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R2R/multibit vs Delta-Sigma - Is There A Measurable Scientific Difference That's Audible

Discussion in 'Sound Science' started by goodyfresh, Aug 31, 2015.
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  1. goodyfresh
    What it says in the title:  Could someone explain to me, in a simple-enough way, the real difference between the two, and exactly why everybody seems to think that R-2R/Multibit is so much "better?"
    And if delta-sigma does in fact suck so very much, why the heck are all the major manufacturers leanign towards using it in almost all their DAC chips these days?

    Finally:  Are there any CHEAP options out there for DAC's (with USB input) which use R-2R instead of delta-sigma?  Like, below 300 or 400 dollars?

    Edit:  I changed the title of the thread, at @x RELIC x's suggestion, to better reflect what I was actually trying to ask.
    TronII and landroni like this.
  2. goodyfresh
    Buuuuump! If nobody's going to respond to this, could someone at the very least point me int he direction of pre-existing threads that will answer my questions?  It's kind of disheartening that apparently 40 people have viewed this thread of mine and yet no one has responded!
  3. obobskivich
    I'm not sure if you can/should group R-2R in with "multibit" since there are multibit delta-sigma DACs (in fact, many modern designs (since 2000) are multibit), and often when I see "multibit DAC" written it is usually talking about multibit delta-sigma, as opposed to some other principle. As far as explaining the differences between them, the really short version is that R-2R (or "resistor ladder") DACs and delta-sigma DACs perform their conversion in different ways, and some people preference one over the other (some like their toast buttered up, and others like their toast buttered down). For a somewhat longer answer, see the Wikipedia article: https://en.wikipedia.org/wiki/Digital-to-analog_converter#DAC_types (you only need to read the giant block starting with "Oversampling DACs or interpolating DACs" and the section on R-2R in relation to your original question; that article is not exclusively about audio either (DACs don't just exist in/for audio)). Both are ultimately seeking the same result: good quality analog output. They just mean to arrive there in different ways, informed by different design decisions and limitations.

    I would not honestly go as far as saying delta-sigma "sucks so much" but more that R-2R is seemingly the buzzword du jour. Eventually the hypetrain will move on to something else. This doesn't mean you should avoid R-2R-based products, but instead realize they're just another way to skin the same cat, and depending on your personal taste, you may like that way better than some other way, or you may not (or you may not even notice much of a difference).
  4. x RELIC x Contributor

    This blog helped me understand the basics. Though it's a bit biased in its conclusions I would agree with what he states at the end based on the differences I've heard.


    There's a lot of reading and learning ahead.

    Delta-Sigma doesn't 'suck so much' on its own. It's just that after hearing a good R-2R implementation compared to a good Delta-Sigma implementation many people prefer the R-2R DAC for its superior natural reproduction of music. Purrin's thread is a good one to read on Head Fi (it's locked now). You also may want to go over to the DAC-19, Master 11, Master 7, Schiit Yggy, and Gungnir multibit threads. I should point out that I don't hear any less detail in R-2R than Delta-Sigma. I actually hear finer detail that gives me more cues to the timbre of real instruments. In comparison Delta-Sigma sounds unnatural while missing the low level detail.

    Purrin's thread:

    The basic reason all the major manufacturers are using Delta-Sigma instead of R-2R is cost of production, implementation, and size. Plain and simple. Here's a few good articles on the differences and a bit of history on the devepment of Delta-Sigma.





    Delta-Sigma is essentially a rough approximation (a very good one) of the original signal, and the birthing point of DSD (or is it vice versa). In my opinion DSD and is a compromise and is basically a low resolution (1 bit) format that is simply super sampled out of necessity, not for audio fidelity. Hearing the difference first hand I now 'get it'. I'm picking on DSD because R-2R can't do DSD (and for a good reason) and recreates PCM in basically a 1-1 fashion without the rough approximation. Delta-Sigma = DSD.

    In the end my conclusion is that once you've heard a good R-2R implementation it's hard to go back to Delta-Sigma. To me it was similar to going from a stock iPod Classic to the X5. The iPod was great, until I heard differently. I don't use my iPod anymore.

    More on the differences between R-2R and Delta-Sigma (part 1 and part 2).


    As a side note here's a very good article on when higher sampling rates help or hurt audio fidelity. I learned a lot from this one.


