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Need to find NTC resistor for thermometer

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soldar:
I have one of those inside / outside digital thermometers that has the outside probe at the end of a long cable but somehow the cable was cut and the probe is gone forever. I assume it was probably some simple NTC resistor.

I have put a variable resistor in its place and recorded the temperatures it read as a function of the resistor value.


--- Code: --- Ohm - - - TºC
95000 -31.0
92000 -30.0
51800 -21.4
27000 -10.0
 8800 +11.0
 5640 +19.8
 4990 +22.2
 4400 +25.0
 3780 +27.8
 3010 +32.3
 1933 +40.7
 1537 +44.5
--- End code ---

I could spend an afternoon relearning about NTC curves and equations but maybe someone can help me out.

It looks like I need an NTC resistor of 4K4 at 25ºC.

Then there was some coefficient that defined the exponential resistance curve and that is where I get lost.

Anyone?

And, before anyone says it, yes, this is an academic exercise done for pleasure and not for profit. I know I can probably get a new digital thermometer cheaper than I can get the NTC resistor.

E.T.A.: I found some software that says it will calculate coefficients given the table of values but I do not know where to even start.
https://sourceforge.net/projects/thermistor/files/
http://thermistor.sourceforge.net/

mikerj:
4400 ohms @ 25C is not a preferred value.  You table is a pretty good fit for a 4700 Ohm @25C with a Beta of 3500 which is a common part.

soldar:
Thanks mikerj.  Knowing R25ºC and Beta is there a simple equation that will relate R with T?

Looking in Mouser I only see SMD components which should not be a problem as I just need to solder a couple thin wires and encapsulate it in a blob of epoxy or hot glue.

The thing is that it will cost much more to mail than the cost of the part. Since this is just for play I might wait until my next visit to some electronics market in China.

mikerj:
The standard Beta equation is:

\$R=R_0e^{\beta(\frac{1}{T}-\frac{1}{T_0})}\$

Where
\$R\$ Is the resistance you wish to find at temperature \$T\$
\$R_0\$ Is the known thermistor resistance at temperature \$T_0\$
\$\beta\$ Is the beta value

All temperatures are in Kelvin i.e. subtract 273.15 from the temperature in Celsius.

Note that the Beta characteristic only gives a good fit for a limited range of temperature.  Often a thermistor manufacturer will specify multiple beta values for different temperature ranges.

soldar:
Thanks.

>> All temperatures are in Kelvin i.e. subtract 273.15 from the temperature in Celsius.

I know what you mean. You mean "add" 273.15 to Celsius to obtain Kelvin.

I have been playing around with the spreadsheet and T25 = 4400 and Beta = 4000 gives better approximation to my results but, as you say, that is a non-standard value.

I have seen online some sensors with NTC resistors will add a fixed resistor in parallel in order to flatten the response.

This may be more complicated than is worth pursuing.  The unit still has the clock and the indoor sensor working so I might just forget about the remote sensor.

On the other hand I might assume both sensors were alike and I could take out the included sensor and measure it at different temperatures and see if I learn anything from there. Or just put the internal sensor at the end of a cable and use it as remote.

It is incredible how little it takes for me to waste a lot of time.

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