I remember a Mechanical Drafting class from long ago and far away, when that kind of thing still existed. I'd sketched in a radias'd corner, and the teacher asked how I made the corner. I confessed, so he asked how I should have done it. I explained the proper procedure and he was satisfied.
Simulations are fine if the underlying model and algorithms are understood, but can lead us down dark paths if the model's simplifications and assumptions aren't understood. "The map is not the world."
All good fortune,
Chris
Simulations are fine if the underlying model and algorithms are understood, but can lead us down dark paths if the model's simplifications and assumptions aren't understood. "The map is not the world."
All good fortune,
Chris
Good post.
I also never heard the term 'Baxandall distortion' before. What I mentioned and posted was a graph of harmonic levels versus distortion that was put together by Peter Baxandall many years ago, showing that moderate amounts of feedback in a certain setting make matters worse.
Maybe the name stuck that way, maybe we just witnessed the birh of a new, wrongly-understood term that will lead to lots of new fighting threads here ;-)
See attached, part 5, the penultimate part. Fig 6 is the test circuit, fig 7 is the graph. ASlso you should read the conclusions at that same page, they summarise the discussion. (Part 6, the last, does the same for BJTs.In Part 6, Peter also formulates a Distortion Theorem which leads him the term Inverse Distortion, which most probably is not what you though!).
I also find the 'term 're-entrant distortion' very misleading as it goes back to the 'going around and around' thing that doesn't happen, as it all is a continuous process.
People have a habit of compacting whole narratives in a few or just one word,. That normally isn't an issue during a discussion where everybody knows about it. But come back later and those terms start to lead their own lives and often are misunderstood.
Jan
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And after all this, I still contend that it does go "round and round". Feedback is causally recursive, and if it were not we wouldn't have the Feldtkeller/Farren/Baxandall/Putzeys effect. The finite (non-zero) propagation time stretches this a tiny bit (for audio) but that doesn't matter for the argument. Recursion is common in the living world (growth) and new and surprising outcomes often result. It could even be looked on as the complement to evolution by selection - instead of winnowing, recursion generates new variety.
I wonder what Bruno Putzeys would say about such a philosophical topic.
Much thanks, as always, and Happy Birthday to me,
Chris
At least we know that as an engineer he use multiple negative feedback loops to control his amps. As a manufacturer he use positive feedback reviews to boost sales of his amps. 😀
Well, I don't agree, because if it were recursive, there would be a signal difference in time between before the 'going around' signal arrives back at the input, and after it does, a small window in time that the distortion is not yet reduced, and then it is. There's no trace either in the physical world or in the math that such a different exists.
But you know what, I'll ask Bruno's view. Don't know if he can be bothered, but I'll ping him.
And happy birthday to you!
Jan
Reading (and thinking) about it again, I think I can see my own confusion.
For me, the term recursive meant something discrete, something non-continuous.
But I think that's wrong, something can be at the same time continuous and recursive.
Right?
Waiting for Bruno to chime in.
Jan
For me, the term recursive meant something discrete, something non-continuous.
But I think that's wrong, something can be at the same time continuous and recursive.
Right?
Waiting for Bruno to chime in.
Jan
Norvegian Nobel committee? 🤔 Everybody knows that the Nobel prize is awarded to the best scientists by the Finnish king.
If the rest of this thread has the same relation to reality, then...
Likewise approaching the problem mathematically with a physically impossible simplifying assumption; a perfect error amp with ideal feedback cancellation. If that was achievable feedback wouldn't be necessary.
My thinking with Spice is much simpler. An ideal differential gain block summed with a AC voltage source operating at twice the frequency of the gain block's input, the latter multiplied by some arbitrary negative scalar representing percent thd. An ideal amp with a single harmonic. Two fundamental and fully understood ideal elements to see the what before diving into the why.
Bruno's contribution, without comment:
Yes, feedback is recursive. Given a DC input, a [stable, negative] feedback system simply solves an equation by successive approximation (see also my reply to Menno in LA). In the classical case of a perfect polynomial nonlinearity you get new harmonics after adding feedback because the solution is not a polynomial. Its Taylor expansion goes on forever. Menno’s point was that real life nonlinearities aren’t perfect polynomials either, so with a few exceptions the “Baxandall effect” is really only observed in systems specially contrived to exhibit it. In fact, you could do the opposite and design a circuit whose open-loop transfer follows a square root law. Without feedback that gives you an infinite series of harmonics. Then you will see all higher harmonics drop away rapidly as you put feedback around it. It works both ways. So you can’t use the Baxandall effect to make general predictions of “what feedback sounds like”. Its only practical use lies in understanding why specifically people who try a small amount of feedback on e.g. a SET amplifier tend to dislike the result (and spend the rest of their lives talking about it).
So if you want to have an intelligent discussion about this, take the generalised view that feedback, in the extreme, first inverts the nonlinearity and only then proceeds to hammer it into the noise floor.
But note that it’s the equation-solving behaviour of a feedback loop that causes this inversion, not the fact that it solves the equation using recursion.
I’m hard pressed to see the point of the discussion though. Any system whose state depends on its state in the past is a feedback system. I’m inclined to consider feedback and recursion as synonymous. A falling rock is a recursive system. After all, the rock’s current position is highly contingent on where it was a microsecond ago and how fast it was going. Back to audio, any filter, even a passive one, is “recursive” in that sense. Fun fact: if you build a simple 1st order RC LPF with a non-linear capacitor and/or resistor, you get the classic rising THD vs frequency in the passband. Exactly like a simple 1st order feedback amplifier.
