# Tutorial - A tale of 6 amps THD+N and THD specifications

Discussion in 'Sound Science' started by atomicbob, Aug 5, 2018.

1. Trust the numbers? Maybe not so much.

Another Grim Fairytale on why I hate numerical specifications for audio components, especially THD+N and THD.

This is a brief, visually oriented tutorial.

Prerequisite reading:
Tutorial - Interpreting THD and THD+N specifications and graphs
https://www.head-fi.org/threads/tutorial-–-interpreting-thd-and-thd-n-graphs.885876/

Please read the above and familiarize yourself with the various information available on the graphs that will be presented below. I don’t wish to resort to eight-by-ten color glossy photographs with circles and arrows and a paragraph on the back of each one explaining what each one is (kudos to those who know this reference.)

Here are THD+N measurements for six hypothetical amplifiers, left and right channels:

Each amplifier measures very close to 0.01%. Given these measurements all six amps should be identical and sound the same, correct? No! While the THD+N numbers are almost identical, each one was derived from a different set of conditions occurring in the respective amplifiers. The resulting numbers are an oversimplification of the complex spectrums from which they were computed.

In reality unit variance from the production line is larger than those measured for our six hypothetical simulated amplifiers. The purpose here is to demonstrate how the same measurement number may be achieved in a variety of ways.

In each spectrum graph that follows, the second highest spike from the 1 KHz stimulus will dominate the measurements except the last one. Please note the dBu y-axis, which is held constant between graphs.

BS-1

Our first hypothetical amplifier has a 60 Hz mains spike dominating the THD+N measurement. Note that THD and harmonics are quite low. Easily observed in the spectrum above.

BS-2

The second amplifier has a 2nd harmonic dominating the THD+N and THD measurements. No AC mains noise to be seen.

BS-3

Our third amplifier THD+N and THD measurements are similar to the 2nd amplifier but now are dominated by a 3rd harmonic.

BS-4

The BS-4 distortion is dominated with a 4th harmonic for both THD+N and THD measurements.

BS-5

Our 5th amplifier has a 180 Hz mains noise harmonic dominating the THD+N measurement.

BS-6

The last of our hypothetical amplifiers has residual broadband noise dominating the THD+N measurement and contributing to a slightly higher than expected THD though there are no specific harmonics clearly responsible.

From the preceding it is obvious numeric representations of complex spectrum information is a tremendous oversimplification. These amplifiers each have a specific sonic signature differing from all others. They will sound different to those with trained listening skills. Yet their respective THD+N measured nearly identical.

In a similar fashion, the BS-2, BS-3 and BS-4 all measured close to 0.01% THD. Yet each one had a different harmonic dominating the THD measurement. Based on empirical listening evidence, the BS-2 might be described as warm sounding, the BS-3 as bright and the BS-4 having something about the sound that is fatiguing, possibly sour sounding. Please be aware these descriptions are highly subjective. However, the measurements are not.

Some general observations. The BS-1 has a lone 60 Hz mains component contributing to the THD+N, which is likely not to be noticed by most listeners in average ambient conditions. The BS-5 has a 180 Hz mains harmonic which is more likely to be heard due to increased sensitivity of the Human Auditory System (see Fletcher-Munson curves) at this frequency. As described in the previous paragraph the BS-2, 3 and 4 are all THD dominated with their respective subjective traits. Finally the BS-6 has broadband noise which will be readily apparent as hiss, especially to IEM listeners.

Hopefully this tutorial will raise awareness of how some numeric representations are just short of worthless given the drastic differences presented above resulting in almost identical computed results.

