[landroni]

'The new R-2R DAP Thread', or something. Upon popular (and valid) request I'm spinning this R-2R vs Delta-Sigma DAPs off from the X7 thread.
 

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http://www.head-fi.org/t/713735/x7-the-flagship-dap-from-fiio-updated-on-15-12-2014/5775#post_12015898
"All valid assumption except there is no good multi-bit DAC chip out there to test out the theory. You have to realize that chip manufacturer abandon the R-2R ship long before any portable audio companies even use it, or even before 'DSD' becomes a buzz word. The reason has less to do with marketability but technical limitation (okay, maybe marketability has something to do with it too). High end R-2R chip is neither cheap nor easy to make - and the higher-end it goes, the much harder it becomes. Chip maker simply realizes it is not worth spending huge amount of money in R&D trying to push for small amount of uncertain breakthrough but rather more economical to develop a less ideal tech that is more promising in the future, simply in the hope that one day it will be good enough to excess the older tech - for the most part, I think that's exactly what D-S has accomplished."
 
@ClieOS
I think you're making valid points. The old "golden" R-2R chipsets were discontinued mainly for production costs and complexity. Manufacturers used marketing to disguise the loss in effective functionality (they never put forward in their specs and marketing the real low-bit limitations, or the insane amounts of noise produced, but talked the talk of "equivalent" functionality and support for higher sampling rates and higher bitrates).
 
However, from what I see, DS has reached more or less a dead-end. Decades of industry R&D culminated into the latest ES9018S chipset, yet it still falls short when compared to similarly priced R-2R implementations, very old or very new. While obviously DS has its uses in many contexts (e.g. slim built smartphones), IMO it has no place in flagship, high-fidelity territory. And this is what we're all here for, whether we talk Yggy, X7 or HM901s. After all, people are already forking insane amounts of money for incremental improvements --- might as well use the right technology for it.
 
To reach its full potential DS needs insane sampling speeds and ungodly storage space (it's irrelevant if the chip supports 768 KHz, since no one has a handy copy of such an audio file available), yet there is simply no such bandwidth available today, nor there needs to be. Even those with sizable DSD/SACD collections will admit to relying mostly on PCM. What's more, in my understanding R-2R simply does not need so-called "high-res" for human applications: theoretically and practically 96 KHz is already more than humans will ever need, well, until they evolve that is. And 16 bit vs 24 bit is again more of an arcane, theological debate: each easily covers and goes beyond human perception limits.
 
So if we're talking high-end, high-fidelity for humans, R-2R seems like the no-brainer technology for me. In comparison, DS seems like a fundamentally limited if avowedly glitzy overkill.
 
Now, as you say, if only manufacturers of DAC chips caught up with this and provided some useful toys to play with. After all, vinyl did make a revival from the dead (even if it remains relatively niche), and maybe the digital world needs a new DAC chip manufacturer to step in and seize the R-2R niche...

 

[Joe Bloggs]

Crossposting over from the X7 thread:

Also, read the following:

http://sjeng.org/ftp/SACD.pdf

I agree with everything written in the linked article but that has nothing to do with the choice of sigma-delta as the design principle for a DAC. The mistake of SACD is with using sigma-delta as the storage medium for the source music data. There's nothing in the article protesting the use of sigma-delta in DACs.

Sigma-delta as used in DACs, when coupled with a simple low-order lowpass filter, is a great economical solution to the problem of D/A conversion, yet with top-tier performance. It avoids the linearity problems of high-bit-count multibit designs. It should be noted however that the ES9018 is internally not a 1-bit converter but 6-bit, running at multi-MHz sample rates. In any case, the lowpassed output has been measured to achieve the lowest distortion figures within audio frequencies in any DAC in the market, which by definition points to high fidelity and no discernible sigma-delta "sound" (because for a DAC to have any "sound" in the sense of coloration, distortions of the intended signal in the output inevitably result).

 

[landroni]

Crossposting over from the X7 thread:
I agree with everything written in the linked article but that has nothing to do with the choice of sigma-delta as the design principle for a DAC. The mistake of SACD is with using sigma-delta as the storage medium for the source music data. There's nothing in the article protesting the use of sigma-delta in DACs.

Sigma-delta as used in DACs, when coupled with a simple low-order lowpass filter, is a great economical solution to the problem of D/A conversion, yet with top-tier performance. It avoids the linearity problems of high-bit-count multibit designs. It should be noted however that the ES9018 is internally not a 1-bit converter but 6-bit, running at multi-MHz sample rates. In any case, the lowpassed output has been measured to achieve the lowest distortion figures within audio frequencies in any DAC in the market, which by definition points to high fidelity and no discernible sigma-delta "sound" (because for a DAC to have any "sound" in the sense of coloration, distortions of the intended signal in the output inevitably result).

