> We aren't changing the mu with the control grid voltage
Some. Never enough to be useful.
You have two problems.
You want gain to change.
And in a compressor or limiter, you want minimum gain at maximum output.
But minimum gain means minimum current.
So on one hand, we want to approach Power Matched condition at minimum current and gain. And as the plot NYDave showed shows, this suggests a load like 20K or more. Which gets you into high inductance for bass, and stray capacitance treble troubles.
Also, if it is Power Matched at minimum gain and current, then it is mismatched at higher current, and gain hardly changes as current changes. For 6386 at 240V and 20K load, at 25mA the gain is about 15 and at 5mA the gain is about 10. And we get that much change mostly because the 6386 really does change Mu from 20 to 5.
An alternative is to match at max gain and let it go mis-matched at low gain. 3K load gives gain=7 at 25mA and gain=1.5 at 5mA. Better, but still only 13dB GR. We'd want to push down to say 2mA where gain will be (squint) 0.6, 21dB GR. So the load impedance should be as low as or lower than the max-current plate impedance.
But now look at the low gain high output condition. 1mA current in 3K is 3V and 3mW peak at high distortion (even doubled in push-pull). Taking 10dB headroom we have 1V and 0.3mW peak output. If we want to apply 20dB GR and get an 80dB dynamic range signal, the noise floor at plate must be 100dB below 1V. With 14dB of no-GR gain, that's 114dB re:1V or 2 microVolts at the grid. That's a low noise number for a hot-cathode device. And the 6386 is far better than most tubes.
I like to estimate the unbalanced DC "could be" 20% of the maximum current, and will happen around half current or around 3dB GR. If you use the limiter as a safety fudge, tapping just a few dB GR fairly frequently, the unbalance thumps could be bothersome. Not so much for the iron, because E-I cores comfortable for 25mA balanced DC will usually tolerate 2.5mA unbalanced DC. If you have a crate of tubes you could tediously select better-matched pairs.
I have a feeling the core should be big enough to work the GR tube as a Power Amplifier with low THD down below 50Hz. That may mean a lot of iron even for miniature tubes. Edcor does have a good pound/$ ratio. At the lower impedances, a big hunk of ordinary iron is probably better than a small chunk of magic iron.
Input noise is a function of Gm. We want low Gm for high grid signals and high Gm for low noise. The real answer is to find "bad" tubes, which have high current for moderate Gm, so when we push them to lower current we still have lots of current to make lots of max output. 6L6 comes to mind, but nobody seems to be that heroic. Of the not-so-insane schemes, 12AU7 working near 120VDC with a 10KCT 2W winding should beat some meat without much stink, and at stupid low cost.
A figure of merit might be to take the spec-sheet's boast condition and figure I/Gm. That gives a voltage. In fact it is the maximum input voltage for low GR and high THD. You need to derate for low THD, and derate some more for the amount of GR you will need, but these factors tend to be the same for all tubes. However I/Gm is a figure of DE-merit for amplifiers. Tube designers spent 50 years trying to improve Gm/I, meaning I/Gm got worse. Some of the oldest tubes may be the "best". Of the modern sort, 12AU7 is a sloppy job and "better" for our purpose than 12AX7 or 6DJ8.
High plate voltage improves maximum grid voltage. However we normally idle near zero grid, and most tubes will burn-up if plate voltage is set high. High plate voltage also means high control voltage and heroic sidechain. On some tubes the plot of I/Gm is S-shape, and the best part is below the inflection. Gm falls faster than I. That's a secret of the 660. Then you idle at significant negative grid voltage, and can run high plate voltage. In any case, high plate dissipation is good. (Again 6L6 comes to mind.)
The secondary side depends what you want for an output amp. The 660 parallels ~3mW pairs to get a "Pro" power on 600 ohms, but it is hard work with little headroom. If you want a 1-stage output buffer, you may need to step-up the 1V-3V plate level to the output grids. If you go voltamp poweramp, you want to match for noise, and 10K:10K is not bad for 6386, but 10K:2K may be better for less beefy tubes to get plate resistance stepped down below grid noise resistance.
Note that the Vari-Gu input must run at high idle current for good max-output performance. This means it may be the lowest grid-noise stage in your studio (though push-pull works against that). It might be that the best place for the gain cell is at the mike, right after a fairly low-ratio transformer. Or maybe no tranny: the 660's four-pair input has a noise resistance near 300 ohms, which is quieter than many condensers, and not a lot higher than some dynamics. In many low-buck studios, room noise may mask mike and tube noise. You'd have to float the mike guts at CV level, and make Phantom follow it.... a transformer may be useful.
But putting a Vari-Gu cell after any other amplifier, you just about have to have a loss.
