Electronics > Metrology

Spread sheet aided calculation for standard resistor measurement

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zlymex:

--- Quote from: dacman on March 25, 2016, 01:31:14 am ---One problem with the example is that the definition of the US legal Ohm changed in 1990 and the 1982 value hasn't been corrected.

--- End quote ---
That's right, good point, I forgot that.
Now I made a suggested calculation of the annual drift based on US Ohm adjustment in 1990 of -1.69ppm, and the drift rate of 0.053ppm per year before. The user has to input his own value of his/her choice(of the suggested value or his/her own calculation) because the adjustment of other countries were different.

e61_phil:

--- Quote from: zlymex on March 21, 2016, 12:24:51 pm ---
For example, by using an 3458A to measure the unknown, you got Rxm=1000.155 Ohm, this is not the result of Rx. You have to measure the Standard as the comparent. 
You substitute the unknown with the standard, measure again, you got Rsm=10000.123 Ohm, this is again not the result of Rs. However, the difference(Rxm-Rsm = 0.032 Ohm) is much more important, which will be used to calculate the final result of Rx.
If your standard was calibrated as 10000.002, then the Rx would be Rx=Rs+(Rxm-Rsm) = 10000.002+0.032 = 10000.034, correct?

Well, if there is no aging of the standard, and no temperature variations, it's correct. But if not, you can refer to the spread sheet for the right calculation.


--- End quote ---

I have a question to your calculation: Why is an offset expected? I would expect a gain error in a DMM which reads another than the true value (offset should be eliminated by auto zero features). Therefore, my calculation would (in the simplest case) more like this:

Measured Standard reistance divided by calibrated values gives the gain error:

10000.123 / 10000.002 = 1.0000121

And now I would divide the result of my unknown resistor measurement by this gain error:

10000.155 / 1.0000121 = 10000.034


The result is the same due to the very small deviations, but which way is the right one?


Another way could be the measurement of the resitor ratios by the DMM and multiplication of the ratio with the known resistor.

zlymex:
To: e61_phil
Your way is correct. My way is the simplified version of your way. That is, use addition and subtraction instead of multiplication and division.

e61_phil:
Thank you for the clarification :)

dacman:
Addition and subtraction only work because the standard is close to nominal.  If the standard had an offset of, for example, -900 ppm, then there would be an error of about 1 ppm in the result when compared to multiplying and dividing.

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