So as the correction signal already arrives four orders of magnitude faster than the signal it is correcting, the differentiation hypothesis is neither necessary nor sufficient.
An afterburner from Bruno
In the continuous case (Continuous Time system) the system converges gradually, in the discrete time (DT) case step-wise. And, what happens in a CT system between 0 Hz and infinite Hz happens in a DT system between 0 Hz and Fs/2 Hz.That's the only difference. Class D is also DT and there it doesn't work any less. But even that's beside the point. There are DT systems where the distortion remains the same with every iteration. Those systems keep on flapping about simply because there is no possible output for the non-linearity. These are called Sigma-Delta modulators, and I haven't heard anyone complain that these use so much feedback and keep on recursing.
Jan
In the continuous case (Continuous Time system) the system converges gradually, in the discrete time (DT) case step-wise. And, what happens in a CT system between 0 Hz and infinite Hz happens in a DT system between 0 Hz and Fs/2 Hz.That's the only difference. Class D is also DT and there it doesn't work any less. But even that's beside the point. There are DT systems where the distortion remains the same with every iteration. Those systems keep on flapping about simply because there is no possible output for the non-linearity. These are called Sigma-Delta modulators, and I haven't heard anyone complain that these use so much feedback and keep on recursing.
Jan
I'm not sure where the differentiation thing arose, because feedback is an integrating function. Signal arrives at an amplifier's input. It passes through the amplifier, with some hopefully small error and some intractable time delay. This resulting output is then compared with the input and integrated over a time constant much larger (for audio) than the intractable time delay and appears at the amplifier's loop's output. Rinse and repeat.
The key to a practical (for understanding) model for audio feedback is the integrator. Within the working time frame of an audio signal, the input signal and all of the successive approximations of the infinite series integrate step-wise towards, but never reach (noise limited) an exact instantaneous voltage answer.
Update: Bruno is, as always, way over my head, but useful later if/when I get smarter. Fat chance, but ya never know.
All good fortune,
Chris
The key to a practical (for understanding) model for audio feedback is the integrator. Within the working time frame of an audio signal, the input signal and all of the successive approximations of the infinite series integrate step-wise towards, but never reach (noise limited) an exact instantaneous voltage answer.
Update: Bruno is, as always, way over my head, but useful later if/when I get smarter. Fat chance, but ya never know.
All good fortune,
Chris
Last edited:
I agree that the integrator view is key here, although I confess I don't completely grok it yet.
Also, the idea that you can use feedback around a continuously switching class D loop, get a stable system and THD below that of a good class A amp sends my brain reeling.
Jan
Also, the idea that you can use feedback around a continuously switching class D loop, get a stable system and THD below that of a good class A amp sends my brain reeling.
Jan
If I understood anything about class D I'd be a danger to myself and others around me. It's just too volitle a chemical. To an "innocent eye test" it looks like any small errors in timing would cause monotonicity problems at low levels. You may need to be B.P. himself to be dedicated enough to get that stuff right.
https://www.metmuseum.org/art/collection/search/484972
Much thanks, as always,
Chris
https://www.metmuseum.org/art/collection/search/484972
Much thanks, as always,
Chris
Errors in timing are responsible for 99.999% of the distortion in class D amps. To make a class D amp comparable to the best class AB ones or even approaching class A the dead time needs to be down in the single digit nanoseconds. Only when there is ZERO dead time is the amplitude perfectly proportional to duty cycle. But that results in exploding mosfets as soon as you start putting out any real power with it. A few ns is a good compromise, but that does result in Class D’s version of “crossover distortion”. It can go pretty damn low, but never go away entirely. Rise and fall times also contribute to timing error, but cancel if the two switches are the same. The usual 100ns dead time in a big pro amp is a huge timing error at 20 KHZ, and reduced by the usual 40 or so dB of NFB that most regular amps have at that frequency.
Why does the dead time to be down to single digit nS? You mean open loop?
If closed loop, it's pretty irrelevant (from THD perspective).
Jan
If closed loop, it's pretty irrelevant (from THD perspective).
Jan
The feedback phase corr. cap was put in just to eliminate any confounding phase error issues in the FFBP discussion. Instead, it seems to cause endless confusion. Forget the damn cap.
