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  1. #1
    Senior Member barrows's Avatar
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    Multi Bit DACs vs. Delta Sigma DACs

    Pursuant to the thread hi-jack that developed in the USB DAC/Alan Taffel thread, I would like to start a thread specifically to consider peoples experiences with Delta Sigma vs. Mutli Bit DACs. Everyone is encouraged to offer any opinions, theories, and hopefully experiences, they may have had.
    Unfortunately, Multi Bit DACs are few and far between these days-Less Loss being one that I know of offhand-there is a belief amongst many that the PCM1704 DAC chip was the pinnacle of dAC development, and was the last Multi Bit chip before the big manufacturers switched to developing the Delta Sigma designs that dominate today.
    In this thread we can also discuss non over sampling (NOS), and perhaps the related concept of filterless DAC designs.
    What does everyone think, and what have you heard?
    EVERYTHING MATTERS

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  2. #2

    Too polite

    Without going into specific models, I've generally found the delta-sigma DACs I've heard to be 'too polite' for my liking. Is this due to the necessary 'massive' oversampling that needs to take place? I don't know...

    But my experience also suggests that the whole DAC architecture is important, not just the chip. The DAC I've been using for the last 7 years is based on the PCM1704U-K chip... and sounds positively flat, lifeless and boring compared to my current (also multi-bit) DAC.

    Mani.
    Playback ('true PCM'):
    XXHighEnd/HQPlayer @24/768 -> Phasure NOS1​a
    Recording ('true PCM'):
    Pacific Microsonics Model Two @24/192 -> Weiss AFI1 (with Paul Hynes linear PS)

  3. #3

    Do people understand the difference

    between multi-bit and not?
    Should they care?
    If so, I may be able to write an idiot's guide... ( including such bombshells as why sine waves are used for DAC testing... )

    your friendly neighbourhood idiot

  4. #4

    "Do people understand the

    "Do people understand the difference between multi-bit and not?"

    I don't understand it in detail, and am quite interested.

    If multi-bit does not equate exactly with NOS, then an explanation of these differences would also be useful.

    While we're on this topic, I'm not sure I understand the significance between 'oversampling' and ASRC.

    I get the impression that both are evil, but that oversampling is considered more of a 'necessary' evil than ASRC. Perhaps this is because oversampling is a 'feature' of sigma-delta chips?

    Anything you'd care to share, I'm interested.

    Grasshopper



  5. #5
    Senior Member PeterSt's Avatar
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    Should they care ?

    I am out of opinions for now, but would love to read something from an i_s, especially if it sprung from his own mind. This one should make you hot :

    "Delta-Sigma trades amplitude resolution for frequency resolution".


    XXHighEnd (developer)
    Phasure NOS1 24/768 Async USB DAC (manufacturer)

  6. #6

    Write the guide

    IS please write the guide! Delta sigma / multibit /ladder dacs , why over/up sample ? I for one would be extremely interested, regards Keith.

  7. #7

    I_S - Ditto the 'Yes Pleases'..

    And to give you an idea of the level of understanding you're up against......

    I had a really lovely day at the seaside recently. Whilst sitting and contemplating the nature of DAC's, as you do at such times, I noticed that none of the incoming waves had sines on them. Also, none of them were square. In fact, they were all sorts of different shapes and sizes. And yet, they all seemed to make the same 'scrunchy, splashy, whoooooshy' sort of sound. Most pleasant, but not really Hi-Fi. I found this most confusing.

    I did test my DAC by placing it in a number of different sorts of wave but unfortunately, rather than enlightening me about its performance, it seems to have stopped it working!

    Your, somewhat short of information.

  8. #8

    Since you asked...

    We'll start with a multi-bit, or ladder DAC. We'll ignore all oversampling and filtering discussions for a bit, so bear with me

    To understand this, we'll go over a few basics: In digital audio, a simplified view, which will do for now, is that audio is represented by a series of samples, taken equally in time. For our example, we will consider an 8 bit DAC, and the sampling rate ( the space between samples isn't very important ).
    An 8 bit DAC means that is takes in an 8-bit number, which represents a value between 0 and 255 ( in our example ) - this DAC is just to explain the theory.
    This works using something called binary:
    Each bit is is a 1 or a 0, and where they are in the word corresponds to magnitude, as follows
    128 64 32 16 8 4 2 1

    so to represent, say 7, we write
    0 0 0 0 0 1 1 1 - this equals "4 + 2 + 1" = 7
    and to represent say 78 we write
    0 1 0 0 1 1 1 0 - this equals "64 + 8 + 4 + 2" = 78

