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Old 7th November 2007, 04:17 PM   #1
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Default Distortion Neutralizer for Odd Harmonics

I was toying around with a class A, P-P amplifier design recently using cross-coupled resistive neg. feedback from the output plates back to the screen grids of the driver tubes. The drivers are configured in an differential LTP arrangement.

I started thinking about what would happen if the LTP used just a resistor in the tail instead of a CCS, and came across an interesting mechanism that appears to cancel only odd harmonics.

The idea of crosscoupling canceling odd order distortion I believe has been mentioned by Thorsten earlier in a thread on partial feedback to the driver grids and I think I also heard it mentioned for the Wolcott design too. At the time(s) I couldn't see how two inversions (1st from moving the feedback to the driver grids instead of the plates, the 2nd from the cross coupling) could account for any effect particular to odd harmonics other than the normal negative feedback action. And no explanation was offered at the time as to how this could happen. And I still think that in the ideal case of a perfect LTP there would not be any effect.

However, for a resistor tailed LTP, the variation of tail current with a common mode signal on the grids, causes a variation in gain of the LTP stage. Which potentially can be used to cancel gain variations elsewhere (like the outputs!). Now a perfect P-P output transformer will only have differential signals across the plate terminals (unless the B+ sags). But a real xfmr will have some winding resistances which act as current sampling resistors.

For a distortion where one tube increases in gain by the same amount that the other tube decreases in gain, no common mode voltage droop will appear. (ie. for perfect class A and also for this quasi-complementary distorting example of class A operation, constant B+ current is drawn.)

But for even order distorting devices like tubes and Mosfets (outside of their square law region), errors in gain are monotonic in polarity. Ie, their gain typically increases with increasing turn-on (well, untill saturation is hit) This means that one P-P output device will increase it's conduction more than the other device decreases its conduction, causing a common mode current change.

Increased common mode conduction thru the xfmr resistance causes the common mode plate voltages to drop, and the LTP grids will also drop correspondingly in common mode, which lowers the current in the LTP tail. This in turn lowers the LTP gain, which if adjusted for the correct amount can compensate the output stage's net increase in gain.

Near saturation, this common mode mechanism will also operate, since only one output device enters saturation at a time causing a large common mode current change. But the error effect is much larger there, and the common mode error correction loop gain is fixed ( by tail resistor value) at the lower level needed for the correction in the nearly linear region of operation. So saturation will still be soft and tube like. (notice that this common mode mechanism operates with a finite loop gain, just like Hawksford Error Correction, but is specific to only odd order distortion in this case)

Certain types of output device distortion, such as Mosfet square law conduction, will not be corrected by this scheme. There, the transconductance increase of one device is matched by the transconductance decrease (in class A only) of the other device, causing no common mode feedback. But this has no net affect in class A, since the total signal transconductance remains the same.
So no correction occurs when none is needed.

Obviously, this scheme only works for class A operation of the output devices. And requires strictly regulated B+ for sure.

Don
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Old 7th November 2007, 05:35 PM   #2
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Default odd-order cancellation

You have stumbled upon what Western Electric called "harmonic equalization" and a version of it was used in its 92A push-pull 300A amplifier in 1936. This seems to have been forgotten up until recently, although it has been used in the Dynaco power amps (the common-cathode current sense resistor) and in the Scott 340 receiver (as a unbypassed common screen resistor).

Your explanation is quite clear. Another was of looking at this is from the point of view of an RF SSB balanced modulator. In a push-pull circuit, a signal taken off of a common load gives the balanced modulator output. Adding this signal back in can cancel odd-order harmonics. In the long-tailed pair, this happens automatically.

I have experimented with this using a test amp where I could dail-in the amount of common cathode impedance from infinity (i.e. a CCS) to zero. Using push-pull 6CK4s, I found that the odd-order distortion could be significantly reduced, and that the null was not too sharp. With infinite resistance (CCS in the cathodes) the odd-order distortion was much higher than with grounded cathodes, arguing against the use of a CCS in this location. The amount of common-cathode resistance needed for minimum distortion depends on the tube type, which reflects the different distortion characteristics of each type.