Major take-aways from this tutorial:
1. don't use a single numeric metric as a goodness indicator when comparing audio components
2. numbers typically represent oversimplifications of more complex data observed in spectrum graphs
3. learn what purpose a measurement serves, methods used to perform, and how to interpret results

For a great audio / visual by Avermetrics on this topic look at this video:

Further reading:
Fundamentals of Modern Audio Measurements, Richard C. Cabot
http://www.aes.org/e-lib/browse.cfm?elib=7080

*edit* - corrected video link, added take-away message

Last edited: Aug 8, 2018
2. Contributor
maybe reformulate this so it's less misleading. THD was never the only variable defining sound, so there is no reason in the first place for amps to necessarily sound the same even if they had strictly identical harmonic distortions and noises at all frequencies. only with everything else considered equal can your point make sense IMO. which is not something we see often.

the highest extra crap is 80dB below signal, so yes let's double down on the highly subjective aspect of those descriptions. I don't know where to put the threshold of perception for harmonic distortions, even a safe one(anybody has some research on that?), so I won't make any grand claim about those variations being audible or not. but if I could get clear listening fatigue from stuff strictly 80dB below music, that would really make me rethink audio altogether. it would probably be the most eye opening experience since I'm in this hobby.
if those impressions came from proper listening tests, it might be relevant to check that no other aspect of the sound coming out of the headphone(not the just the amp) was at a level we can expect to notice.

help me here. we're talking about something down at, let's say -118dBu for the noise in the upper range, the rest sticking pretty well to harmonic freqs. I take my old HF5 as reference, not the most sensitive stuff in the world but still clearly on the sensitive side of things. enough to make me hate 4 out out of 5 amplifier outputs on which I notice background hiss. unless I messed up somewhere(wouldn't be the first time), I end up expecting something around 2 or 3dB SPL at 1khz. and that's if the noise doesn't move at all when I change the volume.
edit for those who care to be less silly than me: the noise floor isn't the level shown on the graph at -120dBu, the FFT length will change the level of noise on a graph and must always be accounted for. that's what I weirdly forgot in my reasoning.

I'm sort of with you on the idea that specs like one sterile value of THD can be a little misleading and really of no help at all to guess how something will sound(if the distos are at audible levels). but then again any measurement is just a partial view onto something. maybe the big issue is just that people always overreach when they interpret measurements? or worst, thinking we know how to interpret measurements despite not even knowing how the measurement was obtained.
but the single THD value isn't guilty of anything. numbers are people too... ok maybe that's one step too far. ^_^

if I knew a consistent alternative I could trust for the gears I can't try myself, I'd completely disregard those barely indicative specs with almost always incomplete nomenclature(that pisses me off soooooo often). but I don't have that good alternative. only a minority of gears are given a more in depth measurement to be available publicly(thank you for being a provider of such measurements!!! no matter how much of a jerk I am, I'm very grateful for your efforts toward the community over the years).
professional reviewers... well let's just say that they have to play nice for various reasons and I now feel naked since innerfidelity has been given to a noob.
and random guys giving a feedback is something I will never trust to estimate sound quality. fool me once, shame on me. foll me 50 times a day for decades and even I will get a clue. so in that sad excuse of a context, default specs like THD @1khz with hopefully some way to know the level of the tone, often becomes my one eyed king in a blind world.

Last edited: Aug 7, 2018
3. When it comes to distortion, measurements are good, but if it's audible, then it becomes a problem. Do you have sound samples illustrating various types and degrees of distortion? I'd be very interested in that.

4. The tutorial is about one example of numbers vs. spectrum. The use of THD and THD+N was not by any means meant to imply a single variable defining sound quality.

Careful with these two thoughts. The test in the tutorial was performed at 0 dBu, which is an absolute level. 0 dBu = 0.775 Vrms sinusoidal stimulus. 60 and 180 Hz mains noise will remain constant as they are residual noise. So will a high noise floor (hiss). Now consider a Campfire Audio Andromeda IEM user encountering -80 dBu of hum, buzz or noise. Andromeda has 115 dB SPL / mW sensitivity at 12.5 R impedance. Let's ignore for the moment frequency response and impedance bumps. With 0 dBu, 0.775 Vrms the Andromeda will consume 48.1 mW producing 115 + 16.8 dB = 132 dB SPL. No one should ever listen at that level. However, 80 dB below that level is 51.8 dB SPL. If the hum, buzz, noise is constant regardless of gain setting, then this is the level that will appear when no music is playing. This is a level audible to all but the seriously hearing impaired.