    Now, for our DAC, we can map this into resistors, each one half in value to the previous one, with the idea that all the resistors being "turned on" sum up to the maximum output voltage of our DAC. We also need some kind of strobe signal to "latch" the data into all the resistors at the same time, and hold it there until the next one is ready.
    So, we have a system that maps beautifully onto the data being sent in, so what can go wrong?
    Well, the first ( and most troublesome problem ) we have is that those resistors have to be pretty tightly matched - they have to be exactly multiples of 2 with respect to each other, which we can just about do for 8 resistors - the one representing the 1st bit must be 128 times exactly bigger in voltage output than the smallest one. However, now consider a 16 bit DAC - the smallest one here has to be exactly 32768 times smaller, and in a 24 bit one 8388608 times smaller ( and the next one up be 4194304 smaller ). In addition, these resistors will probably vary with time and temperature, and they won't vary in the same way ( one resistor being thousands of times bigger than another one means they are pretty dissimilar physically ).
    So what does this mean in terms of the output?
    The biggest problem as I've said, is that the sums no longer quite add up, and they will vary as the signal varies - so an incoming sample that is say 2 bigger than the last one will actually end up being 2 and a bit bigger, or 1 and a bit bigger. There are other, more subtle problems involved, but this is the fundamental problem, which we can measure as distortion - distortion is a separate entity from noise, being something directly related to the signal.

    note, however, that we can vary the input as much as we like, and the output will change more or less instantly between samples, depending on slew rate...

    I'll get move onto delta-sigma later,


    your friendly neighbourhood idiot

    PS most DACs are water resistant not water proof




  9. #9
    Senior Member PeterSt's Avatar
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    As usual, thanks !

    Of course this thread is long from finished, but I can tell you that I not only can measure things being wrong, but also things being right. So, in the exact context of what you just wrote (and nothing more !) you may be surprised how accurately the PCM1704U-K is able to follow the source data. This is up to the Least Significant Bit (the one representing the smallest value (1 (or 0)), although noise will influence its recorded state (analoguely taken).

    Beyond your context is stuff like transients (and the related slew rate), and it is there where things start to be different (well, as far as I found) ...

    Peter
    XXHighEnd (developer)
    Phasure NOS1 24/768 Async USB DAC (manufacturer)

  10. #10

    Thx!

    @i_s

    Nice explanation - I still don't fully get delta-sigma DACS so looking forward to that lesson

    I believe that NAIM CDPs use multi-bit DACS and I think (although cannot confirm, cannot find the link) that this will go into the NAIM DAC.

    PCM1704

    One thing from this paper that I didn't understand was this:

    [wrt multi-bit DACSs] However, even the best of these suffer from potential low-level nonlinearity due to errors in the major carry bipolar zero transition

    Also interested if anyone has information on how accurate the laser trimming of the resistors is and therefore the levels of distortion to be expected and whether these are published anywhere.

  11. #11

    well, this again relates to

    well, this again relates to inaccuracies between the resistors - most signals ( especially small ones ) vary around the middle of our possible ranges - in our hypothetical DAC, if you imagine that 0V is in the middle of our range ( this is known as "offset binary" ), -5V is 0, and +5V is 255, then you will see that our 0V point is 128, or:
    1 0 0 0 0 0 0 0

    so, if the signal you are trying to recreate has a tiny amount of noise, the DAC might be fed
    1 0 0 0 0 0 0 0
    0 1 1 1 1 1 1 1
    1 0 0 0 0 0 0 0
    ( i.e. 0V, - a small amount )
    So the 7 resistors must sum to be exactly 1 less than the big one - i.e. this is the worst case scenario, and unfortunately, is the most likely one!

    your friendly neighbourhood idiot


  12. #12
    Senior Member PeterSt's Avatar
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    Back-to-Back

    Harry, besides what I just said (ans crossed your post I'm sure), the bipolar thing is solved in the 1704 because it's actually two DACs "back to back" as BB says, which may be seen as similar as to how differential (balanced) solves problems.

    I can write the same as the datasheet will say (well, I think it says it somewhere), but bytes are somewhat more complex when used electrically than it seems. This is related to the way plus and minus data is represented, and in short you can say that plus is all zeros except for the real values (like 00000010 means decimal 2), while minus is the exact other way around and 11111101 means -2 (this is not 100% correct, but it will do for the explanation). Now, electrically - going from +1 to 0 to -1 (which is just where voltage goes from plus to minus) this is the biggest step possible, actually unwanted, but it happens all the time. Now think of the back-to-back thing as each DAC halve treating its own part of the spectrum : one deals with plus only, and the other deals with minus only.

