SB3 volume control with 20-bit external DAC

[stefanta650]

I think the easiest way to understand this is to forget about numbers, decibels, and bits per sample for a minute, and just think about what's coming out of the DAC.

To oversimply only slightly: there are two things always coming from the DAC. 1) signal and 2) noise.

The level of the noise output stays the same no matter what signal level is being produced. That is really important to understand!

When the DAC is making a loud signal, there is a lot of signal and a little noise. That's a high SNR, which is good.

However, when the DAC is making a quiet signal, you have a little signal and a little noise. If we now consider the noise level in relation to the signal level, the noise is now louder. The noise level hasn't gone up in absolute terms (eg volts), but relative to the signal it has, so you now have a bad SNR.

Now consider a simple resistor attenuator being fed by a loud (good SNR) signal from the DAC. When the voltage passes through the resistor divider, everything gets attenuated - the signal and noise together. You have the same* SNR coming out of the divider as you had going in, i.e., the DAC's optimal SNR is preserved.

OK, now back to bits per sample. As you can see, the above effects really don't have much at all to do with bits per sample. We could send a million bits per sample, and it would still be the same. So why does bit depth matter? What is the significance of 16 vs 24 bit?

What matters is that we send enough bits per sample that the DAC's full dynamic range is utilized. It is important to realize that the DAC's dynamic range is finite, and is less than its input word size - more like 20 bits, since it is limited by its output noise level.

By "expanding" a 16 bit signal to 24 bit, all we are doing is saying "these 16 bits go in the most significant slots of the 24 bit word". We haven't improved the SNR of the signal, any more than you can "enhance" a digital photo the way they do on CSI.

If we attenuate the 16 bit signal, yes, the zeroes and ones will migrate down into the least significant bits of the 24 bit word, and yes, if we still "have all the bits" we could then mathematically go in reverse and get back to the same data. But that is not what the DAC does with the signal! The bits represent a smaller signal now than they did before. We still have exactly the same decreasing SNR effect. Sending 24 bits into the DAC just means we aren't making it any worse than it already is. We haven't "bought more headroom"... it does NOT mean that those first 8 bits of attenuation are "free".

To prove this, you could play a sine wave through the DAC and measure the SNR at each volume step. We would expect to see the SNR decrease as the volume is decreased. If there were anything special about the point where we start "losing bits", or if we were really getting "extra headroom", then the plot would decrease slowly (or not at all) until it reaches that point, and then there would be an inflection.

However, that is not what you'll see. The SNR will simply decrease with the signal level, all the way down.

I hope this helps... for extra credit maybe someone will try testing this?

* Actally, there are a number of secondary effects which reduce the SNR by the time it gets through the amplifier, but these are vanishingly small in comparison.

Hi Sean!
I'm sorry for activating an old thread - but it features my question :-) Just a couple of weeks ago I got a Squeezebox Classic and I make use of the replay gain function. But even after adjusting the volume of my amplifier (which is connected via analog output of my SB) I think that the sound with RG enables is not that clear dynamic than with RG disabled. So my question is: does RG reduce the quality or is it just because it reduces the digital level so the SNR is lower with RG enabled (as the noise floor remains as it is...).

Thanks for helping and understanding :-)

Stefan

[Triggaaar]

The normal approach with a 16 bit original represented as a 24 bit signal, would be to make the bottom 8 bits 0s - so using the volume control, some of those bits may be turned in 1s, but no 1s will ever be required lower than the 24th bit. If you then throw away the bottom 4 of those 24 bits, you may be throwing away some 1s, and therefore some information. If you use all of the 24 bits you aren't throwing away any information.

This is very useful, thanks. I had wrongly assumed that as you reduced volume, you lost a bit of information at a time, and if you didn't go below the 16 bit original, which DAC you used would be irrelevant.

If we had represented the original 16 bit signal as 20 bits, I assume we'd be able to slightly reduce the volume and pass to an external 20 bit DAC, without losing information (although reducing SNR - which I'm not saying is irrelevant, but in my case, I use a pre amp to set my maximum volume, and then use the sq box to adjust slightly for convenience)[/QUOTE]

[Skunk]

the C-100 integrated seems to produce an improved sound over connecting the SB3 directly to the A-100 amp.

