Delta Sigma Woes

Discussion in 'Digital: DACs, USB converters, decrapifiers' started by Madaboutaudio, Oct 19, 2015.

  1. Madaboutaudio

    Madaboutaudio Friend

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    This is a very Interesting video on the Filter(gibbs phenomenon) issues with Sigma Delta ADC:


    From the video, it seems that Sigma Delta provides signal accuracy but not time domain accuracy.
     
  2. ultrabike

    ultrabike Measurbator - Admin

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    Sounds like a load of bullshit to me.
    1. A sigma-delta IS NOT restricted to 1-bit output.
    2. A sigma-delta in general is not restricted to 24-bit.
    3. The sigma-delta DOES NOT have an internal digital filter. You supply that external to it.
    4. Sigma-delta IS used in many data acquisition equipment.
    5. The overshoot Gibbs phenomenon issue IS NOT the fault of the delta sigma, but of the filtering external to it. It would apply to any DAC architecture using a step filter (such as the burrito combo) and it's not necesarily a bad thing.
    6. The overshoot and pre-shoot is also not a fault of the delta sigma.
    7. Oscilloscopes and the like typically use high speed conversion given the application. But seldom do you see a 24 bit Scope (and if you do see some, likely they use D-S).
    8. The low cost of some well designed delta sigma has to do with volume. In some specific applications, delta sigma designs are not cheap.
     
    Last edited: Oct 19, 2015
  3. ultrabike

    ultrabike Measurbator - Admin

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  4. Madaboutaudio

    Madaboutaudio Friend

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    finally found this "lost" video:
     
  5. ultrabike

    ultrabike Measurbator - Admin

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    LOL! I'll check it out later today. I think it's the ESS guy from the first picture frame.

    I'll try to give a sort of intuitive explanation of the D-S process as well.
     
    Last edited: Oct 19, 2015
  6. Judeus

    Judeus Almost "Made"

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    Why bother eating a nice meal?

    Just throw it all in a blender and drink it through a straw = delta sigma
     
  7. OJneg

    OJneg The Most Insufferable

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    Jason and Moffat are great guys and all, but that's a gross misrepresentation of delta-sigma modulation
     
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  8. ultrabike

    ultrabike Measurbator - Admin

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    Yup.
     
  9. ultrabike

    ultrabike Measurbator - Admin

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    The ESS dude is somewhat correct. It is difficult to explain D-S in layman terms. At least for me.

    It is much easier for me to solve for the D-S linearized equations in the z-domain and call it a day. Because that's how I learned. It is quick and intuitive for me.

    The Equations (simple first order D-S)

    DS_1st_order.png

    e(n) = x(n) - y(n)
    y(n) = e(n) z^-1/(1 - z^-1) + n(n)
    so
    y(n) = (x(n) - y(n)) z^-1/(1 - z^-1) + n(n)
    or
    y(n) (1 - z^-1) = x(n) z^-1 - y(n) z^-1 + n(n) (1 - z^-1)
    which means
    y(n) = x(n)z^-1 + n(n)(1 - z^-1)

    That is, the output is basically a one-clock delayed version of the input, plus the quantization noise n(n) going through a 2-tap "flat-top" high-pass filter (noise transfer function). There are ways to possibly remove the signal delay, but in HW one sometimes wants to keep the delay there for timing closure.

    One can generalize this and add arbitrary transfer functions in the feedback and the feedforward path with some more interesting signal and noise transfer functions.

    One can add more stages and go through the equations.

    One can add multiple D-S blocks dealing with the signal and the differences and come up with more interesting structures.

    One may quantize to 1-bit, or to 20-bits.

    One may add all kinds of dither with this or that probability density functions to avoid limit cycles.

    Hopefully more layman explanation

    The D-S system maybe thought of as a feedback system that tracks the output signal. Consider the situation where there is no quantization noise (i.e. say 24-bit in, 24-bit out). Then the output is the same as the input. Basically the D-S is able to perfectly track the signal.

    Now add noise (i.e. say 24-bit in, 5-bit out). Then the D-S will attempt to track the signal, and it will do fairly well at the lower frequencies because they are easier to predict and correct, but not so good with higher frequencies that change quickly.

    So one oversamples, which in turns allows the D-S to track input signal with high degree of accuracy, depending on architecture, because relative to it's sample rate, they are somewhat low in frequency and easier to track.

    This is a bit of an oversimplification. It maybe possible to do some fairly weird noise transfer functions and other crazy things. But hopefully this gives an idea or a flavor of what's going on.

    Why should anyone do this?

    Some say it's because it's cheap. Yes. And no.

    D-S may allow one to use less levels, say 3.5-bit, at the output which maybe easier to put together than say a 24-bit R-2R. But one still might like to do a fairly good job at representing those 9 levels. Hopefully with high linearity. And depending on what one ends up doing, this may not be cheap. Though it could. Just as one could put together a POS 32-bit R-2R with horrible linearity and no monotonicity what so ever.

    My understanding is that the problem with 24-bit or more R-2R DACs is that is very difficult to put together resistors and current sources with the required tolerances. There maybe temperature dependencies. And even if one could (after perhaps some cleaver ways of calibration and so forth), one could use delta-sigma to increase the bits out of such R-2R arrangements. Hell, if a 20-bit R-2R can do 2 MSPS and noise floor in the front end is low, it may be possible to milk it to do more than 20-bits in the audio range.

    The trade off is not accuracy. AFAIK one gets more accuracy. The trade off is bandwidth (i.e. conversion speed). And BTW, if your input is 24-bits and come out less than that, well, R-2R or not you obviously just lost the LSBs of your sample, so output is not exactly the same as the input. Add to it noise and distortion at the front end, which happens to varying degrees all the time, and there you go.

