I would argue that the theory is being written right now. Feedback theory began with Black in 1934; adjustments to his simplifications were made by Feldtkeller in 1936, Farren in 1938, Baxandall in the mid-1960s? and summarized by Putzeys in 2011, all adding the effects of recursion. To this point all ignored propagation time, which is plenty close enough for government work, but not exact. smoking-amp's contribution, right here right now in this very thread, is to include propagation time.
The subject of feedback seems to bring a lot of craziness out of the woods, don't know why, but in the case of this thread some real progress has been made, by some.
All good fortune,
Chris
The subject of feedback seems to bring a lot of craziness out of the woods, don't know why, but in the case of this thread some real progress has been made, by some.
All good fortune,
Chris
I'm reminded of a lesson from Putzeys (who Jan brought into the interminable Blowtorch threads to help me) that all feedbacks are the same: local degeneration is no different from long loops or any combination thereof. If I could work the search engine I'd point to a pair of graphs posted by N. Pass (dropping a lot of names here) comparing the output spectrum of a single MOSFET stage with and without a source degenerating resistor, confirming this. Without was a "clean" second order spectrum, "with" included all the possible higher order products.
All good fortune,
Chris
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"Many processes involve dead times, also referred to as transport delays or time lags. Controlling such processes is challenging because delays cause linear phase shifts that limit the control bandwidth and affect closed-loop stability.
Using the state-space representation, you can create accurate open- or closed-loop models of control systems
with delays and analyze their stability and performance without approximation."
https://www.mathworks.com/help/control/ug/analyzing-control-systems-with-delays.html
For you serious folk who do real world stuff it may be obvious, but for audio electronics it's a whole new critter. Nothing better than learning something new. Nothing.
All good fortune,
Chris
All good fortune,
Chris
Yeah, I doubt I'm onto anything new here. Just a more intuitive view hopefully. Audio amps are pretty simple compared to the stability of say a rocket or fighter plane (taking off or landing vertically lately). It would be useful if we could find a more intuitive model of how Fdbk works for our amplifiers, since Laplace transforms and the like are not real friendly or intuitive.
One thing that might be of use for N Fdbk could be to also use the 2nd derivative of the input signal to refine the signal projection from the 1st derivative, since that tells you how the 1st derivative will be changing during that coming interval. Class D amplifiers adopted such predictors to improve their fidelity since they don't get continuous output (before filtering) to compare with.
One thing that might be of use for N Fdbk could be to also use the 2nd derivative of the input signal to refine the signal projection from the 1st derivative, since that tells you how the 1st derivative will be changing during that coming interval. Class D amplifiers adopted such predictors to improve their fidelity since they don't get continuous output (before filtering) to compare with.
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Dropping below a nice clean 2nd harmonic line with the Discrete FFT gets you a long spray of higher harmonics with alternating signs, just because the Discrete transform can't model a 1.9 harmonic well. (only discrete integer harmonics). So it could just be a representation problem. Would be interesting to find out if degeneration causes additional re-entrant distortion. I don 't see any obvious mechanism to affect the future from the past like a loop provides, other than junction capacitance maybe. An analog spectrum analyzer could work, but the expected extra dist. is probably too low to see.
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My takeaway from Bruno's comments was that the same model of feedback would apply to any feedback, irrespective of race, creed or national origin. We accept this easily WRT issues of stability - for example cathode followers with significantly capacitive loads - but we have historical bias against applying the same rigor to recursion (without saying it in those terms). Been there, t-shirt. Once accepting that level of granularity, a broader but more consistent viewpoint emerges. Messier but not only knowable, but known.
Your thoughts about the "predictive" properties of the integrator I rate at the same light-bulb level of new insights.
Much thanks, as always,
Chris
Your thoughts about the "predictive" properties of the integrator I rate at the same light-bulb level of new insights.
Much thanks, as always,
Chris
So another way to say it is that there's always a loop, and always an integrator. They just get really small over a single stage.
ch
Take a triode that has nice evenly spaced curves. It has gain, and we generally think of the electrostatic effect of the plate V on cathode emission as N Fdbk. But it doesn't generate re-entrant distortion. (does it?) You could draw a load line on it's curves with very little distortion. The Fdbk there is speed of light, without any device resonances to get in the way. So any kind of re-entrant effect is only a few pSec delayed. Any recirculating stuff is looking just like the original signal with a microscopic phase delay.
So, seems to me that the usual looped circuit N Fdbk successfully time aligns the Fdbk for subtraction purposes (using its predictor), but it does not prevent actual physical delay from causing re-entrant distortion. Or can it?
Can the re-entrant dist. corr. be brought into time alignment with the incoming signal generated distortion so they just sum to zero? The re-entrant stuff is inverted after all. Obviously this needs some thinking over and maybe some checking out.
