Hi Bruno,
Before I let you go, you make one interesting statement in your reply to Menno Van Der Veen's LTE: "Conclusion: Negative feedback does not attenuate the harmonics of the open-loop nonlinearity, but of its inverse."
The math is heavy on an empty stomach and I disagree that discounting "distortion of distortion" is right.
Further, there are implications from your conclusions that are no doubt clear to many but I think it may be worth elaborating.
Ciao T
Before I let you go, you make one interesting statement in your reply to Menno Van Der Veen's LTE: "Conclusion: Negative feedback does not attenuate the harmonics of the open-loop nonlinearity, but of its inverse."
The math is heavy on an empty stomach and I disagree that discounting "distortion of distortion" is right.
Further, there are implications from your conclusions that are no doubt clear to many but I think it may be worth elaborating.
Ciao T
Scott,
Wrong in what? That your results are NOT results a JC-3 would produce?
You mean in YOUR circuit they do nothing useful. What they do in the JC-3 can not be concluded from your sims...
As they say in German "getroffene hunde bellen" (dogs that have been hit bark").
Ciao T
Wrong in what? That your results are NOT results a JC-3 would produce?
You mean in YOUR circuit they do nothing useful. What they do in the JC-3 can not be concluded from your sims...
As they say in German "getroffene hunde bellen" (dogs that have been hit bark").
Ciao T
For intermediate values of loop gain "distortion of distortion" may only be "very nearly" negligible instead of entirely. The difference being exactly that between the curved lines and the straight asymptotes in my graph. And your point is?
Occasionally not elaborating every implication spurs people on to think for themselves. That ability comes in handy sometimes.
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WOOF! WOOF! (Or is it woffen woffen wackle wackle mit den hueften) No I meant the JC-3 circuit or for that matter any simple folded cascode gm gain stage like that (whice includes the AD844 and its ilk).
Hi,
First, given your original "conclusion" it would obvious what.
You note (I have not checked the math but I take it to be correct) that feedback produces an inverse function from original non-linearity of the circuit. What then happens when this non-linearity is applied to the original non-linearity.
Of course, we are back to what some call "re-entrant distortion".
Ciao T
First, given your original "conclusion" it would obvious what.
You note (I have not checked the math but I take it to be correct) that feedback produces an inverse function from original non-linearity of the circuit. What then happens when this non-linearity is applied to the original non-linearity.
Of course, we are back to what some call "re-entrant distortion".
Ciao T
You are failing to state your case. I am not going to enter a discussion with someone who simply barks "don't agree" without making a counterpoint he is willing to defend.
And just what do you think is re-entrant distortion other than the fact that the inverse of a low-order function has an infinitely long series expansion and hence more harmonics? I just gave you the bloody general mathematical explanation of re-entrant distortion. What will you do next? Tell Newton his gravitational law is incorrect because stuff just falls down?
Bruno,
Okay, more clearly, as the feedback's distortion reduction based on your math is not a linear function "distortion of distortion" becomes a significant term, not one to be swept under the carpet.
Not quite, you oversimplified. But yes, the mathematical foundation is there. However, have you ever attempted to go through enough iterations to get a precise result? Can the result even be made to converge?
Pullllease, Newton. Pshaw. Newton lived in a Universe that strongly diverged from the one we live in now. And even now, we do not know what gravity is.
Ciao T
Okay, more clearly, as the feedback's distortion reduction based on your math is not a linear function "distortion of distortion" becomes a significant term, not one to be swept under the carpet.
Not quite, you oversimplified. But yes, the mathematical foundation is there. However, have you ever attempted to go through enough iterations to get a precise result? Can the result even be made to converge?
Pullllease, Newton. Pshaw. Newton lived in a Universe that strongly diverged from the one we live in now. And even now, we do not know what gravity is.
Ciao T
Back around 1975 there was an interesting article about distortion in cable television amplifiers. Sensitivity to distortion for televisions is not quite as high as it may be for audio, but the bandwidth is so wide that there is a much greater chance for it to occur.
The first example was the normal signal level out of a line amplifier is around 100 mV for each channel. As some systems may have 150 or more channels that could in theory require 15 VRMS out if all the channels were to hit peak voltage at the same time. As they were AM modulated and not in sync that would be unlikely to happen. As the power supply voltage was often 24 VDC the maximum output could only be about 8 VRMS. So there was a minimum power supply voltage required based on probability and VHF transistors of the day had quite low voltage limits. (The solution became bridged amplifiers.)
