Inherent distortion in class AB

[Malcolm Irving]

It does not seem to be widely known that class AB introduces inherent distortion. Here is my reasoning:
The diagram below represents the idealised plate characteristics of one pentode of a push-pull pair. The load lines are for class AB operation.



Point Y is the quiescent, or bias, point where this pentode is conducting 30mA. The other pentode is also conducting 30mA, but the current in the load at this point (under dynamic conditions) is zero.
Point X is the point where the other pentode cuts off, and can be regarded as the transition point between class A and class B operation.
If dynamic conditions move from point X to point Z the current in the load doubles (it is a transformed version of 60mA to 120mA) and this would require a change in Vg of 6V.
But to move the output current from a transformed 60mA to zero (from point X to point Y) it is only necessary for Vg to change by 3V.
This shows that there is an inherent nonlinearity (and hence distortion) in class AB, even if the pentodes were perfectly linear.
Global negative feedback will easily reduce the effect of this nonlinearity.
This type of distortion is sometimes mentioned in the hi-fi literature, where it is known as ‘Gm doubling’.

[Jazz P Bass]

Yup.

[Mike Sulzer]

But is this not where the inherent non-linearity of the pentode or beam power tetrode saves the day? Look at this: http://www.keyboardpartner.de/hammon...r/6L6GC_P8.GIF
Notice how for equal changes in vg, the resulting change in plate current is small at low current and large at large current. Therefore, having both tubes on at idle makes the total gm higher, just what you need. Then as you apply the inputs with opposite polarity, the gm of one increases, and the other decreases. Of course, to take full advantage of this you have set the idle current for minimum harmonics over this range. But everyone has a spectrum analyzer these days!

It does not seem to be widely known that class AB introduces inherent distortion. Here is my reasoning:
The diagram below represents the idealised plate characteristics of one pentode of a push-pull pair. The load lines are for class AB operation.

[ATTACH=CONFIG]37385[/ATTACH]

Point Y is the quiescent, or bias, point where this pentode is conducting 30mA. The other pentode is also conducting 30mA, but the current in the load at this point (under dynamic conditions) is zero.
Point X is the point where the other pentode cuts off, and can be regarded as the transition point between class A and class B operation.
If dynamic conditions move from point X to point Z the current in the load doubles (it is a transformed version of 60mA to 120mA) and this would require a change in Vg of 6V.
But to move the output current from a transformed 60mA to zero (from point X to point Y) it is only necessary for Vg to change by 3V.
This shows that there is an inherent nonlinearity (and hence distortion) in class AB, even if the pentodes were perfectly linear.
Global negative feedback will easily reduce the effect of this nonlinearity.
This type of distortion is sometimes mentioned in the hi-fi literature, where it is known as ‘Gm doubling’.

[ThermionicScott]

I think this doesn't get as much press precisely because pentodes and beam power tubes are non-ideal. Amplification is greater near saturation and lesser near cutoff, so the doubling-up of signal compensates for that effect. But as long as the amp is somewhere between class A and class B, that kink will end up somewhere, so NFB is good for cleaning that up.

[nickb]

Which is just as well since for real non-linear tubes the gm is smaller at low currents - e.g for a 6L6 about 3mS at 40mA and 10mS at 200mA. It is why biasing the tubes helps to reduce crossover distortion - you double the low end gm of 3mS to 6mS.



As a consequence, the actual transfer function looks like this:



And much the same is true for transistor AB stages too.

But I know you already knew that. I have a suspicion you just wanted to put the fox in the hen house

[Malcolm Irving]

Yes, the above posts are correct. The effect is compensated for, in practice, by the reducing Gm as the pentode approaches cut-off. The difficulty of cutting-off a pentode also means that the class A to class B transition is smoothed out.
I think the effect might be significant for amps such as AC30 which has a wide class A region and no feedback.
In a lot of solid-state amps the class A region is very narrow, and is only used to avoid the possibility of cross-over distortion in class B (if component values drift).
The ‘Gm doubling’ doesn’t seem to get mentioned much in tube guitar amp circles – so I just wanted to check if folk are aware of it. But always happy to put the fox in the hen house!

[ThermionicScott]

I think it might depend on your perspective. If the amp were biased so that the tubes never went into cutoff (not to be tried with an AC30!), then even though the Gm doubling was still happening, it would also never not happen, so could you still call it "distortion"?

ISTM that the effect should be less pronounced at higher bias currents and a higher primary Z, so that's why cathode-biased amps seem to get along without NFB, whereas it's hard to find fixed-biased amps without it.

[Malcolm Irving]

.... If the amp were biased so that the tubes never went into cutoff (not to be tried with an AC30!), then even though the Gm doubling was still happening, it would also never not happen, so could you still call it "distortion"?
....

That would be a class A push-pull amp, which is sometimes used in hi-fi, but (as far as I'm aware) has not been used much in guitar amps. The output power would be much less than you could get, with the same output tubes, in the usual class AB design. But, as you say, no distortion from this effect, as Gm is double all the time.

If you tried to get to that point by warming up the bias (e.g. in an AC30) you would exceed the quiescent plate dissipation limit before you got there.

[ThermionicScott]

Yep!

[printer2]

But what is wrong with distortion?





Hen house? Who, me?

[Mike Sulzer]

But what is wrong with distortion?





Hen house? Who, me?

Low level crossover distortion is different from clipping. You would need to listen carefully to see if it is what you really want.

[pdf64]

Is it good to refer to this effect as crossover distortion?
It would be strange for an AC30 to be used as an example of that.

I guess that the distortion created by this effect is low order odd harmonic, eg 3rd?

[Malcolm Irving]

A while ago I did some Fourier analysis, using Fourier Series Calculator - Fourier Series on line - Mathstools on a theoretical signal based on a pure sine-wave input, with Gm doubling for half the time. To be more precise, the Gm doubling occurs in the intervals (-pi to -3pi/4), (-pi/4 to pi/4) and (3pi/4 to pi) and Gm is not doubled in the intervals (-3pi/4 to -pi/4) and (pi/4 to 3pi/4).

The Fourier analysis, for this case, showed 6% third harmonic, 1% fifth harmonic and just below 1% seventh harmonic, plus lower levels of other odd harmonics.

I've got a feeling that it would be a 'nice sounding' distortion, but that would be subjective of course.

[Mike Sulzer]

Whether it is good or not I do not know, but i think it is appropriate because it results from crossing over from one tube to the other in a push pull amplifier. But I would be just as happy with another name if you have one.

Is it good to refer to this effect as crossover distortion?
It would be strange for an AC30 to be used as an example of that.

I guess that the distortion created by this effect is low order odd harmonic, eg 3rd?

[Mike Sulzer]

A while ago I did some Fourier analysis, using Fourier Series Calculator - Fourier Series on line - Mathstools on a theoretical signal based on a pure sine-wave input, with Gm doubling for half the time. To be more precise, the Gm doubling occurs in the intervals (-pi to -3pi/4), (-pi/4 to pi/4) and (3pi/4 to pi) and Gm is not doubled in the intervals (-3pi/4 to -pi/4) and (pi/4 to 3pi/4).

The Fourier analysis, for this case, showed 6% third harmonic, 1% fifth harmonic and just below 1% seventh harmonic, plus lower levels of other odd harmonics.

I've got a feeling that it would be a 'nice sounding' distortion, but that would be subjective of course.

The harmonics produced by this type of distortion have maximum percentage values at some not so high power rather than increasing at high power like clipping. So I guess that gives it a different feel, if it has a feel at all.