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Consideration of resistor tolerance.

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C. Garrett said this needed addressing. I agree.
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Robin Clark 2011-02-20 15:53:46 +00:00
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pt100/pt100.tex
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@ -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}