    Well, that's the problem. For an R-2R DAC to be 300-400 dollars it more than likely will sound like crap because of the implementation requirements.

    As far as FOTM comments I feel it's more of a re-awakening than a FOTM, in no small part to the exposure Schiit has brought with the Yggy. I hope more manufacturers bring back R-2R, similar to how vinyl is making a mainstream comeback.
  5. goodyfresh
    Thanks guys!
  6. obobskivich

    DSD came second; it was developed as an archival format modeled on the internal working of 1-bit delta-sigma (it essentially contains *that* digital bitstream, since that was believed to be a better choice for digital archival storage). DSD isn't fairly characterized as "low resolution" though - it's a serial data format that can achieve very high resolution (comparable or better to PCM at 16-bits), but goes about it in a different way from PCM or other formats. It also has different pros and cons, like needing low-pass filtering to remove noise at the output section (one of your sources, from Craigman Digital, explores this).

    I'm not meaning to say FOTM/hypetrain is "evil" - it benefits consumers because it usually means new gear at lower prices, as different manufacturers try to compete with "me too" products. I think the example of vinyl is great - a few years ago there weren't many good options for new turntables, and now the market is flooded with choices. IMHO choice is a good thing for consumers.

    On your sources, I dislike the Audio-Mojo, AnkAudio, and Mother-of-Tone articles because they're heavily/overtly biased and trying to sell us stuff. The CraigmanDigital, Trust Me I'm A Scientist (as well as the Xiph.org article it links to/cites), and Positive Feedback articles are good places to start beyond Wikipedia (which also has a huge article on delta-sigma for those interested: https://en.wikipedia.org/wiki/Delta-sigma_modulation); they all address legitimate issues and all raise the $64,000,000 question of "that's nice, but can we actually HEAR it?" - which is an inherently personal/subjective debate at the end of the day (and I think PF does a great job of comparing this to the debate over feedback in amplifiers - it's never-ending and ultimately comes down to the listener).

    As far as "gearquest 2015" - you may try looking for used components based on an R2R design; not sure where you'd find a comprehensive list though. Might be easier to find a list of R2R DACs themselves and then work up from that.
    Traveller likes this.
  7. x RELIC x Contributor
    Ha, "gearquest 2015", I like the term. :)

    obobskivich I agree with you on most points, and of course we all hear differently and value sonic traits differently. The non-prefered blogs / articles you dislike I am well aware of the biases involved, however, they do simplify things to a degree. It was after reading these articles that I was better able to understand the others I linked.

    As far as my assertion that DSD is low resolution..... Well, without implementing the noise shaping for quantization errors and the multi level filtering required to bring the signal back in line with the original I feel this is what makes it fairly low resolution. It's only after extensive 'treatment' that the outgoing signal ends up representing the incoming signal. Based on my (admittedly limited) experience. When the signal is modified to the extent that it is in D-S and DSD I would doubt the theoretical bits of what reaches our ear equal the actual resolution we hear. I agree though, is it audible? What I do hear is that D-S just sounds more 'one note', more lifeless.

    As for vinyl, my daughters friend bought her a turntable and a few records for her 21st birthday last year. How awesome is that? Love that it really is coming back in to focus.
    TronII likes this.
  8. obobskivich
    You could test the output of a DAC's "faithfulness" with a null in theory (like craigman did, but with actual audio), but IME sometimes gear that measures badly (wrt conventional wisdom) can sound good. Look up the TDA15xx for example (for a really dramatic example, look up the Zanden 5000 on Stereophile - I've never heard that specific one but the discussion around it seems pertinent here).
  9. x RELIC x Contributor
    goodyfresh you may want to check out this post for an inexpensive R-2R Theta DAC.

  10. goodyfresh

    Looks interesting!  But I can't seem to find any info by searching online as to where I can buy it or exactly how much it does cost >_<
    TronII likes this.
  11. x RELIC x Contributor

    I found some that were sold already for $175. Like the post says, if you're patient you can find them. They were made in the early 90's so you need to look out for them.
    TronII likes this.
  12. goodyfresh
    Ah yes, okay :)  Making them work as a USB DAC shouldn't be too hard either, I'd just need an adapter for USB-to-COAX

