Temperature sensing with NTC circuit

Question

I am reading through this document by TI on designing a temperature sensing circuit with an NTC thermistor. I'm having some trouble understanding the design steps though. Here are some snippets from the application note: -

They state that they want the op-amp to operate in the linear region which I guess means that they don't want the op-amp output voltage to exceed the supply voltage (saturation). For that, they need a certain value of \$R_1 \$ to limit the input voltage. However, in their calculation they don't take the supply voltage into account at all, but only use the min and max value of the thermistor.

My question is how can they neglect the op-amp's supply voltages when calculating \$R_1 \$? And also, why do they calculate it like this \$R_1 = \sqrt{R_{NTC,max}\cdot R_{NTC,min}} \$?

Why is it not, for example, \$R_1 = \frac{R_{NTC,max}+R_{NTC,min}}{2} \$?

Answer 1

The supply voltage is in the formula for calculating the op-amp output voltage, so it is not left out.

But as the NTC and the fixed resistor use the op-amp supply and ground for the voltage divider, all it is needed to know is that the divider output will be within the supply voltages.

The R1 value is calculated with a geometric mean instead of arithmetic mean, because it will result into a value that maximizes the divider output voltage swing based on the NTC resistor range. The R1 value that maximizes the voltage swing does not depend on supply voltage, it maximizes it for any supply voltage.

The values for NTC resistor at 25 and 50 degrees is used because that is the range defined in the design specs that the circuit must operate. There is no point using the full NTC range of values at say 0 and 100 degrees.