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

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

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.

For a great audio / visual by Avermetrics on this topic look here

 

Having an FFT plot showing the actual content of the THD+N is far more informative than just a simple number and plenty of things can be hidden in there.

Still, at 80db down, most of the differences would be on the bleeding edge of audibility. The increased noise on #6 with super-sensitive IEMs seems the most likely real world difference. I think most of the rest would require at least live-venue listening levels in a library-quiet room. Once you get down to an honest .001% THD+N I don't think any harmonic composition would yield different audibility outside of an acoustics lab.

At least with full size headphones. There always seems to be an even more sensitive multi BA IEM around every corner which demands an even lower noise floor...

 

Alice's Restaurant.

 

Earlier in my career I would have made a similar statement. I was fortunate to meet some really smart psycho-acoustic researchers from Bell Labs. They helped me to figure out that I indeed had a lot to learn. So much depends on so many conditions. Blanket statements don't apply. Ask any of the lossy compression algorithm developers about this. Masking can be a lifetime study topic.

 

This might seem needlessly philosophical, however I'd like to point out that measurements are only indicators of real world phenomena. For example - in room acoustics a strong early reflection will be seen both in frequency and time domain measurements as a certain deviation. However, looking at a single static set of measurements won't reveal the full complexity of the phenomenon.

I'm inclined to say that same will apply to electronics. Usually a lack of linear and non-linear distortion at required power levels is a good indicator that the said device will perform an honest translation of the input signal to output. If distortion is present, some kinds will be less audible than others and some types of audible distortion will appear less annoying than others.

 

The way I see it, "lack of distortion" is a non-issue, as we have yet to see a perfect amp. Especially in real life situation, which are infinitely more complex and demanding than what's usually used to make measurements.

Unless you go into "audibility at -dB level" which Bob already addressed earlier.

 

You have links to any reading on that? It sounds interesting.

 

Not free but a good reference in this chapter:
https://link.springer.com/chapter/10.1007/978-3-319-07974-5_2

 

Looks interesting. Now I have to see if I can find my way past the paywall...

 

Continuing https://www.superbestaudiofriends.o...mirs-hack-job-part-ii.6449/page-2#post-236511. There shouldn't be identical 2 devices that measures identical, but at least very similar. I only care about 2nd and 3rd harmonics and mains hum to be kept below -90dB from the reference signal.

BS-6 has no audible harmonics nor hum, so it should sound very well; I don't think the residual broadband noise will ever become an issue and will not interact with the audio tracks.

Wondering if you have the time to give'em some A/B tests, it should be fun to identify from the above pictures few of the "audiophile terms".

 

Please note those are hypothetical amplifiers, created in the measurement domain for educational purpose. They do not exist in the real world, though the concept still applies. Remember the chief point is measurement numbers are lossy data reductions for complex data sets. This particular exercise demonstrates how the same number is achieved through at least six different complex data sets.