## Computing Uncertainty (Spreadsheet)

### Computing Uncertainty (Spreadsheet)

At the power calibration tutorial at Measurement Science Conference in Anaheim on 25 March, 2009, a spreadsheet was shown that implemented the calculation of uncertainty of a single Gamma-Corrected frequency point. Several students requested the spreadsheet, so I'm posting it here. I didn't make much of an attempt to document the workings of the sheet (hoping that the slides would help with that), so please use replies to this topic to ask any questions that arise.

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### Re: Computing Uncertainty (Spreadsheet)

I work at a primary standards lab, and we currently calibrate F1109's and F1116's for our customers (secondary reference labs). These same customers also own M1110's and M1111's that we calibrate. We are currently looking at options for these secondary labs to calibrate their own feed-thru mounts using these standard mounts. If this is done, the secondary labs would not disassemble the splitter from the mount to obtain gamma values. With no gamma values on the F-series mounts, our concern is the effect on calibration factor uncertainty? We do not want to pass significant uncertainties to power sensor users down the chain.

I have been looking at this spreadsheet and have managed to decipher some of it. I wasn't sure about the most important part though.

Is "Gamma Error uncorrected" (Block O20) the uncertainty without correcting cal. factors for Gammas? If so, are these expanded uncertainties?

Just curious if we can compare blocks I18 and O20 to get the comparison we need.

Thanks for any assistance you can provide.

I have been looking at this spreadsheet and have managed to decipher some of it. I wasn't sure about the most important part though.

Is "Gamma Error uncorrected" (Block O20) the uncertainty without correcting cal. factors for Gammas? If so, are these expanded uncertainties?

Just curious if we can compare blocks I18 and O20 to get the comparison we need.

Thanks for any assistance you can provide.

### Re: Computing Uncertainty (Spreadsheet)

Hi, Van; Thanks for the question.

You are correct that the "Gamma Error Uncorrected" on line 20 is the estimate of the error due to mismatch in the case that the phase of the port parameters are unknown. This uncertainty is reported at a 95% interval, or "k=2".

There is an added complication, though. In this calculation, both magnitudes (Rho) of Gamma were 0.1, equivalent to VSWR of 1.22. If you were using the spreadsheet with supplied or measured *data* of Rho, you'd probably have the angles, too, and could go ahead and "Gamma-correct". If you don't have the data, then you have to assume some worst-case value, usually larger than the actual measured value. Even with all that, with M1110 and F1109's, the Rho's are lower and the total mismatch error isn't too bad even if uncorrected. I think it will turn out to be less than 0.8% at 18GHz. When you RSS that with the other contributions, it may be acceptable.

If it was up to me, I'd consider having them do a corrected transfer using the "old" S22, and investigate possible changes in S22 if the calibration failed.

You are correct that the "Gamma Error Uncorrected" on line 20 is the estimate of the error due to mismatch in the case that the phase of the port parameters are unknown. This uncertainty is reported at a 95% interval, or "k=2".

There is an added complication, though. In this calculation, both magnitudes (Rho) of Gamma were 0.1, equivalent to VSWR of 1.22. If you were using the spreadsheet with supplied or measured *data* of Rho, you'd probably have the angles, too, and could go ahead and "Gamma-correct". If you don't have the data, then you have to assume some worst-case value, usually larger than the actual measured value. Even with all that, with M1110 and F1109's, the Rho's are lower and the total mismatch error isn't too bad even if uncorrected. I think it will turn out to be less than 0.8% at 18GHz. When you RSS that with the other contributions, it may be acceptable.

If it was up to me, I'd consider having them do a corrected transfer using the "old" S22, and investigate possible changes in S22 if the calibration failed.