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Audibility thresholds of amp and DAC measurements

j_j

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I was thinking of including level dependent effects too like poorly chosen transformers and other non-linear effects. I have some vinyl rips from "The Final Cut" using a notorious pre-amp reviewed here. I might rum them to see what comes out. That LP was one of very few that used Zuccarelli Holophonics and some difference experiments that I did had bizarre results.
Level effects (gain, frequency shaping) are linear effects. If there are nonlinear effects we want to know them. Now distortion and compression are nonlinear effects. Noise, of course, is just noise, but yes we will measure that as well by using error spectrum.
 
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bennetng

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@nhatlam96


Apart from @Blumlein 88 's explanation in this post, you can also see my illustrations in the post below:
https://www.audiosciencereview.com/...d90-balanced-usb-dac-review.10519/post-291483
We don't listen to a high amplitude single tone, so this "filter attenuation issue" is essentially nonexistent in real audio content. If you do listen to a single tone, you have to listen it at reduced volume, otherwise it will result in deafness. Also, with reduced volume, the filter residues will fall into the analog noise floor anyway. Always remember that filter attenuation is relative to signal strength, analog noise floor of a DAC is constant.
 

RichB

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@nhatlam96


Apart from @Blumlein 88 's explanation in this post, you can also see my illustrations in the post below:
https://www.audiosciencereview.com/...d90-balanced-usb-dac-review.10519/post-291483
We don't listen to a high amplitude single tone, so this "filter attenuation issue" is essentially nonexistent in real audio content. If you do listen to a single tone, you have to listen it at reduced volume, otherwise it will result in deafness. Also, with reduced volume, the filter residues will fall into the analog noise floor anyway. Always remember that filter attenuation is relative to signal strength, analog noise floor of a DAC is constant.
There are many amplifiers that 0.03 distortion that would not look good on this chart, not that I mind.

- Rich
 

Spocko

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It's safe to say that in this modern era, we have reached a point that competently engineered DACs and amps exist for under $1000 that offer more than adequate performance because any measurable shortcoming is below the threshold of audibility due to real world noise floors masking these issues. Paying a premium for more expensive products may improve these measurements, but the listener will be unable to detect these improvements unless they (1) significantly reduce their noise floor in a sound insulated environment or (2) listen to single tone sign waves in lieu of real content.
 

j_j

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Paying a premium for more expensive products may improve these measurements, but the listener will be unable to detect these improvements unless they (1) significantly reduce their noise floor in a sound insulated environment or (2) listen to single tone sign waves in lieu of real content.
To put it another way, I think many people would be amazed at what we CAN measure with a simple USB dongle DAC/ADC.
 

rkbates

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Have you tried these tests?

Audible Dynamic Range Sound Test
https://www.audiocheck.net/audiotests_dynamiccheck.php

Blind testing a 24 dB Dynamic Range
https://www.audiocheck.net/blindtests_dynamic.php
Disclaimer - couldn't be bothered connecting the laptop to the 'good' gear so used the laptop sound card and some Bose noise cancelling headphones. 66db dynamic range 100%, 72db pure guessing. 1dB level change 100%, 0.5 db pure guessing. Not flash, but better than I expected. The big shock was 8 bit vs 16 bit music sample - no difference. I have previously tested my high frequency hearing and not much left above 12 kHz. For me then, MQA is the perfect choice for shifting high frequencies I can't hear into least significant bits that I can't hear. Probably no need to buy that $10,000 power cable now either.
 

peng

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Can someone please help me understand the SMPTE/DIN Ratio (dB) graph?

If I look at the green, "lenient" line, I can see that at 0 dBFS, IMD is about -66 dB but at -55 dBFS, IMD is -11 dB, and at -25 dBFS IMD is -41 dB. so why is -66 dB considered the lenient threshold?

