Amplifier harmonics and load stability

[A.S.]

Next let's look at the characteristic 'sonic signature' of certain harmonics which we'll deliberately add to a pure tone. That may help us attribute a character to what I've described as '2nd harmonic', '3rd harmonic' or whatever. Within the limit of my test equipment I can generate any whole harmonic of the fundamental, or even any in between frequencies such as the '3.7th harmonic' which, believe it or not could conceivably be generated by an instrument or hifi system, including the speakers. But let's keep it to the basic exact-multiples-of-fundamental for now.

9. First we should acclimatise ourself with 440Hz (Concert A), pure tone for ten seconds. This should sound sweet and completely free of any edginess. If you are listening on cheap PC speaker, they almost certainly will have some distortion but hopefully not so much.

Loading the player ...

This is the reference sound.

10. Now we will add 10% 2nd harmonic distortion to that 440Hz. The second harmonic of 440Hz is 880Hz, so I've mixed in 10% of 880Hz on top of the 440Hz. Is the 10% second harmonic distortion audible?

Loading the player ...

11. We increase the 2nd harmonic distortion of Example 10 from 10% to 50%. Is the 50% second harmonic distortion audible?

Loading the player ...

9a. And back to the reference pure tone again (as Ex.9)

Loading the player ...

12. Finally, can we hear 3% 2nd harmonic distortion?

Loading the player ...

I would anticipate that now you've trained yourself to recognise second harmonic distortion, you may just about hear it* at the 3% level (assuming your speakers are not themselves generating even more than 3%) - that is, 3% relative to 100% of the pure 440Hz tone. But if we used music rather than a pure tone, it would be virtually or actually impossible to identify harmonic distortion at such a low level; the musical instrument themselves would be generating so many harmonics that a few percent added from the recording or reproducing equipment would merge with the instrument's own sound and be undetectable except under very carefully controlled conditions. Second harmonic distortion at around 3% would be typical for a pickup cartridge tracking a loud disk, analogue magnetic tape recording and even quality loudspeakers working hard in the low frequencies.

So that's second harmonic distortion. What about third harmonic? That means, taking our 440Hz pure tone we need to add-in some 1320Hz tone at varying levels.

*Don't worry if you can't identify 3% 2nd harmonic distortion especially on cheap PC speakers. You should be able to distinguish 10% 2nd harmonic more easily.

[A.S.]

In post No. 41 we listened to the addition of varying amounts of second harmonic distortion to our pure 440Hz tone. We compared 10%, 50% and finally 3%. But what if we introduce some third (3rd) harmonic distortion - will that have the same corrupting character as the 2nd harmonic distortion or not. Let's put it to the test.

9b. Here again is our nice pure 440Hz reference tone. There is no added distortion to this tone - it will replay as perfectly as your equipment will allow.

Loading the player ...

10a. And just to refresh our memory, here is what 10% second harmonic distortion sounded like (Ex. 10 from post #41)

Loading the player ...

13. And now, here is what 10% third harmonic distortion sounds like:

Loading the player ...

Hopefully you can hear 10% of either 2nd or 3rd harmonic distortion. But would you agree that the sonic character of these two rather subtle distortions is very different?

Now what happens if we combine the 2nd and 3rd harmonic distortion with the original pure tone into one example:

14. Pure tone with 10% 2nd harmonic and 10% 3rd harmonics:

Loading the player ...

And there is something rather interesting about Ex.14 (so much so that I double checked I'd made it correctly). Compare 10a and 13 with 14 and what do you conclude about the audibility of the distortion in Ex. 14?

[A.S.]

In post #42 we sonically compared 2nd harmonics with 3rd harmonics. Hopefully you could hear a difference in the characteristic sonic nature of even order harmonics (2nd) and odd-order harmonics (3rd).

We can add a whole series of even order harmonics or odd order harmonics and see what they sound like. I'm going to add them in the same quantity, to emphasise the point.

[I have run-out of available MP3 in-thread players (temporarily) so am reverting to the Flash audio player for now and will re-encode for MP3 later]

15: Our 440Hz pure reference tone again:



16: 440Hz tone plus 10% 2nd, 4th, 6th (even order) harmonics:



17. 440Hz tone plus 10% 3rd, 5th, 7th (odd order) harmonics:



What I hope we can hear now is that Ex.16 with the even-order harmonics sound like a cheap electronic organ. You could play simple chords on this and it would sound 'robotic' but nevertheless passable as a child's toy. But in the case of Ex. 17, do you think that the presence of such strong odd-order harmonics could ever sound tuneful, no matter what notes were actually being played? The point is, just as the text books warn us, even order harmonics at moderate levels (say, a percent or two) blend very nicely with the music and are masked by it. But odd-order harmonics have a nasty, rasping edge which never sounds musical and are much more audible and irritating.

