For low distortion, the phase angles must be small. 180 degrees is a large phase angle, what is accomplished is signal cancellation not distortion cancellation.
Thinking back to the original multiple phase shifts paper, some extended/reduced ideas might be developed.
Instead of multiple phase shifts and multiple "identical amplifiers", let us sequence several SMALL phase shift networks (wideband) in SERIES in front of a SINGLE amplifier. Even harmonics are easy to get rid off, so lets start with 3rd order distortion products.
According to the paper, these 3rd order products would suffer 3X the phase shift (versus the non shifted signal) after being formed into distortion products. So let us tap off some appropriately attenuated amplifier output and send that back to sum into the phase shifter sequence before the amplifier, at a point where it would cancel out with the subsequently 60 degree shifted main signal. These 3rd order products would need to be effectively 180 degrees out of phase with the input signal there, and would propagate thru as first order products at 180 degrees, cancelling out the 3rd order distortions at the output (with a correct level selected).
Similarly, other appropriately attenuated output signal paths would be sent back to appropriate phase shift points in the input phase shifter sequence to be summed, causing cancellation of each order of distortion product needed. So one will end up with some attenuation pots to null out each order of distortion. Since these are distortions, only very tiny signals will be fed back to effect cancellation of each order.
Some refinements might be required after doing a full mathematical analysis no doubt (8 pages maybe! ), there will be positive and negative 1st order Fdbks occurring here also. But just to give the general idea a name, how about "Phase Order Partitioned Neg. Fdbk" or POP FDBK.
It may also be possible to place the series phase shifters into the feedback network instead, and then pick off properly attenuated phase order feedbacks from that sequence to all be summed together at a conventional amplifier input, like Neg. Fdbk is normally done. This may make better sense, since the output signal amplitude is large and needs attenuation anyway for feedback purposes. (each broad band phase shift section will be causing some attenuation already and the higher order distortions would presumably be smaller corrections)
Instead of multiple phase shifts and multiple "identical amplifiers", let us sequence several SMALL phase shift networks (wideband) in SERIES in front of a SINGLE amplifier. Even harmonics are easy to get rid off, so lets start with 3rd order distortion products.
According to the paper, these 3rd order products would suffer 3X the phase shift (versus the non shifted signal) after being formed into distortion products. So let us tap off some appropriately attenuated amplifier output and send that back to sum into the phase shifter sequence before the amplifier, at a point where it would cancel out with the subsequently 60 degree shifted main signal. These 3rd order products would need to be effectively 180 degrees out of phase with the input signal there, and would propagate thru as first order products at 180 degrees, cancelling out the 3rd order distortions at the output (with a correct level selected).
Similarly, other appropriately attenuated output signal paths would be sent back to appropriate phase shift points in the input phase shifter sequence to be summed, causing cancellation of each order of distortion product needed. So one will end up with some attenuation pots to null out each order of distortion. Since these are distortions, only very tiny signals will be fed back to effect cancellation of each order.
Some refinements might be required after doing a full mathematical analysis no doubt (8 pages maybe! ), there will be positive and negative 1st order Fdbks occurring here also. But just to give the general idea a name, how about "Phase Order Partitioned Neg. Fdbk" or POP FDBK.
It may also be possible to place the series phase shifters into the feedback network instead, and then pick off properly attenuated phase order feedbacks from that sequence to all be summed together at a conventional amplifier input, like Neg. Fdbk is normally done. This may make better sense, since the output signal amplitude is large and needs attenuation anyway for feedback purposes. (each broad band phase shift section will be causing some attenuation already and the higher order distortions would presumably be smaller corrections)
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Yeah, I like the phase shifter sequence in the Neg. Fdbk path better. Much easier to analyse, and the inadvertent main signal components fed back will just act like conventional Neg. Fdbk. in addition. Maybe workable. So one is just tuning up a little extra 180 deg Neg. Fdbk for each distortion order left over by the conventional Neg. FDBK (which might have nothing to do if the distortion is exactly cleaned up by the POP FDBKs, and so eliminating the dreaded "re-entrant N FDBK" effects). (although my gut analysis of "re-entrant" N Fdbk is that it is harmless BS, it's just the mathematical effects of transfer curve straightening)
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That’s why I suggested alternating the phases using using a digital pulse to select the phase being sent/received. No cancellation but using a small reconstruction filter means you don’t see the switching.
