2nd vs. 3rd order harmonics

[rabies]

IIRC, class A circuits produce 3 order harmonics and class AB circuits produce 2 order harmonics (or vice versa?)

what's the difference and can solid state amps do this as well or not?

[defaced]

You've got it backwards. Class A is more second order. The natural phase cancellation of class AB reduces the second order harmonics, but that can be overcome by not using matched pairs, playing with the balance of the phase inverter and I'm sure many other things.

Even order harmonics reinforce the fundamental (original note), odd order work against the fundamental (and if you get enough of them, make a square wave). Solid state devices make more odd order harmonics. Human ears like the sound of even order harmonics which is why alot of people prefer the sound of tubes over solid state.

Harmonic addition: This example uses all harmonics to create a square wave, but simply using odd order will do it too.

[loudthud]

Odd harmonics are created when a waveform is distorted symmetrically. Asymmetric distortion has more even order harmonics. Most push-pull circuits tends to clip waveforms symmetrically so even harmonics are low. Single ended circuits usually won't clip equally on both top and bottom parts of a waveform so more even harmonics are produced.

Op-Amps usually clip symmetrically. Part of this is the way they are designed and the excessive feedback forces them to do it. Preamps with discrete transistors or FETs are warmer sounding IMHO and they don't use very much feedback (there are exceptions). Solid state power amps are usually more like Op-Amps.

The advantage of a tube is that the grid draws current with sever overdrive and that skews the symmetry of the clipping (too much and you have blocking distortion). The common push-pull tube power amp with a LTPI will produce even harmonics when over-driven because the input of the phase inverter skews the symmetry and limited feedback doesn't correct it. The inherent imbalance of the PI also contributes.

A square wave with 50%-50% symmetry sounds hollow but a square wave with 40%-60% symmetry sounds more musical.

[teemuk]

I was planning to post something very long but Loudthud got ahead of me and basically wrote out most of the things way better than I could…

I’ll just add that,

A pure sine wave contains only the fundamental harmonic whereas triangular waves and square waves consist of only odd order harmonics. Square wave signals are basically created out of an unlimited number of such components, like the animated demonstration showed. In triangular signals the amount of high order harmonic components is lesser. (Or more precisely, these components have lower amplitude). The more the signal resembles these waveforms, the more the signal must therefore contain odd-order harmonic components, and possibly more higher order harmonics as well.

[Rick Erickson]

[Most push-pull circuits tends to clip waveforms symmetrically so even harmonics are low. Single ended circuits usually won't clip equally on both top and bottom parts of a waveform so more even harmonics are produced.]

Given that - and I'm not suggesting it isn't correct, but it does raise a question to me:

Why do so many people (think they) like the sound of power tube clipping over preamp clipping? By definition, the preamp distortion should be adding lots of second harmonic distortion, and the power tube clipping in most amps will be lacking in 2nd harmonic.
In reality, most of the really sweet/smooth sounding non master-volume amps seem to be designed so that the preamp sections and the power amp distort together. Food for thought.

RE

[teemuk]

One reason for this, I think, is that these "sounds of harmonics" rules are clichés, started by Russell O. Hamm, and tend to not correlate with actual preferences of people.

It is not like odd harmonics=bad, even=good. That's too black and white way to look at it. It's more like a proper balance of many ingredients: To produce certain types of tones you inherently need more odd than even and possible a higher amount of high order harmonics too. For some other types of tones some other recipe might work better. And all that distorting usually co-exists with pre- and post equalisation that has a VERY BIG effect to the overall tone. People tend to give this harmonics stuff way more value than I think it actually deserves.

[loudthud]

+10E6 teemuk

[Why do so many people (think they) like the sound of power tube clipping over preamp clipping? By definition, the preamp distortion should be adding lots of second harmonic distortion, and the power tube clipping in most amps will be lacking in 2nd harmonic. ]

The magic comes from the LTPI's imbalance when overdriven. That's why it's the most popular by far in guitar amps. Most "improved" phase inverters reduce or eliminate the imbalance and don't sound as good (possible exception Hiwatt). You won't find the LTPI in HiFi circuits without significant modifications.

When a power amp is driven to clipping it starts to present a non-linear impedance to the speaker. If you turn down a master volume control below clipping, the impedance becomes more linear and the sound produced changes. Another thing that comes into play is affect of power supply ripple and regulation. These and other factors combine favorably to what we call tube power amp distortion and it's not the same as the preamp distortion that you get by turning down a master volume control.

[rocket]

Originally Posted by defaced

You've got it backwards. Class A is more second order. The natural phase cancellation of class AB reduces the second order harmonics, but that can be overcome by not using matched pairs, playing with the balance of the phase inverter and I'm sure many other things.

Even order harmonics reinforce the fundamental (original note), odd order work against the fundamental (and if you get enough of them, make a square wave). Solid state devices make more odd order harmonics. Human ears like the sound of even order harmonics which is why alot of people prefer the sound of tubes over solid state.

