We're making good progress. Here is our design so far:
To eliminate negative feedback from cathode degeneration, the bypass capacitor CK needs to be large enough to short all audio frequencies. The required value depends on the cathode impedance ZK, which is equal to the 820-ohm cathode resistor RK in parallel with the reciprocal of the tube's transconductance gm that we estimated earlier:
ZK = 820 || [1 / (1.5ma/V)] = 368 ohms
The lowest note on a guitar with standard tuning is 82 Hertz. So if we select a capacitor whose impedance is equal to the cathode impedance at a frequency 10 times lower, 8.2 Hertz, then we can be fairly certain that we've eliminated negative feedback:
CK = 1 / (2*pi*368*8.2) = 53uF
50uF will work just fine. Let's pull a similar trick to solve for the screen capacitor CS.
A pentode has screen resistance rs that is analogous to the plate resistance rp in a triode. Since the ratio of plate current to screen current is about 6 to 1, the screen resistance rs is about 6 times greater than the plate resistance when the tube is triode-connected. Here are the triode-connected plate characteristics:
From the red line in the vicinity of the DC operating point, we observe that the plate voltage increases 22 volts when the plate current increases 1 milliamp. According to Ohm's Law this represents a plate resistance of 22k, so screen resistance is about 6 times greater: 132k. To make the impedance of the screen bypass capacitor CS equal to 132k at a tenth the lowest frequency of a guitar, the capacitor value is
CS = 1 / [2*pi*132k*8.2] = 0.15uF
The EF86 has about 5 picofarads of capacitance between the grid and cathode and only 0.05pF between the grid and plate. Because of the Miller Effect, the capacitance between the grid and plate is multiplied by 1 plus the stage gain of 100, so the total Miller capacitance is
CM = 5pF + (1 + 100)(0.05pF) = 10pF
A 12AX7 has ten times more parasitic capacitance, which is bad news for radio and why you won't find Marshall's favorite triode in the front end of my Philco. To ensure that radio-frequency suppression in our EF86 preamp begins at a cutoff frequency of 100 kHz, the grid stopper resistor value needs to be
RGS = 1 / [2*pi*100kHz*10pF] = 159k
We'll use 150k. A grid resistor value of RG = 1M is a standard that places only a light load on the guitar circuit while providing sufficient grid leak. Why argue with success? We'll use 1M.
As a final order of business, power supply filter capactor C3 needs to be large enough to mitigate AC ripple and decouple the preamp from later stages. The specific value depends on the rest of the amp, but since R3 is a respectable 47k, setting C3 to 50uF creates an impressive 65dB of ripple suppression, as shown by this snapshot of our RC Ripple Filter Calculator:
If we want to penny-pinch a bargain basement amp, we can reduce the capacitor size based on the ripple suppression upstream of R3. On the other hand, let's spare the math for once and bestow a quality capacitor on a very deserving tube. Here is our final design.
1Richard Kuehnel, Vacuum-Tube Circuit Design: Guitar Amplifier Preamps, 2nd Ed., (Seattle: Pentode Press, 2009).
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