Firstly apologies if this is not the correct place to post this but wasn't sure which site would be good to ask regarding about measurement uncertainty calculation.

I am trying to calculate the combined measurement uncertainty, however the uncertainties I want to combine are using different scales:

Carrier level uncertainty: ±0.5dB (logarithmic)

Modulation uncertainty: ±5% (linear)

Converting either from one format to another will not give me a simple ±value in the other format

What is the best way to combine these uncertainties?


You can convert to percent. $0.5 dB=10^{0.05}\approx 1.122$ so this uncertainty is about $\pm 12\%$ Yes, on the down side you can say it is $\frac 1{1.122}\approx 0.891$ so the uncertainty in that direction is only $11\%$, but that is close.

  • $\begingroup$ Hi, thanks for the answer. Yes I did consider this but the fact that when converting dB to % the positive and negative side were different seemed mathematically incorrect. I guess I could take the higher amount of the two to be safe. Again this was just one example but in cases where uncertainties are higher the difference is greater $\endgroup$
    – kewsvnet
    Jun 5 '14 at 8:25
  • $\begingroup$ Error analysis most commonly is not exact-you want a rough value for what the error could be. We tend to root-sum-square errors, knowing that in the worst case it could be worse than that. Of course, if you want the truly worst case, you add them linearly. It is also not required that errors be symmetric. You could quote a value as something $+12\%-11\%$ if it is important to you. This often happens if the lower limit approaches zero. $\endgroup$ Jun 5 '14 at 13:08
  • $\begingroup$ Yes, you are right in most cases the + / - conversions are close and if we stick using the positive dB value when converting to % it is the worse of the two. Once I have all my values in % I am also using the root-sum-square of the errors. Thanks again for your help! $\endgroup$
    – kewsvnet
    Jun 6 '14 at 13:34

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