pt100 vrange diagram

pt100/pt100.tex

@@ -40,6 +40,25 @@ current resistance of the platinum wire sensor. The resistance
 of this is directly related to temperature, and may be determined by
 look-up tables or a suitable polynomial expression.
 
+
+\begin{figure}[h]
+ \centering
+ \includegraphics[width=150pt,bb=0 0 273 483,keepaspectratio=true]{./pt100/vrange.jpg}
+ % pt100.jpg: 714x180 pixel, 72dpi, 25.19x6.35 cm, bb=0 0 714 180
+ \caption{PT100 expected voltage ranges}
+ \label{fig:pt100vrange}
+\end{figure}
+
+
+
+
+The voltage ranges we expect from from this three stage potential divider
+are shown in figure \ref{fig:pt100vrange}. Note that there is
+an expected range for each reading for a given temperature span.
+Note that the low reading goes down as temperature increases, and the higher reading goes up.
+For this reason the low reading will be reffered to as {\em sense-}
+and the higher as {\em sense+}.
+
 \subsection{Accuracy despite variable resistance in cables}
 
 For electronic and accuracy reasons the four wire circiut is used
@@ -74,6 +93,8 @@ 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}
@@ -86,6 +107,16 @@ 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
@@ -96,14 +127,14 @@ $R_p$ is the PT100 thermistor and $R_{2}$ connects the thermistor to ground.
 %   R         &    wire        & res +         & res -    & description
 \hline
 \hline
- $R_1$ SHORT    &  High         &  -       &  Value Out of Range Value \\ \hline
-$R_1$  OPEN     &  Low          & Low      &  Both values out of range \\ \hline
+ $R_1$ 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           & High       &   Both values out of range \\ \hline
- $R_p$  OPEN     &  High          & Low      &  Both values out of range \\ \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    &  Value Out of Range Value \\  
- $R_2$ OPEN     &  High          & High      &  Both values out of range \\ \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}
@@ -126,7 +157,8 @@ resistors in this circuit has failed.
 \label{pt100temp}
 PT100 resistors are designed to 
 have a resistance of ohms{100}  at 0 \oc \cite{eurothermtables}.
-A suitable `wider than to be expected range' was considered to be {-100\oc} to {300\oc}. 
+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
@@ -154,10 +186,10 @@ $$ lowreading = 2^{12}.\frac{2k2}{2k2+2k2+pt100} $$
  \textbf{Temperature} & \textbf{PT100 resistance} & 
 \textbf{Lower} & \textbf{Higher} & \textbf{Description}   \\ 
 \hline
- {-100 \oc} &  {\ohms{68.28}} &  2.46V         &   2.53V      & Boundary of   \\ 
-            &                 &  2017\adctw   &   2079\adctw  &   out of range LOW \\ \hline
-  {0 \oc}   & {\ohms{100}}    &  2.44V         &   2.56V       & Mid Range         \\
-            &                 &  2002\adctw   &   2094\adctw   &          \\ \hline
+% {-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
@@ -176,7 +208,7 @@ we would get from the resistor failures to prove that they are
 `out of range'. There are six cases and each will be examined in turn.
 
 \subsubsection{ Voltages $R_1$ SHORT } 
-With pt100 at -100\oc 
+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..