My specific questions are:

1. What exactly does -66 dB IMD mean in terms of the SMPTE/DIN Ratio?

2. Do I convert the SMPTE/DIN Ratio (dB) to IMD (%) the same way I would convert SINAD (dB) to THD+N (%)

3. If the answer to 2. is affirmative, then -66 dB is about 0.05% and is therefore acceptable based on the lenient green line then wouldn't -11 dB at -55 dBFS level, that is 28.2% IMD distortion be terrible? In that case, why based the IMD at 0 dBFS and ignore the the 28.2% IMD at the lower level such as -55 dBFS, or the -41 dB/0.89% IMD at -25 dBFS? Don't we listen to music at well below 0 dBFS most of the time?

Thank you.

MD, THD+N vs frequency
For IMD, the same distortion thresholds as for FFT apply: -120 dBFS for the strict and -66 dBFS for the lenient.


1615916096930.png


1615917577984.png
 

peng

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@flipflop , can you help me in the questions I raised in thread#508 above?
RT60 at low frequencies ? | AV NIRVANA

Are you saying that at the -30 dBFS level, that I supposed for a 100 W rated amp, it would be at about 1 W output into 8 ohm, IMD (understood noise included) level of -6 dB would be acceptable based on "lenient" (the green trace) per NewAVGuy? It just seems to me the IMD vs Output graph is easier to understand and visualize as the IMD vs dBFS (I assume that's the input test signal magnitude), to visualize how bad/good it is, I would have to know the actual SPL of the test signal, but I am sure I really don't know how to interpret that graph correctly.

Thanks you.
 
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flipflop

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Thread Starter #511
2. Do I convert the SMPTE/DIN Ratio (dB) to IMD (%) the same way I would convert SINAD (dB) to THD+N (%)
The answer to your question requires some nitpicking for clarification:
a) SMPTE/DIN is a technique for measuring IMD. The 'SMPTE/DIN Ratio' is the amount of IMD measured. More info here: https://www.ap.com/technical-library/more-about-imd
On the graphs with the thresholds, the IMD is expressed in dBFS, which can be converted to a percentage.

b) SINAD is the opposite of THD+N. SINAD tells us how much of the signal is reproduced cleanly, i.e., without harmonic distortion and noise. So when you convert -66 dBFS THD to percentage, we get 0.05% THD. To get SINAD, you would simply remove the '-' and the 'FS' from '-66 dBFS': 66 dB.
Technically, SINAD could also express what we see on the IMD graphs, but you would probably confuse other ASR members if you started talking about IMD SINAD.

Getting back to your question, the answer would be "no" because converting IMD/THD (dBFS) to IMD/THD (%) isn't exactly the same as converting SINAD (dB) to IMD/THD (%).
If you had asked "Do I convert the IMD (dBFS) to IMD (%) the same way I would convert THD (dBFS) to THD (%)", the answer would be "yes".
3. If the answer to 2. is affirmative, then -66 dB is about 0.05% and is therefore acceptable based on the lenient green line then wouldn't -11 dB at -55 dBFS level, that is 28.2% IMD distortion be terrible?
The mistake you're making here is that you read the distortion level from the x-axis (Generator Level (dBFS)) when it should be read from the y-axis (SMPTE/DIN Ratio (dB)).
When you're at generator level 0 dBFS, the lenient threshold is -66 dBFS IMD. When the generator level drops to -11 dBFS, the lenient threshold becomes -55 dBFS on the y-axis, because -11-55 = -66, meaning the actual threshold remains unchanged.
Are you saying that at the -30 dBFS level, that I supposed for a 100 W rated amp, it would be at about 1 W output into 8 ohm, IMD (understood noise included) level of -6 dB would be acceptable based on "lenient" (the green trace) per NewAVGuy? It just seems to me the IMD vs Output graph is easier to understand and visualize as the IMD vs dBFS (I assume that's the input test signal magnitude), to visualize how bad/good it is, I would have to know the actual SPL of the test signal, but I am sure I really don't know how to interpret that graph correctly.
I agree that the IMD vs Power Level graph is easier to comprehend than the IMD vs Generator Level graph, but the former is for amps while the latter is for DACs, so they serve different purposes.
 