Harmonic addition: This example uses all harmonics to create a square wave, but simply using odd order will do it too.

in a squarewave there are NO even order harmonics at all! as another poster states here even order harmonics are found in unsymmetrical waveforms like a sawtooth (violin!) or in asymmetrically clipped waveforms.
Therefore single ended designs have more even harmonics than PP, regardless of Class A, AB or B. (of course all SE- designs are class A, though)

[defaced]

Then it looks like the animation is wrong!

[BackwardsBoB]

I think you're missing something if you limit your understanding of odd/even harmonics to symmetry.

The first, second, and fourth harmonic (the fundamental and loud even harmonics) are octaves. You can play any note with these harmonics present, and only get tones that are in the scale and blend well with the other notes you're playing.

But the third harmonic is a fifth above the second harmonic and I'm not sure what the fifth harmonic is, but you could figure it out, and it sure isn't some octave above the fundamental. If you're in the key of C and you play a B, you're going to get some F#, and if you play a C chord, you're going to get some B from the third harmonic of the E. Whether this sounds complex or bad is subjective, but it's not a problem with even harmonics, at least until you get to the sixth harmonic.

Go here and play with the Java applet:

http://blackstoneappliances.com/dist101.html

[Steve Conner]

The real magic of tube distortion lies in how the orders of harmonics change with the drive level. Different stages in the amp overdrive at different levels, and as tubes get overdriven, they rectify the drive signal and shift their own bias points, which causes an even more complex variation of harmonic spectrum with drive and time.

But generally, as you drive harder, the amount and order of harmonics both increase. On a good amp, you can go from a little touch of low-order sweetness, to an aggressive blat full of high- and odd-order harmonics, just by picking notes harder. It's not unlike the shift in tone caused by blowing a wind instrument harder (I think Russell O. Hamm even mentions this in his paper) and it adds another dimension of expressiveness to your sound.

Oh, and when people say that an amp "chimes", that's probably dissonant odd harmonics you're hearing. Bells and chimes all have dissonant partials, too. (I say "partials" because they're not necessarily at all harmonically related to the fundamental.)

PS: A square wave has no even harmonics: it's made of f, 3f, 5f, 7f, etc. If you want a wave that contains all harmonics, that would be the sawtooth. See your Minimoog manual for more details :-)

[Steve Conner]

The real magic of tube distortion lies in how the orders of harmonics change with the drive level. Different stages in the amp overdrive at different levels, and as tubes get overdriven, they rectify the drive signal and shift their own bias points, which causes an even more complex variation of harmonic spectrum with drive and time.

But generally, as you drive harder, the amount and order of harmonics both increase. On a good amp, you can go from a little touch of low-order sweetness, to an aggressive blat full of high- and odd-order harmonics, just by picking notes harder. It's not unlike the shift in tone caused by blowing a wind instrument harder (I think Russell O. Hamm even mentions this in his paper) and it adds another dimension of expressiveness to your sound.

Oh, and when people say that an amp "chimes", that's probably dissonant odd harmonics you're hearing. Bells and chimes all have dissonant partials, too.

(I say "partials" because the process that generates them doesn't mandate any harmonic relation to the fundamental, unlike distortion harmonics in an electronic circuit, which can only be harmonics.)

PS: A square wave has no even harmonics: it's made of f, 3f, 5f, 7f, etc. If you want a wave that contains all harmonics, that would be the sawtooth. See your Minimoog manual for more details :-)

[Steve Conner]

The real magic of tube distortion lies in how the orders of harmonics change with the drive level. Different stages in the amp overdrive at different levels, and as tubes get overdriven, they rectify the drive signal and shift their own bias points, which causes an even more complex variation of harmonic spectrum with drive and time.

But generally, as you drive harder, the amount and order of harmonics both increase. On a good amp, you can go from a little touch of low-order sweetness, to an aggressive blat full of high- and odd-order harmonics, just by picking notes harder. It's not unlike the shift in tone caused by blowing a wind instrument harder (I think Russell O. Hamm even mentions this in his paper) and it adds another dimension of expressiveness to your sound.

It seems remarkably difficult to emulate this effect with solid-state circuitry. You can do it. I remember the guy who made an AC30 simulator out of op-amps and zener diodes, and it was good enough that Korg bought him out and burnt the plans ;-) And the Blackstone guy seems to know where it's at with his MOSFET overdrive pedal. (Yes, I want one.) But generally, on a hobbyist scale it makes more sense to just use actual tubes.

Oh, and when people say that an amp "chimes", that's probably dissonant odd harmonics you're hearing. Bells and chimes all have dissonant partials, too.

PS: A square wave has no even harmonics: it's made of f, 3f, 5f, 7f, etc. If you want a wave that contains all harmonics, that would be the sawtooth. See your Minimoog manual for more details :-)