  13. landroni

    Another way to get a modern and relatively inexpensive R2R device is Schiit Bifrost multibit (600$):
    Schiit seems to have taken great care when designing this product, to keep costs down and sound-quality on-par with good R2R implementations:
    The Schiit designers compare it precisely to the Theta Cobalt, placing them both in the historically appropriate technological and pricing context.
  14. landroni
    I feel that the R2R vs DS debate is intimately related to the current cacophony over sampling rates. Higher sampling rates are either better, worse, or don't make a difference: go figure. Monty Python and Dan Lavry say that 192 kHz sampling speeds are silly, and actively damaging for playback fidelity. Neil Young and even James from FiiO say that 192 kHz and 384 kHz are useful to improve sound quality in the audible band. While this is clearly something akin to the theater of the absurd, I suspect that they're all right. They're just talking about different things.
    Lavry clearly talks about multibit converters (and probably Monty, too), those R-2R (aka "ladder") converters that take the full samples provided by a lossless audio file and convert them at hardware level before passing the signal to the analog output phase, with no oversampling (NOS). This technology is somewhat rare nowadays (and these DAC chips are more expensive and require extreme manufacturing precision when getting into 19-20 bit territory), and has been dying a slow death before seeing somewhat of a revival lately. Some of the products using R2R converters are old Theta (e.g. DS Pro Generation V), and newer Schiit multibit (e.g. Yggdrasil) or Audio GD (e.g. Master 7 or DAC-19). R2R DAPs are even rarer, the few existing breeds being the HM801, Hifi E.T MA9 and... surprise... Tera Player.
    While this may be a bit of a stretch, these are apparently the only DACs/DAPs around which are bit-perfect, and they're definitely fewer than 0.5% of the market. They use the original samples in full depth (up to the hardware limitations, usually ranging from 17-18 bits up to about 21 bits max), as these are high-bit, low-speed devices just like redbook PCM is a high-bit, low-speed format: 16-bit/96 kHz is ALL they need for perfect retrieval of analog waveforms within the audible band, and 16-bit/44.1 kHz works very well, thank you. What's crucial here is that 16-bit/96 kHz R2R technology exists, is proven, doesn't require ever changing formats and complex digital processing, does much less aggressive filtering of the data stream/sound signal, is perfectly suited for 99.9% of available audio material (slow PCM), and the only R&D required is care in real-world device implementation.
    Neil Young and James however clearly have in mind Delta-Sigma D/A converters (e.g. the DACs in Pono or X7), low-cost 5-6 bit devices which use complex digital-feedback techniques and algorithms (e.g. noise-shaping) to approximate analog waveforms. If with R2R we are hearing the device, with DS we are hearing the algorithm. DS is the direct successor of 1-bit D/A converters and are thus at heart low-bit, ultra-high-speed devices that rely on oversampling techniques (e.g. 2^8 = 256 times the sampling rate). This is probably why many report that the low-bit, ultra-high-speed DSD format sounds so much better and more "natural" on them. This is also what makes them quite... err... awkward with high-bit, low-speed PCM, because the two are fundamentally mismatched. This is probably why manufacturers like FiiO, Hifiman and AK are constantly seeking to support ever higher sampling rates, to infinity (which is in many ways irrelevant, as how many copies of 768 kHz PCM files do you have?).
    What's most disconcerting with DS converters, is that they are dropping original samples: since they can't handle more than 5-6 bits natively, it really doesn't seem to matter if you pass them an 8-bit or a 24-bit file, as they will still drop all the bits until they get to a 5-6 bit sample, and proceed from there to the analog conversion. (Talk about wasted space in a world awash with 16bit PCM played back almost exclusively on DS devices.) In order to operate, they need to slim down the high-bit PCM file into a low-bit version. And since they use so few bits, they produce a boatload of noise (i.e. a very high noise threshold), which is why they need to use oversampling to increase the bitrate and then use aggressive noise-shaping techniques to shift the noise just outside the audible band, a process which can go wrong in many ways. Since DS are fundamentally low-bit devices, it appears that they need ever higher sampling speeds in PCM to do their best, which along with DSD are merely cumbersome attempts to work around the fundamental limitations of the technology. I'm no engineer, but overall it looks to me that all this is hardly suited for high-fidelity applications, not least because they're not bit-perfect. But hey, they currently occupy 99.5% of the market, including "high-fidelity" flagship territory.
    Sometimes I get the feeling that Delta-Sigma is so attractive to manufacturers mostly for scoring marketing points: "high-resolution" support up to 768 kHz and 32 bits, DSD, DXD, DSD512... Compare this to the paltry "up to 24 bits and 96 kHz" that R2R manufacturers often whisper. But if we avoid the polemics, on a theoretical level I see two big issues with DS.
    First, this is a lossy conversion process that uses decimation to partially drop data, and then proceeds to digitally synthesize high-bit performance. And after 15 years of R&D, the digital "glare" reported from the very beginning is still being reported today with top-flight DS DACs (when they playing back slow PCM). From my (approximate) understanding of DS technology, first they lose data from the original samples by downconverting each sample to 5-6 bits, then DS oversamples the data by some 2^8 or 2^10 (256 to 1024 times the sampling speed of 44100) to add an additional 8-10 bits of performance, then proceeds to using complex and obscure digital-feedback noise-shaping techniques to clean up the gargantuan levels of noise introduced by the earlier process and "sweep them under the rug" by shifting them just above 20 kHZ to where dogs and cats can hear it but not humans (so forget of using DS technology to test classical music on animals), thus adding a further ~8 bit performance. For instance ES9018 is rumoured to work at 6 bit + 8 bits + 8 bits, for a marketed headline 22.5 bits of effective performance. BTW, we should forever forget about "32 bit" DACs as neither technology is currently capable of handling it, each plateauing neatly around 21-22 bits, and apparently no standard digital audio file contains more than 24 bits worth of data...
    My other theoretical concern also relates to oversampling, but from a different perspective. The Metrum document above, from another believer in R2R, focuses precisely on why so many DACs sound so differently from live performances. Ultimately this really is what we're all here for: recreate a live performance in our living room. It talks about "realism", "natural" sounding, purity of the sound, absence of digital artefacts (“rubbish”) and the like. They point among other things to FIR filters used in DS oversampling technology, the absence of FIR filters in old R2R chipsets like TDA1541, and the ear acting as a naturally sharp filter ("like a band-pass filter") meaning that adding one such filter in the audio playback device would be an overkill.

