Why is resistor temperature coefficient given in a +/- number?

Question

For a given resistor you might see a TCR of +/-25ppm/C, but I'm not sure I quite understand that number. As far as I know, a PTC resistor like a basic thick film always increases in resistance as temperature rises. So where's the +/- coming from? Is it just saying that when the temperature decreases that the resistance will also equally go down by -25ppm/C? I don't see the spec given as like 100ppm +/-25ppm/C, that I'd understand but this makes me feel like I'm missing something.

Answer 1

A PTC or NTC resistor is designed to have a large tempco.

A PTC may have a nominal TCR of (let's say) +2000 ppm/C. Now this 2000 wouldn't be exact, due to material, manufacturing and measurement tolerances, so it might be better to quote it as being a TCR of 1950 to 2050 ppm/C, or equivalently a TC of 2000 +/- 50 ppm/C.

A standard resistor would ideally have a zero TCR. Cheap ones somewhere near zero, expensive close tolerance ones very close to zero indeed. Rather than quote the TCR as 0 +/- 25 ppm/C, it tends to be just quoted as +/- 25 ppm/C. Due to the tolerances, the manufacturer doesn't know, or is not prepared to warrant, whether it goes up or down in resistance as you increase the temperature, just that it's within 25 ppm/C either way.

That +/- 25 ppm you quote represents quite an expensive resistor, cheap ones tend to be more in the +/- 100 to 200 ppm ballpark. As the cheap resistors are cheap, it's usually the case that even if the manufacturer knows which way the TCR is going to go, he's not going to warrant it or specify it, and just give a blanket +/- tolerance.

There are several ways to make a low TCR resistor. One way is to deposit the resistive film on a substrate with a different thermal expansion coefficient, so that the thermal strain generated as the temperature changes cancels out the TCR of the resistive film. Another way is to make the resistive film with a mixture of both NTCR and PTCR components. Obviously if the cancellation is intended to be exact, and you don't get complete cancellation, you'll get a deviation one way or the other.

You can assume that at the 25 ppm/C (expensive) level, there is some sort of TCR cancellation going on, which can error in either direction.

Answer 2

In order to get better performance, resistor makers use materials and constructions that often result in a more complex curve, especially for high precision resistors.

Here, from a major resistor manufacturer (Rohm) is a curve that they say is typical of thick film construction.

The temperature coefficient, when measured as in MIL-STD-202, by default has a reference temperature of 25°C and is measured above and below the reference temperature.

T.C.R. = \$\frac{R_2 - R_1}{R_1(T_2 - T_1)}\cdot\$100

That method appears to assume that the change will be relatively monotonic above and below 25°C. Note that the slope of Rohm's curve, depending on the end measuring points, can be considerably higher than the average T.C.R. specification, especially at the temperature negative extreme in the example shown.

For high precision resistors they can mix element composition and use substrates that have a coefficient of thermal expansion that causes compensating changes in resistance.

Answer 3

don't standard resistors always increase resistance with temperature?

No, they can rise or they can fall.

Making a resistor to have a very low temperature coefficient is tricky to do and requires a manufacturer to make them to a high precision and consistent standard but, nothing is perfect and, some material in the make-up of the resistor will have a positive tempco and some material will have a negative tempco and, one will slightly dominate over the other and dictate whether a specific resistor from a specific batch is slightly positive whereas another from the same batch might be slightly negative.

The general idea is to try and make the resistor tempco zero but, slightly over-compensating with one added material may force it to have a small negative tempco whereas under-compensating might make it slightly positive.