CHANGSTAR: Audiophile Headphone Reviews and Early 90s Style BBS
Lobby => Amp and DAC Measurements => Topic started by: Marvey on September 30, 2014, 08:13:00 PM
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Just a had thought. Again, could be talking out of my ass. All conjecture. Could differences among the types of DACs, resistor ladder, 1-bit, multi-bit/hybrid, SABRE (who knows since no public documentation) be a result of the types of linearity errors.
For resistor ladder DACs, the linearity errors would be of a certain sort. Resistors trimmed slightly off. Like bit 4 output is 16.3 (instead of perfect 2^4=16) to 32768 from bit 15 output(assumming bit 15 output is perfect). No matter what, the bit 4 output is always going to be in slight error, and consistently of that slight error.
For sigma-delta, noise shaping would be used. This of course would introduce a entirely different type of linearity errors, but given how sigma-delta works, the overall error would be less. It would seem much more difficult to get the ladder DACs to be just as linear given the difficultly of precision trimming of the resistors.
Now how does this correlate to what we hear? Those of you who have heard enough DACs, quality DACs that is of both kinds, know that resistor ladder and sigma-delta sound different and have different strengths. The best sigma-delta implementations sound highly detailed with sharp attacks. The best resistor ladder DACs sound smooth with natural timbre.
Would in interesting to see some linearity plots (output vs. bitcode), DNL, and INL plots of both kinds. Maybe there is something. Maybe not.
Maybe greater linearity = more resolving (it's true mathematically, but is it true subjectively?) Maybe linearity error plots with certain more predictable patterns = smoother more natural sound?
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Added by Anaxilus for other considerations. All comments welcome.
http://www.youtube.com/watch?v=HIAqtblSmjQ
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Just a had thought. Again, could be talking out of my ass. All conjecture. Could differences among the types of DACs, resistor ladder, 1-bit, multi-bit/hybrid, SABRE (who knows since no public documentation) be a result of the types of linearity errors.
For resistor ladder DACs, the linearity errors would be of a certain sort. Resistors trimmed slightly off. Like bit 4 output is 16.3 (instead of perfect 2^4=16) to 32768 from bit 15 output(assumming bit 15 output is perfect). No matter what, the bit 4 output is always going to be in slight error, and consistently of that slight error.
For sigma-delta, noise shaping would be used. This of course would introduce a entirely different type of linearity errors, but given how sigma-delta works, the overall error would be less. It would seem much more difficult to get the ladder DACs to be just as linear given the difficultly of precision trimming of the resistors.
Now how does this correlate to what we hear? Those of you who have heard enough DACs, quality DACs that is of both kinds, know that resistor ladder and sigma-delta sound different and have different strengths. The best sigma-delta implementations sound highly detailed with sharp attacks. The best resistor ladder DACs sound smooth with natural timbre.
Would in interesting to see some linearity plots (output vs. bitcode), DNL, and INL plots of both kinds. Maybe there is something. Maybe not.
Maybe greater linearity = more resolving (it's true mathematically, but is it true subjectively?) Maybe linearity error plots with certain more predictable patterns = smoother more natural sound?
TBH, I dunno either.
What I can say though is that if a ladder DAC uses sample and hold, that automatically will introduce a little bit of roll off at the top and some amount of ultrasonic stuff.
Delta Sigma will not be nearly as rolled off at the top, but it will produce quite a bit of ultrasonic stuff.
There might be some interactions with the board, other components regarding the ultrasonics, but I dunno.
For sure the frequency response will be slightly different unless some sort of compensation is introduced for the ladder DAC.
Like you said, there will be different sources of non-linear issues due to precision. With 1-bit delta sigmas, if the signal does not follow a certain assumed uniform distribution model, things can get weird and spurs can appear at the output. There will also be some residual precision error form what I remember. Multi-bit, multi-stage, high-order delta sigmas with different levels of feedback (not just unity) can yield more interesting noise shaping characteristics, lower precision errors and maybe less prone to non-linear data dependent issues... also from what I remember.
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TI DAC8581. Industrial DAC chip which could be the one used in a well known NOS DAC.
It's a "16-bit" DAC. Well sort of. Look at the LSB error in the INL plot. I believe that INL error pattern is typical of ladder DACs.
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The DLE graph is pretty good, though.
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The DLE graph is pretty good, though.
Of course, it's a differential.
Anyways. This DAC is scary. Scary good. It's a 20-bit ladder (with tweaks I don't understand or are unclear) DAC with better than 1 LSB accuracy.
AD5791. $55 a pop at Mouser. And not because crazee audiophiles want it so Kingwa needs to buy 100s of them.
This DAC chip is definitely for missiles or MRIs.
(http://www.analog.com/library/analogdialogue/archives/44-04/AD44_04_FIG_04.jpg)
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TI DAC8581. Industrial DAC chip which could be the one used in a well known NOS DAC.
It's a "16-bit" DAC. Well sort of. Look at the LSB error in the INL plot. I believe that INL error pattern is typical of ladder DACs.
Um. Wow.
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It's a voltage output DAC, Kingwa won't like that facepalm
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Um. Wow.
I think Chrysler used for those DACs for manufacturing. :-)
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The DLE graph is pretty good, though.
Of course, it's a differential.
Anyways. This DAC is scary. Scary good. It's a 20-bit ladder (with tweaks I don't understand or are unclear) DAC with better than 1 LSB accuracy.
AD5791. $55 a pop at Mouser. And not because crazee audiophiles want it so Kingwa needs to buy 100s of them.
This DAC chip is definitely for missiles or MRIs.
(http://www.analog.com/library/analogdialogue/archives/44-04/AD44_04_FIG_04.jpg)
Its also interesting to note that Analog Devices billed it as "THE INDUSTRY'S FIRST TRUE 20-BIT DAC" when it was introduced...in 2010.
It's unlikely that this would ever be used in audio, since it does not accept standard audio data formats (and, in fact, if you look at the datasheet for what you have to write into the DAC for every sample, it's even scarier.) Plus there's no EZ-Bake Oven "How 2 Uze 4 32/768 Arrdio" application note for it with Konvenient Plug-N-Go™ reference design. And, only 20 bits! Where's your buzzword compliance?
Another random note, taken from a quick scan: AD has a bunch of very linear DACs, including ones we'd kill for in the early days of audio, like quad 16-bit parts with less than 0.5 LSB nonlinearity across the band.
