An experimental 4-th order linear audio power amplifier

[dom0]

I guess technically you are right, although differential signaling isn't commonly used without balanced lines, even in digital circuits.


As I understand GKs explanations the dominant pole fallback is around to force the amplifier into stable operation even if it is strongly clipping, because an oscillation once occured in this system doesn't die down. Really sounds more like a safety net, nothing that should be active in regular use.....

[Richard Head]

I wonder what the transient response would look like?

[T3sl4co1l]

Should be a little slow to get going, then an increasingly rapid slope (you might not be able to see the slopes transition as each integrator saturates), then as it settles down, a very long settling time, to an extremely precise level (though ultimately still limited by the offset and GBW of the amps involved).

A fascinating implication of such a network is it seemingly implies that, if stages are transitioned continuously, then one would get a continuously variable (i.e., fractional) integral.  In analogy to a saturating chain of ampilfiers, the sum of which exhibits a log(Vin) curve (log base being the gain per stage).

The biggest downside is, the 'plant' (last integrator / gain stage / output) needs to be incredibly fast, because each integrator takes off a factor of 3 or more from the GBW.  I think.  "Very long settling time" is relative to this final bandwidth, which I suppose would have to be in the several MHz range, for an audio application (20kHz+).  Which doesn't really sound so bad, at least.

Also, the settling would be in terms of not just voltage, but "jerk" (derivative of acceleration, V/s^3)!  Actual voltage settling may be good or poor (I'm not sure; depends how much voltage over/undershoot is required to adjust those derivatives; and the compensation*, of course), and will take all that extra time, but we're talking asymptotic reproduction of ramps and second order curves, which means fantastic AC reproduction.

*A 4th order controller plus single pole 'plant' implies we can solve for coefficients (hopefully -- if possible) that satisfy a particular filter polynomial, such as a 5th order Bessel.  That would be a sweet amplifier indeed.

Tim

[dom0]

https://www.eevblog.com/forum/projects/an-experimental-4-th-order-linear-audio-power-amplfier/msg240562/#msg240562

[wiss]

Just a thought (subscribe), THD must be dominated by the input stage in this design. In my experience it gets difficult to get that below -150 dB

[nano]

Any ideas? Sounds good? If the Hypex “N-core” amplifier modules were not so expensive I would have bought one already to reverse engineer it, with particular interest in the saturation detection circuitry.

The analog switches can probably be replaced by OTAs, or even just clamp diodes (back to back zeners from OUT to -IN) on the integrators really, so that a more modest nonlinearity can be used to transition from integrator to inverter behavior.

This very nice publication describes a fairly simple saturation circuit which improves upon the zener method.
As far as I know this solution is very very similar to what hypex uses in the ncore amplifiers.

[GK]

Hmm, I didn't see this. Fascinating as usual, GK

Only problem I have, which is rather fundamental in my opinion, and I'm sure you're aware of the drawback: why screw it up by introducing explicit discontinuities?! 

You obviously need to think this through some more.

As I understand GKs explanations the dominant pole fallback is around to force the amplifier into stable operation even if it is strongly clipping, because an oscillation once occured in this system doesn't die down. Really sounds more like a safety net, nothing that should be active in regular use.....

Correct.

Should be a little slow to get going, then an increasingly rapid slope (you might not be able to see the slopes transition as each integrator saturates), then as it settles down, a very long settling time, to an extremely precise level (though ultimately still limited by the offset and GBW of the amps involved)*snip*

Not a single integrator even comes close to "saturating" during slew-rate limiting.

https://www.eevblog.com/forum/projects/an-experimental-4-th-order-linear-audio-power-amplfier/msg240562/#msg240562

I get the impression that hardly anyone has properly read through my posts.

This very nice publication describes a fairly simple saturation circuit which improves upon the zener method.
As far as I know this solution is very very similar to what hypex uses in the ncore amplifiers.

Interesting paper, but the scheme is totally unworkable/inapplicable in this design which, having multiple cascaded integrators, is topologically vastly different in operation to the discussed class-d designs (which have ~constant loop gain throughout the audio band).

[GK]

@GK,

I've been reading through your 4th order power amplifier topic with great interest. You mention that this design has been featured in Linear Audio magazine, however I can't seem to find in what edition? Now it so happens I own every edition, and have looked through a number of them, but can't seem to find your article, could you perhaps point me in the right direction?

Thanks and best regards,

Sander.

Thanks for the interest. I sent the pictured amplifier overseas for independent measurement on an AP system 2, to someone who was going to co-author (simply write up their independent testing) the article for LA.