You nailed the intent of the tutorial with "(many) people (often) overreach when they interpret measurements?" That is the whole point. Latching onto some specific measurement number and using as a "goodness" indicator while comparing spec sheets, is a REALLY BAD IDEA(TM). I am using THD and THD+N as an example in this tutorial, as I see this one misused, misapplied and generally misunderstood all the time. The data produced can be somewhat useful when properly understood, applied correctly. However the spectrum provides the details as to how the numbers were obtained, which is far more useful.

Consider that not only are there a variety of measurement data but listeners also have preferences. Matching data to preferences is a better use model of measurement data, and I mean the more complex spectrum results I have been worked hard to provide (when time permits), in a consistent suite of such data. Avoid getting caught up in the numbers game. Look at the spectrum that produced the numbers.

Last edited: Aug 6, 2018
RCBinTN and Currawong like this.
5. Please watch the video linked in the original post.

6. Contributor
eheh, I don't disagree with the ideas, or that estimation with the Andro. but then you just used the wrong examples in the little feedback about the subjective impressions of some of the amps. the suspicious stuff in the low end happens on BS-1 and BS-5. while you mentioned BS-2, 3 and 4 in OP, all pretty clean when it comes to noise. and I expect THD to go mostly follow the output signal and pretty much disappear because of auditory masking from the music itself. that's why I only quoted those parts in my previous post, I'm very much in line with you for everything else.

same with hiss. in that quote you mentioned BS-6, where the overall noise is close to -120dBu, not -80. so even with the Andro, we shouldn't really be at "readily apparent" level of hiss.
edit: same as previous post, I kept going with my numbers without checking if they were correct in the first place... bad castleofargh!

Last edited: Aug 7, 2018
7. Outside of pathological system setups and extremely sensitive transducers, where more careful research may be advised; generally speaking, with most transducers, the answer to your rhetorical question is "yes!", these amps should all sound the same. Those that frequent these forums regularly have oftentimes pointed to similar issues with manufacturer specifications.

This is a link I reference every now and then:

http://www.rane.com/note145.html

I understand where your post is coming from, but I think it may generally confuse a lot of people into believing that all amps are drastically different with a majority of transducers, and it is really the opposite. Most amps are perfectly fine for most transducers, provided they adhere within the acceptable specifications provided, and audible differences are typically not identifiable.

That is not to say that all amps sound the same, but that statement is more likely to be correct in most rational scenarios than claiming all amps sound different or have their own sound signature.

Thanks for detailed measurements. Good stuff!

8. What I would like to hear is recorded music with audible levels of distortion that matches distortion specs for typical amps. I haven't run across an amp with audible distortion yet. I'd like to hear what that sounds like with real world examples. Are there music samples out there somewhere with gradually increasing distortion so I can get a feel for the thresholds?

9. THD will usually track level with respect to the stimulus.
However, consider a brief, incomplete and overly simplified discussion of auditory masking and the basilar membrane. I'm going to reference Equivalent Rectangular Bandwidth (ERB), Critical Bands (CB), and the Bark scale.
Some information on ERB here:
https://ccrma.stanford.edu/~jos/bbt/Equivalent_Rectangular_Bandwidth.html

Referring to equation 28 in that paper
ERB(f) = 0.108f + 24.7

at 1000 Hz ERB(1KHz) = 132.7 Hz for moderate sound levels. Not the entire 20 Hz to 20 KHz audio band.

Now consider a Bark scale chart describing critical bands for some pre-determined frequencies. In reality the CB are continuous and not discrete, but the discrete chart allows a simplified discussion,
https://ccrma.stanford.edu/courses/120-fall-2003/lecture-5.html
Using a Bark scale approximation (look at last graph on page)

For 1000 Hz
2nd harmonic is approximately 4 critical bands higher
3rd harmonic is approximately 7 critical bands higher
4th harmonic is approximately 9 critical bands higher

The basilar membrane treats signals outside a stimulated critical band differently than inside. Outside may be detected in presence of a masker inside a given critical band.

In dense, complex musical passages with many maskers present, then detection may not occur. If presented with sparse or less complex signals, say a bell or triangle, piano in solo or nearly solo role, as examples, then the harmonics may not be masked and detection possible. 2nd and 3rd harmonics are musically related so they are likely to be enjoyed as described in the OP, but 4th harmonic is not musically related and can appear to be that something slightly sour about those sparse passages.

