dCS Ring DAC - A Technical Explanation

My confusion is with how the 16-24 bits of the input digital signal gets converted to 5 bits going into the mapper? It would seem this is a big loss in dynamic range resolution, so I must be missing something…

If I were to venture a guess, I’d say that “5-bit modulator” stage is a digital multibit sigma-delta modulator.

Looking forward to James’ reply :grin:

Many thanks, James, really helpful!

Am looking forward to the next instalments of your Technical Explanation papers.

Best wishes


Thanks Pete

All adds to my understanding!



Thank you.

I appreciate I don’t need to know this but I’ll ask anyway as it’s very interesting. Is left and right divided in the ring or can the latches switch sides.


By no means am I an expert on the maths behind this, however… The more appropriate way to describe the modulation stage would be as a “noiseshaper”, as the audio community is pretty firm on the definition of delta-sigma modulation with one specific implementation.

That said, the key aspect to consider is that even with DSD running at the same rate as the Ring DAC with only 1 bit, you get close to 24-bit performance. We are working with a much greater word length here, and while it really isn’t an apples to apples comparison (DSD to the Ring DAC format), it stands to show that a lower bit depth and higher rate – if handled correctly – can produce excellent results.

It is separated, yes – one side of the DAC board handles one channel of the audio. This avoids crosstalk between the left and right channels.


The following is taken from a response we put on another forum, but I think the information is really pertinent to the discussion here…

To improve the state of the art you need subject matter expertise. Only by understanding the benefits and limitations of various approaches to A-D and D-A conversion can we design a DAC that we feel is best in class. Of course what we deem as a critical performance requirement may not be the same as other manufacturers or hobbyist engineers, however we are one of a select few manufacturers who have designed world-class ADCs, DACs and sample rate converters for both studio and consumer use.

So, we are trying to point out the issues that exist in common architectures, which to sum up are:

You can have lots of weighted current sources at a low sample rate – the challenge here is matching these current sources, and keeping them matched over temperature variations and time. For audio, the side-effect of this is that any errors in this matching cause unnatural distortion (due to correlation), which the human auditory system is very sensitive to. On the plus side, because we don’t have to run that fast, jitter is less of an issue.

You can have conceptually a single current source, and run it at a much higher sample rate. This fixes the matching issue (because it’s self-referencing – on or off, and any drift will manifest as DC rather than distortion). Unfortunately to deal with the quantisation noise generated, you have to heavily noise shape this and move it up in band. This can cause issues because if you keep the clock at sensible rates, the quantisation noise is very close to the audio band, and if you move it too high in frequency jitter becomes a real issue (due to switching noise), at which point you may have to perform some quite horrible (and sometimes impossible) maths to match rates.

What the Ring DAC does is effectively a hybrid – the clock can run at sensible rates (so 3-6MHz) and the noise shaping can be gentle, but because we have multiple codes to represent, we need a way to match them exactly - whilst bearing in mind that components age, temperature can become a factor and so on. This is the job of the mapper, and it has numerous attractions, including distributing DAC errors away from where we are interested (audio frequencies) to where we are insensitive (very high frequencies), without altering the data presented to it, whilst at the same time ensuring all the sensitive components age in the same way.

We can definitively state the that the Ring technology is not multiple DSD streams, and is not random – if you read the writeup, we even say “may appear random”.

It is quite correct to say that you cannot decorrelate noise that is already part of the signal. However, it is worth thinking about this as a philosophical point. One view is that noise shaping and filtering are evil because they somehow ‘guess’ and don’t reproduce the ‘original’ signal, and the ‘fewest steps must be the best’. Now, this may sound strange coming from us, but one of our beliefs can be attributed to Einstein – “Everything should be made as simple as possible, but no simpler ”. So what is the original signal we are trying to reproduce? This will be covered more in the filtering article.


Right, that makes sense. Perhaps a more appropriate term I should’ve used is Noise-Shaping Requantizer. :smiley:


@James the series seem to be halted. Will there be a next post?

I read this expanding thread with great interest, but fear like my understanding of Relativity, which I was taught at A level, I’m somewhat behind the curve. But it is very enlightening thanks.

Will you be at some future point explaining the effects of the filters ( for vivaldi). I’m a little lost despite reading round this as to what their sonic effects are and would be most interested.

Yes listening is recommended, but backing it up with some science would be much appreciated.


The series is definitely still going ahead. The next post will be coming very soon, but we’re working on preparing some additional information that we hope will address some of the questions that we have received over the past few weeks.

Thanks for your patience, and I’ll be back with a new post on filtering within the next two weeks.

The next post(s) we have planned are on filtering, so once those are ready hopefully you will feel much more comfortable with the topic!