I asked the moderators to move this, not just to avoid an off-topic debate, but to have a place to analyse where the limits of current amplifier theory lie and how they can be improved.
Hopefully the improved theory will lead to improved amplifiers.
Amplifiers are Minimum Phase at low frequencies.
They inevitably become Non-minimum phase at some point, eventually.
From time delays in transistors and wires if no other reason.
These delays are often invoked by opponents of feedback.
They are equally as often dismissed by sensible analysis, they are too small to have the impact claimed for them.
The rejection of this cause of Non-MP has tended to extend to any possible Non-MP behaviour.
This may not always be accurate.
Practically all current analysis assumes perfect MP behaviour.
But Non-MP does set limits to what is possible for feedback to achieve.
So it is important to include Non-MP to determine these limits.
I want to move from a simple first order approximation to a more advanced second order model.
David
Hopefully the improved theory will lead to improved amplifiers.
Amplifiers are Minimum Phase at low frequencies.
They inevitably become Non-minimum phase at some point, eventually.
From time delays in transistors and wires if no other reason.
These delays are often invoked by opponents of feedback.
They are equally as often dismissed by sensible analysis, they are too small to have the impact claimed for them.
The rejection of this cause of Non-MP has tended to extend to any possible Non-MP behaviour.
This may not always be accurate.
Practically all current analysis assumes perfect MP behaviour.
But Non-MP does set limits to what is possible for feedback to achieve.
So it is important to include Non-MP to determine these limits.
I want to move from a simple first order approximation to a more advanced second order model.
David
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I would apologize to everybody, we had an off topic discussion about practical aspects of an audio power amplifier, I was quibbling about SOA design, while Mr. Zan had some very practical points about the non minimum phase characteristics.
I would say your comment is truer than you intended.
A quick look at Toni's thread, from where the circuit under discussion was copied (post#457), shows that in post #537 I recommended to Toni how to neutralise the non-minimum phase (RHP) zero.
Toni replies that it helps and his subsequent versions all use this technique.
That's very practical😉
On the other hand your comments on SOA have been dismissed.
That's a quibble.
I could, of course, be incorrect, so rather than just bicker let's put it to the test - and ask Toni who's comments have been practically useful and who's quibbles?
In the meantime, to return to the point before you commented on the SOA, where do you think the non-minimum phase behaviour comes from?
Really, I would be interested to learn your ideas about this, hence my persistence.
Best wishes
David
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I have no idea and honestly I don't care.
That's after I noticed you used 18ohm output devices base stoppers in the asc file you quoted at as an example. I didn't even bother to re-capture that thing. Life is to short, even for me.
Tony's amp didn't explode because of the power supply collapsing, I already mentioned that. Yet another method for SOA protection (no pun intended, many commercial amplifiers are using such). Otherwise, those drivers don't have a chance to survive any worst case conditions (load, thermal), with a stiff +/-70V power supply (as it IMO should be, to justify 8 output pairs).
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Your excuses become more and more implausible😉
Any reasonable output base stopper makes essentially no difference to the VAS Non-MP behaviour.
It's not even what I use in my amp, just happened to be what was in an example.
Use what ever you like, it's conveniently parameterised, takes <5 seconds
For someone for whom "life is to[sic] short" it's odd that you spend more time to type an excuse than it would take to do.
Even if your claim is correct, he presumably doesn't have worst case transistors, he doesn't run it in a room heated to uninhabitable temperatures and he doesn't have an arc welder for a power supply - from memory it's only 650 VA toroids. So just another quibble.
Best wishes
David
Could you, for the non-experts who want to dip in and out, please explain what "minimum phase" means and what it assumes and what effects that has on the output signals.
Then tell us what "non minimum phase" means.
Then tell us what "non minimum phase" means.
For an amplitude response A and w= 2pi*f, a minimum phase system will have by definition a phase vs frequency response of dA/dw.