peng

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The mistake you're making here is that you read the distortion level from the x-axis (Generator Level (dBFS)) when it should be read from the y-axis (SMPTE/DIN Ratio (dB)).
When you're at generator level 0 dBFS, the lenient threshold is -66 dBFS IMD. When the generator level drops to -11 dBFS, the lenient threshold becomes -55 dBFS on the y-axis, because -11-55 = -66, meaning the actual threshold remains unchanged.
Thank you very much for explaining, but I actually didn't read the axis wrong. My question#3 was "3. If the answer to 2. is affirmative, then -66 dB is about 0.05% and is therefore acceptable based on the lenient green line then wouldn't -11 dB at -55 dBFS level, that is 28.2% IMD distortion be terrible?" So I was in fact reading the distortion level on the Y-axis but I picked the generator level drops to -55 dBFS on the X axis whereas in you example you picked the generator level drops to -11 dBFS on the X axis.

The way you explained though, the result would be the same either way if we are looking at the threshold line, because it would be constant at 66 dB at intended.

I guess my other mistake is a conceptual one. I keep thinking IMD in dB or % in concept (mathematically speaking) the same as THD+N (or SINAD with the opposite sign) in dB or %. So I am thinking that if IMD is -11 dB (on the Y axis) when the generator level is -55 dBFS, it is 11 dB below the test signal and that would be huge, and that's where I got stuck because for THD+N, you would never consider -11 dB a possible threshold regardless of the output level.

In other words, I thought for the threshold to be -66 dB, IMD at generator level of -55 dBFS would be -66-55 = -121 dB in absolute sense, that is, reference to 0 dBFS, now that you explained it, it is -11 dB below -55 dBFS, and that is -66 dBFS. I still find it confusing but at least now I know how to read that graph.

Obviously I need to read the definition of the SMPTE/DIN (dB) ratio more carefully, thanks for that AP link.

I agree that the IMD vs Power Level graph is easier to comprehend than the IMD vs Generator Level graph, but the former is for amps while the latter is for DACs, so they serve different purposes.
Got it, thanks again. By the way, why don't we see ASR measure IMD for amps more often? In fact the WXA50's graph I attached was the only one I could find, though I remember seeing may be one or two more but that's it. I suppose its not fair to ask you the question, I should ask Amir lol..

Thanks again for your help, and creating the thread, I bookmarked it in a hurry. Any chance you would be open to creating a downloadable PDF file as well?
 
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flipflop

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Thread Starter #513
Thank you very much for explaining, but I actually didn't read the axis wrong. My question#3 was "3. If the answer to 2. is affirmative, then -66 dB is about 0.05% and is therefore acceptable based on the lenient green line then wouldn't -11 dB at -55 dBFS level, that is 28.2% IMD distortion be terrible?" So I was in fact reading the distortion level on the Y-axis but I picked the generator level drops to -55 dBFS on the X axis whereas in you example you picked the generator level drops to -11 dBFS on the X axis.
Right. My bad.
By the way, why don't we see ASR measure IMD for amps more often? In fact the WXA50's graph I attached was the only one I could find, though I remember seeing may be one or two more but that's it.
I think it's because IMD+N vs power level and THD+N vs power level graphs generally show the same thing for most amps: a steady decline in noise (as power goes up) and then a sudden spike in distortion (as clipping sets in).
A lot of amp reviews actually do feature IMD measurements, though, in the form of the 32-tone test.
Thanks again for your help, and creating the thread, I bookmarked it in a hurry. Any chance you would be open to creating a downloadable PDF file as well?
You're welcome.
I haven't kept the notes and pictures I made while working on this thread.
Anyone is welcome to create a PDF of it if they want to.
 
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flipflop

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Noise doesn’t actually go down as power goes up. Signal goes up and demands more power, and the percentage of output that is noise goes down. Absolute noise may actually go up.

Rick “often seeing confusion about this” Denney
True. I didn't mean it in the literal sense. It was a different way of saying "moving along the x-axis".
Thanks for pointing it out, though. Don't want anyone to get the wrong idea.
 
