AC Operating Conditions

We're making good progress. Here is our design so far:

To eliminate negative feedback from cathode degeneration, the bypass capacitor C_K needs to be large enough to short all audio frequencies. The required value depends on the cathode impedance Z_K, which is equal to the 820-ohm cathode resistor R_K in parallel with the reciprocal of the tube's transconductance g_m that we estimated earlier:

Z_K = 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:

C_K = 1 / (2*pi*368*8.2) = 53uF

50uF will work just fine. Let's pull a similar trick to solve for the screen capacitor C_S.

A pentode has screen resistance r_s that is analogous to the plate resistance r_p in a triode. Since the ratio of plate current to screen current is about 5 to 1, the screen resistance r_s is about 5 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 72 volts when the plate current increases 1 milliamp. According to Ohm's Law this represents a plate resistance of 72k, so screen resistance is about 5 times greater: 360k. To make the impedance of the screen bypass capacitor C_S equal to 360k at a tenth the lowest frequency of a guitar, the capacitor value is

C_S = 1 / [2*pi*360k*8.2] = 0.05uF

We'll use 0.068uF.

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 the stage gain of 100, so the total Miller capacitance is

C_M = 5pF + (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

R_GS = 1 / [2*pi*100kHz*10pF] = 159k

We'll use 150k. A grid resistor value of R_G = 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 56k, setting C₃ to 50uF creates an impressive 66dB 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.

Did I mention that Georg Simon Ohm is also available on Amazon?

Reference