Or using components that are vastly faster than the signal frequencies so there is no appreciable loop delay.
Suppose the distortion N Fdbk were just slightly enhanced so that it does completely cancel out the generated dist., would that help? (I'm thinking Error Correction technique, which can adjust the distortion down to "near" zero. Is that "near" null just the re-entrant stuff slipping by?) Could EC be adjusted just a little past the null point so that a small amount of (inverted) single pass dist. comes out, but no re-entrant crap?
So, seems to me that the usual looped circuit N Fdbk successfully time aligns the Fdbk for subtraction purposes (using its predictor), but it does not prevent actual physical delay from causing re-entrant distortion. Or can it?
Can the re-entrant dist. corr. be brought into time alignment with the incoming signal generated distortion so they just sum to zero? The re-entrant stuff is inverted after all. Obviously this needs some thinking over and maybe some checking out.
Or using components that are vastly faster than the signal frequencies so there is no appreciable loop delay.
Suppose the distortion N Fdbk were just slightly enhanced so that it does completely cancel out the generated dist., would that help? (I'm thinking Error Correction technique, which can adjust the distortion down to "near" zero. Is that "near" null just the re-entrant stuff slipping by?) Could EC be adjusted just a little past the null point so that a small amount of (inverted) single pass dist. comes out, but no re-entrant crap?
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Late addition:
The Baxandall graphs indicate that re-entrant distortion vanishes with high N Fdbk. And EC does have extremely high internal N Fdbk (but by using positive Fdbk to get the gain) So it's a good question whether that would work to eliminate re-entrant dist., IF the positive Fdbk doesn't spoil the show. Could the re-entrant stuff maybe have a different null point from the usual dist. null?
Time to get out the old Tek 7L5 Spectrum Analyzer. No discrete aliasing effects there.
The Baxandall graphs indicate that re-entrant distortion vanishes with high N Fdbk. And EC does have extremely high internal N Fdbk (but by using positive Fdbk to get the gain) So it's a good question whether that would work to eliminate re-entrant dist., IF the positive Fdbk doesn't spoil the show. Could the re-entrant stuff maybe have a different null point from the usual dist. null?
Time to get out the old Tek 7L5 Spectrum Analyzer. No discrete aliasing effects there.
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I'm not sure I understand how this term is being used. Distortion is internally - in the tube - generated by the error correction stage after input/feedback entry. The error amp adds new errors to the errors it corrects.
I was using it for the inverted error coming back in ( for a multi-stage circuit N Fdbk ) which then generates the Baxandall type distortion by re-distortion of that Fdbk. giving higher order distortions.
EC does have distortion problems from the extra arithmetic, ending up in the distortion null that won't quite go to zero. But does that "null" still have this Baxandall type distortion in it too?
For the very linear triode it may simply be working the other side of the equation for avoiding Baxandall distortion, namely just low dist. too start with, nothing obnoxious recirculating to re-distort, if there even is any re-circulation.
Now that I think of it, I guess there is re-circulation in a triode. Let's say the triode V changes as a result of the grid V input. That plate V change affects the cathode via electrostatic field, changing the current flow to the plate. So the plate re-adjusts again and so on. This re-circulation occurring in a multiple few pico seconds and reaching convergence to the Mu factor.
So I guess a device like a pentode would prevent this recirculation, unfortunately they aren't linear for gain like the triode, but maybe as a follower this works well to prevent Baxandall dist. But then there is no gain..
So it seems that devices that don't have back effects could avoid Baxandall type distortion. A linear triode driving a pentode (or Mosfet) cascode above it should work to get high linear gain without Baxandall effects. Ugh, except the triode doesn't work linearly anymore with the cascode loading. There must be some solution.....
Well, this brings back the triode puzzle once again. Its NOT linear until the N Fdbk works on it. So how does it avoid Baxandall distortion?
EC does have distortion problems from the extra arithmetic, ending up in the distortion null that won't quite go to zero. But does that "null" still have this Baxandall type distortion in it too?
For the very linear triode it may simply be working the other side of the equation for avoiding Baxandall distortion, namely just low dist. too start with, nothing obnoxious recirculating to re-distort, if there even is any re-circulation.
Now that I think of it, I guess there is re-circulation in a triode. Let's say the triode V changes as a result of the grid V input. That plate V change affects the cathode via electrostatic field, changing the current flow to the plate. So the plate re-adjusts again and so on. This re-circulation occurring in a multiple few pico seconds and reaching convergence to the Mu factor.
So I guess a device like a pentode would prevent this recirculation, unfortunately they aren't linear for gain like the triode, but maybe as a follower this works well to prevent Baxandall dist. But then there is no gain..