And guess what type of harmonics are typical of amplifiers? As a rule of thumb, tube amps will generate significant even order harmonics and poorly designed transistor amps mainly generate odd order harmonics. And hence there is some objective fact behind the 'warm' tube sound and the (sometimes) 'hard' solid state sound. But whilst the even order harmonics just can't be removed from the tube amp because that are the very nature of the valves themselves, a well designed transistor amplifier can have (as we observed in post #24) effectively zero harmonic distortion of either even-order or odd-order harmonics. But would you prefer zero harmonic distortion when a little second order distortion could nicely warm-up the sound?

Subject now open for debate.

[weaver]

And there is something rather interesting about Ex.14 (so much so that I double checked I'd made it correctly). Compare 10a and 13 with 14 and what do you conclude about the audibility of the distortion in Ex. 14?

On first listen I thought 14. less distorted than either of the other two.

[A.S.]

On first listen I thought 14. less distorted than either of the other two.

Ummm. That's not what I expected you'd say although I can image a reason why you deduced that.

What I was hoping you'd say was that in Ex. 14 (Pure tone with 10% 2nd harmonic and 10% 3rd harmonics) that the dominant distortion appeared to be the 3rd harmonic one, and that the 2nd harmonic was buried 'under' the third harmonic. Agree?

And how about in the real world? How much distortion does a typical loudspeaker generate in normal use? We can look as an example (although distortion is a little on the high side) at a sealed box, very highly regarded, well reviewed and innovative speaker system popular in the late 1980s (I just have this review to hand - there may be other better examples). What we can see is that at 100Hz @ 86dB - what we here consider to be a normal, safe-on-the-ears domestic listening level - this highly respected speaker generates about 9% second harmonic distortion and under 1% third harmonic. At 96dB, quite loud domestically, the second harmonic distortion is about 15% and the third at about 2.5%. This is not atypical for a good speaker system. And is far, far more distortion than all but the very worst audio amplifier you could find at a junk store.

One wonders how "rhythm and pace" may relate to an abundance (or not) of distortion.

>

[weaver]

Ummm. That's not what I expected you'd say although I can image a reason why you deduced that.

What I was hoping you'd say was that in Ex. 14 (Pure tone with 10% 2nd harmonic and 10% 3rd harmonics) that the dominant distortion appeared to be the 3rd harmonic one, and that the 2nd harmonic was buried 'under' the third harmonic. Agree?

Almost.

Can we just bring a little theory of music in at this point?

The 2nd harmonic of A 440 Hz is 880 Hz which is another A but an octave up.

The 3rd harmonic is 1320 Hz which is an E above the 2nd harmonic A and in musical terms is another fifth up (and in musical terminology is actually called the dominant.)

An A major chord would consist of A, C sharp and E - a major chord is probably the most 'normal' chord that we hear and in this context the combination of A and E doesn't have any of the negative sounds that we associate with 3rd harmonics in a hifi context.

(the 3rd video in post 37 shows this nicely)

Playing A 440 with it's third harmonic - 1320 Hz is a relatively large interval - an octave plus a fifth. Adding in the 2nd 'bridges the gap' to an extent.

Sounding notes an octave apart will always sound as normal as it gets - otherwise they wouldn't be the same note. Any other interval will always sound more 'odd', ie. more distorted in this context.

So, yes I agree with you but looked at in musical terms rather than plain 'harmonic distortion' terms.

One further thought: the 6th harmonic will be 2640 Hz which is actually another E - so now 'E' gets to be an even order harmonic as well!

[EricW]

What I was hoping you'd say was that in Ex. 14 (Pure tone with 10% 2nd harmonic and 10% 3rd harmonics) that the dominant distortion appeared to be the 3rd harmonic one, and that the 2nd harmonic was buried 'under' the third harmonic. Agree?


>

That was definitely my initial perception, although as I went back and kept re-listening to the samples, I started to second-guess myself a bit. Perhaps I was gradually becoming more sensitized to the presence of the second harmonic "under" the third. But yes, the third harmonic was definitely dominant: it had a sharper tone, with a greater sense of "presence".