The second issue was that of IM distortion particularly in multi-stage amplifiers. As the channel spacing is fixed at 6 Mhz. there could be build up of cross products that would affect certain channels.
The third and interesting issue was that sometimes the distorted products of a single stage would have some of the products returned to the correct result by a second stage of amplification (W/ it's distortion).
In audio as you are aware 9th harmonic distortion is particularly objectionable. So where the third order product may be considered adequate at -40 db re the source a 9th order product may not be at -80.
When the error product is included with each stage then each stage's contribution to the final product is more obvious and allows additional design decisions.
Now to me the actual issue on applying classic control theory could be that audio reproduction may be more critical of the small errors than most other control systems. I suspect a gun turret does not require -80 db precision.
ES
Read the equations carefully exponents have been dropped and there might be other fonting errors.
Who wants to apply local feedback and rerun the equations.
EDIT - I forgot, John you love to quote this PIM article but it's also where Barrie says it's the Vbe/Ic relationship that is all important, beta does not matter.
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Recently in this thread there was a listening experiment introduced by Janneman that provides some further evidence of the importance of PIM in the following sense. There where two music files which only differed in that one of them had a 360 degree phase shift centered around 2KHz.
I could not distinguish the two files when AB-ing them with a short pause in between, but with instantanious switching, there was quite an obviuous difference in the transition between files with a phase shift. SY also indicated he had noticed this effect.
What this showed at least to me, is that absolute phase (static phase shift) is not all that important, which is fortunate, because all loudspeakers introduce phase shifts. However, a dynamic phase shift, such as introduced by rapid AB-ing Janneman's test, is highly audible.
All this is congruent with my understanding of the way the human brain processes sound. Time information is preserved up till about 3.5Khz on the auditory nerve, and plays key role in localization. Any phase intermodulation would wreack havoc on this process.
I don't think the above is very contentious.
The question I have not been able to answer from this whole discussion above on feedback is the impact this might have on phase intermodulation.
vac
Scott,
So, let me see, the JC-3 is a folded cascode Gm Stage? I mean, you looked at the circuit, right?
I see two distinct stages and a quite modertly degenerated VAS in this, the circuit is not folded cascode, but often referred to as Lender circuit... And I see a completely undegenerated differential input stage stage (at least originally it used moreate gm J-Fets...).
The VAS is not loading the IPS much, but the load of the EF2 output stage on the VAS output junction is substantial (EF3 or BiMos would be better).
And that is one of the reasons why your sims return rubbish.
GIGO.
So, if you are at all interested in the FACTS you have a closer look and rework your sim's to make sense, if you want to thumb the same old tub and ring the same old welkin you will not and insist that is black is white and four is five, as will JCX with his particular brand of sims, be my guests...
Ciao T
So, let me see, the JC-3 is a folded cascode Gm Stage? I mean, you looked at the circuit, right?
I see two distinct stages and a quite modertly degenerated VAS in this, the circuit is not folded cascode, but often referred to as Lender circuit... And I see a completely undegenerated differential input stage stage (at least originally it used moreate gm J-Fets...).
The VAS is not loading the IPS much, but the load of the EF2 output stage on the VAS output junction is substantial (EF3 or BiMos would be better).
And that is one of the reasons why your sims return rubbish.
GIGO.
So, if you are at all interested in the FACTS you have a closer look and rework your sim's to make sense, if you want to thumb the same old tub and ring the same old welkin you will not and insist that is black is white and four is five, as will JCX with his particular brand of sims, be my guests...
Ciao T
How precise do you want it? I think what Bruno has shown is that in the limit of infinite loop gain, the distortion in the output is an attenuated version of the inverse of the transfer function. With finite loop gain it will only be approximately equal to this. I don't think convergence is an issue, as we don't get singularities popping out of our amplifiers.ThorstenL said:
Another way of looking at it is to consider that the feedback equation for second-order distortion only is analogous to 1/(1+x). A simple enough rational function - in fact almost the simplest possible rational function. Yet it has an infinite expansion:
1/(1+x)=1-x+x^2-x^3+x^4 . . .
In genuine 'no feedback' situations we need a transfer function which is relatively 'clean', with low-order terms only. In feedback situations, if enough feedback is being used, we instead should ideally have a transfer function with a clean inverse even if this means the forward function looks worse. Can anyone design an amp with a square-root forward transfer function. as that would give pure 2nd with enough feedback?
Another name for a dynamic phase shift is a frequency change.vacuphile said:
Feedback networks are usually simple and unlikely to create dynamic phase shifts. Amplifiers, on the other hand, can be more complex and a dynamic phase shift could happen e.g. a stage whose output impedance is level-dependent feeding a capacitance.