Final random note: The $55 AD5791s look to be the cheap "A" grade. "B" grade is actually better in AD-speak. $65 in 1000 pc quantities. That's about 10 top-shelf delta-sigma DACs there, or 40 AKM4396s, which are still very good.
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OK trying to find INL plots for audio DACs... Can't seem to find them. Now I wonder about those 20-bit, 24-bit and 32-bit claims. I can find graphs for a lot of high accuracy ladder DAC type chips on the Analog Devices site though. All the audio chips seem to omit this measurement.
For the heck of it, I'm going to write a computer simulation for an INL plot a typical ladder DAC. I can probably assume the resistor values / errors will follow a bell curve and we already know how a ladder DAC is laid out...
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So I talked to some friends much more on the analog side of things... I know some of that shit, but I tend to focus more on the digital side of things (both systems and ASIC). This is all in their opinion I guess (but these are IC analog designers so I kinda value their opinion)... Almost verbatim:
"...don't think ladder DACs are better (vs delta sigma), but think INL and DNL have more direct physical interpretation for ladder DACs. Guess is that INL and DNL are specified less often in delta sigma DACs because they are just part of the story when it comes to distortion. So more often than not, it is preferred to think of just total distortion specified as SNDR or even two-tone intermodulation. ENOB and/or SNDR probably tell a more complete story."
When doing systems bit exact models we did as good of a job as we could to model not only channel (cable model), but also front end limitations for the IC communications devices we built. Non-ideal conditions were usually specified in terms of ENOB and sometimes a PA model would be included. We got very close results to what we got in the lab. The requirements for the DACs and ADCs where pretty stringent.
I'm not going to say INL and DNL don't matter. I think they do. But I don't think they are the tell all, and definitively feel more comfortable with ENOB specifications than with INL and DNL, though I know those can be dressed.
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Here is some more about the subject:
1) http://www.analog.com/static/imported-files/tutorials/MT-003.pdf
2) http://www.analog.com/library/analogdialogue/archives/39-06/Chapter%205%20Testing%20Converters%20F.pdf
Reference 1) is good for understanding concepts on ENOB and SNR stuff. Reference 2) talks a bit about the same and INL and DNL. Flip to page 5.12 on the second reference and one may find a possibly explanation as to why INL and DNL are not commonly provided in some audio DAC datasheets:
"Finally, there are several types of DACs which generally do not have static linearity specifications, or if they do, they do not compare very well with more traditional DACs designed for low frequency applications. The first of these are DACs designed for voiceband and audio applications. This type of DAC, although fully specified in terms of ac parameters such as THD, THD + N, etc., generally lacks dc specifications (other than perhaps gain and offset); and generally should not be used in traditional industrial control or instrumentation applications where INL and DNL are critical. However, these DACs almost always use the sigma-delta architecture (either single-bit or mult-bit with data scrambling) which inherently ensures good DNL performance. DACs specifically designed for communications applications, such as the TxDAC-family, have extensive frequency-domain specifications; but their static specifications make them less attractive than other more traditional DACs for precision low frequency applications. It is common to see INL and DNL specifications of several LSBs for 14- and 16-bit DACs in this family, with monotonicity guaranteed at the 12-bit level. It should by no means be inferred that these are inferior DACs—it is just that the application requires designs which optimize frequency-domain performance rather than static"
BTW: I'm not sure about the Analog Devices "should not be used in traditional industrial control or instrumentation applications". Not saying it isn't true. Just not sure about that. What is a little more clear to me though, is that for delta sigma INL and DNL are not as straight forward measurements as with ladder DACs. I can say also I didn't use those (INL/DNL) for modeling communication system performance either.
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After reading a little more, I think one might be trading resolution (bits) for BW (samples per seconds) when going from delta sigma to ladder. Also here goes a uber part specifically for MRI. It's not ladder, it's pipeline (which might be sorta related):
http://www.ti.com/product/ads5263&DCMP=hpa-med-ads5263-en&HQS=Other+PR+ibistool-pr
These gives you 100 MSPS 16-bit... for just about $278 a pop.
This seems also like good material to browse:
http://www.ti.com/europe/downloads/Choose%20the%20right%20data%20converter%20for%20your%20application.pdf
According to the above presentation, for some defense systems BW requirements might be in the order of 1M to 1G which might be too much for some delta sigma stuffs (*that kind of depends on application though, don't think all things defense have that kind of requirement). If one flips to page 51 there is a chart for bits vs settling time (BW), and delta sigma is sitting in the lowest speed highest resolution area. R-2R is in the a bit lower (maybe mid) resolution area but a bit faster.
That AD5791 has a 1μs settling time. That's pretty freaking fast. Add to that 20 bits per sample and we proly talking $$$. But for audio applications uber fast may not be that necessary, but resolution might be a different story (i.e. number of bits).
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Alright, so I did some more digging into audio DACs. Most of them are indeed delta sigma. Most of them cannot do more than 20 bits of resolution. They seem limited by noise.
Again, there seem to be a trade-off between sampling rate and number of bits, regardless or architecture.
If one feels comfy with ladder DACs and those give out 20 bits, I guess life is good. One might need to take care of the sinc frequency response shaping that comes with it though, but that's another story. I do think there are flagship delta-sigma DACs that can give 20 bits of resolution. Perhaps the PCM1795, CS4398, or maybe the ES9018K2M can (last one gets closer to 21 bits). IMO it's just another way to get from point A to point B.
It maybe possible to come up with a DAC (delta sigma or ladder) with higher resolution. But so far I haven't seen > 20 bits of effective resolution, INL/DNL plots or not, and either ladder or not for BWs that will cover the audio range. I definitively could be wrong.
I also do not subscribe to the belief that we have gone back 20 steps back with delta sigma and that proof of that is that one will never put that technology in critical applications. I also don't like the bringing up of military applications and credentials. Proly an irrational pet peeve of mine. I believe that for the sampling rates that those applications require, delta sigma may not be appropriate. But I do not currently feel that has anything to do with "accuracy".
Furthermore, all of this does not take into consideration implementation, which can render those wonderful 20 bits of resolution to crap.
All of what I write here is IMO, and I could be completely wrong, and I'm more than open to be corrected in my mistakes. I also have a lot of respect for Schiit products and expertise.
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Delta-sigma (and everything associated with it, including implementations) = one step forward (resolution) and two steps back (tone color, grain, timbre).
The thing I'm interested in is how the INL plots look like between the ladder and SD DAC implementations. Maybe there are patterns there which correlate to what we hear between those two types of DACs. What's the nature of the error?
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Just had another thought.
