Q. Can you explain audio interface input sensitivity?

My interface allows me to switch line‑input sensitivity between +4dBu and ‑10dBV. My calculations suggest that should be a difference of 14dB, but it looks more like 12dB on my DAW’s meters. What’s going on?

Via SOS web site

SOS Technical Editor Hugh Robjohns replies: 

As anyone with a GCSE Maths qualification knows, the difference between +4 and ‑10 is, indeed, 14. However, as any audio engineer knows, the difference between +4dBu and ‑10dBV is actually 12dB. So your meters are telling the truth!

This is a very common, but very basic, misunderstanding for a lot people (and even some manufacturers), but it is well worth understanding the facts.

The reason for the apparent discrepancy is that the two standard operating levels your interface allows you to select are quoted in respect of different reference signal voltages. Those little letters after the dB values are there for a very important reason!

It may seem obvious that the difference between these two input sensitivity settings is 14dB, so you may be surprised when your DAW measures it as 12.

The professional operating level of +4dBu is measured with respect to a reference signal level (denoted by the little ‘u’) of 0.775Vrms, and works out at a signal voltage of 1.228Vrms. (The ‘rms’ appendage basically means that we are assessing the average signal level — and we’re talking about sine-wave test‑tones here.)

The semi‑pro operating level of ‑10dBV is with reference to 1.000Vrms (denoted by the big ‘V’) and works out to 0.316Vrms. The difference between the two is 11.790dB, although, unless you wear anoraks or have a PhD, it’s probably much easier and more convenient to think of it as a 12dB difference. If you want the maths (which is still only GCSE level, thankfully), here it is:

Decibels = 20 x log (signal voltage/reference voltage)

So:

20 x log (1.228/0.775) = 4dBu (Note the term dBu to denote the 0.775Vrms reference.)

And:

 20 x log (0.316/1.000) = ‑10dBV (Again, the use of dBV denotes the 1.000Vrms reference.)

To calculate the difference between the two standard operating‑level voltages:

20 x log (1.228/0.316) = 11.79dB ~ 12dB

Note that in this case, where we are simply calculating the ratio of two signal voltages, no reference is involved, so the letters ‘dB’ are used on their own.  

Published in SOS February 2011