AES E-Library Estimates of Nonlinear Distortion in Feedback Amplifiers
Cherry shows another version of the Baxandal "harmonic growth" math, "inverts" distortion, shows how do do simple power series inversion math for 2nd, 3rd order nonlinearities of real amplifier individual parts from models, measurements, relates the calculated results to the measured amplifer's output distortion, gains, feedback
an insight is that high gain reduces signal levels in early stages - which are easily made "deep Class A", can have lower distortion/"declining harmonic structure" to begin with - the latter stage gain makes the earlier stages operate even more linearly by requiring less signal amplitude at fixed bias for smaller signal/bias ratio
then "re-entrant" distortion terms being powers of very small quantities can ignored as being way below the cirucit's noise floor in these early stages
if we can make few 0.1% distortion output stages then the "2nd pass" "distortion of the distortion" is parts-per-million
even if you find Cherrys earlier AES papers less useful due to impedance matrix math I think this later paper is more accessable, gives more potential design guidance principles rather than just illustrating how to apply upper level EE analysis tools
Cherry shows another version of the Baxandal "harmonic growth" math, "inverts" distortion, shows how do do simple power series inversion math for 2nd, 3rd order nonlinearities of real amplifier individual parts from models, measurements, relates the calculated results to the measured amplifer's output distortion, gains, feedback
an insight is that high gain reduces signal levels in early stages - which are easily made "deep Class A", can have lower distortion/"declining harmonic structure" to begin with - the latter stage gain makes the earlier stages operate even more linearly by requiring less signal amplitude at fixed bias for smaller signal/bias ratio
then "re-entrant" distortion terms being powers of very small quantities can ignored as being way below the cirucit's noise floor in these early stages
if we can make few 0.1% distortion output stages then the "2nd pass" "distortion of the distortion" is parts-per-million
even if you find Cherrys earlier AES papers less useful due to impedance matrix math I think this later paper is more accessable, gives more potential design guidance principles rather than just illustrating how to apply upper level EE analysis tools
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Sorry I was trying to make a list and was typing too fast, I meant to be inclusive to most if not all input circuits that output a differential current in response to a differential voltage. You love the opportunity to jump on any mis-speak. In polite conversation you usually ask if someone really meant to say what they did.
The circuit simmed was the 4-JFET and two bipolar gain stage as I said the other night. A classic diamond input folded cascode CF input has the same issues. You have yet to provide even one counter example except vague appeals to authority/name dropping of folks you claim without concrete evidence disagree.
Barrie's paper relies on gm upon C as the transfer function, and since the C in his case is connected to the output and there ain't no way to get into gm, I guess the inner loop is SOL. And futhermore the output stage really doesn't matter, it's ideal.
So now the loading of the output stage matters? It is assumed that this is rolled into output stage distortion at least around here, i.e. the Cje modulation with the crossover voltage becomes a current error, the Cje's often larger that Cdom, etc. The inner loop makes all these considerably worse, that's obvious by inspection.
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Pavel,
I suspect you have read some of the equipment reviews and seen products offered for sale that have more than that. Some of those products are even called "Musical."
So where you and I would not design for such high harmonics some folks actually seem to do so!
But I think you understood the real issue. Do all the math so you can see all the results. Shortcuts are nice, but you have to be aware of what you might be missing when you use them.
Of course after you have done the math or simulation, you really do have to test the results!
I have a great simulation of an almost distortionless amplifier of great power (1Kw) unfortunately in reality it is horrible. Yes some folks understand more details such as the accuracy and even level of the models etc. But the final critic is actually listening to it.
I don't know if you followed the thread where someone asked about running 120 volt gear on 220 volts. One of the suggestions was to put a diode in series with the line as that would cut the voltage in half! Worked in his simulation! He did try it and reality reared it's head.
ES
Ed,
I know what you mean, but certainly you are aware of the fact that I not only simulate the amplifiers, but also design and build them. I cannot imagine the situation how to get -80dB at 9th with even average design. -80dB at 9th may result from:
- very poorly designed underbiased output stage, i.e. crossover distortion
- very strange circuit design (yes I know examples of such amplifiers)
Regards,
I know what you mean, but certainly you are aware of the fact that I not only simulate the amplifiers, but also design and build them. I cannot imagine the situation how to get -80dB at 9th with even average design. -80dB at 9th may result from:
- very poorly designed underbiased output stage, i.e. crossover distortion
- very strange circuit design (yes I know examples of such amplifiers)
Regards,
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