But to clarify where the integrator shows up. Assume for a moment there is -just- the cap in the feedback path. That is the standard arrangement for making an integrator with an OpAmp. Looking at its operation, the cap differentiates the N Fdbk coming from the Op Amp output. Since the two inputs to the Op. Amp are forced to match each other, that means the Cap derivative is forced to match the input. Since the amp output is the same as what is going -into- the cap, it must be the integral of what is coming out of the cap. So the output of the Op. Amp must be the Integral of the input signal.
For phase correction purposes, the tiny cap placed across the Fdbk resistor is used to bring the N Fdbk up to date with the now slightly later input arriving. The tiny derivative component from the cap adds a prediction of where the N Fdbk -should- be at this later moment. Not much later, like nSecs. It isn't much of a correction, but is used to bring the output of the N Fdbk amp into perfect phase alignment with say a sine wave input. Providing time coherence across the circuit. The Fdbk resistor of course is operating the standard error correcting effects. This phase correction is what quashes the often heard complaints that N Fdbk is correcting the errors after the fact.
Since the FFBP dist. is hypothesized to result from re-circulation and re-distortion, the phase corr. cap can be used to keep time alignment error, or phase error, from building up over multiple loops. Still a small effect, but possibly affecting the higher harmonics. The higher harmonics, being higher freq. are more sensitive to time errors, beside the possible multi looping build-up.
But to clarify where the integrator shows up. Assume for a moment there is -just- the cap in the feedback path. That is the standard arrangement for making an integrator with an OpAmp. Looking at its operation, the cap differentiates the N Fdbk coming from the Op Amp output. Since the two inputs to the Op. Amp are forced to match each other, that means the Cap derivative is forced to match the input. Since the amp output is the same as what is going -into- the cap, it must be the integral of what is coming out of the cap. So the output of the Op. Amp must be the Integral of the input signal.
For phase correction purposes, the tiny cap placed across the Fdbk resistor is used to bring the N Fdbk up to date with the now slightly later input arriving. The tiny derivative component from the cap adds a prediction of where the N Fdbk -should- be at this later moment. Not much later, like nSecs. It isn't much of a correction, but is used to bring the output of the N Fdbk amp into perfect phase alignment with say a sine wave input. Providing time coherence across the circuit. The Fdbk resistor of course is operating the standard error correcting effects. This phase correction is what quashes the often heard complaints that N Fdbk is correcting the errors after the fact.
Since the FFBP dist. is hypothesized to result from re-circulation and re-distortion, the phase corr. cap can be used to keep time alignment error, or phase error, from building up over multiple loops. Still a small effect, but possibly affecting the higher harmonics. The higher harmonics, being higher freq. are more sensitive to time errors, beside the possible multi looping build-up.
Last edited:
This thread is really about nonlinear control systems theory. It's way beyond my pay grade. There's a reason moldy college textbooks are hundreds of pages long.
It's fine. This isn't a PhD. thesis defense. The Moldovian Nobel Prize committee doesn't read diyaudio.com.
Meanwhile, we can celebrate the discovery of French Fry Bagel Popcorn distortion!
I will leave you now. Thanks for giving me something interesting to think about. We're all friends here, no offense intended. Life is good (as long as you don't read the news).
It's fine. This isn't a PhD. thesis defense. The Moldovian Nobel Prize committee doesn't read diyaudio.com.
Meanwhile, we can celebrate the discovery of French Fry Bagel Popcorn distortion!
I will leave you now. Thanks for giving me something interesting to think about. We're all friends here, no offense intended. Life is good (as long as you don't read the news).
Non Linear Control Theory
Here is a choreographed Youtube video illustrating FFBP distortion. The girls are the pristine input signal, and after they go around the loop they are covered with FFBP "dirt". Enjoy. 😉
Here is a choreographed Youtube video illustrating FFBP distortion. The girls are the pristine input signal, and after they go around the loop they are covered with FFBP "dirt". Enjoy. 😉
FFBP
Getting rid of the error before it re-circulates seems like a good idea. Works for high N Fdbk at least.
Zintolo presented this idea from some French source. Looks suspiciously like Error Correction or EC. It limits the N Fdbk to -just- the error.
