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How important is DAC linearity?

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#1
I'm wondering how important this linearity measurement is. The very well regarded Topping D30 only gets an effective value of 15 bits. Even the topping D10 hits 20 bits (I can't find the image, Amir measured it somewhere on the forum).

I've been looking at the Sanskrit 10th, interested in the AK4490 chip, and I also need a DAC that is powered separately from PC USB and has optical/coax input. But the SK10 doesn't have a great linearity measurement either. The Modi 3 does really well here (the Sanskrit is using the external power supply).

Thanks for any insight.

Here are some example images from Amir:

D30.png


sanskrit.png


d50.png
 

garbulky

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#2
@brydon10
The linearity definitions criteria is something that's too arbitrary for me.

The ratings on linearity used to be given as +/- 0.1 db on this website (later relaxed to 0.5 db). So the moment it exceeded that, that was considered that the dac was able to do 15 bits "resolution". The idea being that 0.1 db would mean that a dac was perfectly linear to differentiate it from one that was not.

But why not 0.00000000001 db as being the definition of linearity in bits? That's even more perfect right? If so, suddenly a whole lot of dacs including the AP machine would fail that and you'll end up with graphs of dacs labelled "4 bits of resolution which makes no sense. Hence the need for a well-accepted standard that's not made up when one defining bit resolution or linearity as being bit resolution.

I've asked to see any kind of scientific literature that has the word "a bit" and 0.1 db (or 0.5db) as part of its definition and still have not seen it. For bits, I have seen 6 db being a 1 bit but not 0.1 db. 6 db is 6000% more than 0.1 db. You see my issue here...
https://hbfs.wordpress.com/2008/12/09/deriving-the-1-bit-6-db-rule-of-thumb/


There is an accepted definition for "equivalent/effective number of bits" which granted isn't really about linearity. But it is an actual defined thing.
(The Equivalent number of bits)= (SNR – 1.76)/6.02

(This equation would likely give you a higher different value for equivalent number of bits - note the 6 db value which is the converter of decibels to bits).
https://www.analog.com/media/en/training-seminars/tutorials/MT-003.pdf
https://en.wikipedia.org/wiki/Effective_number_of_bits
https://www.analog.com/en/analog-dialogue/raqs/raq-issue-90.html


So my fuss this: without an accepted scientific standard, how much you change an arbitary 0.1 db 0.1 db to say 0.5 db or to 3 db makes the linearity figure come out very differently
If you are looking at graphs and you see "15 bits" written there you are likely going to think - this dac can't even do 16 bits! It's not good. CD is 16 bits! I know I did.

But... the SMSL dac can resolve greater than that - just not at perfect linearity. Look at that SMSL dac which looks like it does -80db at 0.1db (13 bits). Relax that to 3db suddenly you are at a whopping -115 db (19 bits) and not -80 (13bits) when using 0.1 db as the limit. That's a large difference in bit resolution and that's why it's important that if we define linearity or resolution this way that we have an accepted standard especially if we use the term bit resolution on a graph.

Imo if you can hear a dacs linearity of even +/-3db all the way down at even 14 bits (-84 db) in music, Good luck to your super human ears! Good luck if you can even hear anything at all at that low volume in music listening (-84db similar to somebody shouting at you from 10 miles away).
(Check out the shoutometer for comparison)


https://www.audiosciencereview.com/forum/index.php?threads/the-shoutometer.2555/


So I'm not sure what real world help this 0.1 db perfect linearity has to your listening experience. I would be interested to find out if listening tests can show anybody able to differentiate even 3 db of linearity at even 14 bits let alone 0.1 db.
 
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#3
Thank you for the great reply garbulky. So you are saying the resolution really depends on the graph and db scale used.

Here is the Topping D10

index.png
 

Veri

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#4
Thank you for the great reply garbulky. So you are saying the resolution really depends on the graph and db scale used.

Here is the Topping D10

View attachment 28172
I personally believe 15-16 bits can represent CD audio in its entirety and should be fine. 19-20-bit audio and 120+dB dynamic range DACs are for those who want the best of the best, even if the difference is probably not really audible. But there is of course the pride of ownership, customisability of certain features, inputs/outputs/...