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I've been playing around a little with some audio gear because of COVID boredom.
I have been listening to my flac audio ripped CDs through a Sonos Connect for a lot of years.
I just added Volumio and a Topping E30 DAC and have done some A-B listening. I can't hear a difference.
I am playing some old DVD Audio and SACD content (stereo not 5.1 :-( ) I had lying around. Usually that content has been remastered so it sounds different from the original CD for that reason. I can't really say I can hear a material difference with the higher res. formats. That's both a testament to the original CD PCM format and perhaps a nod to my hearing which now tapers off between 13-14kHz.
Amir's measurements of the Sonos device showed decent measurements for CD audio. I can confirm that regaudless of the disrespect their brand otherwise gets.

I've had up-market (but not high-end) amp's/receivers and I've always maintained that I couldn't really hear any differences from amps either.
I had a brief experience with a cheap(er) AV receiver and boy did I hear a difference with that. I almost wish that I had taken measurements just to understand why it sounded so "thin" and bad. By all means, buy decent electronics, but really spend your money on speakers because that final step creating sound is fraught with the most peril. You have frequency response, distortion, responsiveness (speed), and directionality all contributing to making any recording sound different. There will always be disagreement about what's the same and what's different, because perception is reality. Go to live music and learn to trust your own ears. Even measurable differences don't really mater if you yourself can't hear them.
 

Descartes

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Introduction
A recurring theme on ASR is whether or not the various measured qualities of the devices are audible. In this post, I'll present some clear and visual thresholds for when those imperfections can be considered a potentially audible concern. I will not explain the basics of amp/DAC measurements.
Feel free to comment if you have any issues with the content of this post, be it technical, grammatical, or maybe just something that's poorly communicated.

Orange marks strict limits while green marks lenient limits.
Strict thresholds guarantee that anything measuring better will be transparent.
Lenient thresholds are only lenient relatively to the strict thresholds. They are also "strict" from an audible point of view. Devices measuring worse than the lenient thresholds might still sound fully transparent to you or anyone else for that matter.


Frequency range of human hearing
Humans cannot hear sounds of every frequency. The range of hearing for a healthy young person is 20 to 20,000 hertz.
When pure sine waves are reproduced under ideal conditions and at very high volume, a human listener will be able to identify tones as low as 12 Hz (Olson, Harry F. (1967). Music, Physics and Engineering. p. 249). Below 10 Hz it is possible to perceive the single cycles of the sound, along with a sensation of pressure at the eardrums.
For these reasons, the audibility thresholds will deal with frequencies from 0 to 20 kHz.


Dynamic range, linearity
CDs, with undithered audio, have a maximum dynamic range of 96 dB (16 bits). Studies, such as the one conducted by Meyer and Moran, have shown 96 dB of dynamic range is transparent for any normal listening conditions.
120 dB (20 bits) of dynamic range is required for transparency. Anything below -120 dBFS is inaudible. Amir wrote an in-depth article about the subject.

View attachment 18959
Allo Boss V 1.2 is unable to reproduce undithered audio from CDs (with content that makes full use of the 16 bits) transparently.

View attachment 18960
miniDSP SHD lands between the two targets.

View attachment 18961
SMSL VMV D1 has more dynamic range than the required 120 dB for guaranteed transparency.


View attachment 18963
Benchmark DAC1 USB doesn't reach the -96 dBFS target.

View attachment 18964
Orchard Audio GALA remains flat up to -96 dBFS, but losses linearity before reaching -120.

View attachment 18965
Auralic Vega measures perfectly at -120 dBFS, but due to the analyzer itself introducing some noise, it doesn't show the ideal flat line, which it should be.


FFT
NwAvGuy's Heaphone Amp Measurement Recommendations - In this article, NwAvGuy provides some guidelines for good amplifier design. He is "an electrical engineer by education (BSEE) and career", not a psychoacoustician, and he does not cite his sources, so his limits will be treated as lenient.
NwAvGuy says that "noise needs to be -85dB below the signal to be inaudible which works out to only 0.005% THD+N. But music masks distortion so 0.01% (-80dB) is considered acceptable." Since I make no assumptions about the listener or listening material, I'll disregard the -80 dB threshold and go with -85 dB.
His guideline for distortion is <0.05% equivalent to -66 dBFS.