Given the same temperature and other conditions, it would seem that the INL/DNL plots of ladder DACs would be reproducible. In effect, they are always going to make the same error.
With SD DACs, would the INL/DNL plots look slightly different every time the measurement is taken because of the randomness of noise shaping?
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Does INL/DNL really matter for audio? It is a static measurement. Don't know if those plots make sense for S-D DAC anyway.
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TI DAC8581. Industrial DAC chip which could be the one used in a well known NOS DAC.
It's a "16-bit" DAC. Well sort of. Look at the LSB error in the INL plot. I believe that INL error pattern is typical of ladder DACs.
Any recommended reading sources that might help someone understand how to read these measurements? (I'm hoping my computer science background will help me get up to speed more quickly, where I did take one class that dabbled with assembly programming and other stuff specific to the bit level, but a lot of that has been dumped from my brain already.)
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Well, would you use one of these DACs for audio?
(http://www.changstar.com/index.php?action=dlattach;topic=1793.0;attach=7688;image)
Do you want to be up to 15 LSBs off? Which for 16 bits, means 4 bits off? So how would you like to 3 to 4 bits louder than you are supposed to be from 0.20V to 0.40V on a 2V output DAC?
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I could tell the measurement wasn't good based on your comments, haha, just wasn't sure what I was looking at. OK, so 15 LSBs would be 4 bits off for 16 bit. Stuff like that is what I was asking if you had recommended reading for. Looking around myself as well to get myself educated, just wondered if you stumbled on anything easy to understand or digest. (Admittedly, this bit-level stuff, especially dealing with LSBs or MSBs went mostly over my head in that class, but maybe something is still stuck in my brain.)
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At least the differential error is low, which means that my sinewave would keep a nice shape and not distort like crazy. That's another way to look into it.
Isn't a 4bit error below the variation between 2 headphones anyway?
You could well design a DAC that has very low linearity error, which would be good for static measurement (voltmeters and all) but would it be able to keep these good measurement with a 10kHz sinewave?
I briefly looked at the datasheet of the super accurate DAC you posted yesterday and could never find any mention of actual sample rate.
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Honestly, I don't think it would be that bad. Maybe the guys at Schiit would differ. :-)
One way to test is to take that graph and make an error function. And then apply to the raw WAVE file. For every word (16bit), fuck up the value a little bit according to the function. And then see how it sounds.
In terms of SD, you are probably right it doesn't apply since error will be different. But what happens (subjectively) to the WAVE file when we feed it into a DAC and add random noise per X sample after conversion of PCM to single or multi-bit?
Again, all conjecture.
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I could tell the measurement wasn't good based on your comments, haha, just wasn't sure what I was looking at. OK, so 15 LSBs would be 4 bits off for 16 bit. Stuff like that is what I was asking if you had recommended reading for. Looking around myself as well to get myself educated, just wondered if you stumbled on anything easy to understand or digest. (Admittedly, this bit-level stuff, especially dealing with LSBs or MSBs went mostly over my head in that class, but maybe something is still stuck in my brain.)
x x x x x x x x x x x x x x x x (16 bits)
MSB LSB
2^15 2^14 ......... 2^2 2^1 1
using signed short 16-bit:
-32768 or 8000 (hex) = -2 volts
0 (dec) or 0000 (hex) = 0 volts
32768 or 7FFF (hex) = 2 volts
shift everything over (add 32768) and the graph should make sense.
or something like that. you get the idea.
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Honestly, I don't think it would be that bad. Maybe the guys at Schiit would differ. :-)
One way to test is to take that graph and make an error function. And then apply to the raw WAVE file. For every word (16bit), fuck up the value a little bit according to the function. And then see how it sounds.
In terms of SD, you are probably right it doesn't apply since error will be different. But what happens (subjectively) to the WAVE file when we feed it into a DAC and add random noise per X sample after conversion of PCM to single or multi-bit?
Again, all conjecture.
I could do that from the LE graph with Matlab. Alas, I only have Scilab at work and it is VERY poor with image processing (to build the mapping function) :/
You reminded me what I wanted to try today :D
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Well, would you use one of these DACs for audio?
(http://www.changstar.com/index.php?action=dlattach;topic=1793.0;attach=7688;image)
Do you want to be up to 15 LSBs off? Which for 16 bits, means 4 bits off? So how would you like to 3 to 4 bits louder than you are supposed to be from 0.20V to 0.40V on a 2V output DAC?
How do you get 0.2 to 0.4V?
15 LSBs for a 16bits / 2V DAC is more like 0.00091V (0.046%)?
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[size=78%]x x x x x x x x x x x x x x x x (16 bits)[/size]
MSB LSB
2^15 2^14 ......... 2^2 2^1 1
Ah, yep. Got it! :)p5
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Marv, if you have the Wav files sent them to me.
One thing though. Use the highest sampling rate you can from your ADC. If its 96 kHz, use that. Also use the highest resolution supported, and if you can use ASIO drivers. Make sure you are using full resolution or somehow have some reference (i.e. try to fully load the DAC).
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LOL, can you just convert one of your songs to WAV?
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Yup. But don't have R-2R goodness.
Can try with whatever I have.
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Well, would you use one of these DACs for audio?
(http://www.changstar.com/index.php?action=dlattach;topic=1793.0;attach=7688;image)
Do you want to be up to 15 LSBs off? Which for 16 bits, means 4 bits off? So how would you like to 3 to 4 bits louder than you are supposed to be from 0.20V to 0.40V on a 2V output DAC?
How do you get 0.2 to 0.4V?
15 LSBs for a 16bits / 2V DAC is more like 0.00091V (0.046%)?
Look at region from slight past 32768 (0 volt) to 40960 (0.5 volt) - assuming +/-2V peak. Get it now? 10 to 15 LSBs off (higher) between that point. 2^3 = 8. 2^4 = 16.
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Yup. But don't have R-2R goodness.
Can try with whatever I have.
ah gotcha. will do
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Well, would you use one of these DACs for audio?
(http://www.changstar.com/index.php?action=dlattach;topic=1793.0;attach=7688;image)
Do you want to be up to 15 LSBs off? Which for 16 bits, means 4 bits off? So how would you like to 3 to 4 bits louder than you are supposed to be from 0.20V to 0.40V on a 2V output DAC?
How do you get 0.2 to 0.4V?
15 LSBs for a 16bits / 2V DAC is more like 0.00091V (0.046%)?
Look at region from slight past 32768 (0 volt) to 40960 (0.5 volt) - assuming +/-2V peak. Get it now? 10 to 15 LSBs off (higher) between that point. 2^3 = 8. 2^4 = 16.