So it seems that devices that don't have back effects could avoid Baxandall type distortion. A linear triode driving a pentode (or Mosfet) cascode above it should work to get high linear gain without Baxandall effects. Ugh, except the triode doesn't work linearly anymore with the cascode loading. There must be some solution.....
Well, this brings back the triode puzzle once again. Its NOT linear until the N Fdbk works on it. So how does it avoid Baxandall distortion?
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Overtime:
Well, this brings back the Triode puzzle once again. Its NOT linear until the N Fdbk works on it. So how does the Triode avoid Baxandall distortion?
Wait, wait! I think I see it now. Inverted Triodes have inverted distortion. The reverse Fdbk path gets anti-distorted. That's clearly the key. Just need to get a coherent model of how its working. 3/2 power law times 2/3 power law equals 1.
So you need to know how the device/circuit distorts, and pre-process the error component Fdbk into anti-distortion. ( inverted being taking the forward distortion function and running the detected error thru it backwards. That new Fdbk^ then just turns into a clean correction offset when re-distorted in the 2nd pass thru the device) No distortion of previous distortion anymore.
Well, this brings back the Triode puzzle once again. Its NOT linear until the N Fdbk works on it. So how does the Triode avoid Baxandall distortion?
Wait, wait! I think I see it now. Inverted Triodes have inverted distortion. The reverse Fdbk path gets anti-distorted. That's clearly the key. Just need to get a coherent model of how its working. 3/2 power law times 2/3 power law equals 1.
So you need to know how the device/circuit distorts, and pre-process the error component Fdbk into anti-distortion. ( inverted being taking the forward distortion function and running the detected error thru it backwards. That new Fdbk^ then just turns into a clean correction offset when re-distorted in the 2nd pass thru the device) No distortion of previous distortion anymore.
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Excessive overtime now:
Well, that solves the mystery of Triodes.
But now is there any practical way to use this for more complex circuits?
How about if we use an inverted -perfectly linear- triode to control the gain of a pentode?
Naw, doesn't work perfectly. An inverted non distorting function is still linear. Same as a resister N Fdbk. Almost linear gain.
How about a diode function in reverse, Maybe!
Yeah, yeah. Working in theory if the diode is a perfect match to the pentode function. 3 ways even.
Can use the reversed diode for feedback to the pentode grid. 3/2 power times 2/3 power.
Or can use the diode as a load resistor. 3/2 power law times 2/3 power law. This is the little known Voltage Mirror. More recently it became the similar Aikido front end stage using two triodes. dist Func1 times 1/ dist func2 to get linear output, if the two triodes are identical.
And lastly, the diode can be used to convert current input to grid voltage for the pentode. 2/3 law times 3/2 law to get linear current gain. Also little known as the tube current mirror.
Well, that solves the mystery of Triodes.
But now is there any practical way to use this for more complex circuits?
How about if we use an inverted -perfectly linear- triode to control the gain of a pentode?
Naw, doesn't work perfectly. An inverted non distorting function is still linear. Same as a resister N Fdbk. Almost linear gain.
How about a diode function in reverse, Maybe!
Yeah, yeah. Working in theory if the diode is a perfect match to the pentode function. 3 ways even.
Can use the reversed diode for feedback to the pentode grid. 3/2 power times 2/3 power.
Or can use the diode as a load resistor. 3/2 power law times 2/3 power law. This is the little known Voltage Mirror. More recently it became the similar Aikido front end stage using two triodes. dist Func1 times 1/ dist func2 to get linear output, if the two triodes are identical.
And lastly, the diode can be used to convert current input to grid voltage for the pentode. 2/3 law times 3/2 law to get linear current gain. Also little known as the tube current mirror.
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Hard to get perfectly matched devices, especially when they are dissimilar types.
I'm thinking the pentode could combine both devices into one, similar to the triode, but with programmable gain.
A resistive divider from plate to screen grid (maybe with a Mosfet follower for driving the screen, but may not be needed actually).
The screen grid acts like the plate in a triode for setting the gain to that point. Since the grid2 V is just a ratio from the plate V, the plate V should be that ratio more than the screen V. Now the screen does have a finite impedance, which will change the resistive divider ratio. Since the screen V is (intended to be) a constant fraction of the plate V, it should intercept a constant fraction of plate current. So that grid2 impedance should stay constant (constant I/V). So you can either figure the screen Z into the divider design, or use a Mosfet follower to drive the screen. Either way you end up with a programmable gain triode, which should be as linear as that internal g2/g1 triode. Unfortunately, not that many tubes have an ideal g2/g1 triode curve set. But I have seen and used this circuit before with pretty good results. A 12HL7, for example, gives really good results. At least Baxandall dist. is hopefully minimized with this setup for moderate gains. One could put a Mosfet follower in to drive the R divider network too. Unload the plate some.
