SBOA505 December 2020 OPA2991-Q1 , TLV197-Q1 , TLV2197-Q1 , TLV4197-Q1 , TMP61 , TMP61-Q1 , TMP63 , TMP63-Q1 , TMP64-Q1

Improving Accuracy of the Sensor Circuit

The temperature accuracy of the circuit can be improved while continuing to use a linear approximation to solve for the resistor network. In this example the temperature range will be optimized from 0°C to 90°C. This is accomplished by decreasing the offset term of the V_OUT(T) equation.
Equation 1. $V_{o u t} (T) = V_{N T C} (T) \times (1 + R 4 \times (\frac{R 3 + R 5}{R 3 \times R 5})) - V_{b i a s} \times (\frac{R 4}{R 5})$
Recall, V_OUT(T) is treated as a linear equation to solve for the resistor network:
Equation 1. $Y (X) = X \times M + B$
Therefore, the y-intercept, B, of the equation can be used to offset the curve along the Y-Axis. In this case the y-intercept of the equation is:
Equation 1. $B = V_{b i a s} \times (\frac{R 4}{R 5})$
To shift the center of the V_OUT(T) curve the negative inverting gain will be shifted 1.86%. The 1.86% shift was selected by calculating the change needed to shift the midpoint of the simulated V_OUT(T) curve towards the midpoint of the theoretical V_OUT(T) curve. The calculations needed to improve the accuracy of the NTC circuit are as follows:
Equation 1. $V_{o u t_s i m} (m i d p o i n t) = 2.34$
Equation 1. $V_{o u t_n e w} (m i d p o i n t) = 2.385$
Equation 1. $(1 - \frac{2.63}{2.68}) = 0.018$
The new V_OUT(T) can be obtained by multiplying the ratio of R4 to R5 by 1.018 as follows:
Equation 1. $V_{b i a s} \times (\frac{R 4}{R 5}) = V_{b i a s} \times 1.018 \times (\frac{R 4}{R 5})$
Equation 1. $5 V \times (\frac{10 k Ω}{6.842 k Ω}) = 5 V \times 1.018 \times (\frac{10 k Ω}{R 5})$
Equation 1. $R 5 = 6.965 k Ω$
The final resistor, R3, can be solved for using the new R5 value. Note, this approach will slightly affect the inverting gain of the circuit however, the non-inverting gain of the circuit will remain unchanged which will not impact the gain of the voltage divider output voltage as a function of temperature (V_NTC(T)).
Equation 1. $4.07 = (1 + 10 k Ω \times (\frac{R 3 + 6.965 k Ω}{R 3 \times 6.965 k Ω})); R 3 = 6.119 k Ω$
Using the linear approximation the resistor network for the desired temperature range is as follows:
1. R1 = 10kΩ
2. R2 = TMP61
3. R3 = 6.119kΩ
4. R4 = 10kΩ
5. R5 = 6.965kΩ
In the following image, the comparison of V_OUT(T) to the linear approximation is used to calculate the resistor values. V_OUT(T) represents the output voltage including the non-linear portion of the TMP61 temperature range. Linear approximation represents the calculated temperature assuming the TMP61 resistance response is linear across full temperature range.
Solving the resistor network for the optimized temperature range improved the accuracy across the overall temperature range of the sensor. The temperature error across the optimized temperature range is approximately 1.65°C which occurs at 49.1°C. The temperature reading from the ADC is approximately 50.75°C while the actual temperature is 49.1°C. However, the error at the end points increases.