... the EF86. ... the amplification factor was only 38. ...
According to wiki it is 185. ...
https://en.m.wikipedia.org/wiki/EF86
This is a perfect example of why Wikipedia is not allowed to be used as a reference in academic work. After all, you could go change that right now to " Amplification Factor 1,004,578,985" if you wanted.
The "gain of 185" for the cited condition comes from the 4th column of the top section on Page 3 of
this EF86 data sheet. And it is "gain" because it is "volts out / volts in."
This same data sheet provides (triode connected) Amplification Factor as 38, because that value is fixed by the relative spacing of the cathode, grid and screen.
Notice that all "Voltage gain" figures on the 3 triode-connected sections on Page 3 show values well below 38. That's because in-circuit gain is always smaller than "Amplification Factor" or "Mu". The plate load resistor (R
L) and the tube's internal plate resistance (r
a) form a voltage divider such that we only exhibit a gain close to Mu when the external plate load is near-∞Ω:
Av = (Mu x R
L) / (R
L + r
a)
The reason I point this out is triode curves are a diagonal line moving upward, while pentode curves are a near-horizontal line. For large changes of plate voltage the EF86's plate current barely changes which indicates a high internal plate resistance. Page 7 of
this EF86 data sheet shows a 2.5v gridline where plate current is 2mA at 100v plate, and increases to only a bit over 2.1mA at 400v:
Resistance = Volts / Current = (400v - 100v) / (2.1mA - 2mA) = 300v / 0.0001A = 3MΩ
Now, try plugging in the Wikipedia Condition's "Amplification Factor" of 185, R
L of 220kΩ and the example r
a of 3MΩ:
Gain = (mu x R
L) / (R
L + r
a)
Gain = (185 x 220kΩ) / (220kΩ + 3MΩ) = 40.7M / 3.22M = 12.6 ---> less than a 12AU7
The math doesn't work anymore, because the internal plate resistance is so high. So if we go backwards and estimate "Mu" from the observed gain of "185" what do we get?
Gain = (mu x R
L) / (R
L + r
a)
185 = (Mu x 220kΩ) / (220kΩ + 3MΩ)
185 x (220kΩ + 3MΩ) = Mu x 220kΩ
Mu = [185 x (220kΩ + 3MΩ)] / 220kΩ
Mu = 2707 (!)
But where Mu is nearly constant in triodes, the implied Mu changes with every condition in pentodes, which is why it is never cited, and why we use a different formula to estimate pentode gain (Gm x R
L).