It does not work like that. I just saw your headphone amp design. It´s horrible (if you ask me).
Almost like a almost unity buffer to rebalance linearity you could feed-forward in that deviation and correct in the next stage. However the next stage error then needs forward correction, and so on.
Better than feedback as the error correction is applied to the signal in error; thatcher than applying to the signal behind (not really a problem given the speed).
Better than feedback as the error correction is applied to the signal in error; thatcher than applying to the signal behind (not really a problem given the speed).
That tube arrangement is simply based on averaging noise and reinforcement of signal (SNR). I’m still playing with that for an output. No distortion correction. I’m not an electrical engineer - software and numerical computation by training and day job..
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For feed-forward correction, you could additionally run the input signal down a delay/transmission line (matched to the amplifier delay) so as to have a time coherent signal for subtraction from the scaled output signal, to use for the feed-forward correction. Won't be a very long transmission line.
The time delay in an amplifier (for audio anyway) is so short compared to the signal bandwidth that this time skew effect is usually not even considered. But for sake of purity, let us fix the problem for a feed-back amplifier too:
Over a very short interval (less than top bandwidth) we can predict the signal via its derivative, just like a PID controller does. So with a derivative function (RC) we advance the phase of the Neg. FDBK signal from the amplifier output before it gets subtracted from the input signal, so as to be time aligned with the input signal. Just a small sub uSec order phase advance needed to keep input and N Fdbk signals time coherent (keeping the OT out of the loop).
Or one could put the small RC derivative phase advance at the amplifier input and return the N Fdbk signal to just before the derivative box, to get time coherence.
The time delay in an amplifier (for audio anyway) is so short compared to the signal bandwidth that this time skew effect is usually not even considered. But for sake of purity, let us fix the problem for a feed-back amplifier too:
Over a very short interval (less than top bandwidth) we can predict the signal via its derivative, just like a PID controller does. So with a derivative function (RC) we advance the phase of the Neg. FDBK signal from the amplifier output before it gets subtracted from the input signal, so as to be time aligned with the input signal. Just a small sub uSec order phase advance needed to keep input and N Fdbk signals time coherent (keeping the OT out of the loop).
Or one could put the small RC derivative phase advance at the amplifier input and return the N Fdbk signal to just before the derivative box, to get time coherence.
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This popped up over at tubecad: Distortion Reduction
Not quite the same as my thinking for the op amp idea.
There’s a couple of patents on feedforward, mainly on chip and not applied by analogue to tubes.
Not quite the same as my thinking for the op amp idea.
There’s a couple of patents on feedforward, mainly on chip and not applied by analogue to tubes.
That's the age old technique of putting some more gain in front of the amplifier and putting N Fdbk around the whole thing, as Broskie points out.
The recent patent version puts some pointless blocks N1 and A2 into the diagram so it looks different (N1 can be factored out, "A1" in the A2 block formula equalizes the phase shift from the real A1 amplifier for loop stability), so they could patent it again. An advertising motivated patent. The extra gain comes from an Op. Amp, A3.
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It would be useful if some general means of eliminating odd distortion harmonics in amplifiers could be found.
The elimination of even harmonics in P-P amplifiers seems impressive until you realize most of them are turned into odd harmonics by symmetry. If the two P-P halves operate in class A, then some real cancellation of even harmonics from each half occurs with the other half, preventing formation of additional odd harmonics from them. But internal odd harmonics don't generally cancel, more generally they add. (ie compression or expansion)
I believe the key to avoiding odd harmonics ( even harmonics too) is for the gm of each half of the P-P amplifier to sum to a constant between them, for any signal operating points.
Several ways to achieve this come to mind.
1) On could just use constant gm devices to begin with, like Crazy drive. Or precisely matched constant Mu tubes like the "new" series Schade ( CED, UnSet)
2) One could monitor the gm of each P-P half by taking derivatives and summing to form a correction signal that would be integrated versus a negative constant and added to the input.
