DACs seem to be popping up everywhere now, especially USB DACs. They are integral to SSPs and receivers, but are also available as stand-alone DACS, some inexpensive, and some very expensive.
DACs are not very well understood by the average audiophile, including yours truly. All we really want is for it to do a good job decoding the digital signal and send high quality analog audio to the amplifiers.
One perfomance characteristic that has not been given enough attention is “Linearity” This refers to how linearly the output follows the input.
The following figure shows a theoretical DAC that has perfect linearity. It’s expressed in dB, since the digital input is dB. So, at 0 dBFS, which is defined as 1 volt, the input and the output are the same: 0 dB or 1 volt. The actual output will be more than one volt, since preamplifiers need several volts to work with. This comes from the op-amp that is fed by the DAC’s own output.
So, let’s take a look at a DAC. I don’t identify the DAC brands because this is not about them. It’s about DACs in general.
DAC 1 is linear down to about -95 dB, where it begins to flatten out. The noise floor is -110 dB. What this means is that all the musical detail that is between -100 dB and -95 dB gets raised to -95 dB. We can’t say if detail lower than -110 dB is raised because that detail is buried in the noise floor.
Somewhere in the range of -80 dB to -90 dB, is the limit of our ability to hear recorded musical detail. Of course this depends on several factors, such as how good your hearing is to begin with, or if you are using headphones, but it is a good rule of thumb.
So, if DAC 1 has a noise floor is -110 dB, and it is linear to -95 dB, musical detail that was recorded at -1oo dB gets raised to -95 dB, and you just might be able to hear it if you have good hearing and are using headphones. This would give the sense that the music has a lot of detail, when actually it is detail that you shouldn’t be hearing at all, because it was recorded at -100 dB, well below audibility.
The Y axis on the right is the output, expressed in dBr. The Y axis on the left is voltage output, corresponding to the dBr values on the right. The X axis is the input, expressed in dB. So, at 0 dBFS input (X axis), the output is 32 dBr (right Y axis) and 4.4 volts (left Y axis). Click on the Linearity graphs to see an expanded version that makes it easier to read the X axis.
Of course, this depends on the DAC having good Time Domain response. Here is a Time Domain spectrum (1 kHz, 24 bit) for DAC 1 at -110 dB. Notice that the waveform is clearly defined. So, with this DAC, you would hear that -110 dB detail rather distinctly, particularly during quite musical passages.
Here is the linearity curve for DAC 2. The linearity begins to flatten out at about -85 dB. The noise floor was -120 dB. So, all musical detail between -85 dB and -120 dB would be raised to an audible level (-85 dB). If the noise floor were -85 dB, then the flattening would have been due simply to the noise floor, and no detail lower than -85 dB would be audible.
The Time Domain spectrum for DAC 2 is shown below. The waveform is not as distinct as compared to DAC 1, so the fine musical detail would not be quite as clear.
If the flattening out of the curve at -85 dB were actually just the noise floor, the -110 dB sine wave would not be seen. It would have just shown a noise spectrum.
Here is a 1 kHz sine wave at 0dBFS from DAC 2. Note that the noise floor is at -120 dB. Both the linearity curve and the 1 kHz sine wave spectrum shown below use dithered test signals. The Time Domain is measured using an undithered test signal.
DAC 2 is actually much more expensive than DAC 1 (in the thousands of dollars), and yet the time domain is not as good. I liked the sound of the enhanced detail, which was very noticeable, but if you didn’t know that it was due to the DAC, you could attribute it mistakenly to the SSP or receiver.
I will be adding more data to this particular blog as I obtain a few more DACs, particularly the inexpensive USB DACs that proliferate the market (e.g., $399).
John E. Johnson, Jr.
Editor-in-Chief
The author wishes to acknowledge the comments and suggestions from Nelson Pass and David Rich.
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I'm surprised that you want to make this argument. It comes over as an attempt to post-rationalize reasons for DACs to sound different, other than frequency response, loudness, and impedance matching.
Try this test. Prepare a .wav file of a section of music at normal levels. Now make a duplicate but at -85 dB lower level. Play the normal piece at a loudness you are happy to listen at. Now play the quiet piece without changing system volume. Can you hear ANYTHING AT ALL?
Now consider this: the quiet (silent?) piece was all of the music, whereas your hypothesis only relates to the portion of the music that lies below -85 or -95 dB, being a tiny glimmer of the full signal. Or, try the above test, but the quiet piece being the original piece with all content stripped above -85 or -95 dB. It will only be harder to hear (essentially noise).
