Hello,
sorry your wording is difficult to understand at least for me as a non native speaker.
I never could imagine that you really want me to take my precious hobby time to grab out all the data.
Up to now you cry for data without telling what you really want to do.
My apologies. I had assumed that the data was as accessible as the plots. I use a single directory for small projects. For large ones I use more elaborate structures. One really does not want to put 40,000 files in a single directory. Access gets rather slow.
I want to develop models of the variation of precision references caused by age, temperature, humidity, barometric pressure and any other identifiable sources of variation which are measurable and relevant. The purpose of these models is to be able to make measurements of a device during an initial test period which will be able to accurately predict the value and uncertainty of the reference for some period of time into the future.
The motivation is quite simple. In metrology, the particular value is of little consequence so long as it is known. It is the uncertainty of that value that matters. Traditional reference designs have expended great effort and cost producing specific values when all that is really required is any nearby value which is known with low uncertainty.
The length of time that such predictions are accurate is dependent upon how long a history one has for the device and whether any extraordinary events take place such as happened to one of @cellularmitosis' references.
Hysteresis associated with environmental changes requires having the environmental history. Such data is easily collected with an inexpensive MCU which can run off a coin cell for several years. But to be useful for reducing the uncertainty, one must have sound predictive models of the relationship between the reference value and the environmental history. That requires a lot of data to assure that the models are statistically valid.
Now with the pictures I get the image that you want to solve a problem that is long solved on my side
every time I draw a LMS curve it is actually a 3rd order polynom.
2nd order does not fit in all cases and 5th order usually does not improve the result.
I omitted the result for 10k#8 because I had questions about the proper equation and with a sample size of one did not wish to pursue the matter.
What you have provided in the overview and the CSV file version is an approximation based on an assumption that the T.C. is a straight line.
No, the 25 deg C value is actually the linear (1 st order) coefficient of the 3rd order polynominal.
Interestingly the 2nd order coefficient is around 0.032 +/- 10..15% on this batch of the PTF56 resistors.
So the 25 deg C value is a good measure for the fitting.
Then the information you presented is misleading. A proper presentation should have included the other coefficients and the form of the polynomial. As presented, the reader would expect that the curve was the RMS average of the rising and falling passes oddly labeled by a non-native speaker.
Once I have the correct polynomial form I can generate a random set of resistors and determine how many measurements are needed to calculate the change in the voltage of a divider over a specified temperature range. This is an afternoon's work if I have your actual measurements.
you are loosing yourself in a dream world in generating artificial data.
Reality will differ: in the PPM range you have to treat every resistor as a individual.
The creation of synthetic data is often used and well respected in the scientific community. There are a tremendous variety of ways of creating synthetic data. Which should be used is dependent upon the problem. In exploration seismology multicompany consortia expend millions of dollars to create synthetic datasets for which all the relevant parameters are known so that one can evaluate how well algorithms for recovering such information from field data perform. Most of the cost is the many hours of supercomputer time it takes to create the datasets.
In this instance, given the mean and standard deviation of the coefficients of the polynomial, one creates a suite of resistors from which one chooses randomly. Generally referred to as the "Monte Carlo" method. This method is used for combinatorial problems because they are inherently NP-hard and cannot be solved for even a rather small number of samples. So one makes enough trials to determine the mean and standard deviation of the combination being studied.
Edit: I digitized a few points from 10k#8.
attached the normalized result of 1 minute averages of deviation from 25 deg C value (in ppm) over temperature difference to 25 deg C in (deg C)
(ignore the first 3 lines they are only the instruction for my solver).
good luck
Andreas
Two series are rather less than needed to arrive at any definitive result on the hysteresis. However, it is more data than I had, so I shall be happy with that for now. And press forward with the construction of my own temperature chamber.
As you have taken the time to determine the hysteresis and have much more data than you have made available to me, would you be willing to share your insights? Is the behavior on the RH & LH portions of the curve the same as in the center?
This is rather important to the construction of traveling references.
Have Fun!
Reg