Again, be careful. One must sum the levels in all the FFT bins to obtain residual noise level. Summation is not direct but through the following equation:

FFT size process gain:
http://www.analog.com/media/en/training-seminars/tutorials/MT-001.pdf
https://www.designnews.com/aerospace/where-does-fft-process-gain-come/100022666833951

For post #1 tutorial above FFT size is 128K (131072). For M = FFT size
FFT process gain = 10*log(M/2)
In the tutorial examples, process gain calculates to 48.16 dB
Now looking at the average of the FFT baseline noise floor for BS-6, estimate -125 dBu.
-125 dBu + 48 dB process gain = -77 dBu.
-77 dBu from our reference of 132 dB at 0 dBu given for the Andromeda IEMs results in 55 dB SPL.
This will be audible hiss.

Another example would be Focal Clear with sensitivity of 104 dB/mW and 55R nominal impedance. Running the calculations results in 33 dB SPL for the same BS-1, 5 and 6 hum, buzz, or hiss.
33 dB SPL may or may not be audible depending on ambient environment of the listener. Fan noise is likely to mask. Quiet rural bedroom the residual noise between tracks, if not using track overlap fades, may be annoying.

If you were located near my lab I could demonstrate this, audibly, as I have done for many of my colleagues. My lab space often achieves 22 dBA and 28 ~ 30 dBC SPL ambient. Hum, buzz and hiss annoy me personally, others may not be bothered.

castleofargh likes this.
10. Dennis Bohn wrote many great papers. I reference his writings frequently. A shame when Rane was acquired by InMusic and eventually terminated all the talented staff. Rane was located only a few miles from me.

For the purpose of the OP tutorial I would ask you to consider the psycho-acoustics discussed in the previous post. As we continue to research, we learn more and all is not as it appeared only a few years ago. There may be a potential to reconcile objective with subjective by considering measurements beyond numbers and subjective experiences beyond over-compressed, dense source material.

A good point about not implying drastically differences from the OP. Different yes, but at 80 dB below for THD harmonics, not drastic. Some of the subjective discussion does appear exaggerated at times. Hum, buzz and hiss are another story.

The psycho-acoustic researchers (of which I know an ex-bell lab type for example, he mentors me best he can, I'm not on his level, yet) have plenty of demonstrations that opened my ears.

Last edited: Aug 7, 2018
11. I know I can't hear anything that is -80dB down under music. I can't even usually hear -40dB under music. In my sig, Ethan Winer takes a horrible buzzing sound and plays it continuously under music at various levels. It becomes completely inaudible relatively quickly. If you are talking about distortion that follows the modulation of the music rather than being a continuous buzz, I would think it would become inaudible even faster. I'm interested in what I can hear in real world use. Is there any reason I should be concerned about audible distortion using say a midrange AVR? Do you know of any amps or receivers with audible levels of distortion in normal use?

12. This reply will be potentially unsatisfying.

If one is a hard core objectivist then there won't be any differences to be heard except with badly engineered components suffering serious deficiencies, such as loud hum, buzz, hiss etc.
If one is a hard core subjectivist then there are differences to be heard in all components.

Next up is the environment in which evaluation, AB or ABX testing is to occur. Even moderate ambient noise may cause masking. No point in attempting such auditory discrimination next to a loud appliance, as an example. HVAC running is another big masker at the levels being discussed.
Electroacoustic transducers also create issues with such testing with their frequency responses, distortion signatures. If using speakers in a room, room reflections will introduce challenges if not managed. I personally favor Sennheiser HD800 and Focal Clear headphones for easiest discrimination. Eliminates room acoustics but at expense of ear canal coupling issues. One headphone is 300R and the other 55R to roughly cover both ends of impedance spectrum. IEMs are used for residual noise detection.

Strongly consider ear training:
http://harmanhowtolisten.blogspot.com/
http://www.moultonlabs.com/full/product01

I too have created masking demonstrations similar to Ethan's and with appropriately dense material and the right type of distortion can mix distorted signals only 20 dB below the main signal that is not audible. Choosing source material that allows discrimination is also important. Training to learn the sounds. Start with obvious and work toward subtle. Both ear training suggested employ this strategy. Some brief thoughts on examples were posted above.