    Something like that ... :-)
    Peter
    XXHighEnd (developer)
    Phasure NOS1 24/768 Async USB DAC (manufacturer)

  13. #13
    Senior Member PeterSt's Avatar
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    As said, something like that

    My example was too difficult, and not even true for the internal DAC working (I think), and i_s' example is better. Both, however, come down to the exact same problem : the current of nearly all the bits need to change at once, which is not exactly a "nice" thing to desire (and keep in mind that we're actually talking about 24 bits).

    I guess my example is more about the application you can have, which is about two DACs in differential mode (which is a back-to-back principle just the same).

    Don't confuse this with two DAC chips in parallell mode (like you can say Doede Douma got famous for), which (hopefully) evens unlinearities.

    I can add that these both principles (as far as I know) only can be applied with multi bit DACs.
    My own latest comprises of both at the same time : one half is setup differential, the other half parrallel (totalling 8 mono DACs).

    Peter
    XXHighEnd (developer)
    Phasure NOS1 24/768 Async USB DAC (manufacturer)

  14. #14

    Nice Explanations!

    @i_s, @peter

    Nice explanations thx. I get it now - don't understand about the back-to-back DAC solution but armed with the explanation I can revisit the paper and see if I can figure it.

    @peter

    yes, our posts did cross!

    @peter

    you may be surprised how accurately the PCM1704U-K is able to follow the source data

    Do you mean by this that we can assume the resistors are extremely accurately trimmed meaning that the output voltage always accurately represents the levels in the bitstream (assuming no noise issues).

    This sort of info is extremely important for me as if it is true the NAIM DAC (when it arrives) uses this or a variant of this DAC and it buffers and re-clocks the data (as is being assumed) it becomes a very interesting design to audition.

  15. #15

    Found this.

    Not sure how accurate the metaphor is but gives a good feels for what happens:

    How DACs Work

  16. #16
    Senior Member PeterSt's Avatar
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    Ideas ideas

    I would be the last to downgrade the work from MSB, but as I said elsewhere, websites aren't their best art. I am fairly sure that the page you presented is out dated to their own idea, as are their DACs fitting those ideas (now try to find which they are actually selling right now :-).

    Anyway, when you want to know about these things it is always good to read it BUT, read more of those and compare. You will find discrepancies all over, and don't forget that this is 2009, and already in 2004 things were VERY different (for ideas about everything). Also, back when the CD/DAC was invented, there were even less ideas as to how we all have them now, but the principles nevertheless were the same - when talking about "NOS". Again look at the data sheet, and see that the 1704 does 24/96 only (for implied input). But it really does more, however, who had the idea (back then, 1998) to commercialize that ? AFAIK there just was no material higher than 24/96, and so the IDEAS were different because of that reason alone.

    Do you mean by this that we can assume the resistors are extremely accurately trimmed meaning that the output voltage always accurately represents the levels in the bitstream (assuming no noise issues).

    Well, as is claimed, yes ("laser trimmed" blabla). THD+N claims at -0dBFS to be better than 0.0008%, and this is what I can measure.
    Keep in mind though that this is often with given arranged for circumstances, like no varying temperature. When temperature changes, resistance changes. This is important for a ladder DAC, BUT !! there are several multi bit topologies, and they sure not all work with R2R like i_s explained it. The 1704 does though (but keep in mind the "sign magnitude" thing which adds a little smartness to it) and for 24 bits there are no others anyway.

    accurately trimmed meaning that the output voltage always accurately represents

    Just because you want to know :-) : R2R DACs have current output (the "R2R calculations" are done with current, because current can be added (from math) easily- voltage cannot (well, it can actually, but I guess that wasn't invented when the chips were)). So, this is where "I/V" comes from, and it means "from current to voltage", I to V. Thus, a multi bit DAC needs an I/V stage. A Delta-Digma does not (it works with voltage to start with).

    Peter

    XXHighEnd (developer)
    Phasure NOS1 24/768 Async USB DAC (manufacturer)

  17. #17

    OK, I'm back, and I see in

    OK, I'm back, and I see in my absence there has been some discussion, which is good!
    As Peter has correctly pointed out, my simple little DAC I have been describing is simple - this is for the purposes of letting everyone keep up, so there are other implementations, but the basic problems of multi-bit DACs remain true - no matter what you do, at some point the mismatches between resistors, or current sources become an issue, and especially around specific transitions. I'll skip over the 2's complement discussion for the moment, but we can return to it later, because I'd like to give a brief overview of Delta-Sigma implementations.

