Great topic. This has got me digging and googling. Brain muscle is getting tired!
I'm not sure if we're talking about the same thing, or not. Just for clarification, if the cathode R is unbypassed, then you automatically have cathode feedback (also known as cathode degeneration). The SVT schematic linked to by iiipopes (on page 2?) shows unbypassed cathode resistors. Thus, cathode feedback. (Don't know about the amp shown on page 4 -- its cathode resistors are off-page).
I've pretty much convinced myself that cathode feedback lessens the effect of transconductance mismatch upon gain (Check this link: http://www.angelfire.com/planet/funwithtransistors/Book_CHAP-4A.html . If you are masochistic, scroll down to section 4A.3 "small signal analysis" and take a look at the equation for gain without the cathode bypass cap (4A.10.10). First, keep in mind that gm (transconductance) is directly proportional to mu, so when we talk about gm variation, that is equivalent to talking about mu variation. Now, back to that equation... you'll see mu on top, and mu+1 on the bottom, so in the ideal case where the sum of Rbc+rp is less the mu*Rk, and mu is, say, 10 or more, mu (and thus transconductance) drops out of the gain equation and the gain becomes simply -Rbc/Rk (exactly analogous to a transistor amp with emitter degeneration). Gain is now independent of mu (and thus transconductance).
Now, I can't speak to how much less Rbc+rp actually is to mu*Rk (and this might be where my flaw is -- those who have studied this stuff, help!!!). But I will say that paralleling tubes has the effect of reducing rp by the number of tubes paralleled. Therefore, in an amp with 3 tubes on a side, rp on each side is reduced by a factor of 3.
Thanks very much for the link -- very interesting!
Regarding the paragraph you pointed out, the next two sentences are also important. They state:
I agree with this, but I would like to dig down a bit deeper and clarify what they're taking about.
1. Most of what that section discusses is the necessity of matching the gains of the two "halves" of a push-pull amp (per iiipopes comments). They really aren't talking about matching transconductance of multiple tubes within a side (at least, not per my reading), and I completely agree with what it says, at far as it goes.
2. They also don't discriminate between amps with and without cathode degeneration. I believe there is a difference between the two. If the cathode resistors are not bypassed, they are a form of negative feedback. As such they also act to equalize the gains of the two side of the push-pull amp and thus lessen the effects of transconductance mismatch between the two sides. In other words, matching transconductance has just become less important.
So what this means to me: if the goal is to have the two sides of a push-pull amp have equal gains (to prevent even-order harmonics, etc.), then, in amps without cathode feedback (that is, amps in which there is no cathode resistor, or the cathode resistor is bypassed with a cap), you must match transconductance between the two sides of a push-pull amp in order to match gain.
But in amps in which there is cathode degeneration, matching transconductance between sides becomes less important, as long as mu*Rk >> Rbc+rp.
Anyway, maybe I'm completely wrong or I'm missing something. But this makes sense to me.
Cathode bias, not feedback. In cathode bias the tube self biases through a resistor and bypass cap. Lower power option with interesting distortion character, no feedback loop. Basic triode to a transistor; Plate-collector, grid (control)-base, cathode-emitter.
I'm not sure if we're talking about the same thing, or not. Just for clarification, if the cathode R is unbypassed, then you automatically have cathode feedback (also known as cathode degeneration). The SVT schematic linked to by iiipopes (on page 2?) shows unbypassed cathode resistors. Thus, cathode feedback. (Don't know about the amp shown on page 4 -- its cathode resistors are off-page).
I've pretty much convinced myself that cathode feedback lessens the effect of transconductance mismatch upon gain (Check this link: http://www.angelfire.com/planet/funwithtransistors/Book_CHAP-4A.html . If you are masochistic, scroll down to section 4A.3 "small signal analysis" and take a look at the equation for gain without the cathode bypass cap (4A.10.10). First, keep in mind that gm (transconductance) is directly proportional to mu, so when we talk about gm variation, that is equivalent to talking about mu variation. Now, back to that equation... you'll see mu on top, and mu+1 on the bottom, so in the ideal case where the sum of Rbc+rp is less the mu*Rk, and mu is, say, 10 or more, mu (and thus transconductance) drops out of the gain equation and the gain becomes simply -Rbc/Rk (exactly analogous to a transistor amp with emitter degeneration). Gain is now independent of mu (and thus transconductance).
Now, I can't speak to how much less Rbc+rp actually is to mu*Rk (and this might be where my flaw is -- those who have studied this stuff, help!!!). But I will say that paralleling tubes has the effect of reducing rp by the number of tubes paralleled. Therefore, in an amp with 3 tubes on a side, rp on each side is reduced by a factor of 3.
There is something else going on. In part it has to do with how the tubes interact with the transformer and noise. Check out this link at the end, the paragraph starts with "Transconductance matching is important for AC (signal) balance in the output stage." There are other useful points made in this document.
Thanks very much for the link -- very interesting!
Regarding the paragraph you pointed out, the next two sentences are also important. They state:
"A push-pull amplifier has inherent power supply hum rejection and common-mode input rejection due to the symmetry of the output stage. If one side has a different amplification factor than the other, this symmetry is lost, and the amplifier won't be able to reject power supply hum and noise as well."
I agree with this, but I would like to dig down a bit deeper and clarify what they're taking about.
1. Most of what that section discusses is the necessity of matching the gains of the two "halves" of a push-pull amp (per iiipopes comments). They really aren't talking about matching transconductance of multiple tubes within a side (at least, not per my reading), and I completely agree with what it says, at far as it goes.
2. They also don't discriminate between amps with and without cathode degeneration. I believe there is a difference between the two. If the cathode resistors are not bypassed, they are a form of negative feedback. As such they also act to equalize the gains of the two side of the push-pull amp and thus lessen the effects of transconductance mismatch between the two sides. In other words, matching transconductance has just become less important.
So what this means to me: if the goal is to have the two sides of a push-pull amp have equal gains (to prevent even-order harmonics, etc.), then, in amps without cathode feedback (that is, amps in which there is no cathode resistor, or the cathode resistor is bypassed with a cap), you must match transconductance between the two sides of a push-pull amp in order to match gain.
But in amps in which there is cathode degeneration, matching transconductance between sides becomes less important, as long as mu*Rk >> Rbc+rp.
Anyway, maybe I'm completely wrong or I'm missing something. But this makes sense to me.