Oh, I thought you meant 3-4 bits off was like 0.2 to 0.4V off a 2V scale. I was scared for a bit :D
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Also, your sinewave won't be 3-4 bits louder. Again, this is a static measurement. Your sinewave is made of many word codes (each with their own error).
It will for sure result in a distorted sine wave and it would be interesting to do a simulation and get the classic THD and SNR out of it.
This could actually result in a "tube like" distortion (which sounds cool 8) )
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Also, your sinewave won't be 3-4 bits louder. Again, this is a static measurement. Your sinewave is made of many word codes (each with their own error).
It will for sure result in a distorted sine wave and it would be interesting to do a simulation and get the classic THD and SNR out of it.
You are right. Sine wave don't get louder given the randomness of nature and how it evens out. But parts of the sine wave will be louder, and parts softer. Yup. Think of the curved lines of the sine wave being all crooked and shit. Lack of relative accuracy = distortion. Hmmm. Makes me wonder about a measurement of a specific DAC where there was a lot of high frequency hash on the distortion measurement.
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The high frequency distortion will likely get filtered out down the chain, unless it folds over or makes other things sweat blood.
Also, if you have an ideal situation, the S/H will produce high frequency out of band crap anyway. Maybe less than DS but still would need to filter that out.
I think one difficulty I can see with DS INL measurements is that the signal doesn't "stay" fixed in between samples the way a ladder DAC does (which BTW is distortion in itself given the original signal did not look like an aztec piramid in the first place). The delta sigma output will have to go through a filter to make any sense (at least the other DAC gave an Ziggurat looking waveform), and in between samples it will get smoothed out by the filter. One would have to recover the clock or align things up, but filters will introduce an offset which will make alignment difficult (not to mention phase distortion). That's my best guess of what it is meant by DS not being static.
ladder DAC after filtering will not be static either...
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May or may not be related (as you can tell, I'm pretty uneducated in this area), but one of these DACs with these supposed chips did have some interesting measurement results from an unorthodox test. With a 1-minute sample of some 16/44.1 music, measured and averaged in ARTA (exp mode) and zoomed in to show small differences, there were noticeable variations with the three test results. When upsampled to 24/176.4 via playback software, the results matched much more closely. Almost identical. Related or not, or what that would mean in the end exactly, I'm not sure. (Would have to run tests on other DACs to see how they handle this weird test - thought this was done, but can't find evidence of it here...faulty memory, perhaps.) Again, not an expert, so apologies if this is dumb.
So, going back to the LSB errors, it is interesting to speculate and test A) how that might affect other, more commonly used DAC measurements and B) how that might affect what we hear subjectively in the end.
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Another thought: how did they measure this LE plot? Is it a statistical deviation for multiple chips? One chip?
Stacking multiple chips could be a way to partially cancel these non-linearity (if the chart is not already a statistical mean/median for several chips).
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It's Typical Chart, so proly one sample chip. Not sure if it would be a median though.
LOL, that's a 3 MSPS DAC.
http://www.ti.com/lit/ds/symlink/dac8581.pdf
BTW: One thing that maybe done is to set the delta sigma to fixed DC codes and get points out of it. But that will include not just the IC, but the entire solution and it could be a little time consuming (2^24 codes! ... and forget about 32 bits). One would have to wait for the DS to settle. Maybe one could do jump multiple steps? Not sure about automation.
Ha, say we take a DC value 1 second and a time... We will be done in 6.5 months. 70 years for a 32 bit DAC. Would have to skip or take samples quite a bit faster. But again, that would require some automation. Maybe play a stair case deal. Dunno how long to wait for the settling time. Will think.
EDIT: Forget it. Delta Sigma has memory and outputs will depend on previous inputs. That means that if we did the stair case deal, we would likely be off still. Thats because if we tried a different random stair case or indeed any other signal, we might get completely different results. LOL! Guess that explains why we didn't get those INL/DNL specs from the analog dudes, and worked of the ENOB and SINAD... I did also work on some digital delta sigma stuffs, but did not have to deal with this INL/DNL crap. We were more concerned with ppm jitter which I guess is kind of related. The part that made it easier is that we only had to be concerned with certain discrete codes.
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I guess I can try comparing source from recording using my crappy 2i2 DAC, filters, board, amp, wire, and so on. And hope my 2i2 ADC + whatever other randomness is in the signal path doesn't crap things up :-[
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Well, would you use one of these DACs for audio?
(http://www.changstar.com/index.php?action=dlattach;topic=1793.0;attach=7688;image)
Do you want to be up to 15 LSBs off? Which for 16 bits, means 4 bits off? So how would you like to 3 to 4 bits louder than you are supposed to be from 0.20V to 0.40V on a 2V output DAC?
I have a completely different view than you have.
Here it goes:
1LSB = 1/65536 x 5.657V (for a 2Vrms out DAC) = 0.086mV
The DAC can be off +/- 15 bits
This is due to tolerances of the MSB, 2SB and 3SB which needs an extremely small tolerance because of the LSB.
So the DAc can be 'off' 15x the 'size' of 0.086mV = 1.29mV (which still is a LOT) in an absolute sense.
so a 2VRMS sinewave may be 'off' 0.9mVRMS around the '0V' line (-67dB).
It looks like 'crossover' distortion.
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Y'all need moar of this in yo life - http://www.diyaudio.com/forums/vendors-bazaar/259488-reference-dac-module-discrete-r-2r-sign-magnitude-24-bit-384-khz.html
I'm 95% sure that I'll build one if nothing too nasty pops up in the initial tests of the production boards.
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I've been keeping my eye on that.
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The guy uses 0.01% accuracy resistors (you can also order one made with 0.02% and 0.05% accuracy resistors)
AFAIK (but may be wrong here)
This may yield an ENOB of around 13 bits
The 0.05% ladder may even end up with just 11 bits ENOB (depending on the actual accuracy of the MSB and 2SB resistor)
To create a ladder that has 16 bit accuracy the MSB resistor has to have 0.0015% accuracy
To create a ladder that has 24 bits accuracy the MSB must be 0.00006% accurate
The culprit lies in the 0V audio line where 100000000000000000000 switches over to 011111111111111111111111 (this is for 24 bits)
All those 011111111111111111111111 bit values added must sum to the same value as a single MSB (-LSB)
Now you know why it is so hard to create a good (high ENOB/accuracy) ladder DAC chip and why the ones with a high ENOB are expensive.
undoubtably the DAC will sound good though.