    Anyhow. This is my lame attempt to give this stuff an explanation that hopefully folks can follow.

    And no, I don't think R-2R DACs are crap. As in most things, you can do a good job or a bad job with what you have. IMO, one can put together a fantastic set of R-2R audio DACs, which I think is what Schiit did.
     
    Last edited: Oct 20, 2015
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  10. Judeus

    Judeus Almost "Made"

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    fine... more accurately it would be chopping everything up and laying it flat on a table to make it seem like there is more food then there is, then glueing it back together back to its orginal state
     
  11. ultrabike

    ultrabike Measurbator - Admin

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    [​IMG]

    You are getting closer Jude-Us, but not exactly. :confused:

    I think the reason one does D-S is because multi-bit R-2R are relatively coarse. So you exploit the high resolution in time afforded by the clock.

    So your knife in the y-axis is not as good as your knife in the x-axis. So you use your x-axis knife. Or something like that. And then BAM!
     
    Last edited: Oct 20, 2015
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  12. feilb

    feilb Coco the monkey - Friend

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    It is true as @ultrabike says that the quantization part of DS is not limited to one bit, but most of the time it is anyway. This is, infact, the entire reason that DS is very popular. Unlike multi-bit R2R networks that require laser-trimmed resistor networks to provide an output, DS uses a very simple high/low output and a simple low pass filter to reconstruct the signal. As @ultrabike mentioned, this has generally yielded much better accuracy because it is much easier to chop something up into accurate time segments and provide a single value output than it is to accurately trim a bunch of on-die resistors. Thus, making highly accurate DACs is much less expensive.

    In order for DS to work, however, the clock rate must be significantly higher than the data rate. Because the output of the modulator is 1-bit (high or low), the resolution comes from chopping the sample time up into many small pieces and averaging 1s and 0s over this diced time period to give you the correct average value. In order to produce an accurate result there usually IS an upsampling filter of some sort in the DAC to provide an interpolated value to the modulator at each of the clock cycles.

    Upsampling does introduce ringing effects, particularly on high impulse sounds, and the choice of filter topology has an impact on how the ringing is distributed (pre v post). Linear phase filters produce symmetrical ringing about an impulse. Minimum phase filters demonstrate no pre-echo but significantly more post-echo. Many find the pre-echo more offensive (as do I). You can check this blog for a nice experiment on linear vs minimum phase filters. It has a nice experiment you can do to test whether you can hear the difference. I found it quite easy to pick between the two:

    http://archimago.blogspot.com/2015/04/internet-blind-test-linear-vs-minimum.html
     
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  13. ultrabike

    ultrabike Measurbator - Admin

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    Pre-echo or ringing does not bother me much. But to each its own.

    Lots of TOTL delta sigma chips seem to do at least 5 levels now though (check out TI, Cirrus and AKM data sheets). Some call these DAC chips "segment" or whatever.

    1-bit first order DS are easy to explain (relatively). But much more complex structures are typically used.
     
  14. OJneg

    OJneg The Most Insufferable

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    Most (good) audio D/A chips use multi-bit DS modulators, not 1-bit.
     
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  15. purr1n

    purr1n Finding his inner redneck

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    It's more like flicking a light switch on and off at a zillion times per second with different intervals for the on and off states to simulate a dimmer / different light intensities.
     
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  16. purr1n

    purr1n Finding his inner redneck

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    I find the filters that try to eliminate the pre ringing at the expense of slightly increased post ringing (in math, nothing is for free) to sound worse - more harsh. I'm simply for as little ringing as possible.
     
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  17. ultrabike

    ultrabike Measurbator - Admin

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    That's right. I think you do need more samples (ringing) on a minimum phase filter than a linear phase filter for the same performance.
     
  18. Madaboutaudio

    Madaboutaudio Friend

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    From what I read from the Ess sabre whitepaper:

    It seems that sigma delta has issues with handling fast changing signals like transients. Maybe the noise shaper(or feedback loop) has problems deciding between what is noise and what is signal?
     
    Last edited: Oct 20, 2015
  19. ultrabike

    ultrabike Measurbator - Admin

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    Nope. That, IMO, is the ESS dude trying to sell his delta-sigma approach.

    As long as the input bandwidth is well bellow the oversampling rate, to the delta-sigma, "fast transients" are slow and should be able to track them.

    How well certain frequencies are going to fare depends, among other things, in the noise transfer function which may not necesarily be a simple difference high-pass filter.

    I'm not 100% sure about the ESS approach, but from a quick look at their patents, I tend to prefer the approach by TI, AKM, and Cirrus used for their TOTL stuff.
     
    Last edited: Oct 20, 2015
  20. firev1

    firev1 Friend

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    Going by the ringing or settling time logic, ADC wise SAR has settling times in the order of nanoseconds compared to similar DS chips(usually in microseconds). Regarding SD, even the APx555 with -120THD+N specs is using some form of sigma delta DAC. edit: They use a AKM5394s in parrallel and AD1955s for the DAC end.

    Notably Mola Mola or Hypex's Bruno's Mola Mola DAC uses 32 1 bit modulators with each modulator fed the audio input with time delay between each modulator to resolve the 32 bits in time.

    Not adding anything new but SAR/R2R are really good with noise with high bandwidths and don't really require noise shaping to get true 16 bit specs in the audio region while having no deterministic noise/distortion components up to 500kHz or 1mHz. I think its easier to design around that than regular SD chips.
     
    Last edited: Oct 21, 2015

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