# Combining ±% with ±dB in measurement uncertainty

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.
• 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. Jun 5 '14 at 13:08