[A.S.]

Ok. So it seems that the odd-order third harmonic (and this is also true for 5th, 7th, 9th, 11th etc.) draw more attention to themselves than the even order harmonics (2nd, 4th, 6th, 8th, 10th etc.). So as a general guide, minimising the odd-order harmonics even if it means that the even-order harmonics inevitably increase (a little) may be an attractive design goal.

But as an audiophile chasing every last degree of performance (cables, stands, room tuning) aren't you even a little shocked that a highly respected speaker system can generate 10% or more second harmonic? 10% is so significant that you can actually observe the distortion of the waveform on a 'scope (picture later): a pure sine wave no longer looks pure. If the speaker generates 10% distortion, is it really a worthwhile goal to engineer an amplifier with 0.1 or 0.01 or 0.001% distortion? Isn't it logical that 10% speaker distortion completely swamps the much lower distortion of the electronics?

Those with a long memory may recall the Leak 'Point One' tube amplifier - from the 1950s (or was it 60s?). The point one name referred to a the target specification of achieving 0.1% distortion (total? harmonic?). And at the time, it was concluded that 0.1% amplifier distortion was a really worthwhile (and low) target to achieve.

[Labarum]

Try this

http://www.nutshellhifi.com/library/tinyamps.html

Not sure I understand it all, and I cannot find details of the distortion-weighting arguments referenced.

This seems to be the core of the matter:

The problem with using THD as a yardstick of quality is the order of the distortion term has a far more audible effect than its absolute magnitude. When you have 3 or more fundamental tones, the number of IM sum-and-difference terms are much worse when you have to contend with a large number of harmonics past the third. This was first discussed by Norman Crowhurst and D.E.L. Shorter of the BBC in the mid-Fifties, so it's hardly a new or radical concept.

Regrettably, the single-tone additive THD . . . tests in common use today do not take this into account, thus ignoring the far more audible effects of the upper harmonics with real musical sources . . .

The market-driven pursuit of the ever-lower THD number is why the audio industry progressively abandoned of linear amplifying devices in favor of less linear devices with more gain, and turned to circuits that used greater and greater amounts of feedback. With each step the THD figure moved downward, while the harmonic structure became less predictable and more complex . . .

The thrust of the argument seems to be that for a generation we have been measuring the wrong things, which may account (in part) for subjectivists maintaining their choice sounds better in spite of the science.

[A.S.]

...The thrust of the argument seems to be that for a generation we have been measuring the wrong things, which may account (in part) for subjectivists maintaining their choice sounds better in spite of the science.

Well, of course, you are pre-supposing that the subjectivists can/will be proven right under objective blind listening tests. In other words, that they are hearing something which we ordinary mortals are not hearing or measuring. I seriously doubt that is true. Once the loudness of A is equalised with the loudness of B, I really don't believe these night and day differences are still audible. Of course, they are audible in an uncalibrated, any-old-loudness comparison, even an instantaneous A-B one.

I'm glad you introduces the distortion weighting point. You will notice that in my audio clips #16 and 17, that I introduced an equal amount of 2nd (or 3rd harmonic) distortion. So, for example #16, I took the fundamental at 100% and added in with it 10% of 2nd harmonic plus 10% 4th and 10% 6th. That was to make a point. You are most unlikely to find that equivalence of distortion (10% fixed) as you step up through the harmonics. In the real world, the harmonics of the fundamental tend to diminish in quantity (percentage) as the frequency increases. So an audio signal with fundamental 100% and 10% + 10% + 10% harmonics doesn't exist in the real world. A more likely scenario is 100% + 10% + 5% + 2% + 0.5% as frequency increases. You can see that generally downward sloping trend in harmonics if you look at the harmonic make-up of musical instruments and audio amplifiers. Do you have an example?

[Labarum]

1. I should have known better that to reference the subjectivist/objectivist debate!

2. Do you, Alan, have access to the work of "Norman Crowhurst and D.E.L. Shorter of the BBC". It would be fascinating to see that, and their reasons for proposing that distortion figures should be weighted.

3. I have not yet seen any reference in this thread to non-harmonic distortion - when an amp adds components not found in the natural harmonic series - components that cannot hide in the timbre of the instruments. I can find it no more simply described than here

http://stereos.about.com/od/faqs/f/imd.htm

These spurious noises are the nasty ones.

