I would be very grateful if someone could explain to me why, in a vacuum tube, signal gain is INVERSELY related to maximum plate current.

In the 12A_7 series of tubes, the 12AX7 has the highest signal-gain factor (100), the 12AT7 an intermediate gain factor (60), and the 12AU7 the lowest gain factor (19).

However, the 12AX7 has the lowest maximum plate current (6 mA); the 12AT7 an intermediate max plate current (15 mA); and the 12AU7 has the highest max plate current (22 mA).

This is counterintuitive to me, but that's probably because I don't understand much about electronics. Can anyone explain to a layman why signal gain rises as maximum plate current falls? Thanks!

There is the need for the driving force, the voltage, and the power, the current. Some things are current hungry but don't require much voltage and the other way around. Tubes can put out a lot of voltage but not as much current when compared to solid-state devices. Also there is an inverse going on that with higher current the voltage must drop or a tube of a certain design will need to be made, as in power tubes. Take a EL34 running at 350 volts on the plate with 25 mA of bias. You will get around 16 to 17 watts of power output. If the tube were not built to handle this, as a 12AU7 is not, it would burn up. So you have the small signal tubes like the 12AX7, 6SL7, 12AU7, 6SN7 and so forth but what they do is amplify at different amounts as delivering different current amounts for the needs of the application. So the 12AX7 can deliver a higher amplitude of a signal but less current and if the less current is all that is needed, what is being driven will work just fine. You see 6SN7's and others in the same amplification range being used because they can also deliver current to drive the transducer. The 12AX7 would not have enough current to do this even though the signal is amplified more. I have paralleled 6DJ8's to get twice the current and it works very well but they are also in the same amplification area as the 12AU7 and the 6SN7.

Thanks for the answer, John; I'm grateful.

By the way, I really like the photographs on your website!