Apples and Oranges IMHO. As we've learnt, relying on the digital volume controls is a handicap to the Sb3's SNR. A proper comparison might be the integrated amp or a seperate amp+pre versus fixed/stepped passive attenuators and limited use of the volume control.

The digital volume control is great, and with the integrated you should not be afraid to use it for casual to semi serious listening. When you're all ears though, setting the Sb3 to max is the best idea, and if a comparison is to be made it should be at maximum digital volume for both setups.

[USAudio]

... all in all, it's probably best just to alter level in the analogue domain - at least we all get to sleep nights! ...

You got that right Phil! I've been struggling over this issue for awhile now with the new system I've been putting together.

I came to the same conclusion the other day and decided to replace my PS Audio A-100 amp with their integrated C-100. I was connecting the SB3 directly to the A-100 amp. I received the new unit today and, while I've only had the unit a few hours, the C-100 integrated seems to produce an improved sound over connecting the SB3 directly to the A-100 amp. Some of my recordings that sounded a bit thin before now sound more substantial.

[Phil Leigh]

Yes sorry I didn't (obviously!) mean upsample...what is the correct term for altering the bit-depth of a sample? "re-fathoming"?

a-ha!...

I get it (at last) you can alter the extra bits as much as you like until you happen to cause an effect on one of the original 16...and once you do that you lose information? - that all makes perfect sense.

all in all, it's probably best just to alter level in the analogue domain - at least we all get to sleep nights!
Cheers
Phil

[Patrick Dixon]

So Patrick - to (try and) cut a long story short...

... if only.

In the SB implementation, if you take a 16-bit file, the SB internally upsamples to and outputs at 24 bits

Err, that's not upsampling - upsampling is something completely different!

...if those 24 bits are sent to a 20-bit DAC do you lose any information (at full volume).

My guess is NO since the original 16 bits are preserved (within the 20). This is surely the case otherwise the SB would only be "bit perfect" with 24-bit DACs which is not the case AFAIK.

Please see my previous post - at full volume the bits are passed through unchanged - therefore there can be no loss of information.

I'm happy with the idea that any lowering of the digital volume potentially loses information, regardless of bit-depth

It doesn't! (It has implications on the SNR when the signal is converted back to analogue though.)

[Phil Leigh]

So Patrick - to (try and) cut a long story short...

In the SB implementation, if you take a 16-bit file, the SB internally upsamples to and outputs at 24 bits...if those 24 bits are sent to a 20-bit DAC do you lose any information (at full volume).

My guess is NO since the original 16 bits are preserved (within the 20). This is surely the case otherwise the SB would only be "bit perfect" with 24-bit DACs which is not the case AFAIK.

I'm happy with the idea that any lowering of the digital volume potentially loses information, regardless of bit-depth

[Patrick Dixon]

Ignoring SNR, what is confusing me particularly, is how according to the statements I've quoted, reducing the volume to a certain point will not result in losing original information if using a 24 bit DAC, but it will if using an external 20 bit DAC.

The volume control settings are carefully chosen so that with a 16 bit original no bits lower than the 24th one will be changed. The normal approach with a 16 bit original represented as a 24 bit signal, would be to make the bottom 8 bits 0s - so using the volume control, some of those bits may be turned in 1s, but no 1s will ever be required lower than the 24th bit. If you then throw away the bottom 4 of those 24 bits, you may be throwing away some 1s, and therefore some information. If you use all of the 24 bits you aren't throwing away any information.

It may be helpful to think of SNR as an 'analogue' thing and information as a 'digital' thing. The digital signal in this case is a representation of an analogue signal, and how you represent it digitally has an implication on the maximum SNR attainable in the analogue domain.

In the digital domain you can represent and manipulate the signal in all kinds of different ways, but so long as you don't discard any bits, you retain all the information and you can still get back to the original digital signal.