Distortion cancellation should always be approached with caution, since usually the reduction of low-order terms either (in the best case) leaves the higher-order terms the same or increases them. This alters the sonic signature of the amp, usually to the worse. However, my limited experience with the harmonic equalizer shows that it doesn't seem to significantly increase the high-order terms, and can thus be used to tailor the sound of the amp.

This is an area that needs more exploration. Congratulations on your discovery and clear explanation.

- John Atwood
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Old 7th November 2007, 06:28 PM   #3
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Thank you John.

As usual with tube circuitry, someone has thought of it before. But the idea doesn't seem to have made it into the textbooks, much like inner positive feedback loops didn't either.

The common resistor in the P-P screens idea is interesting. I had some while ago looked at optimizing a single ended "triode" wired pentode. I came up with an equation that indicated that there is an optimum resistance and voltage drop to put between the screen grid and plate when the plate was loaded with a finite load resistance. My guess is the P-P case is related, with the SE signal part nulled out in the P-P pentode case.

Now if someone can just figure out how to do the harmonic fix for class AB!

Maybe one could run the driver stage as a class A LTP and then feedback it's common mode current signals to a LTP pre-driver stage to sort of mimic the correction for the output stage. Then possibly some sort of partial feedback from the output stage to the driver stage to make them track load-wise. But the match won't be all that good with one in class B and the other in class A. Hopefully one can find some kind of null with a pot in the pre-driver LTP tail to adjust correction.

Don
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Old 7th November 2007, 06:30 PM   #4
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steve bench has played with this too... didn't tacle AB, but did get A2 operation.

A2 PP 801's

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Old 7th November 2007, 08:23 PM   #5
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Hi Dave,

Hmmmm, this A2 PP 801 circuit of Steve's is a little puzzling. The 12AX7 common mode correctors are monitoring the 801 grids instead of the plates. This would seem to me to be correcting the V3 (5687) CFs, not the 801s. Maybe this is intended, due to the class A2 drive?

The actual common mode gain control however would appear to be the increase in gm of the 801s as the grid bias is changed (since no LTP tail modulation is used). But then the corrections will only show up at the 801 plates then. Also, both 12ax7s appear to be doing the same thing (except for the DC bias setting pots) since they monitor the same input signals. Am I missing something here?

I'll have to look at the WE86 and WE92A circuits.

Don

edit: I just noticed the 50 Ohm cathode resistors in the 801 cathodes, which provide common mode feedback indirectly thru the 801 grids in class A2. I guess this is how it is monitoring the output.
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Old 7th November 2007, 08:27 PM   #6
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Don,

To be honest, the whole thing goes a bit over my head and beyond my interests. I just know that the Harmonic Equalizer was the inspiration for his amp I think he will be taking it to the ETF this fall. You could ask him the questions you asked me, I'm sure he would be glad to discuss. I just posted the link because of the seemingly common interest.

dave
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Old 7th November 2007, 09:41 PM   #7
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Assuming the intended mode of operation (A2 PP 801) is to monitor the cathode currents by means of the cathode resistor feedbacks, I am now wondering what this does with varying load impedance. It would appear to vary the correction loop gain depending on speaker Z. And a reactive speaker Z???? Hmmm....
I'm at a loss here now too.

Jumping back to the earlier cross-coupled scheme, I have been thinking about how it would react in class AB to one tube cutting off. This does ,after all, just look like a bad case of low gm in one tube. Which the scheme is already tuned to correct. But I think it will need a tracking change to its loop gain at the class B threshold, since it suddenly has a much larger error to correct with less common mode gain to do it with.

(The correction loop gain being dependant on the effective combined output tube gm as well as the corrector stage common mode gain) (ie, for small corrections it will have nearly unity error correction, but at large corrections it will compute too small a correction with a low gm or low gain in the loop, this is very similar to Hawksford EC by the way) So there is some hope of solving this for class AB too. I think one needs something like a square law corrector maybe instead of the present linear one. (needs to be able to tell the difference between one tube gaining gm or the other tube losing gm obviously, more thinking to do!)

Don
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Old 7th November 2007, 10:11 PM   #8
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A related approach on the output side?: http://www.diyaudio.com/forums/showt...79#post1268379
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Old 7th November 2007, 11:36 PM   #9
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Steve Bench does like clever circuits. Good for him that he's able to pull them off!