We are probably all too quickly in the 'measurebating' territory, but even still so many of us here don't think the super budget $100 DAC is 'adequate' for whatever personal reason(s). The tone board is probably sufficient for just about anyone shy of someone needing balanced outputs.

I think it's quite neat that the tone board + Atom $200 stack is really popular inside and outside the ASR forum. :) certainly not wasting any money considering the performance of these two combined! But then the KTB balanced is coming out soon, EL Amp with atom specs is too so there's always some upgrade on the horizon, that's how it always is in this audio game! Stay away if you want to hold on to dear wallet :D
 
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#5
Thanks Veri. I have a Topping D10 DAC and I'm very satisfied with it. I'm just also looking for another DAC to run to my stereo amp, feeding it with the Optical output from the D10, so since I was looking I came up with this question. I might just go with the Sanskrit 10th because I can get one for a great price. I guess using a Y splitter cable from the D10 is another option, but I'm just not a huge fan of the idea.
 

garbulky

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#6
Thank you for the great reply garbulky. So you are saying the resolution really depends on the graph and db scale used.

Here is the Topping D10

View attachment 28172
Well I don't know. I think there's an issue when stating "bits of resolution" using linearity and using an arbitary 0.1 db variation of a flat line as a cut off and using that to state "bits of resolution" as you are seeing in those graphs. I'm unsure if bits of resolution can be defined by linearity (in a well accepted manner). Maybe it can. I haven't seen evidence of this.
In case I'm being unfair, I would like to mention Amir has defended his use of the 0.1 db (and 0.5 db) cutoff extensively. I'm not convinced that it is an accepted standard so I'm presenting my POV but he is clearly way more educated than me in this aspect.

I am not familiar enough to say for sure what is the scientifically correct way to state bits of resolution.
However there is an equation called effective/equivalent number of bits that is an actual standard which I mentioned. Whether that's the best way to state bits of resolution - I'm not sure.

I doubt you'd be able to hear any difference simply due to a varying linearity in music listening at 14 bits or greater though. I doubt I could hear anything at all at that level so far reduced in volume.
 
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Veri

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#7
Thanks Veri. I have a Topping D10 DAC and I'm very satisfied with it. I'm just also looking for another DAC to run to my stereo amp, feeding it with the Optical output from the D10, so since I was looking I came up with this question. I might just go with the Sanskrit 10th because I can get one for a great price. I guess using a Y splitter cable from the D10 is another option, but I'm just not a huge fan of the idea.
If you can get the Sanskrit 10th for a good price it will suffice I guess, just make sure to power it from external power as per Amirs' recommendation/finding in the review. I believe several people own it on this forum and it seems like a nice enough DAC.

Y-splitter is possible and perhaps worth a try but as you say, it's not as much of an elegant solution.
 

Blumlein 88

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#8
One reasonable idea about linearity is it should be within +/- 1 LSB or least significant bit. You don't want a bit level input to the DAC to output something that could be from another input level. That measurement would be far smaller than Amir's .1 db criteria even at 16 bit.

I don't know how important it is or at what level non-linearity would become an audible problem. There are different ways to measure this. Amir's method which is I believe the one AP suggests is somewhat effected by noise I think. So sometimes noise from other sources interferes with measuring the underlying linearity of the DAC. But the people at AP and Amir do know what they are doing.

I use a different way to measure linearity, and find modern delta sigma DACs to have pretty much perfect linearity even to 24 bits hidden in the noise. Multi-bit or ladder DACs have problems reaching this performance and it is one of the reasons delta sigma DACs have taken over the market. They are less expensive and have better performance.

All of which unfortunately doesn't answer much about whether 15 bit linearity as Amir puts it is audibly different than one clean to 20 bits. The Sanskrit 10th had other issues especially with low frequency noise, and more so over USB compared to SPDIF inputs. For these reasons more so than linearity I'd look elsewhere especially if planning on using the USB input. You indicate you are going to use Toslink so it wouldn't be as much of an issue to you.
 
