Play with harmonics app:
Fourier Series Applet
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One can make a class A P-P stage that mostly makes even harmonic distortion with some trick feedback.
Put a current sense resistor in the B+ lead from the OT center tap. No distortion operation would see constant current here. So the odd order distortion normally made in P-P shows up here as current variation.
For an output stage of differential Voltage gain X, to cancel the odd distortion you feed back 1/X of this signal (V to I and I to V conversion included) as neg. fdbk to both grids to cancel the distortion. (ie, just enough pure error feedback to cancel the distortion) This is the WE harmonic neutralizer.
To convert the distortion from odd to even, you feed back 1/X to one grid (neg. fdbk) and -0.5/X to the other grid (pos. fdbk). This is anti-triode mode. ( somewhat less than -0.5/X to avoid oscillation problems from positive feedback; can also try just the 1/X neg. feedback to just one side)
Fourier Series Applet
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One can make a class A P-P stage that mostly makes even harmonic distortion with some trick feedback.
Put a current sense resistor in the B+ lead from the OT center tap. No distortion operation would see constant current here. So the odd order distortion normally made in P-P shows up here as current variation.
For an output stage of differential Voltage gain X, to cancel the odd distortion you feed back 1/X of this signal (V to I and I to V conversion included) as neg. fdbk to both grids to cancel the distortion. (ie, just enough pure error feedback to cancel the distortion) This is the WE harmonic neutralizer.
To convert the distortion from odd to even, you feed back 1/X to one grid (neg. fdbk) and -0.5/X to the other grid (pos. fdbk). This is anti-triode mode. ( somewhat less than -0.5/X to avoid oscillation problems from positive feedback; can also try just the 1/X neg. feedback to just one side)
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I was speaking of the odd order net distortion produced by the full P-P class A amp stage, not the even order produced by the individual tubes, which does cancel at the center tap due to opposite phase.
In any case, you will see current variation at the B+ center tap when the amp is making the usual P-P odd order net distortion.
In any case, you will see current variation at the B+ center tap when the amp is making the usual P-P odd order net distortion.
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I think maybe we are defining the distortion sources differently or semantics or something. Lets take a tube that has a square law response (generating only 2nd harmonic dist.). So it draws too much current at signal current peaks. When two such tubes are driven in complementary fashion to a P-P OT, the B+ will not sum to a constant current, but will have peaks at both signal peaks. OK, I think I see what you mean, the current thru the tap will have positive peaks at the second harmonic. However, these peaks correspond to the peaking (or flattening for saturation) of the output signal which would be 3rd harmonic distortion. I was referencing the output, that's all.
Since the tubes are generating even harmonic dist. in isolation, it is perhaps clearer to stay in that domain. So the even harmonic current sensed at the tap is fed back to the tubes to either make them cancel their individual distortion or enhance their distortion.
Since the tubes are generating even harmonic dist. in isolation, it is perhaps clearer to stay in that domain. So the even harmonic current sensed at the tap is fed back to the tubes to either make them cancel their individual distortion or enhance their distortion.
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If the output devices have a square law response (plus some linear, of course) then the current through each of them will consist of DC, fundamental and second harmonic. The OPT takes the difference and presents that as the output: fundamental only. The CT takes the sum, which will be DC and second harmonic only. There is no third harmonic so no flattening of the output.
For a real device which generate all orders, the OPT cancels evens so the output just sees odds. The CT cancels odds so the HT current is just DC plus evens. Flattening of output peaks is now possible, but these do not appear at the CT.
For a real device which generate all orders, the OPT cancels evens so the output just sees odds. The CT cancels odds so the HT current is just DC plus evens. Flattening of output peaks is now possible, but these do not appear at the CT.
I still see a different picture here. True, the 2nd harmonic cancels out and appears as 2nd Harmonic AC current through the center tap. But there is still odd (mostly 3rd) harmonic in the output (peaks in this case for square law devices). The gm of the devices are varying, increasing at peaks. More current will be drawn though the load at the peaks than the linear (constant gm) case. The variation of gm which produces the 2nd harmonic in the individual devices, causes 3rd harmonic to appear in the final output.
