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I've read the following excerpt from a book (Passive Circuit Analysis with LTSpice by Colin May page 96) but am not sure what that means (with no relevant explanation before nor after):

On Fixed Resistors: a useful point to consider if good stability and reliability are essential is to derate the resistor so that its temperature is far less than the operating maximum. Thus, if the actual power is 1/10W, instead of a 1/8W resistor, use 1/2W.

Resistance of a resistor increases with temperature. So if the temperature is far less than the operating maximum, we're lowering the specified resistance of the resistor, and as a result the resistor (under lower temperature) will load itself with a higher current. Under such condition (same voltage and higher current) the resistor dissipates more power - hence it makes sense to choose a resistor with higher Wattage rating (1/2W instead of 1/10W). I don't see any meaning to it other than reminding us to change higher rated resistor when temperature gone low.

How does choosing a resistor with a higher rating (1/2W) has anything to do with testing the stability or reliability of a circuit? And why is it considered "derating" when you switch to 1/2W resistor as you lower the temperature?

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    \$\begingroup\$ Some resistors age, changing their value with time, if operated at high temperature. Carbon composition resistors can increase in value by 50% or more over 30 or 40 years of operation. \$\endgroup\$ – user_1818839 Jan 5 at 16:55
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Resistance of a resistor increases with temperature.

Well, they try to make them have low or zero temperature coefficient. When thermal stability is required, you can buy resistors with very low temperature coefficients.

So if the temperature is far less than the operating maximum, we're lowering the specified resistance of the resistor, and as a result the resistor (under lower temperature) will load itself with a higher current. Under such condition (same voltage and higher current) the resistor dissipates more power - hence it makes sense to choose a resistor with higher Wattage rating (1/2W instead of 1/10W).

Well, hold on there. The resistance of a resistor will be specified at 25C (room temperature). It is NOT a given that all resistors will go up with temperature. Typically the resistance is specified to have thermal drift of less than 200 ppm per degree C. That could be plus or minus 200 ppm. 200ppm per degree C does not lead to large resistance changes. Let's go through an example.

Suppose you have a 100 Ohm resistor. Let's assume the temperature coefficient actually is + 200 ppm per degree C.

So if it is 100 Ohms at room temp (25 C) what will be the resistance change at 100C? That is an increase of 75 degrees.

75*200/1000000 = 0.015

So the resistance will increase by 100 * 0.015 = 1.5 Ohms.

The main point of that advice, about de-rating your resistors, is that a higher power resistor will have a smaller temperature rise, and therefore a smaller resistance change. That is it. No thermal runaway feedback loop is implied.

When thermal stability is important, you can choose resistors with much lower thermal coefficients. I chose 200ppm because some cheap and readily available resistors are 200 ppm or 100ppm.

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The statement that resistor resistance changes with temperature is true, but only very little (much below 1000 PPM/°C), so the point where you state that at cold temperatures the resistance is so much lower that it consumes more current is simply not true.

A typical 100 ohm 1% resistor is that at 20°C, and it will have a temp coeff of 250 PPM/°C so it will be better than a 100 ohm 2% resistor at temperatures within 40°C of that.

That is hardly enough to change the resistance to change the current enough to exceed the rated power dissipation limit. And if it is enough, then that is the exact reason to derate the resistor, i.e. change to a resistor that can handle the power dissipation without heating up too much.

Changing to a resistor that can handle more power heats up to less temperature because it can radiate and conduct the heat away better, and it also heats up and cools down slower due to higher mass, so for example the stress due to repeated thermal expansion is less and thus the circuit can handle more thermal cycles and has longer life.

If there are user operable parts like connectors, a higher wattage resistor can survive user induced faults like short circuits, if it is rated to handle it instead of just rated to handle normal operation.

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