NTC and comparator to detect temperature trip point

[Dina1999]

In "The Art of Electronics" the following is said: "A comparator in a circuit is a handy device that switches its output according to the relative voltages at its two input terminals. There is a temperature sensing device, a thermistor, which decreases in resistance by about 4%/°C. So we’ve made it the lower leg of a voltage divider. The comparator then compares the voltage from the thermistor and from a temperature-insensitive resistor. When it’s hotter than 30°C, point “X” (thermistor voltage) is at a lower voltage than point “Y" (temperature-insensitive resistor), so the comparator pulls its output to ground." My question is why the voltage at point X (thermistor) is lower than the other one. I thought it would be more logical that if the resistance of the thermistor decreases, the current would increase so that the voltage would also increase. The comparator wouldn't then measure a lower voltage than at Y. Thanks in advance:)

 

[cnh1995]

In "The Art of Electronics" the following is said: "A comparator in a circuit is a handy device that switches its output according to the relative voltages at its two input terminals. There is a temperature sensing device, a thermistor, which decreases in resistance by about 4%/°C. So we’ve made it the lower leg of a voltage divider. The comparator then compares the voltage from the thermistor and from a temperature-insensitive resistor. When it’s hotter than 30°C, point “X” (thermistor voltage) is at a lower voltage than point “Y" (temperature-insensitive resistor), so the comparator pulls its output to ground." My question is why the voltage at point X (thermistor) is lower than the other one. I thought it would be more logical that if the resistance of the thermistor decreases, the current would increase so that the voltage would also increase. The comparator wouldn't then measure a lower voltage than at Y. Thanks in advance:)

Welcome to PF!

Is it possible to post the circuit diagram?

 

[berkeman]

Welcome to PF!

Is it possible to post the circuit diagram?

It's not in the 1st Edition, must be in the 2nd Edition...

 

[Svein]

My question is why the voltage at point X (thermistor) is lower than the other one. I thought it would be more logical that if the resistance of the thermistor decreases, the current would increase so that the voltage would also increase. The comparator wouldn't then measure a lower voltage than at Y. Thanks in advance:)

OK. The voltage across the NTC is given by $V_{NTC}=V_{ref} \frac{R_{NTC}}{R_{fixed}+R_{NTC}}$. If you want, you can input some values in the formula and verify that the voltage across the NTC decreases as the NTC resistance decreases. If you want a mathematical reason, observe that $\frac{dV_{NTC}}{dR_{NTC}}=V_{ref} \frac{R_{fixed}}{(R_{fixed}+R_{NTC})^{2}}$ which is positive. This again means that the voltage across the NTC changes the same direction as the change in NTC resistance.

 

[Dina1999]

OK. The voltage across the NTC is given by $V_{NTC}=V_{ref} \frac{R_{NTC}}{R_{fixed}+R_{NTC}}$. If you want, you can input some values in the formula and verify that the voltage across the NTC decreases as the NTC resistance decreases. If you want a mathematical reason, observe that $\frac{dV_{NTC}}{dR_{NTC}}=\frac{R_{fixed}}{(R_{fixed}+R_{NTC})^{2}}$ which is positive. This again means that the voltage across the NTC changes the same direction as the change in NTC resistance.

Thank you so much! It makes sense:)