Oh, wait. Poor example. Square law produces linear variation of gm, so the two in class A add up to constant gm. So no 3rd harmonic final output in this case. OK. More complex law devices will give 3rd or odd harmonic final output.
I see your point. Odd harmonics generated in the devices will not show up at the CT, and so cannot be used to cancel this way. The best one can get is constant current, which still has odd harmonic bleed thru. But for devices generating mostly even harmonics, this scheme can be used to restore them (evens) in the P-P output.
Something better or different needed to get rid of the odds yet. If one took the difference of the two tube currents, one should see the fundamental plus the odds (Um, thats just the same as the output). Then subtract out the fundamental and feedback the odds. Err, I think that has a name already, Hawksford EC.
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There is still a bit of a puzzle here, since feeding back the B+ current (neg. fdbk) to both tubes will eventually cause the B+ current to become constant. Yet if the tubes are only producing even harmonics, that should make no difference in the output (evens already cancelled in the OT). But CCS tails do make a difference in the sound. What gives here?
Oh, wait. Poor example. Square law produces linear variation of gm, so the two in class A add up to constant gm. So no 3rd harmonic final output in this case. OK. More complex law devices will give 3rd or odd harmonic final output.
I see your point. Odd harmonics generated in the devices will not show up at the CT, and so cannot be used to cancel this way. The best one can get is constant current, which still has odd harmonic bleed thru. But for devices generating mostly even harmonics, this scheme can be used to restore them (evens) in the P-P output.
Something better or different needed to get rid of the odds yet. If one took the difference of the two tube currents, one should see the fundamental plus the odds (Um, thats just the same as the output). Then subtract out the fundamental and feedback the odds. Err, I think that has a name already, Hawksford EC.
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There is still a bit of a puzzle here, since feeding back the B+ current (neg. fdbk) to both tubes will eventually cause the B+ current to become constant. Yet if the tubes are only producing even harmonics, that should make no difference in the output (evens already cancelled in the OT). But CCS tails do make a difference in the sound. What gives here?
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4. Draw fundamental and harmonic sinewaves according to Fourier on a paper, sum their values, and see how with addition of next harmonic it becomes more and more perfect square.
Yes, THD minimizing is one way to go. But it is not the only way. We have a huge thread in Lounge about measurements and sound quality, no need to repeat it here.
CCS tails in a P-P output force constant average current. Fixed voltage bias forces constant quiescent current. Even order distortion (mainly second) means that when a signal is present average current is not quiescent current (even for Class A) - 2nd gives a DC component as well as second-harmonic. So the two bias methods give different bias when signal is present. Almost bound to sound a bit different. Normal resistor cathode bias is somewhere between the two.smoking-amp said:
Also, CCS bias can give different LF phase shift which can affect LF stability and subsonics.
Not the same thing.
Using the B+ current variation sense as negative feedback to both grids (neg. fdbk to both sides) can be set up to null out the B+ current variation. (ie, common mode feedback)
Presumeably this is nulling out the original even order distortion generated by the individual tubes to arrive at constant current sum operation. (even though the OT cancels the evens out too)
Just removing the original evens would be expected to make no difference in the output sound since the OT already does this. But a CCS tail (also giving constant current B+) does apparently give a different sound than no CCS tail.
I think the missing element here are even harmonics above the 2nd H. Tube 2nd H dist. does not produce odd harmonics in the output due to the constant gm sum. But higher even order harmonics do not produce a constant gm sum, so will produce odd harmonics in the output due to gm variation in odd order (the sum).
So my surmise is that either the B+ common mode feedback scheme, or the CCS tail, removes (some) odd harmonic dist. since it removes the 4th and higher even harmonic gm variations. Ie, it is preventing partial conversion of evens to odds, but not removing original odds.
The gm is found from the derivative of the V to I device formula. For square law devices, the gm drops to 1st or linear which sums to a constant in complementary setups. But 4th law (or above) drop to 3rd (or odd) law for gm. These do not sum to a constant in complement form.
