# How important is the temperature stability for gain - setting resistors?

When two resistors are used to set a gain of an opamp, do I need to care about their temperature stability, provided resistors are from the same series, same manufacturer? Let's say my circuit will operate over temperature range of 85 degrees C and the gain of amplifier is 100.

As Andy said, read the data sheets carefully, and understand how TCR is specified.

Like many specs, it's sort of a lie. A TCR of, say, +/-5ppm/°C is a slope and you might expect if the slope of the Resistance-Temperature curve is guaranteed to have a magnitude of be less than 5ppm/°C, the slope of that curve would be guaranteed to not exceed that magnitude. That's not quite true. What the spec means is that the largest average TCR over one or more intervals is less than the limit. Most precision resistors have parabolic or S-shaped TCR curves, not linear, so there can be significant differences. It's important to know the interval(s) that they are using, and how that fits into your requirements.

Typically parts that are made similarly will have similar TCRs, but it's not good engineering to depend on that, though it doesn't hurt to take it into account to make things typically better than they have to be (Philip Crosby might disagree if he were alive, but if it's free, or close to free, it may be worth doing).

If you need really close matching, but perhaps don't care as much about total resistance, you can buy arrays. Be careful when using parametric search engines-- for example Digikey would probably cause you to ignore the excellent LTC5400 part- which has a horrible tolerance of 7.5% or 15% and a mediocre total resistance TCR of +/-25ppm/°C, but the matching is actually pretty good (+/-0.01%) and the TCR of the ratio is +/-1ppm/°C maximum. Other manufacturers such as Vishay have networks with superb performance.

As a final step if you can't quite get the needed performance even with the finest resistors you can afford, you may be able to characterize the drift and correct it (as I recently had to do for a micro-Kelvin temperature measurement system).

A less pessimistic estimate of errors is Total error = $\sqrt{\sum{{error_i}^2}}$, but it assumes a gaussian distribution, and is a probability, not a guarantee, so I think most Engineers prefer to use worst-case values where resistors happen to be at the extremes of their guaranteed values (perhaps the best ones were selected out of the distribution!).

You may find that some circuit configurations are better than others that perform the same function, so a sensitivity analysis can be useful in evaluating your error budget.

It's also useful to lay out resistors in such a way as they don't see temperature gradients and they track temperature. See "common centroid layout". Sometimes we even route out bits from the PCB to thermally isolate sensitive bits of the PCB, leaving only small connecting strips.

You cannot assume the temperature drift of two resistors next to each other on a reel is similar unless the data sheet, or other documents explicitly state this.

Read the data sheet is my advice. You can buy resistors as a pair whose ratiometric temperature stability is intended to be very small ie if one drifts a little bit high, so will the other one thus ensuring gain is stable over temperature.

• any tips on how do I find such mached resistors on digikey (what keywords/categories to use)? or is it high volume supplier specific stuff? – miceuz Jan 21 '14 at 22:55
• When its real important, don't use an op amp. Go for something like an instrumentation amp, with one resistor to set the gain, and all the internal resistors can be considered precision matched. – Scott Seidman Jan 21 '14 at 23:29
• Sounds like a great experiment. Get a batch of typical resistors and run them from -40 to +85C. I'd like to see the result. – C. Towne Springer Jan 22 '14 at 3:35
• @miceuz Maxim make a sot-23 precision resistor divider called the MAX5491 (google.co.uk/…). It's got 2ppm/degC drift in resistor ratio and resistor ratios from 1:1 to 30:1. See page 4 of datasheet for opamp apps. I'm sure there are others. – Andy aka Jan 22 '14 at 8:14