The prototype amplifier when dud somewhere along the line - the independent linearity measurements did not match the final (comprehensive) measurements I made on the prototype before sending it off.

The amplifier was returned to me and I eventually tracked the problem down to a dud driver transistor with a measured ~25 hfe. The amplifier PCB was dissected in the process and is not rebuildable.

A major PITA all around and I've mostly lost incentive. I have started on a MKII prototype which is significantly improved again but the endeavour is on the backburner.
       

[T3sl4co1l]

Hmm, I didn't see this. Fascinating as usual, GK

Only problem I have, which is rather fundamental in my opinion, and I'm sure you're aware of the drawback: why screw it up by introducing explicit discontinuities?! 

You obviously need to think this through some more.

....

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..And?

You could be less cryptic and more, Idunno, human or something.

Tim

[nano]

Interesting paper, but the scheme is totally unworkable/inapplicable in this design which, having multiple cascaded integrators, is topologically vastly different in operation to the discussed class-d designs (which have ~constant loop gain throughout the audio band).

I always wondered why Class-D amps use contsant loop gain. Putzeys mentioned he does this for audiophile reasons to have constant distortion over frequency. But are there any technichal drawbacks to place the poles at the origin (like you did)?

I’m pretty new to all this control theory stuff and I’m still learning. Would the scheme from the Kemp Thesis work if you added (low gain) local feedback around the conventional power amplifier?

[ssassen]

A major PITA all around and I've mostly lost incentive. I have started on a MKII prototype which is significantly improved again but the endeavour is on the backburner.

That's indeed unfortunate, I would however be interested in learning more about this MKII prototype, is there anything you can disclose, or would you rather this is kept off the forum?

[ssassen]

Interesting paper, but the scheme is totally unworkable/inapplicable in this design which, having multiple cascaded integrators, is topologically vastly different in operation to the discussed class-d designs (which have ~constant loop gain throughout the audio band).

I always wondered why Class-D amps use contsant loop gain. Putzeys mentioned he does this for audiophile reasons to have constant distortion over frequency. But are there any technichal drawbacks to place the poles at the origin (like you did)?

It needs to have a controlled behavior, as without an elegant mechanism to reduce the global loop's order you could end up in a situation where the MOSFETs at the output start conducting at the same time, effectively shorting out the power supply. I guess it needs no further explanation why that is a bad thing?

[dom0]

There are actually Class D controllers around that have neither a controlled dead time nor cross-conduction protection? Ugh!

[GK]

Interesting paper, but the scheme is totally unworkable/inapplicable in this design which, having multiple cascaded integrators, is topologically vastly different in operation to the discussed class-d designs (which have ~constant loop gain throughout the audio band).

I always wondered why Class-D amps use contsant loop gain.

The short answer is that it is simpler; and in a high-order feedback amplifier quadruply so. I presume that you have read the "F word" article. I would take Putzeys claims regarding constant loop gain with a grain of salt. The article was essentially a precursor to the release of the "N-core" amplifiers to the audiophile market place. If you know much about that domain you know about the plethora of boutique audio designers and popular reviewers that differentiate their products with the "negative feedback is bad" religion.

The original gripe with high levels of negative feedback go back to the thoroughly discredited postulations of Otala, which those without a good grasp of control theory continue to perpetuate to this day. It seems intuitively obvious to some that an amplifier with a close enough to theoretically ideal transfer function such that the open loop bandwidth is only perhaps a few tens of Hz is completely inadequate for faithfully reproducing 20Hz-20kHz audio. Personally, I found it a bit cringe worthy that Putzeys, in his article ironically tag lined "there is no such thing as too much feedback", essentially found a different angle to basically argue the exact same thing. Putzeys constant loop gain thing in my view was just a way to make "high level" negative feedback sound palatable to the audiophile crowd. He certainly hasn't managed to produce a credible psycho-acoustic reference for his subjective assertions.

But anyway, a good a reason as any for sticking to constant loop gain throughout the audio frequency spectrum in a high-order feedback amplifier is simplicity, and there is nothing wrong with that. If you want to make, say a fourth or a fifth order design as I have shown here, with an open-loop transfer function approaching the ideal, you need to provide a bucket load of gain. You can't provide for that by simply tweaking some circuit constants. As far as I have managed to figure the most intuitively practical and mathematically obvious way of doing this is to cascade multiple integrator stages with zeros. But that adds significant complexity even before contemplating how to keep all of those integrators under control when the control loop enters saturation.
 
There is no reason that I can see why you couldn't implement a control scheme as per the discussed class-d designs around a class-ab linear amplifier. You could even retain the output filter. That would be another technically interesting avenue to pursue just for the sake of it.