I don't see the advantage of increasing the first stage cathode cap to 300μF. The stock 250μF in parallel with the 1.5K resistor gives a time constant of 375msec, which bypasses the cathode resistor down to 2.7Hz. Correct? Going to 300μF raises the time constant to 450msec, lowering the frequency to 2.2Hz. Unless I'm missing something, forgetting something from my electronics classes. It has been quite a few years...
I think something is wrong with your math. Since your time constant to frequency conversion is correct, maybe the time constants you are coming up with is incorrect or doesn't consider what you are really trying to determine is the cutoff frequency which is normally defined as when the response is 3 db down.
To determine the -3db frequency - when a cap will have a capacitive reactance equal to a resistor, I simply use:
freq = 1 / (2*Pi*farads*ohms)
For a 250μF and 1.5Kohms, I get a frequency of 0.424Hz. I get 0.354Hz for a 300μF cap.
Using the cathode resistor by itself is incorrect. You need to consider that the cathode impedance is acting in parallel with the cathode resistor. The cathode impedance for this stage would be roughly 1.6K, and that in parallel with the 1.5K cathode resistor would be about 774 ohms. So, using the 1.5K resistor alone will result in a number about an octave lower (i.e. 1/2 the frequency) than actual.
Will you hear the difference? Absolutely not. It will be subtle to the point of non-existance. It'll all be imagination. Here's why.
What would be the gain difference of this stage operating without a cathode resistor bypass cap versus operating completely, totally, 100percent with a fully bypassed cathode resistor?
6db. Actually I rounded up it's a couple/few tenths less.
At the -3db cutoff frequency, 3db out of the 6db maximum available has already been eaten up - the stage is already operating with 3db more gain with the bypass cap than without. How long do you think it'll take the stage to max out that remaining 3db of maximum gain potential?
About an octave, or twice the frequency. For all frequencies above this, the stage is already operating at it's absolute maximum potential. That's all there is and there ain't no more.
With either a 250 or 300μF cap, this stage has already reached it's maximum potential well below 5hz. It will not increase or change anything once you feed in a frequency you can actually hear. Even using the more typical 22μF value for a bypass cap (-3db @ 9.3Hz), the tube will be operating at maximum gain for any usable frequency.
In Kevin's books he consistently makes two statements, which I will paraphrase. The first is one we know from our own experience -
a "tight" bass is achieved by reducing bass response. The second is common sense once you think about it -
there is no point in increasing frequency response at frequencies that won't make it through the amp.
Look at the output side of this stage. Two values for coupling capacitors can be determined based on the position of the bass boost switch. The value of the capacitor and the volume control resistance in series with the output impedance of this stage will determine how much bass actually makes it out of the stage and into the rest of the amp. This forms a first order high-pass filter.
The output impedance is roughly 38K, but I will bump it up to 50K so I can get better numbers than actual. The volume control is 500K and I'm going to assume the full value, again for better numbers than actual.
With the .0022μF cap alone, the high pass filter has a -3db cuttoff at 131Hz. Frequencies below this will be reduced at a 6db rate. By the time we get down to our lowest frequency, that 6db gain boost we got from the cathode bypass cap is history.
With the bass boost switch on, the two coupling caps are in parallel giving us a 0.009 and change. Heck, let's just round it up to .01μF, again for better numbers than actual. This is much better, our -3db cutoff frequency is now a hair below 30Hz. Our cathode bypass 6db boost will be eliminated at 15Hz and it's all downhill from there. But the good news is that our cathode bypass efforts will be fully recognized at around 60Hz, a fret or so above the open bass "A" string.
Before I rest my case, I'll leave you with a quote from the Radiotron Designer's Handbook, my third edition being printed November 1941, concerning bypass cap values (Ck):
A cathode bias resistor is usually by-passed by a condenser (Ck) in order
(1) to avoid degeneration and loss of gain, and
(2) to avoid hum.
If Ck were omitted, the amplifier would operate with Negative Current Feedback. The capacitance Ck when used to avoid degeneration should normally have a reactance which is low compared with Rk at the lowest frequency required to be amplified. If accurate calculations of this capacitance for specified frequency response are required the formula at the end of this section may be used. For most practical purposes Ck may be a 25μF electrolytic condenser, and although such a high capacitance is often unnecessary for frequency response it is valuable in by-passing hum voltage originating between the heater and cathode.
Yep, there is much more magic in a bottle of wine.