Thanks Joe for crossposting here. From the off I'm sorry for the length of my answer, but there are several points that need to be addressed and I'll try to go methodically through them. I should mention that I am not an engineer, and this is my honest attempt at understanding the technologies involved, their real advantages and limitations, and I will be happy to stand corrected if need be.
 

1-bit vs 6-bit vs 16-bit vs 24-bit

It is true that ES9018 is natively a 6-bit device, not 1-bit. However 1-bit D/A converters are the direct predecessors of 5-6 bit Delta-Sigma devices, and conceptually work in very similar ways and rely on the same techniques (e.g. noise shaping). DS converters were introduced to work around the deficiencies of 1-bit converters in handling PCM low-speed, and the jury is still out there if they succeeded at that. Even at 6-bit DS converters are still fundamentally low-bit devices which rely heavily on ultra-high sampling speeds to do their best. And therein lies the problem:
http://positive-feedback.com/Issue65/dac.htm
"There are lots of things wrong with delta-sigma DACs—most stemming from the fact they are low-bit devices using extremely complex feedback systems to synthesize high-bit performance.

That puts the 3-bit difference between the class-leading ESS 9018 and the class-leading Burr-Brown 1704 in a different light. The performance of the 1704 is the native performance, akin to a zero-feedback amplifier. What you hear is not an algorithm, but the device itself.

The ESS 9018, along with all the other delta-sigma converters out there (including the latest Burr-Brown products), realize their performance with extremely complex digital-feedback algorithms. You are hearing the algorithm, not the 5= or 6-bit converter, and a lot of very strange things can happen with that algorithm. ESS spent several years and a lot of engineer-hours trying to find out what the "golden ears" were hearing—and found, measured, and then corrected several different problems. Given the complexity of noise-shaping techniques, though, there could still be some surprises to be discovered."
 
1-bit or DS devices do their best with formats like DSD, which are also a low-bit and ultra-high speed (from vanilla DSD 1-bit samples at 3 MHz to the extremes of DSD512 at 1-bit 25 MHz). Yet 15 years on, DSD from SACDs is still an oddball format, unwieldy both in the studio and on the consumer's desk, and definitely not available for mass consumption. Today as in yesteryear, PCM still rules the roost, via CDs, FLACs, MP3s and streaming. Anecdotal evidence suggests that even people with access to significant SACD collections will still have 99% of their audio in PCM. Schiit, who produce both DS and R2R DACs, contend that today DSD is "less than 0.01% of recorded music", which sounds realistic.
 
Bruno Putzeys, then Chief Engineer at Philips Digital Systems Labs, had this to say on the subject:
http://forums.stevehoffman.tv/threads/sacd-fundamentally-flawed.26075/page-3#post-459059
"When sony came up with DSD as an archiving system there was hardly even 96kHz PCM around. If at that time they had some old tapes to archive before they fell apart, DSD was the best available. However, since DSD is a liability in terms of processability, archiving to DSD now is no longer a good idea and use of 192/24 is warranted instead. Since SACD is probably here to stay we should view DSD as strictly a release format [...]"
 
However one of the reasons DSD was introduced in the first place was to work around the fundamental mismatch between 1-bit and DS D/A converters (low-bit and ultra-high speed) and PCM (high-bit and low speed). And as you say, SACD isn't a very good idea for storing source music data.
 
But DS just doesn't play that well with PCM. What's disconcerting is that DS drops original samples. As mentioned before, one fundamental issue is the low-bit nature nature of the device: it can only handle 6 bits natively, which means that when passed a 16-bit sample it must squeeze it through a 6-bit bottleneck. In a sense it probably matters little if you pass a DS D/A converter an 8-bit or a 32-bit lossless file: each sample will still have to be squeezed through that same 6 bit bottleneck. Wikipedia has this to say about DS:
https://en.wikipedia.org/wiki/Delta-sigma_modulation
"a delta-sigma DAC encodes a high-resolution digital input signal into a lower-resolution but higher sample-frequency signal"
 
In order to operate, this low-bit process is utterly dependent on high sampling speeds. Another way to look at it is that DS drops original samples (keeping only 6 bits of each sample), and then uses digital-feedback techniques to attempt to recreate (i.e. synthesize) the information that has previously been discarded. Schiit has this to say on the matter:
http://schiit.com/products/yggdrasil
"We can’t get over the fact that delta-sigma DACs throw away all the original samples."
 
So much for "32-bit" Delta-Sigma DACs... And by now it should be obvious that these devices by virtue of their physical constraints deal well with a rare and unwieldy format (DSD) and handle somewhat poorly the most widely available and versatile digital format (PCM).
 

High-fidelity

If we're talking high-fidelity, then discarding original samples is an issue, and a big one at that. In this sense DS can be viewed as a lossy D/A conversion mechanism. Unless you go into incredibly-high-speed sampling rates (approaching infinity), it's hard to envision DS technology being capable of matching R2R in the quality of the retrieved waveforms. The moment DS drops bits from the available samples it departs from the elegance of digital sampling theory, and relies on averaging ("connecting the dots") to retrieve an approximation of the original waveform.
 