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#9
Thanks for the input guys, I really appreciate it. Maybe I won't put so much weight on this measurement. I highly doubt it would ever be audible from what you guys are telling me. I might take another look at the D30, or some other similarly priced products.
 

RayDunzl

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#10
Since those last bits get used "all the time" when listening to music...

Or when measuring tones whose frequencies are not intimately (integer divisions) related to the sample rate...

Does the low-level non-linearity intrude upon the accuracy of higher level signals?
 
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Blumlein 88

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#11
Here is where I created a 441 hz tone at - 3db FS. I took the lowest non-zero bit and raised its level by .1 db. That would have roughly been the 4th largest bit having .1 db linearity error. It resulted in every harmonic at -99.8 db which altogether would be equivalent to about -83 db THD. I would think having this non-linearity in the 15th bit would result in a proportionally smaller addition of harmonics. Doing the same thing for a smaller signal on the 14th bit appeared to create harmonics at -99.8 db from the fundamental. With that low level the results are below the 24 th bit. This is probably an oversimplified view, but gives one the idea low level non-linearity if not too extreme isn't a big issue.
1561327319234.png
 
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Kmac

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#14
You mentioned you are interested in the Sanskrit 10th - I got one a few months ago and it represents good value. I've been quite impressed and it comes with a good remote control as well. I've got a Topping D50 which cost over 2x price for a similar feature set.
 

restorer-john

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#15
One reasonable idea about linearity is it should be within +/- 1 LSB or least significant bit.
The very first dual 16 bit D/A converter made by Philips (TDA-1541A) had <1LSB error on even the lowest grade of the chip, from bits 1-16.
The TDA-1541S1 (select) had bits 1-7 <0.5LSB, bits 8-15 <1LSB and bit 16 <0.75LSB guaranteed, often bettered.

It's academic, and has been for decades for 16/44.
 

KSTR

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#16
Personally, I find linearity and notably distortion (THD+N) measurements/plots that don't factor out (uncorrelated) noise not very insightful. To see what's going on requires looking down into the noise by some 20dB. Which means time-domain averaging of the data before processing. The AP's can do that even with non sample-synced stimuli (using a trigger, very similar to a digital oscilloscope) but using sample synced record-while-playback is better because it is not prone to trigger jitter which attenuates the higher frequencies.

I would actually dare to say the AP's standard "linearity" plot is quite useless for most DACs because any Delta-Sigma DAC is extremely linear by design (down to the last bit), and the left side of the plot (where the noise kicks in) should be discarded anyway because it does not contain relevant data that only leads to wrong conclusions.
Amir's notion of the "Schiit Mode 3 being way more linear than the SMSL Sanskrit 10th" is not exactly correct, rather the Schiit just has lower noise, that's all that can be read from the plots. Linearity only can be compared to the point where the noise kicks in for the noisier DAC. It could well be the SMSL is actually more linear but it just isn't visible in the higher noise floor. Of course, both being Delta-Sigma designs they will have the same baseline linearity which is perfect, as noted (see my thread about the RME Adi2 Pro's "offset error" where I showed that even the very least siginficant bits are rendered correctly by a Delta-Sigma DAC, -- the error came from the incorrect data stream to the AK4490 DAC chip, not from the chip itself)

With non-Delta-Sigma DACs the scenario is different of course but one must take care again that the measurement has enough signal-to-noise ratio to really make the data valid down to the bit depth one is planning to show.
 

solderdude

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#17
The linearity plots still give insight.
They do show real world situations showing the point where the smallest bit(s) drown in noise and what the practical 'resolution' will be because of this.
 

IVX

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#18
Another view of THD+N. All plots show +db deflection, never negative, hence it is not about the INL, DNL or so. The same THD+N plot, just db instead of % and negative-bottom half of the plot is redundant. +.5db means THD+N = 5.9%. One thing makes that test useful, it can find any auto-mute trick if implemented.
PS: AP is pretty simple analyzer - THD+N, amplitude, frequency, phase, FFT. We can ask Amir to show us the structure of "Linearity" test to make sure it is THD+N vs Amplitude sweep ;)
 
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