3) One could do some kind of cross coupled derivatives that would equalize the change rate on both P-P sides to each other. Sort of like the cross coupled Garter bias scheme. This doesn't guarantee a constant gm sum as well however, unless the tubes are nearly pure 2nd harmonic producers.
Some further development obviously needed. Food for thought at this point.
The elimination of even harmonics in P-P amplifiers seems impressive until you realize most of them are turned into odd harmonics by symmetry. If the two P-P halves operate in class A, then some real cancellation of even harmonics from each half occurs with the other half, preventing formation of additional odd harmonics from them. But internal odd harmonics don't generally cancel, more generally they add. (ie compression or expansion)
I believe the key to avoiding odd harmonics ( even harmonics too) is for the gm of each half of the P-P amplifier to sum to a constant between them, for any signal operating points.
Several ways to achieve this come to mind.
1) On could just use constant gm devices to begin with, like Crazy drive. Or precisely matched constant Mu tubes like the "new" series Schade ( CED, UnSet)
2) One could monitor the gm of each P-P half by taking derivatives and summing to form a correction signal that would be integrated versus a negative constant and added to the input.
3) One could do some kind of cross coupled derivatives that would equalize the change rate on both P-P sides to each other. Sort of like the cross coupled Garter bias scheme. This doesn't guarantee a constant gm sum as well however, unless the tubes are nearly pure 2nd harmonic producers.
Some further development obviously needed. Food for thought at this point.
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Clearest mathematically explanation of harmonics is here: Sources of Harmonics(Odd and Even) - Electrical Engineering Stack Exchange however that doesn't explain the original sources.
So a push-pull, not running pure class A adds additional terms to that decomposed frequency series. At the moment I'm trying to understand why the decomposition is odd (ignoring the cancellation piece).
Cancellation leaves odd - that's easy to understand, but why odd in the first place?
You could suggest that the switching of class B is a form of sampling hence nyquist, thus the sampling leads to being able to generate odd directly. Also that being 1/2 an even waveform each side is therefore odd, being temporally (ie 1/2 wave length and phase) spaced they would not cancel out.
So a push-pull, not running pure class A adds additional terms to that decomposed frequency series. At the moment I'm trying to understand why the decomposition is odd (ignoring the cancellation piece).
Cancellation leaves odd - that's easy to understand, but why odd in the first place?
You could suggest that the switching of class B is a form of sampling hence nyquist, thus the sampling leads to being able to generate odd directly. Also that being 1/2 an even waveform each side is therefore odd, being temporally (ie 1/2 wave length and phase) spaced they would not cancel out.
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This makes sense to me too with PP in A.
I was thinking this morning, of making a LTSpice sim to attempt to replicate in a simplistic form. I tend to think of PP as OTL totem pole rather than PP through a transformer.
It may be worth splitting the problem down the middle (pun intended) for example - tackle the symmetrical separate from the non-symmetrical.
The symmetrical problem of the non-symmetrical crossing at the lowest point in the 1/2 waveform - typically in solid state that would be crossing the compliance zone for AB1, AB2 and B. However I don't have the cause crystal clear in my mind yet.
I can see for a non-clean B transition, that for a 1/2 wave form that has a flat area does so in symmetry within the waveform. For an individual valve, that's harder to nail where that waveform deformation comes from.
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Just thinking we can remove the even harmonics by rescaling.
Distorted waveforms (ie shifted energy in time) are going to immediately decompose into additional terms. In deconvolution of images, you've two options:
* sample based on the known point spread function, scale and reconstruct
* cull based on the point spread function scaled to the psf
The fast options are FFT phase correlation of the images, or FIR but you have the luxury of being offline and not realtime normally.
I wonder if there's anything in the quantum world we could use for harmonics. It depends on the technology in use, but many use a quantum wave function. They use phase resonance amongst other things.
In this: https://core.ac.uk/download/pdf/62861.pdf they transmit a modified waveform, essentially pre-adjusted that then is corrected by the distortion. However you'd need to know your distortion function.
Only other way is to simply compensate for change of the different parameters individually rather than the signal itself.