Anyway, while he was in the process of developing his 801 amp I recall him mentioning that the harmonic equalization (HE) or odd order cancellation or whatever you want to call it, could be applied anywhere in the balanced/differential circuit. It looks to me like he has taken advantage of this 'fact' by not even including the 801's in the loop. The 12AX7's monitor common mode signal at the *grids* of the 801's and apply a portion of it to the cathodes of the 5687 drivers. He has two pairs of 12AX7, one for each driver/output tube. Both pairs perform the same function as far as distortion cancellation is concerned, but both pairs are needed because they also are responsible for maintaining the bias of the output tubes; one pair of 12AX7 for each 801.

smoking-amp: I have been looking at the WE circuit for years. I admit that I have never really gotten my head around how/why it works, but it continues to fascinate me. I regularly try to think up new ways to apply it. In my mind Steve Bench has established a 'reference' to compare any of of my ideas against (if for no other reason than he's built something while the rest of us just talk about it); there's no point in trying anything unless it can compare favorably to his implementation. Fortunately, simple and elegant solutions win major points in my book, and although I admire Steve's work tremendously, simple and elegant it ain't.

On the other hand, your use of DC resistance in the plate to generate a common mode signal and apply it to a LTP driver is very elegant. I love it. Even if I don't ever build it, it will probably influence my thinking about the concept for a while... It might even lead to my figuring out how it really works!

-- Dave
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Old 8th November 2007, 04:08 AM   #10
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Hi Sheldon,
Yes, Allen Wrights use of the 68 Ohm unbypassed common cathode resistor in post 292 by Gingertube appears to be a related method. It measures common mode current, which is proportional to total transconductance, and alters biasing of the tubes to approximately (only approx. unity gain available from CF mode) restore common mode current (or total transconductance) back to the norm.

By including an additional gain stage in the loop, the cross coupled approach or Steve's A2 PP 801/ WE ... designs can more accurately regulate the total transconductance.

Hi Dave C.,
The basic distortion correction mechanism is fairly straightforward in my way of thinking (I hope, but lengthy): The total common mode current is proportional to total transconductance from the two output tubes. If their grid signal drives are truly complementary, then this common mode summed current should remain steady during a signal cycle.

Ideally the output devices would have constant gm versus grid signal drive and so would give constant summed or common mode current during a signal cycle. Real devices however don't meet this high standard, but we can settle for equal increase of one device gm being offset by the same decrease of gm by the other device. Since both devices are operating in parallel AC-wise and effectively sum, this is adequate. This still produces constant common mode (CM) current too, so our measurement technique is safe.

Variation (with signal) from the constant CM current level would indicate a distortion causing variation of total gm. If this variation is polarity sensitive we would be seeing even harmonic distortion. But for a P-P output stage, symmetry prevents this. So any variation must be symmetrical, producing (or indicating) odd order distortion.

Typical 3/2 power current variation (100% component for pentodes or as a distortion component for loaded triodes) will produce an increasing total gm as signal increases from zero in either polarity (for P-P) up until saturation is reached at which point total gm will plunge due to the saturated tube loosing serious gm (and the other tube being almost cutoff by grid signal already). So the 3/2 component will be causing odd order distortion. ( the 3/2 power effect produces a greater increase in gm in one tube than the drop it causes in the other tube for an increasing signal)

The saturation effect is likewise fully symmetrical in P-P so it is producing odd order distortion too.

So by monitoring the CM current we can use it to effect a compensating gain change in some way.

The cross coupled feedback LTP driver, with a resistive tail, uses the CM portion of the feedback signals to alter its tail current. Increasing tail current causes a gm increase in the LTP driver by the same 3/2 power non-linear gm mechanism to, in turn, give a gain boost (or buck) to the incoming grid differential drive signals.
Net effect being to keep the final thru-channel gain constant.

The differential component of the cross coupled feedback, meantime, also makes for a short, nearly local (transformer and input stages not included, so high bandwidth) negative feedback loop to effect conventional NFB error correction of the output stage and to lower output impedance.

So we are getting our moneys worth from the driver stage twice: differential (or P-P) mode and SE (or CM) mode corrections. Only a small amount of CM correction is thus required to fill in for the lack of infinite gain in the differential NFBK loop. So a pot in the tail is useful to set the optimum level of correction.

Hope that clarifies the mechanism. (Take two aspirin and call me in the morning )

Don
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