# 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 have two parameters stated, what's the third (combined) meant to be? At the moment you have eggs and bacon but it sounds like you want to combine eggs and bacon into one parameter. Also, why is the word "uncertainty" used? Normally I'd use "tolerance" – Andy aka Jun 4 '14 at 16:38
• Are you measuring power or amplitude? – The Photon Jun 4 '14 at 17:16

## 1 Answer

Never mind that one scale is logarithmic and the other is linear. Both error specs indicate ratios. I'll assume you're measuring power in some form.

Then an error of +/- 0.5 dB indicates the true value is between 0.89x and 1.12x what you measured (with whatever certainty is assumed by your definition of uncertainty).

And an error of +/- 5% indicates the value is between 0.95x and 1.05x what you measured.

If both uncertainties apply to the same measurement, you can multiply these ratios together and find the overall range is 0.846x to 1.178x the measurement, or that the overall error is +17.8% / -15.4% or +0.71 / -0.62 dB.

If you're measuring amplitudes rather than powers, of course you'll need to convert between dB and ratios differently.

• based on what you said shouldn't the overall error work out to +17.8% / -15.4% or +0.71dB / -0.62dB – kewsvnet Jun 5 '14 at 9:49
• @kewsvnet, good point. Edited. – The Photon Jun 5 '14 at 15:55