Disclaimer: The FFT spectrum shows the noise floor as being lower than it actually is. This is called “FFT gain” and it allows us to see distortion products that may be well buried inside the noise floor of the amp or DAC. The gain can be as much as 30 dB to 40 dB lower than reality. Comments on the noise floors for the following graphs are for illustrative purposes only.

View attachment 18966
Audio-gd NFB-28.28 has a "Massive 3rd Harmonic Distortion" spike that puts it above all 3 thresholds.

View attachment 18967
Parks Audio Puffin fails to meet the strict THD+N criteria and the lenient noise criteria, but stays below the lenient distortion limit.

View attachment 19064
JDS Labs The Element stays below the lenient thresholds, but doesn't stay below the strict threshold.

View attachment 18970
Allo Katana measures well enough to stay below all 3 thresholds.


SINAD
SINAD groups distortion and noise into one figure, meaning the lenient noise threshold of -85 dBFS will be used, because it's not clear whether noise or distortion dominates. When converting THD+N to SINAD, one can simply remove the minus sign and 'FS' like so: 85 dB.

View attachment 43569
The 4 DACs to the left of the orange line manage a signal over noise and distortion of 120 dB or more, exceeding the strict threshold. Totaldac d1-six, and all the other DACs to the right of it, don't make the cut for the lenient threshold.


IMD, THD+N vs frequency
For IMD, the same distortion thresholds as for FFT apply: -120 dBFS for the strict and -66 dBFS for the lenient.

View attachment 18971
Audio-gd NFB-28.28 exceeds the lenient threshold and therefore also the strict one.

View attachment 19063
Musical Fidelity V90-DAC stays between the 2 limits.

I've not come across a device that measures better than the strict threshold.


Like with SINAD, it's not always possible to tell the distortion and noise apart in THD+N vs frequency plots, so we have to go with the lenient noise threshold again.

View attachment 25303
Schiit Yggdrasil doesn't manage to stay below the lenient threshold.

View attachment 25304
miniDSP SHD and Benchmark DAC3 measure below the lenient threshold, but above the strict one.

No device measures below the strict threshold on this test.


Crosstalk
-60 dB is NwAvGuy's guideline for crosstalk, so half (numerically) of the strict limit of -120 dB.
As crosstalk measurements are still scarce on ASR, I wasn't able to found one breaching the lenient threshold.

View attachment 18977
Massdrop THX AAA 789 exceeds the strict threshold at all 3 gain settings, but also stays below the lenient threshold.

View attachment 18978
Gustard A20H stays below both thresholds.


Jitter
Jitter is only found in DACs, so I will stray away from the amp guidelines of NwAvGuy for this section. Thankfully, he wrote another article about the subject where he introduces a threshold for jitter:
View attachment 18990
Despite "all the research [he's] done", he doesn't cite his sources here either, so this limit will also be treated as lenient.
NwAvGuy uses a sample rate of 44.1 kHz and a main tone of 11.025 kHz. Amir uses a sample rate of 48 kHz, hence a main tone of 12 kHz. I've adjusted the threshold to fit Amir's graphs.

View attachment 18980
SMSL Sanskrit 10th exceeds both thresholds regardless of input.

View attachment 18981
Topping DX3 Pro exceeds the strict threshold, but not the lenient threshold.

View attachment 18982
Khadas Tone Board doesn't exceed either threshold.


Frequency response, channel balance
Going back to NwAvGuy's amp guidelines, he recommends a maximum of 0.5 dB deviation (from 0) in the frequency response.
Psychoacoustics: Facts and Models by Hugo Fastl and Eberhard Zwicker is not a very quotable book, but on pages 180-181 it makes it clear that a change in SPL of less than 0.2 dB can be heard by humans.
In 'Sound Reproduction: The Acoustics and Psychoacoustics of Loudspeakers and Rooms' Floyd Toole says the following: "The simplest deviation from flat is probably a spectral tilt. There is some evidence that we can detect slopes of about 0.1 dB/octave, which translates into a 1 dB tilt from 20 Hz to 20 kHz — not much."
0.1 dB is therefore the strict limit.

View attachment 18984
The HP Z series laptop's frequency response takes a nosedive right before 20 kHz and exceeds both thresholds.