    "Because our hearing naturally functions as a strong filter, our brains tend to interpret the signal from the NOS
    DAC as if it has passed through a FIR-filter. This is due to the limited bandwidth of our hearing. Looking at
    the picture on the top of this page, we can wonder how the eventual picture will look if another equivalent
    filter is added by our hearing. It is well-documented by both musicians and authorities in the field of audio,
    that especially percussion instruments suffer from this effect. It is therefore not unfounded when NOS DACs
    are claimed to sound the most natural of all the alternatives. Because at the same time the testresults for all
    NOS DACs fall short, the question can be raised wether the correct tests are being done to accurately gauge
    their quality. All measurements are, after all, performed without the benefit of any filter."

    Apparently while FIR filters (> 4th order) make oversampling techniques possible in the first place, it also plays as a redundant filter given our ears' natural filtering (> 6th order). This might go some way to explain the various reports of "artificial" or "digital" or "unnatural" or "lifeless" sound from DS devices with PCM, as opposed to "realistic" and "natural" sound from R2R products.
    They go on with an interesting discussion of jitter testing, and conclude like this:
    "NOS DACS have been gaining in popularity for the past few years, mostly based on listening reviews.
    Especially people who regulary experience live music, appear to have a strong preference for this type of
    DAC. As Kusunoki had mentioned in his article, it is primarily the behaviour in the time domain which gives
    oversampling DACs their “unnatural” quality. This shows in the way that percussion instruments sound too
    lacklustre and a sort of “excessive detailing”, which causes certain instruments to lose their timbre and
    “warmth”. The question wether we should follow our ears or the results of tests remains on the table.

    The development of digital audiosystems has not reached its zenith yet and we will certainly be confronted
    with new developments in the future. Certain is, that due to High Definition recordings the need for
    oversampling and sharp filters has lessened. How to approach the massive variety of CD’s, with their low
    sampling rate of 44.1 kHz remains the question. To oversample or not to Oversample? Not oversampling
    seems to be the preference of musicians and audio-professionals, despite their “limitations”."

    For a related discussion on R2R vs DS see this thread:
  15. Wildcatsare1
    Excellent post, R2R is in my humble experience offers more musicality. I have not heard most of the extremely expensive manipulations of DS DACs, but apparently you must manipulate them greatly to attempt to approximate R2R.
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