Electrical – Do the temperature coefficients of the resistors in the LM399/LM199 “Portable Calibrator” significantly effect the output stability

Calibrate the instrument

Modern DMM's use internal tables of data to implement multi-point calibration. You will not be able to do this yourself without a service manual and their test/calibration software suite.

Manual calibration with resistors will allow you create your own calibration function, but then you will have to manually apply it to each measurement (or suck the measurements through a data drain and do it there).

Factory calibration is not expensive and you don't need to be a huge enterprise to access it.

There are also 3rd party calibration services and labs. Most test equipment rental companies also have attached labs.

Here is an example of US pricing for reference. It is about 10% of original purchase price.

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.