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The guy basically says that the topology he uses (sign magnitude dac?) doesn't play by the usual R2R rules. The numbers he showed are very good for a 0,05% resistor array. My main worries are about the PPM and how thermal drift will play in this design.
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He says this in the first scentence:
It's a DAC module based on a discrete R-2R sign magnitude DAC design
When he uses 0.01% in the MSB to 3SB positions and uses 0.05% for the rest he may well get decent results.
I did kind of 'miss' the sign magnitude part though.
The sign magnitude part is where the DAC never crosses the 100000000000000000000 to 011111111111111111111111 border so no crossover type of distortion but there still will be the linearity problem.
It is basically 2 R2R ladder DAC's departing from the LSB, one in the negative direction and one in the positive direction of which the signals are combined.
This can also be done with 2 of the shelf ladder DAC chips per channel, but takes a conversion stage so the DAC sections receive the correct bit pattern.
The non-linearities are simply found in other parts of the INL line, just not in the middle any more also the tolerance issues of the MSB are still equally relevant.
The pricepoint is fun though.
I have other worries as well :D
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I would have been happy with 16 real bits and 44.1kHz. My concern is that the design target is too ambitious = wasting time trying to hit those excessive requirements. 24/384 for discrete ladder DAC? Why?
People too concerned with unnecessarily large numbers.
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Does INL/DNL really matter for audio? It is a static measurement. Don't know if those plots make sense for S-D DAC anyway.
This is what ultra and I have mentioned before. The reason you don't see these plots on S-D DACs is because it's not considered a relavent spec for their applications. For other applications, it can be critical.
Although it would be interesting if pirates found a correlation between that spec and perceived sound quality.
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Does INL/DNL really matter for audio? It is a static measurement. Don't know if those plots make sense for S-D DAC anyway.
This is what ultra and I have mentioned before. The reason you don't see these plots on S-D DACs is because it's not considered a relavent spec for their applications. For other applications, it can be critical.
Although it would be interesting if pirates found a correlation between that spec and perceived sound quality.
Challenge accepted!
See you in a year, or 10!
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It can take a long time depending on how one approaches the problem. I can also see INL/DNL measurements being a bit off for delta sigma. Unlike with ladder DACs, if one puts different waveforms to test linearity one might get different results.
Say we use a ramp going from low code to high code, and then another ramp going from high code to low code. Even if we held the ramp values for a while to account for the fact that delta sigma is bandlimited after the LPF filter (otherwise it's just random 1's and 0's/-1's) and therefore not "static", either ramp waveform might yield different linearity results. This perhaps because of the behavior of the DS accumulators (memory). Most designers obviously just go for other metrics.
There might be a way to properly do this, but I don't know how yet. Maybe ignoring the possible waveform dependence and just using a ramp from low code to high code and waiting a few ms per capture is sufficient. There are some cases where delta sigma INL is reported, but mostly in ADCs (not DACs). From the TI military applications catalog: http://www.ti.com/lit/sg/sgzt005/sgzt005.pdf
Consider the ADS1258-EP 24-bit 125 kSPS 24-bit delta sigma:
http://www.ti.com/lit/ds/symlink/ads1258-ep.pdf
Reported INL is 0.0003%, or 2^24*0.0003%/100 = 5 LSB INL
Consider the ADS1278-EP 144kSPS 24-bit delta sigma (about 18 bits of resolution)
http://www.ti.com/lit/ds/symlink/ads1278-ep.pdf
Reported Typical INL is 0.0003% (5 LSB)
Not all military app delta sigma ADC report INL. Don't think PCM4202-EP does.
There is a military audio DACs in that document: PCM4104-EP. It is a delta sigma 24 bits, and it does not report INL information. It is about 19 bits of resolution.
These are proly mostly for audio applications, and not necessarily high rate which might require a different architecture. I can see however a different architecture successfully used in audio applications if sufficient resolution is provided in the audio band.
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I believe JA did it but slightly differently in Fig 6. http://www.stereophile.com/content/quality-lies-details-page-5
He claims that it would be excellent but not necessarily a make or break measurement for a DAC though. Getting to parts and their influence on sound quality, I wonder how would the proposed linearity measurements changed with say different PSUs or parts?
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I believe JA did it but slightly differently in Fig 6. http://www.stereophile.com/content/quality-lies-details-page-5 (http://www.stereophile.com/content/quality-lies-details-page-5)
He claims that it would be excellent but not necessarily a make or break measurement for a DAC though. Getting to parts and their influence on sound quality, I wonder how would the proposed linearity measurements changed with say different PSUs or parts?
Yes, JA measured linearity with 1kHz sine. Different from bit / word code vs. output linearity. Basically steady DC output instead of Sine @ certain dBFS.
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Given Bruno Putzeys approach to DACs I'd love to hear him weigh in on this thread.
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Yes, JA measured linearity with 1kHz sine. Different from bit / word code vs. output linearity. Basically steady DC output instead of Sine @ certain dBFS.
Makes sense, for the same reason he is using dBFS on the x-axis instead of DAC code, and dBr instead of LSBs.
Interesting that JA mentions the practical lower limit for linearity is about 18 bits.
I do wonder how a ladder DAC will perform using this different approach to linearity measurements. It's not classical for ladder DACs based on what I recently read. I expect not too different though and might be more practical for delta sigma DAC measurements. I mean, linearity might be frequency dependent (hopefully slightly), but music is not just 1kHz tones or DC static signal. I do agree is probably not as "clean" or "elegant" or "valid" an approach as the DC one, but it's proly a bit more practical for some architectures...
Measured differences (between approaches even) might indeed correlate to perceived performance differences.
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LE and THD look actually better with software trimming (DAC8581):
(http://clemmaster.free.fr/Pics/DAC8581%20-%20software%20trimmed.png)
It is not impossible software trimming is used in the well known NOS DAC (in the "glue logic" that formats S/PDIF inputs to the DAC's word input).
cf p.11 IMPROVING DAC8581 LINEARITY USING EXTERNAL CALIBRATION
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This is interesting. Said DACs have similar looking THD measurements. 2nd order right in between -70-80dB, 3rd a bit higher, 4th drops a bit, 5th is up a bit from 4th, 6th drops from 5th.
Not an exact match by any means, but the pattern is similar.
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Meaning no trimming is done? Doh...
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No idea. Mind offering a brief explanation or link on what software trimming is exactly?
