Linearity Talk

Discussion in 'Tales from the Bully Pulpit' started by winders, Jun 9, 2018.

  1. winders

    winders Know-it-all boomer, prob racist

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    http://www.analog.com/en/analog-dialogue/raqs/raq-issue-90.html

    According to the article above, ENOB is calculated using this formula:

    ENOB = (SNR – 1.76)/6.02 dB

    It also says that to claim certain number of bits of resolution, the converter’s differential linearity must be <1 LSB at the specified resolution. The formula for this I found here:

    https://masteringelectronicsdesign.com/an-adc-and-dac-least-significant-bit-lsb/

    Based on what we have seen with Amir's plots, is his threshold for bits of resolution <1 LSB? Or is it more or less restrictive?

    I ask because I don't know enough to know how to calculate the answers myself.

    @purr1n It seems clear that Schiit Audio is claiming 21 bits of resolution. Based on the above, is that what your measurements show?

    ENOB based on Schiit Audio's published SNR of 119dB is 19.5.
     
    Last edited: Jun 9, 2018
  2. ultrabike

    ultrabike Measurbator - Admin

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    1 LSB is about 6 dB.

    Amir-bits are defined using a 0.1 dB threshold which requires us to drop the -1.76 factor from the ENOB(SINAD) approximation formula and come up to a < 0.0167 bits threshold right out of Amir's butt.

    https://audiosciencereview.com/forum/index.php?threads/understanding-audio-measurements.2351/

    In other words, according to Amir if there linearity error is above 0.0167 bits as the level is decreased, then that's the lowest the DAC can go relative to full scale before things go down south and so Amir-bits are born by plugging such a dynamic range (Full scale to 0.0167 dB threshold) to the ENOB(SINAD) formula. It makes no sense.

    As far as 21 bits, that is not ENOB. It's related to the number of levels of the DAC. However, 19.5 bits of ENOB is fairly high for a multi-bit audio range DAC (my opinion).

    A couple of severe problems with Amir's article above (beside's his nonsense definition of Amir-bits):
    1. The Audio Precision is much more than just an AD.
    2. FFT size cannot reduce noise floor of an AD on demand. Increasing the # of FFT bins just helps visualizing harmonic distortion. There is no such thing as a free lunch.
    3. I don't know why hiding the bit flipping effects on a J-Test by reducing the # of FFT bins is such a good thing.
    4. Don't get me started on 0.1dB linearity threshold Amir-bits.
    5. THD+N is not a poor metric. It is actually used to derive ENOB.
    6. Inter-modulation distortion (like THD and THD+N) are not psycho-acoustically blind.
    All in all, the only things I find valuable in that posts are his links and references. His own contributions there are IMO misinformed.
     
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    Last edited: Jun 9, 2018
  3. winders

    winders Know-it-all boomer, prob racist

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    Yes, I understand that ENOB and resolution are two different things. That’s why I posted the first link which says exactly that. The second link was included to show the concept of how LSB was calculated.

    How did yet get 6dB as the LSB for Yggdrasil? Finally, what is the resolution of Yggdrasil if we assume the LSB is 6dB and use Marv’s or atomic bob’s results?

    Thanks!
     
  4. murray

    murray Friend

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    At a basic level, one bit is a factor of two (i.e. 2x), therefore approximately 6 dB.
     
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  5. Garns

    Garns Friend

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    To be a bit more precise, a change of one LSB is a particular LINEAR change in voltage level. At the lowest bit itself that is 6db, at the next lowest bit 3db and so on. The notion of resolution you cited @winders is basically an information theoretic measure: 17 bit resolution just means that the voltage levels output are distinct enough that you can distinguish reliably 2^17 different signal values without confusion. In an audio context you could argue that is too weak a measure to claim you have 17 reasonably accurate bits. If the 17th bit deviated by 4db from linearity the transfer function would be a bit wonky and you'd get distortion products.
     
  6. winders

    winders Know-it-all boomer, prob racist

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    I won't argue with you because I don't know enough about this to do so. All I can say is that and Engineer from Analog Devices is the one that suggested linearity needed to be within an LSB to claim that resolution. Is he talking in the context of audio in that article? I can't tell one way or the other.
     
  7. Garns

    Garns Friend

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    In the first article they mention 500Msps, ie 500MHz sampling frequency so probably not audio :)

    You are certainly correct that theirs is the only reasonable definition of RESOLUTION, ie, as the ability to RESOLVE the steps involved in a certain number of bits, and that would be the meaning that AD attach to it in stating their chips are 20bit.

    The linearity graph does tell a richer story such that extracting a single number out of it is a bit reductive. However eyeballing Marv's linearity plots it is clear that Yggdrasil balanced gets down to -117db = 19.5 bits with <1LSB deviation.
     
    Last edited: Jun 10, 2018
  8. winders

    winders Know-it-all boomer, prob racist

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    So, for audio, how many dB can linearity deviate before one should not claim a particular resolution? And how many bits of resolution does that mean Yggdrasil A2 really has? Because Schitt claims 21 bits.....
     
  9. ultrabike

    ultrabike Measurbator - Admin

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    Roughly speaking, every bit of resolution is equivalent to 6 dB. It has nothing to do with LSBs or MSBs.