    Again, we'll start with a conceptual DAC, and be aware that there are implementations that vary from this, but we may talk about them later, OK? We've still got quite a lot of stuff to get through..

    OK, so the problems with multi-bit DACs are mainly linearity/distortion ones caused by mismatches in the values that sum to represent our sample. So how about we get rid of ALL mismatches, by only having one on it's ownsome - there is no possibility of one current source being different to itself, right? And, if you only have one, and it's not too important the precise value of it, you can save money on all that pesky laser trimming of resistors. So how can this possibly work?
    Well, the answer to this is to think of the current source being able to switch off and on very quickly, and by "averaging out" the time it's on and off, and looking at it over time, you will get a really surprisingly accurate representation of the sample.
    The way the DAC determines how much the current source should be on is done by a thing called a "modulator" - this does some quite serious maths, but the upshot of it is you feed in a sample, and out comes a pulse train that represents that sample over time. The main thing a modulator does is "noise shaping", which is where the error you get from the output being 1 bit long is fed back through a filter and accumulated, and again, through the magic of maths, all of that noise gets shifted up very high in frequency ( the noise is bizarrely required for the averaging of the output to work - it helps to linearise the output ).
    How high a frequency?
    Well the first types of DACs to use this sort of technology ( think bitstream ) had the bitstream running at just over 11MHz.
    Now the more astute amongst you may have noticed that this technology effectively moves the problems of the DAC away from being linearity ( because the DAC is now intrinsically linear ), and into the filtering of the noise, and how well we can represent the widths of the pulses.
    To give an example of how good the linearity is, Peters 0.0008% THD figure works out to be 101dB, or linear to about 17 bits, whereas there are delta-sigma designs quoted at 120dB or more, BUT notice how important the widths of the pulses are in our delta-sigma? Surely any jitter in the clock will make these pulses artificially long or short? The answer to that is, unfortunately, yes... Additionally, now we definitely require filtering on the DAC output, the output can't change as quickly as the multi-bit DAC. I'll follow this point up later, as it turns out this doesn't matter take my word for it at the moment, we'll come to it!

    So, for a brief summation as to the pros and cons of each technology ( at it's most basic ):
    Multi-Bit
    Pros
    less sensitive to jitter than delta-sigma
    "easy to build" in digital processing terms
    No HF noise additions
    Cons
    Inherent linearity problems in general
    Real problem with zero-crossing
    Very hard to match
    Likely to vary in performance with temperature
    expensive

    Delta-Sigma
    Pros
    Inherently very linear
    Can be very quiet
    Can get excellent performance at low cost
    Very likely to be more stable
    Cons
    Harder in processing terms
    Guaranteed more HF noise
    More susceptible to jitter
    Can be susceptible to idle tones



    your friendly neighbourhood idiot





  18. #18

    The journey

    On another thread, Peter wrote,

    "On this globe a few people hang around, ever seeking for the best sounding DAC. With this, try to imagine a process of many years, and not something like "I now have the money, let's see what I will spend it on". No, this is a process that actually takes "ages", and I can recognize that -all going through that process- end up with the same : no sigma-delta please !"

    My own journey very much reflects this...

    Mani.
    Playback ('true PCM'):
    XXHighEnd/HQPlayer @24/768 -> Phasure NOS1​a
    Recording ('true PCM'):
    Pacific Microsonics Model Two @24/192 -> Weiss AFI1 (with Paul Hynes linear PS)

  19. #19

    Is everyone OK?

    Is everyone OK with the style, level of detail, etc of what I've covered so far? Too technical? Not technical enough? Or am I completely wrong?

    I'm not going to end with X is definitely better than Y, by the way - I just ( as I keep stating ) want to provide some information as to how this stuff works, and the real pros and cons of the stuff you read about/get told by some dealer or marketing guy,

    your friendly neighbourhood idiot

    PS the next rambling will likely be about filtering

  20. #20
    Senior Member PeterSt's Avatar
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    Ok/2

    Maybe others aren't embarrased if I softly tell you that on the Delta-Sigma you maybe drove off a litte into the effects of it, while the base principle is less clear (should be spent somewhat more lines on) ?

    I think what it comes down to is why that sample rate actually needs to be so high, and what that does to accuracy, apart from creating noise.
    It's not only about linearity of course ... and don't forget about the arguments why analysers must use sines ...

    I am NOT (which means NOT) saying that I can do this better.

    Actually I'm afraid the topic is a little too big. I'd say, don't be ashamed to say so.
    But I am sure it is very much appreciated, for sure after me always buzzing about it !