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I'm thinking the pentode could combine both devices into one, similar to the triode, but with programmable gain.
A resistive divider from plate to screen grid (maybe with a Mosfet follower for driving the screen, but may not be needed actually).
The screen grid acts like the plate in a triode for setting the gain to that point. Since the grid2 V is just a ratio from the plate V, the plate V should be that ratio more than the screen V. Now the screen does have a finite impedance, which will change the resistive divider ratio. Since the screen V is (intended to be) a constant fraction of the plate V, it should intercept a constant fraction of plate current. So that grid2 impedance should stay constant (constant I/V). So you can either figure the screen Z into the divider design, or use a Mosfet follower to drive the screen. Either way you end up with a programmable gain triode, which should be as linear as that internal g2/g1 triode. Unfortunately, not that many tubes have an ideal g2/g1 triode curve set. But I have seen and used this circuit before with pretty good results. A 12HL7, for example, gives really good results. At least Baxandall dist. is hopefully minimized with this setup for moderate gains. One could put a Mosfet follower in to drive the R divider network too. Unload the plate some.
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Electron Tube Design by RCA staff. 943 pages. It's on Pete Milletts book archive. Spangenberg "Vacuum Tubes" 860 pgs, as linked above. And "Thermionic Valves" by Beck. Deketh's "Fundamentals of Radio-Valve Technique" too. And the earlier "Vacuum Tube Design" by RCA 260 pages.
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It's in romanian and probably the source is russian.I need to look up for it.I don't know right now where I have it.
Years ago, I had a long debate with a guy named John Byrns on rec.audio.tubes about whether or not a triode "has" internal negative feedback. I claimed it does not. I showed, among other things, that a plain-old diode has the same negative feedback. I even derived V = I * R in terms of negative feedback.
Lots of ordinary things can be modeled as negative feedback systems. Like an electric motor, or a skydiver with a parachute. Everything we do in electronics is a high-level mathematical abstraction. The actual physical workings of our circuits are strange, incomprehensible, and not at all like we are used to thinking of them. The bloody electrons don't carry the information. They move at a snail's pace, about one millimeter per second.
You choose math models according to their simplicity, clarity, and utility. A periodic waveform is NOT composed of an infinite series of sinewaves, any more than a gallon of milk is composed of 128 individual ounces of milk. Except when it is useful to describe it as such. It's kind of arbitrary.
I've never heard of "Baxandall Distortion." Is this an accepted term? The only references I can find to "re-entrant" feedback are in the field of neurophysiology. Let's not get overexcited.
I find it very helpful to remind myself that circuit models are not "real." There is an infinite number of circuit models. For instance:
V = I * R
V + 1 = I * R + 1
V^2 = I^2 * R^2
And so on.
So, the real question is, if you want to propose a new model, what does it bring to the table that makes it more useful than the standard one?
The original poster asked, "How can a feedback amplifier work if the feedback signal cancels the input?" The correct answer was given, i.e., the cancellation isn't total. A small error component remains. I expanded on this by pointing out that a feedback amplifier computes the output that minimizes the error.
How we think about things matters. Clearer thinking leads to clearer models. Let's not muck things up with muddled theories. FWIW and YMMV.
Lots of ordinary things can be modeled as negative feedback systems. Like an electric motor, or a skydiver with a parachute. Everything we do in electronics is a high-level mathematical abstraction. The actual physical workings of our circuits are strange, incomprehensible, and not at all like we are used to thinking of them. The bloody electrons don't carry the information. They move at a snail's pace, about one millimeter per second.
You choose math models according to their simplicity, clarity, and utility. A periodic waveform is NOT composed of an infinite series of sinewaves, any more than a gallon of milk is composed of 128 individual ounces of milk. Except when it is useful to describe it as such. It's kind of arbitrary.
I've never heard of "Baxandall Distortion." Is this an accepted term? The only references I can find to "re-entrant" feedback are in the field of neurophysiology. Let's not get overexcited.
I find it very helpful to remind myself that circuit models are not "real." There is an infinite number of circuit models. For instance:
V = I * R
V + 1 = I * R + 1
V^2 = I^2 * R^2
And so on.
So, the real question is, if you want to propose a new model, what does it bring to the table that makes it more useful than the standard one?
The original poster asked, "How can a feedback amplifier work if the feedback signal cancels the input?" The correct answer was given, i.e., the cancellation isn't total. A small error component remains. I expanded on this by pointing out that a feedback amplifier computes the output that minimizes the error.
How we think about things matters. Clearer thinking leads to clearer models. Let's not muck things up with muddled theories. FWIW and YMMV.