    From @atomicbob:

    [​IMG]

    THD+N = 0.00233% which corresponds to -92.65 dB. THD+N and SINAD are kind of the same thing.

    Using the approximation formula we get (92.65 - 1.76)/6.02 = 15.09 bits of ENOB.

    The 6 dB per bit is kind of implied in the 6.02 division above.
     
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  10. ultrabike

    ultrabike Measurbator - Admin

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    Schiit laims 21 bits, but that is not ENOB. Schiit claims < 0.005% THD (http://www.schiit.com/products/yggdrasil) and neglecting noise that is -86.02 dB or 14 bits ENOB. They seem to be doing better than that.

    Again, do not confuse number of levels in bits with ENOB. Number of levels may account for quantization but not necessarily distortion and noise floor.

    As far as linearity:

    [​IMG]

    Roughly the 6 dB crossing (1 bit error) is around 108 dB which corresponds to 17.5 bits or so.

    I would go by the ENOB definition and not by linearity. And I would further stay away from claiming any kind of bogus bits using a 0.1 dB Amir-threshold.
     
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  11. winders

    winders Know-it-all boomer, prob racist

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    You keep suggesting I am confusing ENOB and resolution. I am not! I said very clearly that Schiit claims 21 bits of resolution. They also claim an SNR of > 119dB. If:

    ENOB = (SNR – 1.76)/6.02 dB

    Then the ENOB is 19.5 bits.

    I am trying to understand how we can look at the linearity measurement to see what the actual, not the claimed, resolution is.

    Within 1 LSB of linearity is the threshold one Engineer from Analog Devices laid out for claiming a certain resolution (that was in the first article I posted). Again, I don't know enough to argue what that all means. I am just trying to ask intelligent questions so I/we can know how far off Amir's .1dB number linearity number is in reality and to find out what Yggdrasil A2's resolution really is versus the claimed 21 bits.
     
  12. purr1n

    purr1n Building Magnis part time because it's peaceful.

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    SNR <> SINAD = Signal+Noise+Distortion / (N+D)

    Using Analog Devices definition of ENOB, Yggdrasil is about 15 bits ENOB. The Topping D30 (the crappiest DS DAC I've heard in a long while) has THD+N around -105db for 17.1 bits. The Modi 2U is about -107db for 17.5 bits

    Now keep in mind that other people, Amir, JA, etc. may have their own definitions of "bits" or ENOB which are different from Analog Device's.

    How does ENOB or the linearity plot correlate to what we hear? I'd say very poorly, unless the figures are particularly off. It's all useless. There's nuanced stuff in the time domain that our ears can pick up which is destroyed (visually) during the FFT conversion to frequency domain.
     
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  13. dmckean44

    dmckean44 In a Sherwood S6040CP relationship

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    You can't.

    Linearity alone does not determinte resolution.
     
  14. purr1n

    purr1n Building Magnis part time because it's peaceful.

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    Even the linearity measurement from these APs, AverLABs, dScopes, etc. might not be true linearity (via INL / DBL) in the sense of a digital code word relating to a corresponding voltage. From what I understand, the levels in these linearity measurements are based from sine waves from say -120db to 0db. I believe that even distortion can kind of screw these up measurements because the overall level is what is measured.
     
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  15. purr1n

    purr1n Building Magnis part time because it's peaceful.

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    To add, the linearity measurement as we've beeing talking about was sort of a measurement du jour for a while back in "the day" (Theta, Wadia, etc.). JA realized it was useless over time, so he don't do that shit anymore for current DAC measurements.

    You may as well measure chassis weight, power transformer weight, or testicle size.
     
    Last edited: Jun 10, 2018
  16. winders

    winders Know-it-all boomer, prob racist

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    According the docs I have, Analog Devices says this:

    ENOB = (SNR – 1.76) / 6.02 (bits)

    and

    ENOB (BITS) = (SINAD – 1.76 + 20 × log (FSR/Actual FSR)) / 6.02

    I used the first one based on Schiit's published SNR spec of >119dB which comes out to >19.5 bits. I don't have enough data to compute the second formula.

    On the topic of resolution:

    I am a firm believer in the idea that measurements mean almost nothing. I am just trying to get to where we can understand what Amir is doing with linearity to show the number of bits of resolution and show how he is wrong since that is what we have been saying. In other words, we can say that the standard to use is X.XdB versus what Amir is using.
     
  17. ultrabike

    ultrabike Measurbator - Admin

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    SNR is not SINAD and should not be used in the ENOB equation because it is missing distortion.
     
  18. purr1n

    purr1n Building Magnis part time because it's peaceful.

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    I'll bet you would hate a DAC with 3.12% distortion. Measurements are not totally meaningless. That would be the other extreme.

    It doesn't matter what Amir is doing with his interpretation of bits or whether his method is wrong or right. You can use JA's standards or AD standards. Nothing is going to come of it. All of this is meaningless if the measurements are "good enough".
     
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  19. murray

    murray Friend

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    I think that you’re overthinking this. I believe that Schitt are claiming 21 bits simply because they are using a pair 20-bit DAC chips (per channel) in a differential configuration. The factor of two adds the extra bit (1048576 steps x 2).
     
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  20. purr1n

    purr1n Building Magnis part time because it's peaceful.

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    Exactly. Schiit is saying their DAC can process at 21/96 instead of 24/96.
     
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