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In Reply to: RE: LTP VS Differential Amplifier posted by Triode_Kingdom on June 16, 2021 at 06:59:46
Couple of things, the grounded grid amplification factor of mu+1 leaves it requiring that side to have higher gain even with balanced resistors.
That never happens.
So the basic issue seems to be that treating it as a grounded cathode and a grounded grid seems to be improper. I don't see treating it that way when the diff amp model actually seems to give the correct output predictions with grid No.2 signal counted as zero.
cheers,
Douglas
Friend, I would not hurt thee for the world...but thou art standing where I am about to shoot.
Follow Ups:
"So the basic issue seems to be that treating it as a grounded cathode and a grounded grid seems to be improper. I don't see treating it that way when the diff amp model actually seems to give the correct output predictions with grid No.2 signal counted as zero."In Crowhurst's Fig. 626 it is manifest that V1 is driving into the cathode of V2, and since the grid of V2 is grounded, that means that V2 is by definition a grounded-grid amplifier. I don't see that there is any room for that statement to be incorrect.
It may be that one could find some other words to describe the same situation, but they must, logically speaking, be equivalent words describing exactly the same situation.
In any case, whatever words one uses to describe the circuit, there can really only be one set of correct equations that can be written down for the small-signal analysis, and so only one correct prediction for the two signal outputs. The physics, after all, is what it is, and all that is really being done is to apply Kirchoff's law to the currents at each node, employ Ohm's law to relate potential differences across resistors to the currents flowing through them, and employ the small-signal analysis of how the tubes behave under small perturbations around the quiescent conditions. All of these are universally agreed.
There shouldn't really be room for there to be any differences of opinion about what the correct system of equations to describe the circuit should be. And it is a very simply circuit. I think that analysis of Crowhurst's, after correcting the obvious algebraic mistake, is valid.
By the way, what do you mean when you say "the diff amp model actually seems to give the correct output predictions with grid No.2 signal counted as zero"? Correct as judged how?
Edits: 06/18/21
With a grid grounded in a diff amp, that section is not presenting a gain of mu+1 as it would if the circuit could be treated as a grounded cathode and a grounded grid. The balance is dependent on the magnitude of the tail load.The usual implementation of a diff amp third stage in a Williamson is going to behave quite differently vs one with a hard, unsaturated CCS in its tail. The signal at the cathode node will be larger, and the plate output will be different.
If it were acting like a separate grounded grid stage, an LTP built around a pair of 6C19Pi running a hard CCS would show higher gain in the section with a grounded grid since mu/mu+1 is near the minimum practically possible. IOW, if treating the grounded grid as separate were proper, a minimum mu circuit would show the grounded grid section with higher gain. That never happens.
As you said, examining the circuit as a whole is required, and it will not show that the grounded grid side has a delivered amplification factor any different from the other half. The interaction between mu, gm, plate loads and the cathode load show the imbalance generating causes.
Without the equations in front of me, increases to mu and gm will both shrink the imbalance. Differences in the plate loads can work towards correcting this imbalance, and increasing Rk shrinks imbalance...
cheers,
Douglas
Friend, I would not hurt thee for the world...but thou art standing where I am about to shoot.
Edits: 06/18/21
"As you said, examining the circuit as a whole is required, and it will not show that the grounded grid side has a delivered amplification factor any different from the other half. The interaction between mu, gm, plate loads and the cathode load show the imbalance generating causes."One needs to be sure that disagreements are not merely about how the words are being used. In terms of Crowhurst's equations, if the amplification factors are called A1 and A2, and defined to be the changes in the plate voltages of tube 1 or tube 2 respectively, divided by the input voltage on the grid of tube 1, then they can be read off from his equations (92) and (94) respectively (since his Ep1 and Ep2 are defined to be the changes in plate voltages on tube 1 and tube 2 in response to putting a 1 volt input on the grid of tube 1). That is to say,
A1 = Ep1 (in eqn (92)), and A2 = Ep2 (in eqn (94)).
(Actually, there is a further typo, in his eqn (92); there should be a plus sign after Rp1 in the denominator of his expression.)
Using the corrected eqn (96) that I had previously given, these equations then say it all. That is, all the signal voltages, namely Ep1 at plate 1, Ep2 at plate 2, and Eck at the common cathode point, are all expressed in terms of the input voltage on grid 1, the resistors RL1, RL2, Rk, and the characteristics mu1 and Rp1 for tube 1 and mu2 and Rp2 for tube 2.
Crowhurst is, of course, precisely worrying about the fact that tube 1 is driving into the impedance corresponding to the paralleling of the cathode resistor Rk and the input impedance of the grounded grid amplifier that it is driving. That is the basis of his calculation. So he has taken everything properly into account.
By the way, if we assume RL1 = RL2 = RL, and assume identical tubes so that Rp1 = Rp2 = Rp and mu1 = mu2 = mu, the resulting formula for A1/A2 agrees exactly with the one Ralph gave a few days ago, namely
A1/A2= 1 + (RL + Rp)/((1+mu) Rk).
If the tubes are taken to be different in their characteristics (unequal mu and Rp), but the two anode loads are still set equal, RL1 = RL2 = RL, then the ratio of the amplification factors is given by
A1/A2 = 1 + (RL + Rp2)/((1+mu2) Rk).
So the mu and plate resistance of tube 1 do not enter in the expression for the ratio of the amplification factors.
Edits: 06/18/21 06/18/21 06/18/21 06/18/21
What in the hell is eqn 92 and 94?...and feel free to put up the corrected version.
Douglas
Friend, I would not hurt thee for the world...but thou art standing where I am about to shoot.
"What in the hell is eqn 92 and 94?"
Equations in the book by Crowhurst that has been under discussion in this thread. I put the relevant pages in a post on this thread a few days ago, with my corrections indicated on the 4th of the posted pages.
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