Using the B+ current variation sense as negative feedback to both grids (neg. fdbk to both sides) can be set up to null out the B+ current variation. (ie, common mode feedback)
Presumeably this is nulling out the original even order distortion generated by the individual tubes to arrive at constant current sum operation. (even though the OT cancels the evens out too)
Just removing the original evens would be expected to make no difference in the output sound since the OT already does this. But a CCS tail (also giving constant current B+) does apparently give a different sound than no CCS tail.
I think the missing element here are even harmonics above the 2nd H. Tube 2nd H dist. does not produce odd harmonics in the output due to the constant gm sum. But higher even order harmonics do not produce a constant gm sum, so will produce odd harmonics in the output due to gm variation in odd order (the sum).
So my surmise is that either the B+ common mode feedback scheme, or the CCS tail, removes (some) odd harmonic dist. since it removes the 4th and higher even harmonic gm variations. Ie, it is preventing partial conversion of evens to odds, but not removing original odds.
The gm is found from the derivative of the V to I device formula. For square law devices, the gm drops to 1st or linear which sums to a constant in complementary setups. But 4th law (or above) drop to 3rd (or odd) law for gm. These do not sum to a constant in complement form.
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Here I "re-engineered" one famous song making my own text about an audio engineer that wants to sing on a stage.
http://wavebourn.com/music/alisovskiy/SebeNaBis.mp3
Very interesting, boy! I can´t understand what language is the singer using, but music is pretty good, and I can recognize a touch like Stevie Ray Vaughan in the guitar? or I´m delirious?
I fact, may I listen more?
It was MIDI file I found on Russian site.
The "singer" was me, language was Russian.
It was MIDI file I found on Russian site.
The "singer" was me, language was Russian.
OK.
"You appear to be claiming that even-order distortion can produce odd-order products. Not true. Do the maths. "
For square law devices in class A P-P:
(1-x)^2 - x^2 = 1- 2x +x^2 - x^2 = 1 -2x
So linear.
For cubic law devices in class A P-P:
(1-x)^3 - x^3 = 1 -3x +3x^2 -2x^3
So giving both odd and even powers and harmonics as the sum
For 4th power devices ...:
(1-x)^4 - x^4 = 1 - 4x +6X^2 -4x^3
So also giving both odd and even powers as the sum.
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"Nulling something via AC feedback (from CT), or via a bias shift (from CCS), are not the same thing. They are bound to sound different. "
Common mode feedback to the grids from the current sense is almost indistinguishable from the common mode variation of the cathodes for the CCS case (both arranged to give constant current sum). But I was not saying these two were different.
I was saying that these two are different from the grounded cathode case, where the P-P OT removes the even harmonics. The common mode fdbk and the CCS cases are removing even harmonics from the tubes 1st, while the grounded cathode to P-P OT summing is removing them after the fact.
As the cubic and 4th power cases above show, these will not be equivalent.
For square law devices in class A P-P:
(1-x)^2 - x^2 = 1- 2x +x^2 - x^2 = 1 -2x
So linear.
For cubic law devices in class A P-P:
(1-x)^3 - x^3 = 1 -3x +3x^2 -2x^3
So giving both odd and even powers and harmonics as the sum
For 4th power devices ...:
(1-x)^4 - x^4 = 1 - 4x +6X^2 -4x^3
So also giving both odd and even powers as the sum.
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"Nulling something via AC feedback (from CT), or via a bias shift (from CCS), are not the same thing. They are bound to sound different. "
Common mode feedback to the grids from the current sense is almost indistinguishable from the common mode variation of the cathodes for the CCS case (both arranged to give constant current sum). But I was not saying these two were different.
I was saying that these two are different from the grounded cathode case, where the P-P OT removes the even harmonics. The common mode fdbk and the CCS cases are removing even harmonics from the tubes 1st, while the grounded cathode to P-P OT summing is removing them after the fact.
As the cubic and 4th power cases above show, these will not be equivalent.
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Not true it seems..
Cosx restricted to the interval (0,pi) and then indefinitly repeated
will have only even harmonics in its fourier series although in practice
it will not be the case because of the discontinuity at pi , the function suddenly
jumping from its minimal to its maximal value , such a jump will
forcibly take a non zero time in real world.
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