Mixing resistors vs capacitance of the following stage

[Hardtailed]

Take into example the classic 5E6/Marshall Plexi circuit: the lead and normal channels are joined before the DC Coupled Cathode Follower stage via 2 470K mixer resistors.

Those resistors are not before the actual cathode follower, but rather to the common-cathode gain stage driving it.
If I do the math, a 470k serie resistor here, figuring a total capacitance (including Miller effect) of roughly 100pF, that brings the low-pass cutoff point at around 3.4KHz! Some say that capacitance can be as much as 150pF, making even worse.

Is there anything else about this stage that makes my math wrong?

I'm guessing also this is why the lead channel bypasses this resistor with a 500p capacitor. But doesn't that defeat the purpose of the resistor if you bypass it?

And if I wanted to have the frequency response almost identical to if no resistor was there, how do I calculate the bypass capacitor needed? Is there any logic in making it around the same value as the stray capacitance (100-150pF)?

[daz]

I'm certainly not the guy to answer you. But as a non tech who only knows results and not the theory behind a lot of it, i will say this. experimenting with voltage dividers between preamp stages verses using grid leaks to cut gain, i have noticed a huge difference in tone. What you said doesn't surprise me because the difference is so drastic that using a voltage divider in place of a simple grid leak sounds like you turned the treble knob from 2:00 down to 10:00. Huge treble roll off to be sure. Of course i suppose you could always do what they do with volume pots and put a cap across the series resistor. never tried that on a set VD myself but i'm glad you brought this up because i may find that useful. You could even use a trimmer in series with the cap to get the perfect balance. If theres anything wrong with my theory someone please tell me because as most of you who know be are aware of, i'm pretty much the court jester of ampage.

[pdf64]

The actual equivilant source resistance that will form the R bit of the RC filter will be formed by the 2 470k (270k in the fender originals) resistors in parallel, then add in the variable element of the position of the pot wipers and then also the plate resistances of the previous stages - it's complicated and there's no one answer, though it'll range between ~235k (both vols near zero) and ~ 500k (both controls ~ halfway electrically). Other settings will give an R somewhere between these.
So you're right, it's far from ideal. If there was another triode stage available, then an active mixer could be used, or a bootstrapped buffer between the mixer resistors and the next stage, as these have massively reduced the input capacitence compared to a regular gain stage.
Failing that, if you want to mitigate for the top end roll off, it would be best to go with the 270k rather than 470k, and accept that there will be a compromise - if you get one channel flatish (by bypassing it's mixer resistor), the other channel will likely have a lower rolloff frequency than if you'd left the other 1st channel alone, unbypassed (so much depends on the vol control settings).
On that basis, yes, it would be best to bypass one of the mixer resistors with a cap equivilant to the tube's input capacitence,ie 150pF, see Designing Common-Cathode Amplifiers
That way you'll form a capacitive potential divider (bypass cap feeding tube input capaciance to ground) in parallel with the resistive potential divider (the 2 470k resistors), and it should balance out.
You could bypass both mixer resistors, and then ensure that neither volume is adjusted near it's electrical extremes, as if the wiper end of either bypassed resistor as set near to ground, it would cause top end rolloff for the other channel.

[yunger]

i've been thinking about this lately also. in my case, my amp gets too bright with volume up (i play a tele FYI). i was thinking of using the rc filter to my advantage by using a dual ganged gain pot with the second gang as a variable resistor. in theory, increasing grid resistance as the volume gets cranked and taming the fizz a little.

[Hardtailed]

...
You could bypass both mixer resistors, and then ensure that neither volume is adjusted near it's electrical extremes, as if the wiper end of either bypassed resistor as set near to ground, it would cause top end rolloff for the other channel.

That's a lot of useful information! That was my impression that bypassing one resistor would likely mean the other channel would lose even more treble (by way of high frequencies "bleeding" back through the cap to ground via the other channel's volume pot). So, basically if one is using just the Brilliant channel and wants the brightest tone, the best way is to keep the Normal channel volume way up with nothing plugged in!
(Although... the fun is in mixing the channels together)