And in the digital domain, IIR filters are discrete-time approximations of analogue filters, and some DSP folk explicitly refer to IIR filters as “recursive”.
Reality is causal, so it’s recursive.
Jan
Yes, feedback is recursive. Given a DC input, a [stable, negative] feedback system simply solves an equation by successive approximation (see also my reply to Menno in LA). In the classical case of a perfect polynomial nonlinearity you get new harmonics after adding feedback because the solution is not a polynomial. Its Taylor expansion goes on forever. Menno’s point was that real life nonlinearities aren’t perfect polynomials either, so with a few exceptions the “Baxandall effect” is really only observed in systems specially contrived to exhibit it. In fact, you could do the opposite and design a circuit whose open-loop transfer follows a square root law. Without feedback that gives you an infinite series of harmonics. Then you will see all higher harmonics drop away rapidly as you put feedback around it. It works both ways. So you can’t use the Baxandall effect to make general predictions of “what feedback sounds like”. Its only practical use lies in understanding why specifically people who try a small amount of feedback on e.g. a SET amplifier tend to dislike the result (and spend the rest of their lives talking about it).
So if you want to have an intelligent discussion about this, take the generalised view that feedback, in the extreme, first inverts the nonlinearity and only then proceeds to hammer it into the noise floor.
But note that it’s the equation-solving behaviour of a feedback loop that causes this inversion, not the fact that it solves the equation using recursion.
I’m hard pressed to see the point of the discussion though. Any system whose state depends on its state in the past is a feedback system. I’m inclined to consider feedback and recursion as synonymous. A falling rock is a recursive system. After all, the rock’s current position is highly contingent on where it was a microsecond ago and how fast it was going. Back to audio, any filter, even a passive one, is “recursive” in that sense. Fun fact: if you build a simple 1st order RC LPF with a non-linear capacitor and/or resistor, you get the classic rising THD vs frequency in the passband. Exactly like a simple 1st order feedback amplifier.
And in the digital domain, IIR filters are discrete-time approximations of analogue filters, and some DSP folk explicitly refer to IIR filters as “recursive”.
Reality is causal, so it’s recursive.
Jan
rayma, thank you for the link.
dreamth, thank you for replying.
And I like this thread, although most of it is way over my understanding (just like with whatever has to do with audio
)
Chris, Happy Birthday !
George
dreamth, thank you for replying.
And I like this thread, although most of it is way over my understanding (just like with whatever has to do with audio
)Chris, Happy Birthday !
George
Threads where you already know everything that's being said are boring and time wasting ;-)
Jan
Jan
The math behind this very "simple" old technique of negative feedback is pretty difficult for almost everybody here on diyaudio, it's just that most of us are ashamed to accept it publicly cause we might loose "audience" or credibility...but credibility is a function of telling the truth you know, not the lies you don't know for sure.
We can only be thankful to those who show us source material and provide simpler explanations that help those of us who aren't in a good shape with mathematics.
Western sources are a bit better in this regard.In the eastern european system all technical books were 99.99% full of derivatives and diffeential ecuations defining everything in the real world by tons of math equations to an extent that every explanation was a new more abstract mathematical equation and putting a very high fence in front of those who wanted to understand the world in simpler analogy terms .
Audio electronics is that area where analogies or analogical thinking put into words allow for a broader audience , but there's always the danger of getting it wrong as grammar rules aren't so tough as math rules.
I have to admit I got a lot of things wrong over the time, I'm still unsure of many other things, but the beauty of the analogic world is that it allows for recursivity or "negative input" if you want to define negative feedback through negative feedback... thus you can apparently improve your stand without fully understanding it.Truth is that when you got it it you're always facing a deeper mistery...as with everything in life.You're eased with some and burdened with way more stuff...If you got it all it means you're dead...
There will always be someone who gets it better than you anyway 🙂.
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In english this sounds more like pleonasm or redundant, superfluous so some guys invented math to make everything sound more precise and complicated 🙂
We know today that the more greek letters are used instead of latin ones, the higher the IQ of the individual using them, so most probably the orthodox Mount Athos greek priests are the most intelligent creatures in the world cause you need to pay them to mix letters with numbers, they don't do it for free...Athenians too 😉 and the russians...completely forgot them...they had a natural bias to mathematics too due to Kirylic alphabet use...
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Well, I'm sticking with recursion and causality. I guess I'll go to the audio gallows any day. The Laplace transform assumes a continuous sinewave solution from the start, a steady state solution. A transient analysis is needed for something that occurs far faster than the amplifier bandwidth. I do have an 11.5 GHz sampling scope that would see the initial transient stepping thru easily, but the amplifier's limited bandwidth would smear out the input step function anyway.
I suggest putting a delay line cable of 30 ft in the N Fdbk path, or the forward amplifier path, to make the effect visible beyond doubt on a typical scope, with a step function for input. But I'm sure there will some objection to modifying the amplifier (stability).
If the Feldtkeller/Farren/Baxandall/Putzeys.... effect weren't a real issue for low N Fdbk amps, this whole discussion would be like counting Angels on a pin head. The transient analysis converges to the Laplace analysis in uSecs.
I suggest putting a delay line cable of 30 ft in the N Fdbk path, or the forward amplifier path, to make the effect visible beyond doubt on a typical scope, with a step function for input. But I'm sure there will some objection to modifying the amplifier (stability).
If the Feldtkeller/Farren/Baxandall/Putzeys.... effect weren't a real issue for low N Fdbk amps, this whole discussion would be like counting Angels on a pin head. The transient analysis converges to the Laplace analysis in uSecs.
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