Also consider this: the demonstration tests that I proposed are super-resolving tests compared to reality, where the signals you are trying to hear in the above tests are swamped to the magnitude of 90-odd dB but the full-scale musical signal. Truly obliterated and inaudible.
Disappointing to think that Pass and Rich contributed to such loose thinking.
You try your own tests. I already have heard the effect of a low linearity DAC (the 85 dB one - and the low level detail was highly emphasized). If you don't like the data, that doesn't mean they are wrong. Nelson Pass is one of the most respected design engineers in the world. Your proposed tests are your own affair.
You try your own tests. I already have heard the effect of a low
linearity DAC (the 85 dB one – and the low level detail was highly
emphasized). If you don’t like the data, that doesn’t mean they are
wrong. Nelson Pass is one of the most respected design engineers in the
world. Your proposed tests are your own affair.
I am a huge fan of Nelson, his contribution to audio, his original thinking, and his generosity to the DIY audio community (of whom I am one). That's why I am disappointed to see him contributing to an article that reeks of post-rationalisation, i.e. attempting to come up with a hypothesis to explain why some audiophiles react negatively to 'digital sound' in uncontrolled listening conditions, then back it up with measurements and graphs, but make no attempt to close the gap between 'something is measurable' and 'something is audible'.
If my proposed tests "are your (my) own affair", then who was it that wrote "if the musical detail that was recorded at -110 dB gets raised to -95 dB, you just might be able to hear it if you have good hearing and are using headphones" in your article? Was that you? By writing that, the author surely made himself interested in my proposed tests, or test of his own construction to answer his own question. It's YOUR topic, not mine.
I didn't try to rationalize why some audiophiles react negatively to digital sound. In fact, I liked the effect. This was a scientific experiment. I heard an unusual amount of low level detail in the sound when testing a DAC, and I hypothesized that it could be a linearity issue. I measured it with an Audio Precision and proved that the increased detail was due to the linearity flattening at an audible level (85 dB). And, I did close the gap between something measureable and something audible. I heard the effect and I measured it. That was the purpose of the experiment. You need more fiber in your diet.
If you don't make an attempt to isolate and observe the electrical effect in controlled listening conditions, then you have no experiment because you have no proven link between cause and effect. This is fundamental stuff. What you have is an hypothesis with a sense of logic to it. You have no experiment that has any rigour. Not yet anyway. I'm not arguing, I'm advising you. At this point you are seduced by the *apparent* link between your prior casual observations, and a real measurement, that may or may not be audible, but needs to be properly tested for audibility. Not assume that "oh, that's it all right" because of the seductiveness of the logic that links 'detailed-sounding sound' to 'dynamic compression of the quietest signals'.
If you had tried my suggested listening test, instead of typing replies for longer than the test would take you, I strongly propose that you would have found a serious barrier to the hypothesis that you are hearing detailed sound from DACs due to a change in the sonic component that is below -85 dBFS. This would have been very valuable information for your consideration of your hypothesis -- IMHO. I'm only trying to help, with genuine suggestions. Your responses alluding to constipation are rude and unwelcome.
I did isolate and observe the electrical effect. It was a leveling of the linearity at -85 dB. Your comments would have been correct if it were not for the fact that the linearity was the only variable that was different between DACs. I first heard the effect when testing a DAC. I was not expecting it. So, I checked the DAC, not the preamplifier, power amplifier, or speakers. Those were the same as for other DACs that I have tested previously. It had to be the DAC. I tested the electrical characteristics of the DAC and the results were different than the other DACs. The only difference was the linearity. That is proof that non-linearity can cause low level details to be heard. In the DAC whose linearity leveled off at -95 dB, the low level details were not as loud.
I have questions.
1. Define “detail”. This appears to be a subjective term in this context.
2. Is 1 KHz sufficiently comprehensive to correlate with one’s definition of “detail”? In other words, does perception of “detail” depend on the spectra of the content?
3. Do we have a meaningful metric set that we’re willing to apply for the fidelity of this theoretical 16–bit content that has been attenuated by -85 dB, and what is the dither algorithm?
4. Is there value in simulating this linearity effect for both instrumented and listening testing, by applying some kind of dynamic compression to the signal pre-DAC? The dither algorithm should be a control here, as well, hopefully derived from instrumented data.
Detail is a reflection of how much noise there is, and it is affected by a number of factors, including the use of low-output phono cartridges that require 60 dB of gain, the use of tubes, and high number of gain stages. Detail would be defined as the low-level parts of the music, such as a triangle in a classical music recording, a ride cymbal in a jazz recording, etc.