Spend a few minutes with Excel. It will be educational. Put in a frequency response curve of your choice and see what the minimum phase response looks like.
Simple example, when low pass filter has a roll-off as the frequency increases not only does the amplitude decrease but the phase is affected too.
There is a minimum amount the phase must be be affected, this is minimum phase. But the phase can be affected more, naturally this is non-minimum phase.
If you equalize the amplitude of an MP system back to flat then the phase is flat too. This does not happen if the system is Non-MP, the phase shift is not reversible.
Feedback stability depends on phase and amplitude so the difference between the two types of systems is crucial.
It is sometimes expressed by reference to the transfer function of the filter (which is what any amplifier is eventually) in the complex plane. So you will see the terms Left Half Plane LHP zero (minimum phase) and RHP zero Non.
There's a ton of mathematics for this, I have tried to explain the ideas rather than the maths in my Linear Audio articles.
Best wishes
David
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Let's append an RC filter on the input to an amplifier.
Now adjust the output of the amplifier such that it corrects for the input filter to give a flat passband out to a couple of octaves wider than the input filter.
The phase in the new pass band is near zero, because the RC filter and the amplifier and the correction to the amplifier's passband are all "minimum phase".
Is that correct?
This is a bit like a Linkwitz transform ! But it only works when the speaker roll off and the amplifier adjustment and the amplifier are all minimum phase.
Is that correct?
Now adjust the output of the amplifier such that it corrects for the input filter to give a flat passband out to a couple of octaves wider than the input filter.
The phase in the new pass band is near zero, because the RC filter and the amplifier and the correction to the amplifier's passband are all "minimum phase".
Is that correct?
This is a bit like a Linkwitz transform ! But it only works when the speaker roll off and the amplifier adjustment and the amplifier are all minimum phase.
Is that correct?
This is not actually correct. The phase is related to the slope of the amplitude response but is not simply equal.
There are some technical issues to make the definition mathematically strict.
Basically the slope of the amplitude curve affects the phase at that frequency the most and the effect tapers off to infinity.
It is actually a fractional derivative, which I only learned recently.
If you know what a first derivative is then think about a "halfth" derivative!
As only a mathematician "wannabee" that really kills me.
Best wishes
David
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Could you give me a reference for that? All of my textbooks use the first derivative.
Would a halfth derivative of sin(wt) be equal to sqrt(w)cos(wt)? (or halfth of exp(wt) = sqrt(w)exp(wt)?)
Yes!
Phase in multi-way speakers is a bit more problematic, LinkwitzRiley crossovers (or others) are not MP for instance. But I think the transform is.
For a speaker minimum phase is more debatable. I'll pass.
Best wishes
David
http://trs-new.jpl.nasa.gov/dspace/bitstream/2014/19495/1/98-0905.pdf
gives a few of the more useful "Bode Integrals" - including the gain/phase
about 1/2 way thru http://www.ece.jhu.edu/~pi/Courses/454/Notes8.pdf is a few pages more
and this goes a little into nonminium phase http://leo.technion.ac.il/Courses/CT/Lectures/lect02b.pdf (jump to Bode's gain-phase relation section)
(it helps to add coth to the google search terms)
could be a Hlibert Transform - if I understood what that is
but its easy to find statements like:
gives a few of the more useful "Bode Integrals" - including the gain/phase
about 1/2 way thru http://www.ece.jhu.edu/~pi/Courses/454/Notes8.pdf is a few pages more
and this goes a little into nonminium phase http://leo.technion.ac.il/Courses/CT/Lectures/lect02b.pdf (jump to Bode's gain-phase relation section)
(it helps to add coth to the google search terms)
could be a Hlibert Transform - if I understood what that is
but its easy to find statements like:
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Turns out that it's sin (wt + pi/4), which sorta makes sense- you get a 90° phase shift for a "whole" derivative, so a half derivative would cause a 45° phase shift.
But the minimum phase still should look like a Hilbert transform- I can't find a reference that says anything else.
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