So the output gets cleaned up in a single pass?
Maybe it would work for FFBP. Of course it has two potential dist. sources, but gain B could be just unity gain I think.
https://www.diyaudio.com/community/...ces-baby-huey-and-beyond.375236/#post-6763934
Getting rid of the error before it re-circulates seems like a good idea. Works for high N Fdbk at least.
Zintolo presented this idea from some French source. Looks suspiciously like Error Correction or EC. It limits the N Fdbk to -just- the error.
So the output gets cleaned up in a single pass?
Maybe it would work for FFBP. Of course it has two potential dist. sources, but gain B could be just unity gain I think.
https://www.diyaudio.com/community/...ces-baby-huey-and-beyond.375236/#post-6763934
Last edited:
Another note about the integrator: this is already built into feedback amplifiers, for stability. For wide bandwidth (semi-con) transformerless amplifiers, it's commonly the transimpedance stage ("VAS") which includes the dominant pole. For conventional valve amplifiers, it was classically just a shunt capacitor, often with a gain stop.
For class-D amplifiers, no clue. But, there must be one somewhere for stability. Even for a single stage with degeneration, there still has to be an integrator somewhere, and a loop somewhere, however obscure.
All good fortune,
Chris
For class-D amplifiers, no clue. But, there must be one somewhere for stability. Even for a single stage with degeneration, there still has to be an integrator somewhere, and a loop somewhere, however obscure.
All good fortune,
Chris
In the early 1990s, when Wildwood Park for the Performing Arts was still being built, we hosted Riders in the Sky in our backstage space, with an opening act of the cutest little cowgirls in the tightest jeans you could ever hope to meet. Called themselves "The Dixie Chicks". Heard they're doing well.
All good fortune,
Chris
All good fortune,
Chris
My knowledge of class D is very approximate, but I believe there is an accounting trick: errors are called "THD" only when they are harmonically related to the fundamental. Otherwise, errors are called "noise".
The entire technique of "noise shaping" is to randomize errors so that they appear as noise, and then to push the noise to higher frequencies (mostly above the audio band).
Thus, you have to look at both THD and noise.
Ed
Class D simply moves the accuracy problem from voltage to time. (As EdGr says, they may not count as THD.)
ALL amplifiers "integrate"--- none go to infinite frequency. Many also differentiate: don't go flat to DC.
Darn, the amplifier scheme in post 212 requires gain B to be very high to get rid of distortion. No better than the usual N Fdbk scheme. Maybe Error Correction, EC, can do the job, but it doesn't adjust easily or stablely to null for higher gains.
The Dixie Chicks are probably the only country rockers I can stand, and they are just great. Put them with Stevie Nicks of Fleetwood Mac and you have the World's Best:
Chicks alone:
Stevie and Lindsey Buckingham (Fleetwood Mac) she wrote the original:
The Dixie Chicks are probably the only country rockers I can stand, and they are just great. Put them with Stevie Nicks of Fleetwood Mac and you have the World's Best:
Last edited:
Nothing like sister harmonies. You may like the Roche sisters; their first album, produced in "Audio Verite" (with an accent) by Robert Fripp, is special. Here's a seasonal sample:
Seasonally appropriate greets,
Chris Kringle
Seasonally appropriate greets,
Chris Kringle
Seasonal Greetings to everyone too.
They knew how to make real music back then. Thanks.
You don't have to worry about noise or FFBP dist. in your amplifier nowadays.
I got started listening to Fleetwood Mac again recently after Christine McVie passed away. Christine and Stevie Nicks and Lindsey Buckingham...., just Wow! So many great pieces they all did together. Chistine we miss you!! She wrote a lot of the songs, played the keyboards and sang, all of them well. Wow!
They knew how to make real music back then. Thanks.
You don't have to worry about noise or FFBP dist. in your amplifier nowadays.
I got started listening to Fleetwood Mac again recently after Christine McVie passed away. Christine and Stevie Nicks and Lindsey Buckingham...., just Wow! So many great pieces they all did together. Chistine we miss you!! She wrote a lot of the songs, played the keyboards and sang, all of them well. Wow!
Last edited: