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Spread sheet aided calculation for standard resistor measurement

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zlymex:
Spread sheet aided calculation for standard resistor measurement
Precise calculation is required when come to the measurement of standard resistors. The attached spread sheet will help in doing so. It also serves as a documentation for your tests. For the mathematical minded, you can look into the equations to see/verify how they calculated.

Note: when you measure an unknown resistor, you effectively compare it against a standard, whether the standard is explicitly sit there as a stand alone device, or embedded in the instrument you use. When you measure the unknown against the standard, you actually calibrate you unknown, or you transfer to the unknown. The uncertainty of the unknown will be the uncertainty of your standard 'plus' the uncertainty of your transfer/test, thus you cannot get a better uncertainty result than the standard even your transfer is perfect.

Standard resistors on their own are not ideal, there are some changing factors such as long term drift and temperature dependency. We have no ability to control the time, and not many of us have temperature stabilized lab or air bath. Variations resulting from aging and temperature must be taken into account to achieve the best results.


If your equipment is good, you have a good standard(may be borrowed), and the measurement is good, but the calculation is short or incomplete, the result will be ruined. In order to prevent that, here are some of the necessary procedures:
1. The initial calibrated data of the standard resistor must be known. There is a piece of paper inside the cover of any SR104 for instance.
2. A recent calibration is necessary in order to know the average anual drift. This also served as the most updated information for the standard.
3. Your 'measurement' is the comparison of the unknown Rx against the Standard Rs.
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.
4. Type in the measurement data into the spread sheet in light-green-background cells, the result will come out at yellow-background cells.


Apart from the measurement related calculations, an internal temperature calculation for SR104 is also provided.

Edit: I found out an error in the spread sheet, and upload again. If your download is before the data/time I edited the thread, please re-download. Sorry for the inconvenient.

ManateeMafia:
Thanks for the spreadsheet. It should come in handy this summer.

quarks:
Hello zlymex,

in your spreadsheet you have different alpha and beta values.
Are these values expected to change?
Or is this because of measurement uncertainty?

bye
quarks

TiN:
Yay, can I steal this one too? :)

zlymex:

--- Quote from: TiN on March 23, 2016, 09:16:44 am ---Yay, can I steal this one too? :)

--- End quote ---
Sure  >:D

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