Electronic – How to connect 15kΩ NTC thermistor sensor to thermostat which requires 10kΩ NTC thermistor

NTC (negative temperature coefficient) thermistors change their effective resistance over temperature. The most common equation used to model this change is the Steinhart-Hart equation. It uses three coefficients to characterize the NTC material with great accuracy.

The Steinhart–Hart equation is a model of the resistance of a semiconductor at different temperatures. The equation is:

$${1 \over T} = A + B \ln(R) + C (\ln(R))^3$$

where:

• \$T\$ is the temperature (in kelvins)
• \$R\$ is the resistance at \$T\$ (in ohms)
• \$A\$, \$B\$, and \$C\$ are the Steinhart–Hart coefficients which vary depending on the type and model of thermistor and the temperature range of interest. (The most general form of the applied equation contains a \$(\ln(R))^2\$ term, but this is frequently neglected because it is typically much smaller than the other coefficients, and is therefore not shown above.)

— Steinhart-Hart equation - Wikipedia, The Free Encyclopedia

Many manufacturers provide application notes (e.g. here) detailing on how to calibrate a given NTC if you desire accuracy better than the quoted manufacturing tolerance.

The provided B-coefficient can be used in a simplified Steinhart-Hart equation as described on the Wikipedia Thermistor article under "B parameter equation".

This is either dangerous, not advisable or doable depending on...

It comes down to what the "cells" are made up of. Since a bare single cell doesn't have a TH, you are talking about a pack. It may be a pack of 1 single 3.7V cell, in which case it's effectively a cell and you can, to a limit, connect in parallel to your heart's content.

I'd advise you to balance them out to each other with an extra resistance before you hard connect them, though. If they're large cells and 0.5V apart that will mean large currents will flow until they "agree", which is good for neither the low one, nor the high one. It would look a bit like this:

^{simulate this circuit – Schematic created using CircuitLab}

You should pick a TH contact, since it is a temperature sensitive resistance that will be measured, if you connect multiple in parallel it will measure a low resistance, compared to what's expected. Since usually they are NTC 10k, that means the charger will think your batteries are hot when you first connect them, which means it will not charge.

If you have a pack of more than 3.7V, such as 7.2V or 11.1V, then connecting multiple in parallel without any "internal cross connections" will increase the speed at which the first cell will die. If the pack is multiple cells in series without any balancing connections, it can be debated whether that's advisable to start with. But anyway.

If you have a 2 cell in series pack, you will want to connect them like this:

^{simulate this circuit}

This way the odd batteries will join force as will the even batteries and that will severely decrease the statistical chance of a dangerous defect in the pack.

((Of course it's better to start out with resistors for the parallel connections for the first hours to cross-balance again))

If you have a multi cell pack and can't make the cross connections as drawn above, I'd say, on balance, you're better off not connecting anything in parallel at all. Especially for charging purposes.