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.
Allo Boss V 1.2 is unable to reproduce undithered audio from CDs (with content that makes full use of the 16 bits) transparently.
miniDSP SHD lands between the two targets.
SMSL VMV D1 has more dynamic range than the required 120 dB for guaranteed transparency.
Benchmark DAC1 USB doesn't reach the -96 dBFS target.
Orchard Audio GALA remains flat up to -96 dBFS, but losses linearity before reaching -120.
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.
Audio-gd NFB-28.28 has a "Massive 3rd Harmonic Distortion" spike that puts it above all 3 thresholds.
Parks Audio Puffin fails to meet the strict THD+N criteria and the lenient noise criteria, but stays below the lenient distortion limit.
JDS Labs The Element stays below the lenient thresholds, but doesn't stay below the strict threshold.
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.
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.
Audio-gd NFB-28.28 exceeds the lenient threshold and therefore also the strict one.
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.
Schiit Yggdrasil doesn't manage to stay below the lenient threshold.
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.
Massdrop THX AAA 789 exceeds the strict threshold at all 3 gain settings, but also stays below the lenient threshold.
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:
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.
SMSL Sanskrit 10th exceeds both thresholds regardless of input.
Topping DX3 Pro exceeds the strict threshold, but not the lenient threshold.
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.
The HP Z series laptop's frequency response takes a nosedive right before 20 kHz and exceeds both thresholds.
Topping DX3 Pro exceeds the strict threshold in both the bass and treble, but stays within the lenient.
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.
TEAC HA-P50 exceeds both thresholds.
Neurochrome HP-1 exceeds the strict threshold, but not the lenient threshold before running out of power.
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.
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
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.
Allo Boss V 1.2 is unable to reproduce undithered audio from CDs (with content that makes full use of the 16 bits) transparently.
miniDSP SHD lands between the two targets.
SMSL VMV D1 has more dynamic range than the required 120 dB for guaranteed transparency.
Benchmark DAC1 USB doesn't reach the -96 dBFS target.
Orchard Audio GALA remains flat up to -96 dBFS, but losses linearity before reaching -120.
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.
Audio-gd NFB-28.28 has a "Massive 3rd Harmonic Distortion" spike that puts it above all 3 thresholds.
Parks Audio Puffin fails to meet the strict THD+N criteria and the lenient noise criteria, but stays below the lenient distortion limit.
JDS Labs The Element stays below the lenient thresholds, but doesn't stay below the strict threshold.
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.
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.
Audio-gd NFB-28.28 exceeds the lenient threshold and therefore also the strict one.
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.
Schiit Yggdrasil doesn't manage to stay below the lenient threshold.
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.
Massdrop THX AAA 789 exceeds the strict threshold at all 3 gain settings, but also stays below the lenient threshold.
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:
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.
SMSL Sanskrit 10th exceeds both thresholds regardless of input.
Topping DX3 Pro exceeds the strict threshold, but not the lenient threshold.
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.
The HP Z series laptop's frequency response takes a nosedive right before 20 kHz and exceeds both thresholds.
Topping DX3 Pro exceeds the strict threshold in both the bass and treble, but stays within the lenient.
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.
TEAC HA-P50 exceeds both thresholds.
Neurochrome HP-1 exceeds the strict threshold, but not the lenient threshold before running out of power.
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.
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.
Last edited:
I will promote it to an article for home page.
