Changing the temperature coefficient of linear thermistors.

Introduction.

Linear thermistors ( RTDs or Resistance Temperature Detectors ) are used for temperature measurement or temperature compensation in analog circuits.
RTDs are based on a platinum or nickel-alloy film, giving them a positive temperature coefficient ( TC ) in the range of 150 ppm/°C to 7000 ppm/°C.
For temperature measurement circuits, the actual TC is not important - the circuit is designed for the RTD in use.
In temperature compensation applications, the TC is normally the most important parameter. RTD temperature coefficients comes in discrete values ( except the one you need ).
Putting a fixed resistor in series with a RTD will reduce the TC of a RTD to almost any value you want while maintaining its linearity.
As an example a logarithmic amplifier based on the voltage/current ratio of a P-N junction has a gain TC of 3333ppm/°C. This can be compensated by a RTD with a TC of 3333ppm/°C.

All calculations here assumes that the RTD temperature/resistance function is linear ( it is not, but very close ).

RTD.

The resistance of a RTD is:

where:
Tr is the reference temperature, typically 25 °C or 0 °C.
T is current temperature.
THTr is the RTD resistance at Tr.
THTCR is the RTD temperature coefficient in ppm/°C.
THT is the RTD resistance at T.

The resistance of a RTD in series with a resistor is:

where:
R is the series resistor.
RTHT is the series combination resistance at T.

or:

where:
RTHTr is the series combination resistance at Tr.
RTHTCR is the series combination temperature coefficient in ppm/°C.
RTHT is the series combination resistance at T.

To find R:

References.

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