Looking at the Marshall JCM800 Lead 50W 1987 preamp I see that the first preamp stage has a 330uf bypass cap and 820 ohm cathode resistor. Has anyone every tried this in a Fender Champ/VChamp on the first preamp stage? What did it sound like? Is it higher gain? It's an awfully large bypass cap. ...
Your cap/resistor combo will be -3dB when X
c = R ("X
c" meaning capacitive reactance).
The formula to calculate X
c usually assume you know what specific frequency you wish to evalute, but we want to know frequency for a known X
c. So we'll swap those two values.
Frequency = 1/(2*Pi*X
c*C)
"C" is in Farads, so 330uF = 0.00033F, and we calculate -3dB at ~0.59Hz. As Silvergun's plot shows, gain is not "increased" it's just not reduced by local feedback across the cathode resistor even down to sub-sonic frequencies.
The 330uF is a carry-over, as Sluckey said, from the 5F6-A Bassman's 250uF, and rounded up to a value in the modern value scheme (0.01, 0.022, 0.033, 0.47, 0.68, etc).
I've had a theory for a number of years that because this was a bass amp (living in 60Hz and 120Hz), Fender tried every trick to make sure hum was nil in the input stage (except d.c. heaters, because that's just silly for an instrument amp in the 50's). A 12AY7 input tube was used (advertised for "low hum & noise in input stages of high gain audio amps"), and my theory is the super-huge bypass cap was to nix hum in the event an individual tube had heater-to-cathode leakage.
I know a modern boutique amp manufacturer contacted me a number of years ago with a hum they couldn't kill in a series of tweed-style amps. If they powered the heater with d.c. (from a battery), the hum was gone. If the powered the heater from a.c. and used a 25uF bypass cap, the hum was there. If they increased the bypass cap to 220uF on the input tube, the hum went away. Tube-swapping didn't seem to cure the hum. Turns out they had a whole batch of new-production tubes with heater-to-cathode leakage and the big bypass cap eliminated the coupling of that heater hum into the cathode.
Using the X
c formula again, 25uF looks like ~106Ω at 60Hz, while 250uF looks like 10.6Hz. A 330uF cap looks like ~8Ω at 60Hz.