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Measuring the linearity of the errors of the DAC per bit-code and then programmatically adjusting it so the error is less. It's not 100% perfect as linearity will fluctuate with temperature and other factors. Obviously it seems it can only be done with R2R DACs.
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Ah, OK, thanks for the explanation.
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Here is the lengthy explanation:
http://liu.diva-portal.org/smash/get/diva2:559515/FULLTEXT01.pdf (http://liu.diva-portal.org/smash/get/diva2:559515/FULLTEXT01.pdf)
page 47 and up .. put your math cap on !
For Delta Sigma a correction is not needed for linearity as it is enclosed in the algorithm.
(http://archive.siliconchip.com.au/static/images/articles/i1127/112766_6lo.jpg)
picture is from this article: http://archive.siliconchip.com.au/cms/A_112766/article.html (http://archive.siliconchip.com.au/cms/A_112766/article.html)
The Delta Sigma CS4398 chip for instance has great linearity (as shown above).
When considering 16 bit accuracy it isn't even 0.1 LSB 'off' at -100dB
When considering a 24 bit accuracy it is about 2 LSB 'off' at -100dB (it will get worse below -100dB of course)
Even though the Delta Sigma is just an 'approximation' the 'approximation' is more accurate than most R2R DACs
An R2R chip output has 'steps' which has to be 'smoothed' if you want to get rid of HF garbage.
Most NOS DACs that can handle make no effort and expect the speaker or headphone to do the smoothing for you, otherwise your ears will.
Smoothing can be done by either up-sampling (inventing = approximation of in-between values) or by a rather steep analog filter which also basically 'connects' between the output time steps more smoothly (and thus 'approximating' in-between values) by an RC-time constant.
In the end it seems to come down to differences in the 'in-between' values and how they are generated and linearity problems in R2R DACs because of tolerances of the MSB and the bigger bits below the MSB compared to the LSB.
No idea how this would translate to audible effects and can't wait till someone has a clear answer.
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Different kinds of linearity measurements we are talking about. That "linearity" graph for from the siliconchip website is 1kHz sine wave output at different levels. The linearity graphs on page 50 of the PDF is output vs. code bit/word. (specific DC, not sine waves)
R2R can also have great linearity plots if using the 1kHz sine wave. SFD-2 below:
(http://www.stereophile.com/images/archivesart/Sf395fig5.jpg)
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Yes of course it is a totally different type of graph.
Making an INL plot of a SD DAC is pointless.
The INL plot in a ladder DAC tells something about the noise you get switching from bitlevel to bitlevel.
This varies from bit to bit.
With DS the 'jump' in output voltage level (quantisation noise) is always quite similar in amplitude where it is not in R2R (be it signed magnitude or 'conventional').
With a few bit DS there are small errors of course but these are much smaller than multibit ladders of course.
Still the sine linearity does say something about how accurate a DAC is but not in the same way as INL and DNL plots.
The SFD is not your typical ladder DAC though and somewhat differently priced from DS DAC chips and current ladder DAC chips.
The question remains how linearity translates to sound quality.
Given the fact that this linearity subject doesn't come up with vinyl/tape, which suffers from even bigger linearity problems (noise and mechanical 'problems' than digital does, tells me linearity may not be that important to obtain 'natural (organic) sound'.
Digital 'processing' of the signal, upsampling algorithms, DAC chip implementation, signal routing, PCB design, power supply, electric isolation and post/reconstruction filtering seem more important aspects to me than linearity of a chip in the DAC-device.
It stands to reason linearity should be good and at least a decent ENOB should be reached.
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We've already postulated that INL type plots may be pointless / impossible for SD DACs because they add pseudo random noise to the bitstream so that INL results would differ from moment to moment.
But who knows. I've never felt increased linearity (bit code vs output) equated to organic or natural sound. If you go back, you'll notice that my suspicions were that increased linearity = more detailed, higher resolution sound. Is why the modern S-D DACs sound more detailed?
I believe that in most implementations, one bit does have better overall linearity (again bit code vs output) than the R2R DACs. However, I do suspect that the more patterned or consistent linearity errors of R2R DACs maybe have some to do with the more natural sound of R2R DACs since we are not randomly injecting all sorts of noise in time to the bitstream as S-D DACS do. Of course all this noise is filtered and we shouldn't hear it. And obviously maybe it's the noise-shaping and filtering mechanism which results in S-D sounding different.
One thing I've noticed is that companies like MSB - their higher priced DACs have the more linear modules - the MSB DACs sound basically the same tonally as we go up - with the only difference being better extraction of low level information.
Similar thing with my DCX2496. Seemed to be more resolving when I paralleled the three output chips instead of using one.
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One thing I've noticed is that companies like MSB - their higher priced DACs have the more linear modules - the MSB DACs sound basically the same tonally as we go up - with the only difference being better extraction of low level information.
Could it be that in the case of these DAC's the perceived difference in SQ is NOT just DAC linearity related but could just as well be caused by more careful/correct implementation of Digital 'processing' of the signal, upsampling algorithms, DAC chip implementation, signal routing, PCB design, power supply, jitter reduction, electric isolation and post/reconstruction filtering circuitry ?
Except for the obvious digital and analog filtering all the other aspects have nothing to do with tonality and can make a difference.
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One thing I've noticed is that companies like MSB - their higher priced DACs have the more linear modules - the MSB DACs sound basically the same tonally as we go up - with the only difference being better extraction of low level information.
Could it be that in the case of these DAC's the perceived difference in SQ is NOT just DAC linearity related but could just as well be caused by more careful/correct implementation of Digital 'processing' of the signal, upsampling algorithms, DAC chip implementation, signal routing, PCB design, power supply, jitter reduction, electric isolation and post/reconstruction filtering circuitry ?
Except for the obvious digital and analog filtering all the other aspects have nothing to do with tonality and can make a difference.
Hmmm....considering the price & engineering chops behind all the MSB DACs, I think we should expect that even their cheapest DAC ($7k) has all those qualities nailed down. Maybe you could point out the specific differences that would possibly lead to improved SQ/resolution/low-level information extraction using this chart:
http://www.msbtech.com/products/dac4comp.php?Page=dac4home
Or maybe dig up some photos of the DAC insides and tell us where they have to make certain compromises that would lessen SQ/resolution/yadda yadda on their lesser models.
Or just tell Marv that he's a retard and indulging in placebo :spank: walk the plank2
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I think you completely missed my point. :)p8
What I said was that good SQ is not solely determined by linearity but the other aspects I mentioned as well.
