what is the transfer accuracy of this setup?(10kohm transfer to 1ohm)
It's impossible to know without more information. Depends on the accuracy of the hamon standards, the transfer standards, the stability of the standards, the stability of the measurements, etc.
Take all of your uncertainties for each transfer and RSS them.
I am a
newbie,if uncertainty = transfer accuracy?
I found the measurement uncertainty of SR104 is 0.3ppm.
And the transfer accuracy of guildline 9350 is 0.05ppm
The transfer accuracy of this setup are 0.3ppm+(0.05ppm+0.05ppm)x2?
Since tolerances are usually specified as confidence intervals (multiples of standard deviations), you should add them using the root of the sum of squares.
If they calibrated the SR104 over a period of three years, then I imagine they might have them characterized to a lower tolerance.
The best way for you to get an answer to this is to ask the lab that performs the measurement for an explanation. If they are a national metrology lab, they'll probably have this published somewhere, and if they are an 17025 accredited primary lab they have to have extensive documentation of the method and uncertainty analysis.
The transfer accuracy of this setup are 0.3ppm+(0.05ppm+0.05ppm)x2?
No, not exactly. There are three contributors for the overall absolute accuracy of the 1 ohms resistor (which you want to know as I understand):
- 0.3ppm from the SR104
- 0.05ppm from the Hammon divider; two transfers to be considered
- 0.015ppm for the 1:1 ratio transfer of the SR104 to the 10k Hammon divider and the same for the 100 to 100 ohms and 1 to 1 ohm transfers, assuming you use a MI 6020 Accubridge (which is expensive, but required when using such a precise Hammon device; the SR1010 e.g. has a 1ppm transfer accuracy 'only') . So overall three ratio measurements.
Please note that if you use a Datron 1281, 3458A HFL, Solartron 7081 for example (meters with specified transfer uncertainty), that uncertainty increases considerably (see data sheet, and don't forget the factor of 1.41 for the two measurements in each transfer).
The transfer accuracy of this setup are 0.3ppm+(0.05ppm+0.05ppm)x2?
No, not exactly. There are three contributors for the overall absolute accuracy of the 1 ohms resistor (which you want to know as I understand):
- 0.3ppm from the SR104
- 0.05ppm from the Hammon divider; two transfers to be considered
- 0.015ppm for the 1:1 ratio transfer of the SR104 to the 10k Hammon divider and the same for the 100 to 100 ohms and 1 to 1 ohm transfers, assuming you use a MI 6020 Accubridge (which is expensive, but required when using such a precise Hammon device; the SR1010 e.g. has a 1ppm transfer accuracy 'only') . So overall three ratio measurements.
Please note that if you use a Datron 1281, 3458A HFL, Solartron 7081 for example (meters with specified transfer uncertainty), that uncertainty increases considerably (see data sheet, and don't forget the factor of 1.41 for the two measurements in each transfer).
There are way more than three contributors of uncertainty in the traceability chain to the 1 ohm resistor measurement. The SR104 states the measurement uncertainty which is only for the time of measurement of that standard. You still have to take into account the stability of the standard and you have to add in a component of stability of your measurement at each step in the traceability chain. This is really important. I've witnessed measurements where the short-term stability swamps the other sources of uncertainty and to just ignore this is terrible science.
For the Hammond devider and the DCC bridge the short term variations are already included in the uncertainties given, see data sheets (its the transfer/ratio overall measurement uncertainty that is specified; for the 3458A HFL the factor sqrt accomodates for fluctuations). The SR104 has a drift and temperature component, as always, thats pretty trivial.
Sorry, that's just not correct. Any measurement is just a representative of a probability distribution and the parameters of the distribution are a function of all the uncertainty contributors. According to BIPM's published measurement uncertainty guide, you must include a repeatability component as a contributor and is usually just the standard deviation of repeated measurements. This is not included in any device's spec sheet as there is no way to predict this. This repeatability component is included in each transfer measurement in the OP's flowchart.
I think you 2 are talking apples and oranges... While you are both correct, I believe AP is referring to the calculation of the accuracy specifications of said transfer. Moon, you're talking in regards to the calculation of the reported uncertainty of said measurements.
Otherwise, I know as being employed by an A2LA 17025 accredited lab, we have to do things more along the lines of what Moon is saying.
Repeatability and Reproducibility are big contributors of uncertainty calculations.
Take the DCC, it compares two resistors and shows the ratio with a given accuracy. This is done in a single measurement. In line with GUM. Not to mix up with a ohms transfer measurement of say a 3458A HFL; there the repetition needs to be factored in, as stated. And yes, I did not talk about how to calculate the overall uncertainty from the contributors. But we probably leave it there now.
Take the DCC, it compares two resistors and shows the ratio with a given accuracy. This is done in a single measurement. In line with GUM. Not to mix up with a ohms transfer measurement of say a 3458A HFL; there the repetition needs to be factored in, as stated. And yes, I did not talk about how to calculate the overall uncertainty from the contributors. But we probably leave it there now.
CalMachine may be right that we are talking about two different things, but in my mind I can't separate a measurement uncertainty from a transfer accuracy... unless the manufacturer is stating a relative uncertainty. If the DCCs are displaying a measurement result, I would hope the DCC's display (or the software interface) of the ratio & accuracy includes a repeatability component as no signal is perfectly stable. The ratio hardware may not have variability but to get any use out of it you have to supply a source signal, and that will always have some short-term variability. Even CCCs have a stability component.
Rough approximation.
As i remember.. at the time of the use of 10kOhm to 1 Ohm transfer presented on diagram, DFM used Guildline 6675 DCC (Direct Current Comparator).
6675 Comparator has Accuracy <0,1 ppm/year/3degC for 1Ohm...1kOhm, and <0.15ppm/year/3deg C for 1kOhm..10kOhm. Stability is accordingly 0.03ppm/day/1degC and 0.04ppm/day/1degC..
Guildline 9350 transfer has accuracy about 0.05ppm
Comparing 10kOhm to 10kOhm, transfer from 10k to 100 Ohm, comparing two 100 Ohm, transfer to 1 Ohm, and comparison 1 Ohm to 1 Ohm will give
sqrt(,15^2+0,05^2+0,1^2+0,05^2+0,1^2)=0,22ppm.
This is upper limit of uncertainty of transfer from 10kOhm to 1 Ohm, because real uncertainties are lower than specified above.
There are also other components of uncertainty budget, but they are usually smaller than this two main components, taken into account.
Stability of very good SR104 is about 0.05ppm/year, (I think DFM has this kind), so the group of 3 resistors should lower this to about 0.017ppm. This woud be the starting point.
For the Hamond transfer, the errors are expected to be larger for the 100 Ohms to 1 Ohms step, because the contact resistance gets more important. So take a look at the full specs of the Hamon dividers, the sales brochures tend to give best in series values.