First of all, the currents must vary to produce an AC output signal. Generally they would be near complementary currents, the CCS tail ensures they are exactly. This turns out to be not that useful actually for tubes.
Take a look at the E55L datasheet linked below. For linear gain, the sum of the gm's of the two P-P devices must be constant.
Bottom of page 7 (the S curve) shows the gm variation when the cathodes are grounded, ie gm variation versus complementary drive voltages (in class A of course). Flipping one of the tube gm curves around for P-P will come close to a constant gm sum with the original curve. (if the tubes operated with perfect 2.0 power law, the gm curves would be straight linear ramps, and would sum to a constant in P-P configuration. The straight portion of the S shaped gm curves is near 2.0 power law. Mosfets come closer to ramps. But symmetrical S curves, typical for tubes, can work too. )
Now look at the top of page 9, gm variation versus cathode current. Cathode current is the complementary variable with a CCS tail. (the tail voltage varies to modify the grid signals into non-complementary signals, to maintain constant current) Notice the flipped around gm (S curve) will NOT sum with the original gm curve to a constant gm. You get a humped gm sum. This produces odd harmonic distortion. Allen's amplifier is a distortion producer. He later fixed it with the optimum tail resistor given in Kiebert's article "System Design Factors for Audio Amplifiers" which nulls 3rd harmonic. (The optimum tail resistor causes the tail current to vary slightly, increasing at signal peaks. The resistor then causes higher tail current at the peaks, causing higher gm, and so removing the gm hump in the middle by increasing the ends.)
CCS tails only work good with bipolar transistors, which have gm proportional to current.
http://frank.pocnet.net/sheets/009/e/E55L.pdf
Take a look at the E55L datasheet linked below. For linear gain, the sum of the gm's of the two P-P devices must be constant.
Bottom of page 7 (the S curve) shows the gm variation when the cathodes are grounded, ie gm variation versus complementary drive voltages (in class A of course). Flipping one of the tube gm curves around for P-P will come close to a constant gm sum with the original curve. (if the tubes operated with perfect 2.0 power law, the gm curves would be straight linear ramps, and would sum to a constant in P-P configuration. The straight portion of the S shaped gm curves is near 2.0 power law. Mosfets come closer to ramps. But symmetrical S curves, typical for tubes, can work too. )
Now look at the top of page 9, gm variation versus cathode current. Cathode current is the complementary variable with a CCS tail. (the tail voltage varies to modify the grid signals into non-complementary signals, to maintain constant current) Notice the flipped around gm (S curve) will NOT sum with the original gm curve to a constant gm. You get a humped gm sum. This produces odd harmonic distortion. Allen's amplifier is a distortion producer. He later fixed it with the optimum tail resistor given in Kiebert's article "System Design Factors for Audio Amplifiers" which nulls 3rd harmonic. (The optimum tail resistor causes the tail current to vary slightly, increasing at signal peaks. The resistor then causes higher tail current at the peaks, causing higher gm, and so removing the gm hump in the middle by increasing the ends.)
CCS tails only work good with bipolar transistors, which have gm proportional to current.
http://frank.pocnet.net/sheets/009/e/E55L.pdf
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Allen is talking about the AC currents, not the DC average. i.e., when one tube pushes, the other must pull by exactly the same amount (which is true). However, Allen knew very little about fundamental electronic engineering, so you often have to take his words with a big pinch of salt. He was more what you might call a 'technically minded subjectivist'.
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