R2R D/A converters, however, make full use of the 16-bit samples to retrieve the exact waveform at all times, so long as the sampling rate is twice the target bandwidth (the Nyquist rate). The 16-bit/44.1 kHz redbook files have ALL the information needed to retrieve the original soundwave, so long as it's a sound below 22.05 kHz frequency. R2R doesn't need to drop bits, nor does it need ultra-high sampling speeds. Schiit describes this as a "true closed-form solution", something that can NOT possibly be achieved with existing DS technology:
http://schiit.com/products/yggdrasil
"Most digital filters destroy the original samples in the process of upsampling. They’re just like sample rate converters or delta-sigma DACs. We’re all about the original samples, so we created a digital filter with a true closed-form solution, which means it retains all the original samples. This is a major difference between Yggdrasil and every other DAC in the world. "
 
According to Dan Lavry for multibit converters the optimal sampling speed is around 60 kHz, which means that 96 kHz sampling speeds is all that humans will ever need to reproduce music in an R2R context. No need to go into the insanity of 192 kHz, 384 or 768, or anything approaching MHz, as anything higher than optimal is actively damaging playback fidelity. And according to Monty Python 16-bit yields a dynamic range higher than humans need, rendering 24 bits unnecessary for playback purposes. All very well, as even the most advanced R2R DACs hardly reach 24 bits internally, plateauing at around 20-21 bits (e.g. Schiit Yggdrasil).
 
So with R2R 16-bit/96 kHz lossless files are ALL that we need to play back music in high-fidelity and perfect resolution. 16-bit/44.1 kHz will also do incredibly well, thank you, most of the times. While I agree that DS is more economical as it doesn't require laser-like precision manufacturing (as for R2R), it also appears suboptimal for genuine high fidelity. And when you take into account that R2R doesn't need exotic and bandwidth-hogging file formats like DSD or 768 kHz PCM to do its best, then R2R ultimately becomes more economical for the end-user. For R2R, and if you ignore marketing glitz for a second, all you need is a well implemented multibit D/A converter that handles gracefully 16 bit samples and 96 kHz sampling speeds. That's it, it is simple, elegant, the technology is proven and exists, and there is no need to chase ever-higher sampling rates or ever changing formats (DSD, DXD, DSD512, DSD-wide, etc.) to improve playback fidelity. By comparison, Delta-Sigma seems to be too complicated for its own good (what next, 100 MHz sampling rates in DSD2048?), but I digress.
 

The Delta-Sigma sound

While we're at high-fidelity, we may as well discuss the "Delta-Sigma sound". With R2R converters the actual D/A conversion is rather straightforward:
http://positive-feedback.com/Issue65/dac.htm
"The Philips TDA154x series and Burr-Brown PCM 63, 1702, and 1704 operate in a completely different way from the delta-sigma DACs that dominate the market today. They are "flash" DACs with single-pass conversion; there's no feedback of any kind. The signal goes straight through the switch array and that's it, off to the analog world for amplification. Once the difficult part of current-to-voltage conversion is accomplished, the rest is easy—basically, a high-quality microphone preamp and line driver, not the most difficult thing to do in the analog world."
 
With DS however we hear an algorithm with synthesized high-bit performance (because the original samples were destroyed at the start of the conversion process). What does this mean? Many users who have heard both R2R and DS implementations (and only few have ever heard R2R, as DS is occupying 99% of the market while R2R is such a niche these days) tend to describe DS as "artificial" or "digital" whereas R2R as "natural", "realistic" or even capturing "reverberations" and the "acoustics" of the recording studio/hall. Then there is the "glare". Some call it the "digital glare", others the "Sabre glare", but it's clear that when handling low-speed PCM the glare was a thing with Delta-Sigma technology from the beginning and is still a thing today.
 

Final thoughts

Many people who have once been exposed to a good R2R implementation can hardly go back to the DS sound. As one user intimated about DS, "it's an artificial sound and once you hear it, you can't unhear it." Of course many will point to implementation, etc., and while a fair point, I will mention that in the paragraph above we're talking about >$1000 desktop devices weighing pounds. As much as I have high hopes for the X7, there is very little chance the X7 will have managed to address the issues inherent in DS implementations within such a slim and stylish mobile device.
 
To see what I am getting at, see this well written head-to-head comparison of similarly priced R2R and DS implementations (Yggy vs DAC1):
http://www.head-fi.org/products/schiit-audio-yggdrasil/reviews/13419
 
While I understand the attractiveness of DS technology to manufacturers from a cost, simplicity and marketing perspective, DS is mostly a low-cost technology perfectly suited for playing sounds on your average iPhone or laptop while wearing white earbuds. This is what we all have today, and this is the digital sound we grew up with. But once we get into the realm of high-fidelity, where people fork copious amounts of money for brick-like devices because they are seeking "true sound" at home or on the road, then R2R seems like the no-brainer technology to me...