13. I'm a hard core pragmatist! I want to see how measurements relate to what I actually hear when I sit down to play an album in my living room. I find that a lot of objectivists get lost in numbers and charts without ever relating them to their own perceptual thresholds, and a lot of objectivists believe that they can perceive as much as a bat can. They both end up in the exact same place at the bottom of the rabbit hole. I can see establishing a threshold and adding "a little bit of buffer just to be on the safe side". But both objectivists and subjectivists seem to create a buffer that is a couple orders of magnitude beyond anything they can possibly hear.

We had a fella in here a few months back saying that a noise floor at -96dB isn't enough... you really need -120dB. He was an objectivist and knew quite a bit about measuring sound reproduction, but he was convinced he was right about that. He placed his pride in being able to hear things other people couldn't, and he'd cheat listening tests by goosing the volume to prove it. I have normal hearing. I see no reason to be ashamed of that and I feel no need to try to jury rig my listening tests to try to prove anything. I don't understand why someone would invest their ego in hearing the unbearable. Learn to play a musical instrument, become a great artist, build your own home from scratch... those are the things that impress me, not being able to hear noise at -70dB. And I don't believe in normal listening conditions anyone could hear that anyway.

Sometimes I think people spend too much time calculating and recalculating the numbers and searching for worst case scenarios so they can push the goal post a little further away, and not enough time thinking about what the application for all of this technology is.

Last edited: Aug 7, 2018
14. Contributor
all right, now I see where the misunderstandings came from. in your first post the sentence I quoted about hiss was specifically about BS-6 and on that one I went full moron from years of having all sorts of RTAs providing me with a readily available number that took the FFT into account when I was looking for SNR (without a test tone in the way). and somehow, I managed to forget everything I know for some reason and weirdly took the level on the graph for noise as is... that's clearly on me and it's super silly. it's like the second stuff you learn about FFT after how you won't get the lowest freqs properly if you use too short a length. yet here I am failing like a boss. if you didn't mention process gain based on FFT, I might have never realized my mistake, thanks for that.
but then you replied to my mistake with stuff about 60 and 180hz noise, so of course I got my focus shifted on how those were other amps, not BS-6 that you had mentioned as having hiss. maximum miscommunication! ^_^
now I believe that all is clear for me, and you're right the hiss on BS-6 is going to be noticed with both the Andro and my old HF5 simply because it's not at -120dBu. and even the other 2 amps with hum could be a problem.

on the other hand, I'm really not sold on harmonics at -80dB sounding differently. even if we do consider almost single tone "instruments" with minimum harmonic content, we'll still get a bunch from our transducers, probably higher than -80dB. and we'd need to listen at a level loud enough in a room quiet enough as you mentioned, so that -80dB is made into something noticeable on its own. I for one basically never align with such conditions when I listen to music. and my listening tests logically fail. I'm not everybody, but I'm also not very optimistic on people perceiving that sort of difference.

I've edited my previous posts so that other members won't be tempted to follow my erroneous reasoning on the noise floor.

Last edited: Aug 7, 2018
15. Been there, done that, got the t-shirt. I try to be more careful now, especially considering how casual visitors, lurkers and forum interlopers often drop into the middle of a larger conversation. But I still often assume too much while attempting to balance between TMI and TLI. Thank-you both for your thoughts and editing as I can see you are also mindful of the larger audience reading this thread, hopefully benefiting and not misinterpreting.

You are correct that casual listeners and listeners in moderate to high ambient noise environments aren't likely to either notice or benefit from such distinctions. Trained critical listeners in quiet environments have greater potential to care. Those on the sound production side are certain to desire the very best tools for their craft. Spending hours with headphones every day, editing dialog and music, distracting deficiencies become both noticeable and annoying.

The major take-away from the tutorial are the following points:
1. don't use a single numeric metric as a goodness indicator when comparing audio components
2. numbers typically represent oversimplifications of more complex data observed in spectrum graphs
3. learn what purpose a measurement serves, methods used to perform, and how to interpret results

Last edited: Aug 8, 2018