(Digital) Volume Control


There are lots of discussions ongoing if one should go or not go for digital volume control.

This is the way I see it:

It'll depend how well it performs.

First of all it doesn't cost you anything, it is easy to handle, makes certain quite expensive audio HW obsolete, resolves quite some analog volume control associated problems and it can sound damn good.

What are the topics to be discussed?

The key parameters to look at when talking about digital volume are:

1. Quantization errors
2. Dynamic Range
3. Signal to Noise Ratio (SNR).

1. Quantization errors

Only quantization errors are specific to digital volume control! (Assuming that your software doesn't do e.g. any filtering, dithering or other manipulations)

A quantization error gets introduced if you just would cut down 8 non-zero-bits (LSB)  on a 24bit word to end up with 16bit. 
Those 8 non-zero-bits  might contain the remainders from e.g. a digital multiplication process which takes place when doing digital attenuation.
You'd obviously would introduce rounding errors a.k.a quantization errors, if you'd drop those 8 bits.

Solution: Meanwhile most DACs work in 24bit mode. There is no need to go down to 16bit again, if you directly feed your DAC or you store your data with a bitdepth of 24bit..

On 16 bit material, which is probably 99,5% of todays played music, you would have  "theoretically" an 8bit (48db) attenuation range, without facing rounding errors.

Luckily  a device like the Squeezebox Touch runs 24bit throughout. 

2. Dynamic Range (DR)

As a rule of thumb we can assume that 6db attenuation equals roughly 1 bit loss of resolution.
6 db attenuation means reducing your  signals dynamic range by 50%. 

So what!?!??

That'll be the same for analog and digital. That can't obviously be an issue associated to digital volume control.  

I think it is obvious that on either side - analog or digital - it is highly recommended to run the highest possible levels to your amp.

The challenge behind that: To  be able to run your DAC output at highest level, your amp gain, speaker SPL and DAC outputlevel  must be properly aligned.

See example below.

3. Lowering  the Signal to Noise Ratio (SNR)

Another effect is  related to the resulting  lower Signal to Noise Ratio (SNR) when attenuating a signal. 

You'll see a decreasing  SNR the lower your signal gets, no matter if you do it analog or digital. Again - that's not the issue.

There is another effect on the digital side we should consider.

Very good DAC chips manage to deliver SNR levels at around 120db.

Hmmh. Let's calculate a bit.

24bits*6db gives us a dynamic range of 144db. With a SNR of 120db we're  obviously
loosing 24db already at this point.

What does this mean? This means from bit 20 (20bit*6db/bit=120db) onwards the DAC chip itself just adds noise to the signal. You could call it automatic unwanted DAC dithering.

If we look at our earlier quantization problem, I was talking about 8bit volume control range without facing quantization issues. The problem is obviously that 4bit out of 8 are those  (>20bit) . These would end up in the DAC noise.

Based on this, we can conclude, that doing more then 4bit (24db=SB-level 52) digital volume control should be avoided, if you own a DAC with >120db/SNR.

If your entire DAC and not only the DAC chip! comes with a lower SNR your rather lossless range for attenuating the signal will obviously shrink further down.

4. Summary
  1. In any case avoid as much attenuation as possible on either side -- analog and digital. 
  2. Digital volume controls get worse under extensive usage and certain environmental conditions.  By considering its limitations and boundaries, digital volume control usually outperforms analog controls. < 4bit=24bit attenuation should give more then satisfactory results on 24bit DAC systems.
  3. Analog attenuation might be preferred if attenuation ranges  >24db must be achieved
    (Don't forget though  that analog volume controls usually introduce several other problems on top of the digital controls!! In those cases even a much higher digital attenuation might sound better than a rather poor analog volume control))

5. Advise

To keep the attenuation as low as possible you need to have a look at  your  DAC output-level and amplifier gain.

The root cause of the attenuation associated  problems is caused by the attenuation itself.

Why do the majority of people need to attenuate the signals that heavily at all? Typical 25-35db that's a lot.

There are IMO two main reasons:

1. There's a much too high gain on the amplifier and/or at the same time a too high output voltage on the DAC output.
You practically need to drive your DAC output voltage down into the noise floor to avoid frying your speakers and eardrums.  Just to please a kind of industry standard of 30db gain on off-the- shelve-one-size-fits-all amplifiers. 
This doesn't make any sense.

If you'd run 0db digital (SB=100) and your DAC delivers a typical 2V RMS output voltage, feeding your amp (voltage gain of e.g. 28) a 4R speaker,  you'd blow your speakers with 784W!! =(2V*28)^2/4R

The very simple and logical  solution would be: A voltage gain reduction from 28  to  6 on your amp !!  To stay with above example, this amp would deliver a reasonable power of 36W at  0db attenuation resp. SB volume control at 100 to your speakers. All this of course needs to get properly aligned with the speakers efficiency  and your preferred listening level.

2. Loudness War

Modern recordings are very "loud" mastered. Those recordings come with a much lower dynamic range and do sound much louder.
These recordings sound cool on a Boom box and of course sell great.
The problem behind it - even if you have a well aligned and engineered system in terms of gain and digital volume control, you'd need to cater for up to 2bit (12db) attenuation only because of the different recordings levels you'll face.
That means if you would manage to run a classical recording - mastered in the 80ies - at SB100 or 0db you'd need to apply for achieving the  same perceived  sound pressure level (SPL) on a modern recording 12 db attenuation. 2 bits just lost without gaining anything!

If we now stay with the 4 bit volume control range  example from above, you'd have just two bits left for controlling  those high-gain recordings.

There is an easy way out. Let's just assume that those low quality recordings don't belong into an audiophile collection anyway. Problem solved!

6. Closing -- A little test

You might want to run a little test, just to put things into perspective:

Attenuate your digital signal as far down so that you can hardly hear anything from your speakers anymore. 

How far down did you get on your SB volume control ? Level 10=-45db?

What does this mean?

That means the audible range on your system would be down just 45db from a maximum volume control setting of 100(0db) down to 10(-45db).

Effectively -- that's your audible range!
That's not much, wouldn't you agree!
At least compared to those earlier discussed -120db=20bit dynamic range - the value we're talking about all all the time.

BTW: Top-End microphones do not deliver more then 75db SNR!

I think there is plenty of digital headroom left. ;)

7. Closing

Bottom line -- I advise you to try and listen.  Consider above aspects. 

There is no black or white in audio. Audio is always and will always be "grey".

I am running serious audio with a digital VC since almost 4 years. I won't go back.


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