diff --git a/pt100/pt100.tex b/pt100/pt100.tex index e7c6812..14ea229 100644 --- a/pt100/pt100.tex +++ b/pt100/pt100.tex @@ -193,7 +193,29 @@ Temperature range calculations and detailed calculations on the effects of each test case are found in section \ref{pt100range} and \ref{pt100temp}. - +%\paragraph{Consideration of Resistor Tolerance} +% +%The separate sense lines ensure the voltage read over the PT100 thermistor are not +%altered due to having to pass any significant current. +%The PT100 element is a precision part and will be chosen for a specified accuracy/tolerance range. +%One or other of the load resistors (the one we measure current over) should also +%be of this accuracy. +% +%The \ohms{2k2} loading resistors may be ordinary, in that they would have a good temperature co-effecient +%(typically $\leq \; 50(ppm)\Delta R \propto \Delta \oc $), and should be subjected to +%a narrow temperature range anyway, being mounted on a PCB. +%\glossary{{PCB}{Printed Circuit Board}} +%To calculate the resistance of the PT100 element % (and thus derive its temperature), +%having the voltage over it, we now need the current. +%Lets use, for the sake of example $R_2$ to measure the current flowing in the temperature sensor loop. +%As the voltage over $R_3$ is relative (a design feature to eliminate resistance effects of the cables). +%We can calculate the current by reading +%the voltage over the known resistor $R2$.\footnote{To calculate the resistance of the PT100 we need the current flowing though it. +%We can determine this via ohms law applied to $R_2$, $V=IR$, $I=\frac{V}{R_2}$, +%and then using $I$, we can calculate $R_{3} = \frac{V_{R3}}{I}$.} +%As these calculations are performed by ohms law, which is linear, the accuracy of the reading +%will be determined by the accuracy of $R_2$ and $R_{3}$. It is reasonable to +%take the mean square error of these accuracy figures. \subsection{Range and PT100 Calculations} \label{pt100temp} @@ -249,6 +271,37 @@ for any single error (short or opening of any resistor) this bounds check will detect it. + +\paragraph{Consideration of Resistor Tolerance.} +% +The separate sense lines ensure the voltage read over the PT100 thermistor is not +altered by to having to pass any significant current. The current is supplied +by separate wires and the resistance in those are effectively cancelled +out by considering the voltage reading over $R_3$ to be relative. +% +The PT100 element is a precision part and will be chosen for a specified accuracy/tolerance range. +One or other of the load resistors (the one we measure current over) should also +be of this accuracy. +% +The \ohms{2k2} loading resistors should have a good temperature co-effecient +(i.e. $\leq \; 50(ppm)\Delta R \propto \Delta \oc $). +% +To calculate the resistance of the PT100 element % (and thus derive its temperature), +knowing $V_{R3}$ we now need the current flowing in the temperature sensor loop. +% +Lets use, for the sake of example $R_2$ to measure the current. +% +We can calculate the current $I$, by reading +the voltage over the known resistor $R_2$ and using ohms law\footnote{To calculate the resistance of the PT100 we need the current flowing though it. +We can determine this via ohms law applied to $R_2$, $V=IR$, $I=\frac{V}{R_2}$, +and then using $I$, we can calculate $R_{3} = \frac{V_{3}}{I}$.} and then use ohms law again to calculate +the resistance of $R_3$. +% +As these calculations are performed by ohms law, the accuracy of the reading +will be determined by the accuracy of $R_2$ and $R_{3}$. It is reasonable to +take the mean square error of these accuracy figures. + + \section{Single Fault FMEA Analysis \\ of PT100 Four wire circuit} \subsection{Single Fault Modes as PLD}