The curve-fitting-circuit design begins by first wiring the four inputs of IC3 to create a positive square term that is scaled at the chip’s output by an internal scale factor of 1/10V. Then, comparing terms, you find that the coefficient, c, must equal 0.0123. Because R6 and R7 form a voltage divider that attenuates the signal, VT, you can express the coefficient with the following equation:
Select a value for R7—10 kΩ for this design—and then use the preceding equation to find the value for R6.
Resistors R8, R9, and, optionally, R10 form a passive adder to create the offset term, a, and the linear coefficient, b. You apply the output of the passive
adder directly to the Z input, Pin 6 of IC3, which adds the offset and linear terms to the square term to form the system response at Pin 7. Again comparing these terms, note that the offset term must equal 0.0005V. The offset term is only 0.5 mV, and eliminating it would add an error of approximately 0.05°C, so you can initially neglect it. Then, because the linear term’s coefficient, b, must equal 0.8507, you first select a suitable value for R9 and use the following equation to solve for R8: b="R9/"(R8+R9).
If you wish to design the optional circuitry and include the offset term, which is part of the passive adder, choose a stable 2.5V reference for VREF, calculate the parallel combination of R8//R9=REQ (the equivalent resistance of R8 in parallel with R9), and solve for R10 using the following voltage-divider equation: a=(REQ/(R9+REQ))VREF.
To calibrate this circuit, replace the sensor with a precision decade box. Set the decade box to simulate 0°C and adjust the offset trim of R2 for an output of 0V at Pin 7 of IC3. Next, set the decade box to simulate 350°C and adjust the gain trim of R3 for an output of 3.5V. Repeat this sequence of trim steps until both points are fixed. The circuit in Figure 1—which includes optional circuitry—exhibits a worst-case measurement error at 250°C and 2.504V of 0.16%, or 0.4°C. Testing the circuit without the optional circuitry—the reference voltage and R10 —shows no discernible improvement in precision.
Reference
“IC Generates Second-Order Polynomial,” Electronic Design, Aug 5, 1993.
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