My interface converter calibration

fireberd
Are you actually working with equipment that use all those references?

wst3
(just remember, you asked!)
 
The decibel is a power ratio! By definition it is 10 times the log of the ratio of two powers, and it is always RMS.
 
So right there we just shot down using dB for voltages, let alone the number of bits that are turned on.
 
Or did we?
 
Engineers are a curious lot, and once they figured out that we hear things on a logarithmic scale (this applies to apparent loudness as well as frequency - pretty cool eh?) they wanted to apply it to everything!

It turns out that we can do a little algebraic magic and use that same dB to describe the ratio of two voltages - we just have to use 20 instead of 10 as our multiplier. (one of these days I am going to write this up nicely, with equations and all that stuff, for now you'll just have to take my word for it!)

But we still dealing with ratios - how can we use the dB to describe levels?

Instead of measuring input and output we can replace the denominator with a known value, and then our dB measurements will provide us with something we can hang our hat on.
 
This is where it starts to get really messy, and since I'm lazy I'm going to just blow through this  next part.

The original reference was 1 mW across 600 Ohms which turns out to be approximately 0.7746 Vrms. That 1 mW reference was known as 0 dBm, or sometimes 0 dBm0, and it is a power measurement.
 
But wait, if we know that's the same as 0.7746 Vrms we can use that, right?
 
Yup, but you know we have to mess things up a bit first! Some folks starting using 0 dBm as a voltage measurement, with or without the impedance specified. It was ok, but it wasn't completely accurate.
 
So we ended up with a new reference, 0 dBU, which some folks claim stood for unterminated, I've never been able to prove that. But it was better. Then Teac threw a wrench in the works and presented yet another reference, and if you think a little it makes a lot of sense, they proposed 0 dBV = 1Vrms. Makes the math a lot easier. For a while we had all those, and more, but these days we can safely say we have only two references:
- the "professional" reference is 0.7746 Vrms
- the "consumer" reference is 1 Vrms
Keep in mind that each of those voltages is the 0 dB mark for that scale.
 
Which brings us to nominal level or normal operating level!
- in the professional world we use +4 dBu which is equal to 1.228 Vrms
- in the consumer world we use -10 dBV which is equal to 0.3162 Vrms.
And this is where we can finally state the difference between 0 dBu and 0 dBV is about 7 dB and the difference between -10 dBV and +4 dBu is about 11.7 dB,
 
Are you confused yet? Good, I'll spare you the VU scale then, and we'll just carry on.

This is where it gets a bit ugly, since the dB was never meant to be used to describe peak values, but as soon as we enter the digital realm that's all  we have, so we've invented the dBFS, as stated earlier, that's the ratio with respect to "all ones" - the highest level we can represent.
 
There is no standard! None!! Zilch!!! Nada!!!!! Zip!!!!!

Yeah, that annoys me just a little bit.

What we need to do is send a sine wave (mid-band is fine) out through our D/A converter, and measure the voltage.
 
For sake of argument lets assume we have a +/-15VDC power supply, and somehow our circuit will operate from one rail to the other, so the maximum voltage we can generate is 30V peak-to-peak, or about 10.6 Vrms or about 22 dBu or 20 dBV.  That won't happen in the real world of course, if it did we'd have 18 dB of headroom (+22 dBu - +4 dBu = 18 db).
 
Which, as it turns out, is how I've set up my studio, but that's really conservative, and you may wish to use 12 dB down from 0 dBFS as your nominal operating level.
 
To do so you send out your -12 dBFS sine wave and measure the analog output. You'll want to attenuate the output externally till -12 dBFS measures 1.288 Vrms or +4 dBu.
 
I've just re-read this, and I'm tempted to delete it, but what the heck - did this help at all? Perhaps this will generate some questions that I can answer more succinctly!

One other very important note - thus far I've limited the discussion to electrical measurements. When we start dealing with sound pressure level it gets even more complex. And then there is the "K System", but I'm stopping here!