[Triggaaar]

Ignoring SNR, what is confusing me particularly, is how according to the statements I've quoted, reducing the volume to a certain point will not result in losing original information if using a 24 bit DAC, but it will if using an external 20 bit DAC.

[opaqueice]

There are two different issues here, and I think they might be causing some confusion. One is whether information is lost when you lower the volume; in other words, is it possible to reconstitute the original signal from the signal with lowered volume? The answer to this in the case of the SB (and probably TP) is that there is a certain range from 100 down for which this is possible, but that below some setting it isn't any longer (I think this is 35dB, so to lowest setting is 30 on the 100 point scale).
But of course this is not a question of much practical interest.

Another question is signal/noise ratio of the signal going to a DAC. In that case the issue above is probably tototally unimportant, and the only issue is how much of the dynamic range of the DAC is being used. Any digital signal with lower than max volume will suffer reduced S/N, and it shouldn't matter much, if at all, if it is slightly below 30 or slightly above 30.

[Triggaaar]

If you have ripped a file (say FLAC) from a CD, and then stream it from the PC to your squeezebox, does the squeezebox receive a 16 bit signal, and convert it, or does the slimserver stream a 24 bit signal?

[snarlydwarf]

"Yes, you only maintain all the resolution of the original 16 bits by using all 24 bits - so truncating to 20 will loose you some information."

a 24-bit input value some of the lower attentuation values will not end up truncating any bits, in other words.

Thats part of why the input value is 24 bits even though the data is only 16 bits.

reducing the digital volume will NOT take out information from the original signal, providing the input signal is 16 bit audio and you don't go lower than (IIRC) -35dB

The same thing as above: the original value on a CD is only 16 bits.

So if you take a 16 bit value, and left-shift it (effectively) 8 times, rotating 0's into the low order bits, you have more wiggle room.

Or if binary isnt your cup of tea: think of it in decimal. You have a number, say, between 00 and 99, if you make it between 000 and 990, by multiplying by 10, you have a bit extra resolution when you do division without resorting to fractions. In this case, it actually gets you through the first N steps of volume attenuation without any truncation.

[Triggaaar]

Thanks for your time trying to help me understand this. I am sorry if everyone else thinks this is clear, and I'm confusing the issue.

No, I'm not saying that! At 100, the digits will be passed through untouched, it's only if you reduce volume you can loose resolution.

Yes, I realise that at 100 volume, the squeezebox will pass the digits through without degrading the signal - I am trying to understand the following two points, which to me, seem contradictory (ignoring reduced SNR):
"Yes, you only maintain all the resolution of the original 16 bits by using all 24 bits - so truncating to 20 will loose you some information."
and
reducing the digital volume will NOT take out information from the original signal, providing the input signal is 16 bit audio and you don't go lower than (IIRC) -35dB

Thanks

[seanadams]

Sorry about that.

Yes - providing the input signal is 16 bit audio and you don't go lower than (IIRC) -35dB.

The bits don't have the same value that they had before you shifted them!! Attenuate by 6db and you're then using only half of the system's output range - you're closer to the noise floor and you have only half of the available "steps".

I don't know what it means to "slightly reduce" the SNR. The reduction is exactly equal to the amount of attenuation.

[Patrick Dixon]

I'm now more confused than I started.

Sorry about that.

So Patrick is saying that reducing the digital volume will NOT take out information from the original signal, just slightly reduce the SNR.

Yes - providing the input signal is 16 bit audio and you don't go lower than (IIRC) -35dB.

And Patrick is saying that even if you leave the volume at 100, you will lose original resolution of the 16 bits if you have a 20 bit DAC (as you are sending it a 24 bit signal).

No, I'm not saying that! At 100, the digits will be passed through untouched, it's only if you reduce volume you can loose resolution.

The one bit that does seem clear, is that digitally reducing the volume, prior to converting to anologue, reduces the SNR.

Almost everything you do to an analogue signal reduces its SNR too, so what I'm trying to say is that digital volume control vs analogue volume control is something of a trade-off.