail in this way than in any other. +Were we to need a more reliable temperature sensor this would probably +be the fault~mode we would scrutinise first. + + +\begin{figure}[h+] + \centering + \includegraphics[width=400pt,bb=0 0 856 327,keepaspectratio=true]{./pt100/stat_single.jpg} + % stat_single.jpg: 856x327 pixel, 72dpi, 30.20x11.54 cm, bb=0 0 856 327 + \caption{Probablistic Fault Tree : PT100 Single Faults} + \label{fig:stat_single} +\end{figure} + + +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. + +\clearpage +\section{ PT100 Double Simultaneous \\ Fault Analysis} + +% typeset in {\Huge \LaTeX} \today + diff --git a/standards/standards.tex b/standards/standards.tex new file mode 100644 index 0000000..e4fa253 --- /dev/null +++ b/standards/standards.tex @@ -0,0 +1,30 @@ +% +% Make the revision and doc number macro's then they are defined in one place + +\begin{abstract} +This chapter describes the legal frameworks and standards organisations +that exist in Europe and North America. +Some specific standards (that the author has experience with directly) +are reviewed. +\end{abstract} + + +\section{Introduction} + +\section{European Safety Standards Legal Framework} +\section{North American Legal Framework} + +Protection against being sued mainly ! UL - underwriters laboratories.... etc + +\section{Cross Referencing} + +Stabndards of ten reference other - i.e. EMC testing in EN298 refers toEN blah blah to level blah blah + + +\section{EN298} + +\section{UL1998} + +\section{EN230} + +\section{EN61508} diff --git a/standards/standards_paper.tex b/standards/standards_paper.tex new file mode 100644 index 0000000..e4fa253 --- /dev/null +++ b/standards/standards_paper.tex @@ -0,0 +1,30 @@ +% +% Make the revision and doc number macro's then they are defined in one place + +\begin{abstract} +This chapter describes the legal frameworks and standards organisations +that exist in Europe and North America. +Some specific standards (that the author has experience with directly) +are reviewed. +\end{abstract} + + +\section{Introduction} + +\section{European Safety Standards Legal Framework} +\section{North American Legal Framework} + +Protection against being sued mainly ! UL - underwriters laboratories.... etc + +\section{Cross Referencing} + +Stabndards of ten reference other - i.e. EMC testing in EN298 refers toEN blah blah to level blah blah + + +\section{EN298} + +\section{UL1998} + +\section{EN230} + +\section{EN61508} diff --git a/thesis.tex b/thesis.tex index 7814fcc..aee42a3 100644 --- a/thesis.tex +++ b/thesis.tex @@ -128,7 +128,7 @@ Software documentation for fmmd tool. \input{fzd/fzd} \chapter{A detailed look at the safety systems required by industrial burner controller} -%\input{indburner/indburner} +\input{burner/burner} %\chapter{FMMD tool : Algorithms and Euler Diagram Parsing}