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Phrak
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rusty009 said:
The error in the circuit has about four contributing factors:
The tolerance of the bias resistor, or bias circuit
The error of resistance with respect to temperature of the thermistor itself
The curve fitting error you are asking about
The step resolution error of the ADC
The curve fitting error may be reduced by chosing a different curve other than a straight line approximation to fit it to, and/or preforming a regressive analysis (least-squares fit).
The ADC error is usually quoted by the manufacture as 1/2 step over the span. I'd use an error value of one step to be practical.
The tolerances of the input circuity will tell us the error in the voltage actually applied to the ADC. This involves doing a little math--
We need to find the variation of the voltage as a function of temperature and bias resistor.
Given
V = F(R_b,T) \ ,
then
\delta V = \frac {\partial F(R_b,T)}{\partial T}\delta T +\frac {\partial F(R_b,T)}{\partial R_b} \delta R_b\ .
\delta V, \ \delta R_b, and \delta T represent absolute error. We need relative error (And we need to represent relative error as vectors.)
\hat{ \epsilon}_{V} = \delta V / V
\hat{ \epsilon}_{R} = \delta R_b / R_b
\hat{ \epsilon}_{T} = \delta T / T
I could have written \delta T and \delta R_b as vectors, but the form of the equation may already be somewhat unfamilar to begin with.
We are assuming that the errors of the independent variables are independent. The error in the resistor is independent of the error in the thermistor. Abit, \hat{ \epsilon}_{R} and \hat{ \epsilon}_{T} would add like perpendicular vectors. \hat{\epsilon_{V}} , on the other hand is some combination of these vectors, and points-off in a direction within the plane spanned by these two other vectors.
The norm (magnitude) of the vector \hat{\epsilon_{V}} is the relative error in voltage to the ADC input. In general, the form of the result will involve a square root.
\epsilon_{V} = C \sqrt{ A \epsilon_{R_b}\ ^{2} + B\epsilon_{T}\ ^{2} }
where A, B and C are constants to be determined by applying the above procedure.
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