    Peter
    XXHighEnd (developer)
    Phasure NOS1 24/768 Async USB DAC (manufacturer)

  21. #21
    Senior Member PeterSt's Avatar
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    Small intermezzo

    Let me explain something which for many will be abacadabra otherwise, but which really isn't hard to get.

    If i_s says 0.0008% = 101dB I assume he took his calculator and he is right on this.
    Now, how to get to 0.0004% ? not much difference, right ? But hey, this is twice as good ! And twice in dB terms is 6. So, 0.0004% = 107dB.
    Do that again - 0.0002% - and you're at 113.
    Again - 0.0001% - (hey, what's the difference !) and there's 119dB. IIRC this is the spec of the ESS Sabre (24 bit version).

    It doesn't end here, because do it again, and you get 0.00005.

    How's 101dB around 17 bits ?
    6 + 6 + 6 + 6 + 6 + 6 + 6 + 6 + 6 + 6 + 6 + 6 + 6 + 6 + 6 + 6 + 6 (yep, that 17 times) = 102.

    So you see, no calculator needed (but keep in mind "twice as good" is slightly more than 6dB).

    Lastly, indeed it is so that when e.g. distortion is needed to be twice as good, it is really really hard to do that, once it is so good already. It looks like twice as difficult as the before time ...
    XXHighEnd (developer)
    Phasure NOS1 24/768 Async USB DAC (manufacturer)

  22. #22

    IS,I'm behind now, and


    IS,
    I'm behind now, and can't really comment, but will catch up tomorrow. I got sidetracked by all the hoopla about the PS Audio device on a separate thread.

    thanks, I did read it on an iphone earlier while I was distracted. I'll let is sink in and then ask any questions.

    clay




  23. #23

    Just a quick update

    Right, as Peter would like me to elaborate more on WHY a delta-sigma needs to operate at such high rates:
    If you imagine that your pulse width was the same speed as the sample, then your new super awesome DAC would have a S/N ratio of 6dB. Oops!
    So, as I was trying to say earlier, the job of the modulator is to noise shape the data - due to some clever maths, it redistributes the noise in a much higher bandwidth, such that it's much higher in frequency than any possible audio content, but in-band, it's super low - the efficiency of this can be measured by a modern delta-sigma DAC ( like the Sabre, as mentioned by Peter ). Now the way that the noise is "shaped" comes into play here. DSD ( as used on SACD ), which is basically using delta-sigma as a medium. This runs at 2.8224MHz, 1 bit ( which is much slower than the 11MHz rate I mentioned earlier ) - this is problematic, as there is less spectrum to spread the noise over, so the noise rises very sharply above 20kHz.

    And secondly, ( and I'll cover this when I get round to writing about filtering ), sine waves are excellent test waveforms because:
    They have no impulses - so we can guarantee that in our measurements, it doesn't really matter where we start or stop
    They are spectrally pure - ALL of the energy in a sinewave is contained in the fundamental
    We can recreate what they should be mathematically, perfectly.
    And lastly, thanks to the work of Fourier, Nyquist, and Shannon, we know that for a band-limited signal, we can reproduce it EXACTLY by combining sine waves ( of difference frequency, amplitude and phase ).

    your friendly neighbourhood idiot



  24. #24

    Multi bit Dac vs delta sigma

    To Mani,
    I am afraid I am on this journey for an extremely good dac. Not an easy journey...

    This thread and Mani commentaries have triggered my curiosity about those dacs.
    It seems that some of the "said" best dacs are multi bit like Dcs or Lavry Gold.
    Msb technology is also doing ladder Dac.
    Apart from Mani, do we have other listening experience of those dacs?

    I am particularly interested in the Usb Power DAC of Msb technology. Its price is 4300 $ so in between the Weiss Minerva and the Ayre Qb9.
    It is using a buffer (half a second) for jitter elimination not unlike what Chord does I think. It works on battery, an interesting feature I had not seen before. On the usb implementation :"The USB receiver is actually powered from the USB computer power and the data buffered and optically coupled to our board for complete ground isolation and jitter rejection." I like the fact that they use an optical link to the Dac to isolate it from computer noise. On the A1008 the sound is much better when I use a usb sound card (like the terratec dual aureon (20$)) and a optical glass cable to the Dac rather than direct usb connection (even with an ultraviolet wireword usb cable).
    I will try to get one for trial purpose.

  25. #25

    Lavry DCS and MSB

    I have been fortunate enough to live with the Lavry 924 , MSB Platinum and the the full dcs, and they are all good sounding dacs.

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