Distorted waveforms (ie shifted energy in time) are going to immediately decompose into additional terms. In deconvolution of images, you've two options:
* sample based on the known point spread function, scale and reconstruct
* cull based on the point spread function scaled to the psf
The fast options are FFT phase correlation of the images, or FIR but you have the luxury of being offline and not realtime normally.
I wonder if there's anything in the quantum world we could use for harmonics. It depends on the technology in use, but many use a quantum wave function. They use phase resonance amongst other things.
In this: https://core.ac.uk/download/pdf/62861.pdf they transmit a modified waveform, essentially pre-adjusted that then is corrected by the distortion. However you'd need to know your distortion function.
Only other way is to simply compensate for change of the different parameters individually rather than the signal itself.
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Harmonics constitute and characterize every sound. Without them the musical instruments would not be recognizable. Harmonics have an amount, magnitude, frequency and other characteristics. Some harmonics have a too high or a too low (missing) amplified amplitude. In the absence of even order harmonics, the odd order harmonics will be produced with higher level distortion. So why would you want to "eliminate" them?
No, this is about eliminating odd harmonic distortion generated in the amplifier, not the original signal.
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Well, sleeping on the odd harmonic dist. problem seems to have yielded some useful results.
But 1st, one should ground oneself here to actual tube characteristics. (before wandering off into quantum theory or other way too distant ideas.)
If one looks at the gm curves for tubes (E55L / 8233 datasheet gives good gm curves) one will see gm is an S shaped curve (page 7) versus grid V. But gm is a SQRT function versus plate current (page 9).
For a typical voltage driven class A P-P amplifier we get the S shaped gm curves overlapped (with one flipped left to right) which sum to a good approx. as a constant. Explaining why class A P-P gives low distortion.
Class AB P-P, voltage driven, gets a W shape gm sum with flattened out winglets at the edges of the W.
And a differential stage with a CCS tail gets a broad gm hill around the center. This comes about because the CCS tail makes the two currents complementary, so giving the SQRT gm function for each tube added together with one flipped left to right.
SE tube operation gives the S shaped gm curve, producing plenty of 2nd harmonic. (the internal triode N Fdbk helps smooth that out)
Now, looking at the definition of gm = dIp/dVg we'll need to monitor each P-P tube's current and differentiate that. dVg is the same complementary drive for each tube, differentiated also. If we sum the abs value of the two tube dIp portions and compare that to dVg of the input signal, we can servo control the tube operation to keep that a constant ratio for constant gm operation.
This monitoring scheme is a quite useful discovery, since it gives us a means of monitoring current gain -without- having to use a HF carrier and synchronous demod of its 2nd harmonic.
It brings to mind a Linear Tech Op Amp years back that had a secret black box in its circuit diagram for linearizing the Op Amp. Probably all Op Amps have it now.
So we need a differential stage to compare the dIp sum to the input signal dV. The output of the diff. stage then can be used to control gain somehow.
The tail current of an input differential stage could be controlled (as mentioned earlier) to alter the gain of the drive voltages ( or dVg).
Alternatively, one could alter the class A cross thru current (P-P) of the output tubes to control gm there directly, since gm is controlled by SQRT of current. (so a dynamic bias control for both tubes together) (note that increasing the cross current does not affect the monitored sum of dIp's, since they are actually subtracted to get the absolute gm sum.)
One problem with this gm measuring scheme is that load variation will cause more current change by itself. So a lower Rload will cause the controller to lower the drive to keep gm constant. Causing a higher output Z.
So this scheme should be used as an internal tube linearization loop before the OT for good bandwidth correction. But a global N Fdbk loop will be still be needed to control output Z.
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I've started to look into my timesliced phased idea.
Just breaking a 10Khz wave with a 10Mhz sample, to skip every other sample, then apply through a reconstruction step seems to work well - using 12au7s:
The upper noise can be filtered off, and give a standard harmonic wave form. The next step is to bring in phase switching and then we should see the harmonics reduce/disappear.
Just breaking a 10Khz wave with a 10Mhz sample, to skip every other sample, then apply through a reconstruction step seems to work well - using 12au7s:
The upper noise can be filtered off, and give a standard harmonic wave form. The next step is to bring in phase switching and then we should see the harmonics reduce/disappear.