... trying to confirm why fender used a 29k primary impedance for the reverb driver transformer. ...
Do you know how to draw a loadline for a single-ended power stage (http://www.valvewizard.co.uk/se.html)? Have you learned how to graphically determine a tube's plate resistance from its data sheet & an operating point?
You may have to download & zoom-in on the image at the bottom. It is a set of 12AT7 curves from the 3rd page of a 12AT7 data sheet (https://frank.pocnet.net/sheets/093/1/12AT7.pdf).
I snagged a silverface Deluxe Reverb schematic (https://el34world.com/charts/Schematics/files/Fender/Fender_deluxe_reverb_boost_schem.pdf), and noted 6v across a 680Ω cathode resistor and ~400v supply on the other side of the Reverb Transformer.
The data sheet shows a single-triode, so we get half-current on the data sheet curves.
Since we have two triodes in parallel, this implies two 58kΩ loads in parallel for a total load impedance of 29kΩ. The curves will show a single load resistance (58kΩ), and twice the internal plate resistance compared to parallel triodes.
6v / 680Ω = 8.8mA ---> a single triode passes 4.4mA, let's call it "4.5mA" to make graphing easier.
The schematic says, "410v" but 400v is easier for graphing, so I drop a big Green dot at the operating point: 400v and 4.5mA.
You note the Reverb Transformer impedance is 29kΩ; our load for a single triode is then 29kΩ x 2 = 58kΩ.
We need a loadline through the operating point. 400v / 58kΩ = ~6.9mA, let's call it 7mA to make graphing easier. The Red loadline starts at 0v and (7mA + 4.5mA =) 11.5mA. The line passes through the operating point at 400v and 4.5mA. This defines a ~58kΩ loadline because (400v - 0v) / (11.5mA - 4.5mA) = 400v / 7mA = 57kΩ plus some rounding error.
Now we calculate power output:
A Class A amp has a limit of clean output while swinging up to 2x idle current and down to zero idle current. So I used a Blue line along the loadline to a current of 2 x 4.5mA = 9mA. The plate swings down to 140v. As a check, 58kΩ x 4.5mA = 261v, and 400v - 261v = 139v (close enough to "140v").
Multiplying the change from the operating point to this peak found with the Blue line gives us Peak Power:
(400v - 140v) x 4.5mA = 1.17 watts
RMS Output Power is 1/2 Peak Power, or 585 milliwatts. But then we have two 12AT7 triodes each contributing the same power for 1.17 watts.
We figure the internal plate resistance of the triode:
The internal plate resistance is defined by a line tangent to the grid-bias curve at the operating point.
I estimated a compromise slope between the -6v and -7v curves, and plot it as a Purple line.
The line has endpoints of voltage at 500v and 290v. There are endpoints of current at 8.5mA and 0mA.
Internal Plate Resistance (rp) = (500v - 290v) / 8.5mA = ~24.7kΩ
Note: 24.7kΩ x 2 = ~50kΩ ----> the load is nearly 2x rp, where theory predicts maximum output power.
Also, this is the rp of a single triode; 2 triodes in parallel then have an rp of 24.7kΩ / 2 = ~12.4kΩ which is mighty-close to 1/2 the Reverb Transformer load impedance of 29kΩ.
(https://i.imgur.com/0Un0g4h.png)
"But the data sheet says plate resistance of 10-15kΩ"
Yes, but one condition has an idle current of 10mA (much higher, rp will be much lower).
The other condition shows a similar plate current of 3.7mA, but with only 100v on the plate, and 270Ω x 3.7mA = ~1v of bias.
We have much higher plate voltage, but also much higher bias voltage to hold plate current down. The result is the rp shown using the curves (and demonstrated in-circuit) is much higher than the data sheet conditions would suggest.
"But the data sheet says plate resistance of 10-15kΩ"
Yes, but one condition has an idle current of 10mA (much higher, rp will be much lower).
The other condition shows a similar plate current of 3.7mA, but with only 100v on the plate, and 270Ω x 3.7mA = ~1v of bias.
We have much higher plate voltage, but also much higher bias voltage to hold plate current down. The result is the rp shown using the curves (and demonstrated in-circuit) is much higher than the data sheet conditions would suggest.
Starting to make some sense. I’ll have to attempt to figure out what else needs to change then, if it works at all. Thanks for the detailed explanation of drawing load lines. I’ll see what I can come up with.