What dBu is 0dBFS?

just a couple of niggling little clarifications, most of the most recent info is correct, BUT (and in no particular order<G>)...

there is no relationship between signal level, signal balance, and signal symmetry.

- signal balance means that the impedance from each of two conductors to ground is equal. Nothing more, nothing less, and it is the basis for driving a balanced input, where commom mode noise can be rejected through summing. A electronically balanced input can be driven by a single-ended (unbalanced) source with minimal penalty. A transformer balanced input can be driven by a single-ended source with almost no penalty. One of the biggest advantages of a balanced circuit is the twist of the signal pair, which cancels any magnetically induced signal (twist has little or no effect on RF or electrically induced intereference.)

- signal symmetry means that the signal is present on two conductors, but the polarity (not the phase) is opposite, and the amplitude is equal. Symmetry is NOT required for a balanced interface. And symmetry is not possible on a single-ended circuit (yeah, obvious, but in the spirit of completeness).

There is no requirement that either interface operate at a specific level. However, common practice suggests that balanced interfaces operate at a nominal signal level of +4 dBu and single-ended interfaces operate at a nominal signal level of -10 dBV. The former is often referred to as "Professional" and the later as "Consumer". There are balanced interfaces on professional gear that operate at -10 dBV, but they are rare, and most likely the result of non-audio people designing audio gear.

Nominal Levels is a bit more complex!

The whole idea of nominal operating level stems from the desire, on the part of broadcasters and telephone companies, to be able to describe perceived loudness. Good luck with that!

The Volume Indicator was developer to meter audio in a way that was somehow analagous to human hearing. The meter movement is damped such that it indicates volume level to the eye in the same way the ear perceives it.

The Volume Unit was the unit of measure for the Volume Indicator.

There was a need to calibrate the Volume Indicator to whatever was going on in the electronics that were driving it. The first such "standard" was 0 VU = +8 dBu (and yes, I'm skipping an entire generation of metering for simplicity - it was actually +8 dBm). Not a misprint, broadcasters still use +8 dBu as their 0 VU indicator.

The recording industry needed a bit more headroom, and adopted the reference of 0 VU = +4 dBu. The exact reasoning is lost in the mists of time - at least as far as I can tell - but analog tape was capable of somewhat more dynamic range than the typical FM transmitter of the day, so that appears to be the driving force.

There is NO Maximum Output Level, Maximum Operating Level, or any such metric. Each circuit has a level at which it distorts, and it is dependent on the power supply first, and certain other design details, such as the ability of active circuit elements to operate from rail to rail, second.

All of which leads us back to the original question.

There is no standard relationship between digital signal levels and analog levels, as I and many others have pointed out. It is entirely up to the circuit designer to create such a relationship. In the circuits that I've designed I've always favored headroom over S/N ratio, and I choose -18 dBFS as my nominal operating level. Sometimes the marketing guys fight with me<G>!

What this means, among other things, is that there remains 18 dB of headroom after you reach the nominal operating level. That is there to account for both musical peaks (which we've always had to deal with) and crest factor (which was less of an issue in the bad old days.)

One last point before I do the math - dBFS is an instantaneous measurement, that is, it represents the maximum excursion at any moment in time, usually a moment in time is 1/48,000th of a second, or 1/96,000th of a second - the inverse of the sample rate.

So while it is not, strictly speaking, either a peak or a peak to peak measurement we need to treat it as such. I can dig deeper if anyone wishes, but I'll leave it at hand-waving for now.

The math:

I have an analog circuit operating from a bipolar 18V supply,
thus the maximum signal level (*assuming an ideal opamp or transistor) is

36Vp-p = 18Vp = 12.7Vrms = 24.3dBu = 22.1dBV = 0dBFS

This represents the clipping point for both analog and digital domains. The actual voltage presented to the A/D converter depends on the chip, and it ranges from 3V to 5V for most commercially available convters today.

So the next problem is to scale our 36Vpp signal to 5Vp (most A/D chips have a single-ended input, or, if they have a differential input it is halved, still limited to a 5V swing.)

But that's really neither here nor there for our purposes... what we care about is scaling our nominal operating level according to some arbitrary rule that we get to set.

Max input, before clipping, is +24 dBu. Nominal operating level is +4 dBu. That's 20 dB of headroom, which is pretty darned good. Keep in mind that we've already converted from Vpp to Vrms. If we set our digital nominal operating level to -20dBFS then we're done, well, except for the whole scaling bit<G>!

If we decrease the analog power supply to +/-15V we lower our max signal:
30Vpp = 15Vp = 10.6Vrms = 22.7dBu = 20.5dBV, and headroom is decreased to 18dB, thus our digital operating level would be -18dBFS.

Decreaseing the analog power supply to +/-12V gives us:
24Vpp = 12Vp = 8.5Vrms = 20.8dBu = 18.5dBV, headroom = 16 dB, and the digital operating level would be -16dBFS.

Is this making sense?

The last wrench we throw into the works is that some designers prefer to shade things in favor of S/N ratio, and raise the digital nominal operating level to -12dBFS, or even higher.

If -12dBFS = 0VU = +4 dBu then in the analog world we end up with a maximum operating level of +16 dBu before the onset of digital clipping, and therefore we need only +/-7VDC for our power supply. (+16 dBu = 13.8Vpp = 6.9Vp = 4.9Vrms)

In the real world that would probably use a +/-9V power supply, giving us a little more headroom in the analog domain.

That's enough for now I think, let me know if I've created more questions than I've answered! (and feel free to check my math<G>!)