Andreas,
I think that MisterDiodes and I have a very good understanding of what you are attempting to do and how you are attempting to do it, it is a good attempt but it is still flawed when trying to make precision measurements, whether or not you are trying to do absolute or relative is not really the point. The point is that even trying to do relative measurements requires due diligence to eliminate all sources of error in the measurements and even relative measurements requires a 'reference' that is known to be sufficiently stable in its own characteristics, therein lies the conundrum, you cannot use a 'reference' part characterized by the same uncalibrated/relative system you are using to make relative measurements because you do not know what the characteristics of that system is well enough.
For example, I have a 242B bridge, unlike the 242D which is trimmable to ~1PPM, the 'B' is not trimmable and is specified to 0±20PPM accuracy which is quite good. Now let's say I need to measure a resistor to 10PPM, obviously I cannot use the 242B since it is only 'known' to be somewhere within ±20PPM (we are ignoring the fact that I have standards), the fact that the 242B may actually be accurate enough at a given resistance is unknown. What solution do you think will solve the problem? You could possibly purchase a regular resistor with specifications good enough to check the 242B close to the required value or you might know someone with such a resistor you could borrow. My point is that you simply cannot make even relative measurements unless your reference is at least known to be within sufficient parameters to compare to, it doesn't have to be a calibrated standard but its properties must be known. Your ADC, good as it is, does not qualify as a reference because you are not measuring resistance with it, you are measuring the ratio between two resistor voltages, neither of which you know the parameters of well enough to claim one is a reference, the accuracy of the ADC becomes irrelevant per se as you are not measuring its accuracy.
Using a Z201 as a reference, as you apparently are, you can only assume that this resistor is within the maximum stated limits unless it is measured by an actual accurate resistance bridge and tested accurately for its TCR over the temperature range in question, you cannot assume any of its parameters are better than worst spec. Therefore your limits of reading, relative or otherwise, is the worst specifications of the resistor you are using as a reference. Since you folks do not have access to any equipment with which to 'calibrate' with, you cannot assume anything better than worst specs. Your relative readings are no better than the worst specs of your reference and that assumes that you know what all of your error sources are in addition to the 'reference'. Given the limiting specifications of a Z201, your uncertainty of measurement must be equal to the Z201's worst specs, you cannot presume anything else without that resistor's actual specifications being known. In short, your relative measurements are nowhere near as good as you think they are despite some repeatability, repeatability is not accuracy. In your case, all you know is that your Z201 has appeared to remain 'stable' as far as you know but that doesn't change the requirements of measurement.
As I stated earlier, your TCR measurements of my 1K resistors appear to be reasonable, as far as accurate, they look like they are reasonably close but since I did not do TCR measurements on those resistors, I cannot say that your measurements are accurate, only relatively accurate. That said, reread my earlier post, I found that your 'readings' indicating aging or 'cold creep' were not valid for the temperature range you were using. That should have been sufficient to indicate there is a problem of some sort in your system as I nor other demanding customers have found such aging or 'cold creep' in very accurate measurements. Please recall that I am using a fully calibrated resistance measuring system which well exceeds any of your setups in accuracy and repeatability. If such characteristics were present I could easily measure them.
For your Z201, here are the major limiting factors (uncertainties), tolerance (0±50 PPM), TCR +0.8, -0.6 PPM/°C, PCR (depends on power level, <±5 PPM), VCR 0.1 PPM/volt applied. You may be able to get a little better reading on the Z201 resistance if a DVM is available and sufficiently more accurate and calibrated. Unless the actual TCR of the Z201 can be verified, you have a minimum uncertainty of +0.8 to -0.6 PPM/°C, that means a reading of +1 PPM could be anywhere between +1.8PPM/°C to +0.4 PPM/°C, you cannot do any better than that. PCR can be fairly accurately calculated knowing the power dissipation but the uncertainty is still ± whatever that is. VCR is an additional 0.1PPM/volt. We also know that the Vishay TCR curve is not linear so unless it is held steady in temperature, that could also vary by an unknown amount.
The problem is that even relative measurements still have to depend on known quantities of the reference being used otherwise the measurements will be of limited use. You cannot use 'typical' stated values obviously because you don't know that you have a 'typical' part in hand. When it comes down to the details, your 'relative' measurements still depend on having a reference with known parameters, since you are using a Z201 as your 'reference', you absolutely cannot assume that part has specifications any better than the figures I stated above nor is your system capable of verifying those parameters because your system depends on that Z201 as the 'reference'! You are hereby caught in a catch 22 in which the only way to get 'relative' measurements is by having a known good reference, otherwise your 'relative' is tied to the uncertainties.
At 1000 ohms, a TCR of 0.05 PPM is 1,000.00005 or .05 milliohms per degree, that is 9 digits of resolution, well within the range of my 242D, however, my 242D has an uncertainty of 0.2 PPM so that a 'relative' or accurate reading is to the 8th digit, despite the fact that my bridge has repeatability well beyond 9 digits, that does not in the least make those digits of any relevance even for a 'relative' measurement because anything beyond the 8th digit is within the uncertainty of the measurement. I am confident that my 242D can accurately read TCR to a tenth of a PPM with an uncertainty of 0.2 PPM of the reading, I am not confident that any of the 'relevant' measurement systems being used here have an uncertainty of less than 1.4 PPM at best with the provision that all other error sources have been accounted for. That is the problem with indirect measurements, they are never as good as direct measurements.
I must disagree also, you do not have a "bridge of sorts", you have a voltage divider being measured as a ratio, that does not constitute a bridge by definition.
QUOTE: "For relative measurements the statistics of repeated measurements indicates a well below 1 ppm deviation for T.C."
See my comments above, you cannot use math to reduce uncertainties, it doesn't work that way. You appear to be making the mistake that 'relative' somehow removes uncertainty, it doesn't. I suggest you go through and make a note of all of the uncertainties in your system, from beginning to end, I think you will be surprised that they add up to a significant sum. At the very least, your uncertainty for TCR is 1.4 PPM at best without considering any other sources. Unless you can verify your measurements, you must observe worst case uncertainties in the system, you cannot assume anything is better than that.
Your measurements are 'relative', no question about that, the real question is, how relative and to what are they? From all of the comments here, it appears that these measurements are being interpreted as 'accurate' rather than 'relative', the so-called 'golden' Z201 probably is the most stable of the Z201s but you are still chained to the uncertainties, you do not know just where that stability lies because of the facts I've presented above. Relatively, that Z201 probably does have a lower TCR than my resistors, I'm not disputing that, what is in question is just where my resistors really come in at (they might be a little higher in TCR or maybe a little lower in TCR in reality), the assumption is that the golden Z201 has a near zero TCR but in fact, it can be anywhere within that uncertainty range, you don't know where. Even with relative measurements you cannot make such assumptions.
In the case of many resistors tested here, there are obvious flaws in some of the resistors, some are even questionably meeting spec. The real problem begins to show up when the better resistors are closer to the 'reference' resistor, possible errors and uncertainties begin to show up and must be taken into consideration, if not, relative becomes of little use. What you really need is a characterized resistor of known quantities, that would go a long way to improving 'relative'.
I will leave any other comments due MisterDiodes to him if he would like to respond in kind. As you pointed out:
"it's always a good excercise to question a measurement setup. Especially when going hard to the ppm limits."
MisterDiodes and I are only trying to point out discrepancies and what needs to be taken into consideration for better measurements.
If at some time in the future the opportunity presents itself at an convenient time, I will be happy to post some actual readings on some resistors, I generally do not have the free time to setup and run such tests unless a customer requests them and also asks for recorded readings (which has been quite rare).
Best regards
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