Some. Never enough to be useful.
You have two problems.
You want gain to change.
And in a compressor or limiter, you want minimum gain at maximum output.
But minimum gain means minimum current.
So on one hand, we want to approach Power Matched condition at minimum current and gain. And as the plot NYDave showed shows, this suggests a load like 20K or more. Which gets you into high inductance for bass, and stray capacitance treble troubles.
Also, if it is Power Matched at minimum gain and current, then it is mismatched at higher current, and gain hardly changes as current changes. For 6386 at 240V and 20K load, at 25mA the gain is about 15 and at 5mA the gain is about 10. And we get that much change mostly because the 6386 really does change Mu from 20 to 5.
An alternative is to match at max gain and let it go mis-matched at low gain. 3K load gives gain=7 at 25mA and gain=1.5 at 5mA. Better, but still only 13dB GR. We'd want to push down to say 2mA where gain will be (squint) 0.6, 21dB GR. So the load impedance should be as low as or lower than the max-current plate impedance.
But now look at the low gain high output condition. 1mA current in 3K is 3V and 3mW peak at high distortion (even doubled in push-pull). Taking 10dB headroom we have 1V and 0.3mW peak output. If we want to apply 20dB GR and get an 80dB dynamic range signal, the noise floor at plate must be 100dB below 1V. With 14dB of no-GR gain, that's 114dB re:1V or 2 microVolts at the grid. That's a low noise number for a hot-cathode device. And the 6386 is far better than most tubes.
I like to estimate the unbalanced DC "could be" 20% of the maximum current, and will happen around half current or around 3dB GR. If you use the limiter as a safety fudge, tapping just a few dB GR fairly frequently, the unbalance thumps could be bothersome. Not so much for the iron, because E-I cores comfortable for 25mA balanced DC will usually tolerate 2.5mA unbalanced DC. If you have a crate of tubes you could tediously select better-matched pairs.
I have a feeling the core should be big enough to work the GR tube as a Power Amplifier with low THD down below 50Hz. That may mean a lot of iron even for miniature tubes. Edcor does have a good pound/$ ratio. At the lower impedances, a big hunk of ordinary iron is probably better than a small chunk of magic iron.
Input noise is a function of Gm. We want low Gm for high grid signals and high Gm for low noise. The real answer is to find "bad" tubes, which have high current for moderate Gm, so when we push them to lower current we still have lots of current to make lots of max output. 6L6 comes to mind, but nobody seems to be that heroic. Of the not-so-insane schemes, 12AU7 working near 120VDC with a 10KCT 2W winding should beat some meat without much stink, and at stupid low cost.
A figure of merit might be to take the spec-sheet's boast condition and figure I/Gm. That gives a voltage. In fact it is the maximum input voltage for low GR and high THD. You need to derate for low THD, and derate some more for the amount of GR you will need, but these factors tend to be the same for all tubes. However I/Gm is a figure of DE-merit for amplifiers. Tube designers spent 50 years trying to improve Gm/I, meaning I/Gm got worse. Some of the oldest tubes may be the "best". Of the modern sort, 12AU7 is a sloppy job and "better" for our purpose than 12AX7 or 6DJ8.
High plate voltage improves maximum grid voltage. However we normally idle near zero grid, and most tubes will burn-up if plate voltage is set high. High plate voltage also means high control voltage and heroic sidechain. On some tubes the plot of I/Gm is S-shape, and the best part is below the inflection. Gm falls faster than I. That's a secret of the 660. Then you idle at significant negative grid voltage, and can run high plate voltage. In any case, high plate dissipation is good. (Again 6L6 comes to mind.)
The secondary side depends what you want for an output amp. The 660 parallels ~3mW pairs to get a "Pro" power on 600 ohms, but it is hard work with little headroom. If you want a 1-stage output buffer, you may need to step-up the 1V-3V plate level to the output grids. If you go voltamp poweramp, you want to match for noise, and 10K:10K is not bad for 6386, but 10K:2K may be better for less beefy tubes to get plate resistance stepped down below grid noise resistance.
Note that the Vari-Gu input must run at high idle current for good max-output performance. This means it may be the lowest grid-noise stage in your studio (though push-pull works against that). It might be that the best place for the gain cell is at the mike, right after a fairly low-ratio transformer. Or maybe no tranny: the 660's four-pair input has a noise resistance near 300 ohms, which is quieter than many condensers, and not a lot higher than some dynamics. In many low-buck studios, room noise may mask mike and tube noise. You'd have to float the mike guts at CV level, and make Phantom follow it.... a transformer may be useful.
But putting a Vari-Gu cell after any other amplifier, you just about have to have a loss.