[Labarum]

From

http://www.nutshellhifi.com/library/FindingCG.html

so still not the original source.

Areas of the "Soul of Sound" site leave me uneasy, but this quote gets us closer to the BBC work.

The Sound of Different Harmonic Spectra

As mentioned above, odd and even harmonics can be recast as asymmetric distortion and symmetric distortion, thus the very different effects seen with IM distortion tests. As D.E.L. Shorter of the BBC pointed out in the April 1950 Issue of Electrical Engineering, real music is dominated by a great many closely-spaced tones - a choir or massed violins having the most dense spectra of all. Shorter showed that with a few as three closely spaced tones, IM sum-and-difference sidebands outnumber the much simpler harmonic series. In effect, as the number of tones increase, the number of IM sidebands increase at much faster rate than simple harmonics. The boundary case is 3 tones of equal magnitude; for 2 tones, IM is about the same as harmonic distortion, for 4 tones, IM is far greater than harmonic distortion. I leave it to the imagination of the reader to figure out how many simultaneous tones are present in real music — a lot more than three!

The influence of IM vs THD has additional consequences for the type of music we listen to. Jazz and folk music have sparse spectra, thus THD will play a larger role in subjective coloration. By contrast, a cappela singers, large choirs, and massed violins have very dense spectra, with many closely-spaced tones drifting in and out of phase-lock all the time. This type of music will be strongly degraded by even small amounts of IM, but not as sensitive to relatively small amounts of low-order harmonic distortion. Thus the origin of the endless audiophile wrangles that are actually based on the type of music the listener prefers . . .


The Effects of Feedback on Harmonic Structure

The Williamson amplifier of 1947 was the design that did the most to popularise the "feedback cures all ills" philosophy. It is interesting during the period from 1948 to 1956, almost all commercial hi-fi amplifiers were Williamson topologies (with minor exceptions for Quad II, McIntosh, and EV Circlotron). During this formative period the mantra of "more power, lower THD" became the driving force in the industry. By 1960, ultra-wide bandwidth, heavy feedback, and Class AB EL34 and 6550 UL circuits ruled the industry.

In the span of twelve years, the traditional audio-engineering prejudice against high-distortion devices faded, opening the door to high-power pentodes and Class AB operation. Each "improvement" was characterized by an increase in device distortion, which was then "corrected" by more and more feedback. Transistors circuits with even higher feedback ratios were the next obvious step - after all, they had more power, lower THD, more bandwidth, and most important of all, cost less to build.

Norman Crowhurst wrote a fascinating analysis of feedback multiplying the order of harmonics, which has been reprinted in "Glass Audio," Vol 7-6, pp. 20 through 30. He starts with one tube generating only 2nd harmonic, adds a second tube in series (resulting in 2nd, 3rd, and 4th), and then makes the whole thing push-pull (resulting in 3rd, 5th, 7th, and 9th), and last but not least, adds feedback to the circuit, which creates a series of harmonics out to the 81st. All of this complexity from "ideal" tubes that only create 2nd harmonic!

With real devices there are even more harmonics. In terms of IM, actual amplifiers have complex and dynamic noise floors thanks to the hundreds of sum-and-difference IM terms. That's not even counting the effects of reactive loads, which adds a frequency dependency to the harmonic structure! (With reactive loads, additional harmonics appear due to the elliptical loadline seen by the power tubes. The elliptical load-line dips into the very nonlinear low-current region, resulting in an instantaneous increase in upper harmonics. This spectral "roughening" is most audible with strong low frequency program material and hard-to-drive horn or vented bass drivers.)

As Crowhurst noted, feedback mostly reduces the 2nd and 3rd harmonics, leaving the upper ones more or less alone, or sometimes even greater than before. Feedback fools the simple THD meter, but the spectrum analyzer sees through the shell game. Too bad raw power and almost useless THD measurements became the end-all and be-all for more than 50 years. If more engineers and reviewers had access to spectrum analyzers, the misleading nature of raw THD measurements would have been discovered earlier, and amplifier design might have taken a different course.

[Labarum]

A fascinating paper from Wireless World by a BBC engineer is found here

A new distortion measurement
Better subjective-objective correlation than given by t.h.d.
by R. A. Belcher, B. Sc., Ph.D., M.I.E.E., BBC Research Department

http://www.keith-snook.info/Wireless...easurement.pdf

This article gets quite technical, but even skipping the bits not understood would make for an interesting read.