View attachment 18985
Topping DX3 Pro exceeds the strict threshold in both the bass and treble, but stays within the lenient.

View attachment 18986
SpeaKa USB DAC stays within both thresholds.

The channel balance threshold from NwAvGuy mirrors the frequency response threshold: if the FR rises by 0.5 dB in one area and drops by 0.5 dB in another, the total discrepancy will be 1 dB, which will be the lenient threshold for channel balance.
The strict thresholds remains 0.1 dB.

View attachment 18987
TEAC HA-P50 exceeds both thresholds.

View attachment 18988
Neurochrome HP-1 exceeds the strict threshold, but not the lenient threshold before running out of power.

View attachment 18989
Sabaj Da3 doesn't exceed either threshold before running out of power.


Output impedance
NwAvGuy's guideline for output impedance is based on the 1/8th rule, placing it at 2 ohms with a worst case scenario of 16 ohms headphones.
The basis for the 1/8th rule is that it allows up to a 1 dB variation in the frequency response. For a 0.1 dB variation a 1/100th rule is derived, meaning the output impedance should be 0.16 ohms or less with a 16 ohms load.
Keep in mind the thresholds vary with load impedance and can be disregarded entirely with headphones that have a flat impedance curve.

View attachment 18991
All the amps to the left of Auralic Gemini 2000 exceed the lenient threshold.


Recap of thresholds
Lenient
Dynamic range, linearity: 96 dB
THD, IMD: -66 dBFS / 0.05%
Noise: -85 dBFS / 0.005%
SINAD: 85 dB
Crosstalk: -60 dBFS
Jitter: -110 dBFS, -100 dBFS around the main tone
Frequency response: ±0.5 dB
Channel balance: 1 dB
Output impedance: 2 ohms

Strict
Dynamic range, linearity, SINAD: 120 dB
THD, IMD, noise, crosstalk, jitter: -120 dBFS / 0.0001%
Frequency response, channel balance: ±0.1 dB
Output impedance: 0.16 ohms


Changelog
  • UPDATE #1: Elaborated on the meaning of the thresholds.
  • UPDATE #2: Based on feedback from @solderdude and @restorer-john, I've decided to get rid of the THD+N vs power graphs.
  • The lenient threshold line for the IMD measurement of Musical Fidelity V90-DAC was mistakenly 10 dB lower than it should've been. It has now been fixed.
  • UPDATE #3: Dithering was unaccounted for in a couple of descriptions of CD audio. The sentences have been rephrased to accurately reflect the fact that 96 dB is not the maximum dynamic range of 16 bit audio. Thanks to @bennetng and @Francis Vaughan for pointing this out.
  • UPDATE #4: A strict threshold for output impedance has been introduced. The graph has not been updated for practical reasons. Big thanks to @dc655321 for helping with the math.
  • UPDATE #5: Added SINAD to the 'Recap of thresholds' section.
  • UPDATE #6: As pointed out by @daftcombo, the lenient thresholds on the THD+N vs frequency graphs were incorrect. This has now been fixed.
  • UPDATE #7: Added SINAD to the main section. Added a disclaimer to the part about FFT. Moved updates to a new changelog section at the bottom.
Excuse my ignorance, but does this mean that only 4 DACs are worth considering?
 
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flipflop

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Thread Starter #519
Excuse my ignorance, but does this mean that only 4 DACs are worth considering?
There's about a dozen measured DACs worth considering if your goal is to own a provably transparent DAC. But if you just want a good sounding DAC, that's most likely also transparent, pretty much any will do as long as you avoid intentionally poorly designed products such as Audio-gd NFB28.28 and Woo Audio WA7tp.
 

Descartes

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There's about a dozen measured DACs worth considering if your goal is to own a provably transparent DAC. But if you just want a good sounding DAC, that's most likely also transparent, pretty much any will do as long as you avoid intentionally poorly designed products such as Audio-gd NFB28.28 and Woo Audio WA7tp.
So the top 12 from measurements standpoints ?

AC808FC4-2082-4C21-8AA1-6CA7144162CC.jpeg
 
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