Thermistors - (focus on NTC)

A thermistor is a resistor where the resistance is strongly dependent on temperature.

So we can use this for place a thermistor at a location where we want to measure temperature.

Measure the resistance for the thermistor and map it to the temperature.

NTC and PTC

We do have two types

PTC : Positive Temperatur Coefficient thermistor
- increasing temperature = increasing resistance
NTC : Negative Temperatur Coefficient thermistor
- increasing temperature = decreasing resistance

PTC

As we can see there is no uniq mapping between temperature and resistance. Its not trivial to formulate a transfer function which can go from resistance to temperature - not to say impossible.

The PTC is not usefull for temperature measurements and is only mentioned here for info.

NTC - Negative Temperature Coefficient resistor

Image of a NTC of value 47 kOhm (color coded)

NTC can be of various physical size
heavy NTC reacts slow
small react fast ..
small Ohm values and relaively large current adds self heating
- P = U I = I^2 / R
- So beware
Physical larger and heavier NTC gives slower response

An picture says it all. There is a non linear monotone relation between temperature and resistance.

NTC resistance temperature relationship II

Resistance is falling when temperature is increasing
This relation is NOT linear - see fig on left
NTCs are specificed by nominal resistance which is the resistance at 25 C
So - by inspection - this figure is for a 10 kOhm NTC(read resistance at 25C)

By proper modelling of the temperature-resistance relation we can use it to measure temperature as depicted on the figure above.

Steimhart and Hart 3rd order approximation for NTC

Steinhart-Hart did formulate a third order approximation.

We do have three unknown A,B and C. So by measure 3 experimental dataset (temperature and resistance) hopefully covering the intended temperature range we can find the A,B,C coefficients for the model approximation.

See more here

See mockup for measurements

comment: you need to know or set Vs and R

Howto

Follow this link to a page giving an introduction on howto estimate Steinhart-Hart 3rd orders parameters - including a pythonscript for it

Steinhart and Hart 4th order approximination formula

FIY we will not use the fourth order approx. But here it is. The ln(R)^2 term is frequently neglected because it is typically much smaller than the other coefficients, and is therefore not shown above in the third order approx.

There is also a 4th order Steinhartand Hart approximation whichis not so well suited for DIY estimatino of the parameters.

Steinhart Hart formula for calculating Temp from resistance
A1, B1,… are specific constants for a givre NTC.
See datasheet for values

From supplier Vishay here is an annotated datasheet It requires a NTC from Vishay. As you can see the B parameter vary as nominal resistance vary.

It might or should be a little more accurate due to higher order model. We not tested that.

Litt

Jens