You just now assured me they nailed them, so all aspects that lead to 'good sound' are there which was my point.
Its not just linearity, its ALL the aspects that need to be O.K.
Should you have any proof that the most expensive version and the cheapest ones ONLY differ in DAC module (linearity) and THAT's what causing them to sound different/better then I will admit publicly that I am retard. :-\
I may not agree with everything that is written, stated or believed to be 'true' just like you (and a few others most likely) don't agree with what I have to say (and do).
However, you won't see me telling Marv (nor others) they are retards nor that they are indulging in placebo.
Please don't put words in my mouth.
I feel I am free to question everyones thoughts, debate, offer counterpoints and everyone is free to reply (in a civilised manner).
I simply post my opinion, just like the rest of us here, even if you don't agree or don't like me or my opinion.
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You can't seem to take a joke mate.
We both agree that those other aspects affect SQ, fine. But I don't think that the lower tier MSB DACs are behind held back by their PCB layout, routing, etc. Or at least I hope that's not that case.
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Looks like Metrum recently announced a new OEM DAC module, chip, something like that (I'm guessing it utilizes the DAC8581 still): http://www.transient-audio.nl/ (http://www.transient-audio.nl/)
"The Dac One is a modern high precision replacement for old dacs very often used in "non oversampled" systems like the old TDA 1543 and TDA 1541. It is not a pin compatible replacement but a way to build up an converter system which can meet the best systems today in terms of sound quality.
The Dac One is build up around a fast 16 bits and very accurate R2R ladder network. To match this ladder network to real audio formats, fast glue logic is added and makes the dac compatible with RJ16, RJ24 and I2S standards. Like one bit dacs, the Dac One can handle 24 bit resolution due to forward control techniques as realized with our FPGA based "Forward Correction Module"
The ladder network is designed as a current output device so to get a voltage out an I/V converter is needed. Depending on designers needs the Dac One is available in both current and voltage output versions."
Specs (actually lists LSB accuracy and differential non-linearity): http://www.transient-audio.nl/Technical_Specs.html (http://www.transient-audio.nl/Technical_Specs.html)
Datasheet (not as much detail as you might hope): http://www.transient-audio.nl/Dac%20One%20datasheet.pdf (http://www.transient-audio.nl/Dac%20One%20datasheet.pdf)
I noticed this reports lower THD than the Metrum DACs as well, 0.008% vs 0.03-0.04% (Hex measured between 0.01-0.02% when I had it, but official specs say 0.03-0.04%).
Also some recently posted PDF on Metrum's design philosophy. Not that I necessarily buy into some of this, despite liking the Metrum sound, but some interesting ideas: http://www.metrum-acoustics.com/Design%20Philosophy%20Metrum%20Acoustics.pdf (http://www.metrum-acoustics.com/Design%20Philosophy%20Metrum%20Acoustics.pdf)
I think it was solderdude that was curious how NOS would change measurements after going through the chain and coming out of a driver. I noticed the Metrums I tested did NOT sound right if you played high frequency sine waves, especially above 10KHz, unless at levels well below 0dB (to be fair, music likely isn't going to have treble signals at 0dB). Think dial-tone from a 56k modem. The NOS1704 sounded pretty regular up top in comparison, but also had considerably lower measured THD. Both have weird looking sine-wave results straight from the DAC if you test with an oscilloscope, but I have been meaning to run some more tests on HP measurements to see how NOS DACs affect them. Unfortunately, I just sold everything but the Classe DAC-1. Some day...
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Thanks hans!
Isn't their "Forward Correction Module" the software trimming I mentioned few days ago?
They have better linearity specs than the DAC chip, for sure.
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I had the same thought when I read that. I was going to make a joke earlier that Metr...uh, said DAC manufacturer was saving software trimming for future, moar better products (assuming they don't trim already based on measurements)...and now I'm wondering if that would not have been much of a joke.
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Their Evaluation Module can accept I2S.
Anyone willing to get a cheap Audio-gd I2S board and mate it with Metrum's EVA? headbang
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There's some discrete R2R DIY kit that is claiming better performance than the PCM1704 and decodes 24/384 (uses 28-bit path):
http://www.diyaudio.com/forums/vendors-bazaar/259488-reference-dac-module-discrete-r-2r-sign-magnitude-24-bit-384-khz.html
Kind of interesting.
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Some of our guys are on board that ship. I look forward to seeing where they go with it. I think I might hear it sometime since some of the locals in Singapore bought modules too.
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I'm wondering, after hearing the Yggy and reading some stuff on this forum hinted at my Moffat (some of which was echoed by Moffat at RMAF: 'reproducing the bits unchanged'...'military/aerospace accuracy')...if great R2R is all about having enough trim and being able to calibrate a look-up table (or equivalent by knowledge of every resistor coefficient) to generate accurate output voltages. The soekris Reference DAC on diyaudio may just be the thing, if it has enough trim and already comes calibrated or if one has the capacity to calibrate and feed it corrected codes. The distortion plots of the soerkis DAC show a similar character to crossover distortion at higher levels, so I'm not confident. Wonderful board and project though...much jealousy.
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Signed magnitude R2R has the same problem as normal R2R (regardless if Soekris feels this isn't the case) but it just shifted to half the output voltage AND is also non symmetrical.
The problem is thus shifted, and doubled, as it occurs differently on the positive and negative half of the output signal, so is not eliminated nor has it become less relevant.
The 'crossover type distortion' is still there and equally 'bad' and still can affect small signals.
Small signals are superimposed on larger amplitudes and is thus not restricted to the '0V line' for AC signals.
Very similar to amplifiers that are partly in class-A and haven't been designed that well.
It isn't anything 'new' or revolutionary either the 15 year old PCM63 also had this topology but called it colinear.
You could improve this by changing the actual output codes (forward correction) to be closer to the desired output voltage but you would have to do measurements and apply it on each individual DAC/channel and will be hard to do yourself unless you have the needed test equipment and programming stuff.
It will be a different correction for positive and negative halves of the output signal as well.
As I mentioned a few pages back.... even 0.01% parts for the MSB isn't enough.
Still, even with those linearity errors the DAC will, most likely, still sound excellent to many ears.
As it doesn't have a proper reconstruction filter (nor do other NOS DACs in general) for lower bitrates the >6kHz signals will still suffer from 'roll-off' which makes these DACs 'mellow' sounding. That roll-off isn't 'fixed' though and highly depends on the output frequency/sampling frequency relation (whether they happen to be in 'sync' or not at specific points in time).