Designing a test that would provide a number that reflects "detail" has to be carefully thought out. A 1 kHz signal is not, alone, enough to execute the test. I am not sure that compression affects the amount of detail present in the digital to analog conversion. That is something that needs to be tested.
Thanks for the timely reply, following my not-so-timely posting.
The reason I ask is that I’m seeing comments on enthusiast forums that talk about “microdetail” and “plankton” that are exhibited by high-end DACs with instrumented results exhibiting lower SINAD than AKM and Sabre solutions, but offer little explanation beyond “delta-sigma sounds like ass”.
I’m not saying that cheaper delta-sigma DAC solutions sound better than the multibit DACs, but I think that *quantifying* why they sound better to many people is a key to bringing that sound down to a reasonable price point. Or, conversely, there’s the sales corollary “Where there’s mystery, there’s margin.”
Part of the eason that expensive DACs sound better is that they have higher quality analog output stages and stronger power supplies that deliver excellent transient dynamics.
You try your own tests. I already have heard the effect of a low
linearity DAC (the 85 dB one – and the low level detail was highly
emphasized). If you don’t like the data, that doesn’t mean they are
wrong. Nelson Pass is one of the most respected design engineers in the
world. Your proposed tests are your own affair.
If David Rich is part of this, I am willing to give it credence--with proper documentation. But to simply say "I heard differences" is not convincing proof of anything. The problem is that we are talking very fine (at best) distinctions between signals. It is easy to fool oneself, and we live in a world where people claim to hear noticeable differences in expensive "directional" Ethernet (!) cables when inserted into a digital system (this fiasco was reported at Ars Technica). So without more information on "how" you heard the differences, it is reasonable to be skeptical.
Don't get me wrong. I'm all for better gear. But at what point is "better" simply theoretical, and not practical or meaningful?
The differences I heard were not subtle. They were very obvious. It is what convinced me to take a look at the linearity. David Rich looked at my statements, as did Nelson Pass.
It's a beginning. The next step is to level match, and make further investigations. Obvious differences ought to be repeatable within a controlled test paradigm. Others should be able to hear it, right?
However it is, one need not spend "thousands of dollars" in order to obtain SOA performance. For example, the Benchmark DAC2 (representative of a fairly modern design, mentioned only because I am familiar with it) achieves -110dB (and better) in all performance parameters. One doesn't need to spend an exorbitant amount (certainly not thousands of dollars) for excellent performance. So in most ways all this is pretty moot.
Getting to specifics: you say there are "enormous differences" in detail between the two DACs you tested? Enormous? I've yet to hear even subtle differences among stand alone CD players, much less DACs. But that is just me.
I'm trying to figure out where your review fits in the scheme of reviews. Thanks for not being too specific with "enormous." It's better that way. Really.
I've read reviews of SOA DACs where folks write about pace, sound-stage, low level resolution and so on and so forth. One review even talked about "a lack of drive that conveys the ebb and flow of recordings." Huh? Was this a case of their NAS hooked up via a non-directional Ethernet cable, ignoring which end goes where? I looked at the OSI model in order to understand exactly where digital "ebb and flow" were derived--is it part of the data link or the physical layer? Maybe it had to do with some kind of subtle phase problem, so I started wondering about the effects of the moon.
Please forgive my skepticism and crankiness. It's nothing against you personally. It's just something derived from years of audio as a hobby, having to drown in a lot of nonsense. By the way, I owe much of my outlook to guys like David Rich. I learned a lot from his writing during his Audio Critic days. So if he's behind this, then what do I know?, and you can laugh at me because I deserve it.
Still, and once again, speaking from the real world, all of this is meaningless if one uses a reasonably priced and correctly designed DAC.
Making accurate measurements of linearity at very low levels is difficult. Usually the noise of the DUT limits the ability to measure the low level stuff. I believe the AP has some signal conditioning to help it. However both measurements you show are well below what can be had for less than $2.00 in quantity. Page 9 of this data sheet http://www.akm.com/akm/en/file/ev-board-manual/AK4430ET.pdf shows -110 dB for a DAC chip commonly available in the set top box from your cable provider (a very cost sensitive application). Seeing the performance plotted would get me reviewing all the connections and settings of the test system. (Were you measuring with 16 bit audio?.)
There was a big controversy over Bill Waslo's test software http://libinst.com/Audio%20DiffMaker.htm in which he demoed a string quartet with a Sousa band mixed in at -85 dB, which was inaudible.
The one test I would do to validate the hypothesis that the rising low level affects detail would be to transfer a known file at -50 dB and boost it on playback the same 50 dB to see if the detail (which should be much exaggerated now) is more emphasized. obviously this needs to be done with great care.