You can measure resistors all you want OUT OF CIRCUIT, free hanging in air and maybe come up with similar results. I don't care if 2 or 10 or 1000 people measure resistors inaccurately and come up with matching inaccurate results, and I especially don't care when basically none of the measures is verified by an absolute, calibrated measure anywhere. I know all the arguments about "relative measures". I understand that, and I understand what Andreas is trying to do on a low budget. That's not the point here, don't get me wrong - I just don't see where "free hanging" resistor tests really show how anything how resistors work in a real circuit - especially on a ratio pair that you are trying to magically extract TC measures down to sub ppm.
The
entirety of any precision circuit - especially at PPM levels - is taken into consideration when you're at lower PPM. Always, and especially since we're in the metrology section. You must think of the entire circuit as a thermal SYSTEM first as TiN pointed out. With resistors and circuits like LTZ's it's all about achieving stable POWER OUT vs POWER IN, and ONLY when power flow is stable do you get
as a by product a stable Vref output or stable resistance measure. Unless you have a stable thermal / power situation, your "Free Hang" resistor measure is just not very meaningful in a practical sense, no matter how its done.
My point is: Especially on ratio resistor pairs - you always measure those pairs AT BIAS and MOUNTED exactly like they will be in final product. That's because you NEVER know how --each-- resistor in the set transfers power back into the board as heat (which sets the apparent operating point temperature of each resistor), at typical OPERATING BIAS and operating THERMAL condition. Does each individual resistor in the ratio set transfer heat into the board
exactly like it does when it's free hanging? Usually not - far from it especially for an unbalanced pair like 13k over 1k. I don't care if you're using a Vishay Foils or PWW or Film or Diffused pair. The final operating point of EACH resistor in the set matters (sometimes a LOT) when you're reporting TC ratio numbers down into .01ppm.
Even if you see some sort of TC mismatch on your free hanging, unbiased resistor pair test, sometimes you find that once the resistors are actually mounted in position they are more thermally matched and stay at a closer matched internal temperature, and now your ratio TC looks better than the free hang test (or TC even changes direction). Sometimes you see the opposite, for instance when one resistor in the ratio pair is connected to a cooler ground or power trace than its mate, or maybe the position on the board doesn't allow for good thermal coupling, or maybe there is a fan blowing nearby pulling more heat away from one resistor of the pair. Now the mounted resistor ratio TC doesn't look ANYTHING like the free-hanging test showed. This stuff happens all the time in real life when you're exploring the low PPM world.
That's why I suggested: The one and only true REALISTIC and PRACTICAL test of an LTZ heater ratio set is to just run them on whatever LTZ board you've designed, soldered to your traces, mounted in your enclosure, running at equilibrium at your typical operating temperature. That's the only accurate way to really know what you've got for resistor ratio performance. At least you know what parameters actually matter in the final evaluation of the Vref.
The next question is - when you build an LTZ with resistor set X or resistor set Y - take a really hard look at your own ability of measuring an absolute voltage value, and see if spending a lot more $$$ on a resistor set will make any difference in the end. That's all up to what you really need and your lab equipment list - but a lot of times: spending more money on resistors won't make any difference.
Usually what happens is you'll wind up building a Vref that's better than what you can ever really measure on your own equipment (unless you have multiple 732's or similar), or sometimes you realize how noisy that eBay DMM really is @ 7.2V
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Have fun!