So while Kees's (Metrum) theory may be valid for 1kHz sine wave signals (the drivers and ears combined are acting as a >8th order smoothing filter) the drivers and ears do not act as a proper reconstruction filter (it needs to be ringing to do so) at all and thus the higher frequencies DO sound different from the signals that had been recorded.
Of course some roll-off seems to be preferred by many so may be a blessing to some and be viewed as 'increased fidelity' by (varying) lack of upper treble.
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Does anyone have any particular recommendations for vintage DACs out of stuff like the PCM6x/5x, TDA15xx, AD18xx, and so on? Datasheets are helpful but only go so far. Am most curious about performance in good implementations that these datasheets won't say anything about, or just general characteristics (tone, for example) of these various chips. I know they're just one part of a DAC, so a loose or generalized answer is OK.
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Added LH DAC vid to first post for reference and further discussion should it arise.
http://www.youtube.com/watch?v=HIAqtblSmjQ
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Slots and stuff, see that TONS in multimeter and bench designs, but none in audiophool stuff and I don't remember seeing them in AGD DACs too. Ground plane and clock layouts are very thorough and again, I don't see them much in the bareboards I looked at in my limited exp.
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Slots and stuff, see that TONS in multimeter and bench designs, but none in audiophool stuff and I don't remember seeing them in AGD DACs too. Ground plane and clock layouts are very thorough and again, I don't see them much in the bareboards I looked at in my limited exp.
Audio-gd use separate boards for digital and analog altogether (in the TOTL designs, at least).
The clock trace thing is basic electronics, though. You obviously want them to be equal length for both DACs.
I don't like to see different shapes for both traces, though. Placing the clock in the center and a mirror design is more reassuring to me.
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the squiggly line will have different trace impedance, which is bad.. that's what my electronics mentor friend says. It's only a single pcb so maybe it was done this way for space saving? Anyway it's pretty cool for the designer to explain his board layout. This is going to be my first nice dac so I hope it doesn't suck. What exactly do the slots do? does it prevent noise?
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The Master 7's(and their other DACs) routing comes across to me as a little neurotic though, power runs right below the boards with the trannys right beside all 3 boards.
Actually the slots are more to prevent interference by conductivity. You see it all the time in bench equipment and multimeters where the application is to isolate high voltage components from the rest of the board. Below is my Fluke 8060A, you can see a few slots which I reckon are where some of the high voltage components are since its located near to the AC/DC test switches. As my meter is not Cat rated, there are no slots at the inputs which you would normally see in a modern yellow Fluke.
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Placing the clock in the center and a mirror design is more reassuring to me.
I'm glad you said that, because I thought it... and I have no clue about electronics or circuits. p:8
The guy has real geek glasses and a a real geek hat, but that is probably not good judgement criteria. :-[ Interesting to see here what more knowledgeable people have to say.
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I'm glad you said that, because I thought it... and I have no clue about electronics or circuits. p:8
The guy has real geek glasses and a a real geek hat, but that is probably not good judgement criteria. :-[ Interesting to see here what more knowledgeable people have to say.
They are fitting a lot including dual mono, dual femto clocks and integrated dual balanced amp into a relatively small package. Also bear in mind the price point it was offered at.
I would have thought looking at the board it was obvious they were trying to cram as much as would fit into the space available. Maybe I need to borrow your guy's Geek glasses. :)) ;)
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Hmmm... makes me think that both the glasses and the hat might be just very practical choices for the job! facepalm
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there's an english project to make an Integrated amplifier with dac and raspberry pi inside.. the designer goes into detail on his design choices and the internal components and how he programmed the dac.. it's pretty in depth
http://audioberry.com/hardware/junior-versatile-digital-integrated-amplifier/
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Marv,
given your opinion on the Sabre sheen, how different is the implementation in the Geek Out devices such that they are liked in this forum?
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Dunno if anyone cares, but since I mentioned it earlier, I thought I'd dump some of the new info Metrum released on their new DAC. It will indeed be based on the new "Transient" modules, no surprise, though I have no clue if they're still utilizing the same DAC chips as before or not in these modules. Those modules alone on paper had better specs than what Metrum had put out prior.
Metrum recently released info on the FPGA/DSP "forward correction module" they're using in the new DAC (probably software trimming that has been discussed?): http://www.transient-audio.nl/FPGA_module.html (http://www.transient-audio.nl/FPGA_module.html)
Page on the new DAC itself: http://metrum-acoustics.com/PavaneEN.html (http://metrum-acoustics.com/PavaneEN.html)
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What is the module "forwardly correcting"?
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Probably will remain unanswered like all the other things Metrum tries to keep a mystery (i.e. DAC chips, other chips used). Hopefully it's the software trimming stuff mentioned earlier, at the very least, assuming same chips are used.
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forward correction = changing the input code to achieve the correct output voltage = software trimming.
It involves characterising each channel/chip individually and 'figuring out' which input code is needed to obtain the correct output voltage.
This also works for linearizing signed magnitude.
It only takes a database and 2 clockpulses to implement.
The 'incoming' sample code is 'replaced' by a sample code that is closer to the desired value and you are done.
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This came out a while back and maybe some of you guys might be familiar with the stuff being said here but its interesting nonetheless, an article on ultra low distortion design.
http://www.ap.com/display/file/747
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Don't remember seeing it posted here.
An extensive list of DAC / CD players with their DAC chips: http://www.dutchaudioclassics.nl/the_complete_d_a_dac_converter_list/#M
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For sigma-delta, noise shaping would be used. This of course would introduce a entirely different type of linearity errors, but given how sigma-delta works, the overall error would be less.
....
Now how does this correlate to what we hear? Those of you who have heard enough DACs, quality DACs that is of both kinds, know that resistor ladder and sigma-delta sound different and have different strengths. The best sigma-delta implementations sound highly detailed with sharp attacks. The best resistor ladder DACs sound smooth with natural timbre.
....
Maybe greater linearity = more resolving (it's true mathematically, but is it true subjectively?) Maybe linearity error plots with certain more predictable patterns = smoother more natural sound?
Very interesting! I know I'm quite late to the party, but it just struck me how this proposition is somewhat analogous to Nelson Pass' comments about negative feedback in amplifiers - that negative feedback decreases total THD, and improves other standard audio measurements, but at the cost of adding new complex distortion components/nonlinear distortions, particularly of high order, that many people perceive as unnatural. https://passlabs.com/articles/audio-distortion-and-feedback