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I'm simulating a simple circuit with a resistance temperature detector. I want to know if it is possible to simulate the small change in the resistance as the current flowing through the resistor generates heat.

For example, a TRAN simulation where the initial value of the current is simply given by V=RI but after some time the current value would be lower as the own current heats the resistor thus amplifying the resistance.

If it isn't possible to do this in LTspice what should I use?

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There is no thermal information in a SPICE element except a static parameter, temp, which is global and sets the temperature when the whole circuit is functioning, or the temperature coefficients tc1, tc2, etc in the resistor's properties (or others, see the help under LTspice > Cicuit Elements > R. Resistor).

If you need such information then you have to realize that it needs to be dynamic, and it means you will have to concoct your own circuitry that calculates the caloric dissipation as a function of the power.

As an example, look at MOSFET subcircuits that have pins which output the temperature. Those calculate the power through the device then use appropriately scaled RC ladder networks to mimic the temperature coupling from junction to case to air. The circuits are not for the faint hearted, because they involve knowing some intimate details about thermal properties of the device, itself. So for your case you will need to know the exact materials and their thermal properties, the air (which normally will have a feedback on the resistor), the proximity to other materials, whatever others.

At this point, you'll have to flip a coin: if you need to know how much temperature a resistor will dissipate after a while, but not all the way there, FEMM & co might be more useful and more accurate. If you need to watch the evolution of the temperature then one of those additional circuits will be needed for SPICE, though the results might only be approximations.

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Yes! First you need to create a finite element thermal model of the circuit, usually based on a 3D model. Then convert it into an RC network model, using an optimization process that minimizes the number of nodes in the model while maintaining the error within your application-specific range.

Then the RC thermal network model has to be coupled to the circuit network model. Coupling in one direction is done by adding thermal generators into the thermal model - those would be voltage and/or current sources driven by the voltages/currents in the circuit. In another direction, the voltages in the thermal model represent absolute temperatures, and can be fed - with appropriate scaling - back into the circuit model.

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