Yes, there is definitely a mistake on the negative side of the doubler and those three capacitors, C30A, B and C go to ground OR the positive corner of the valve heater supply bridge. I'd be tipping the chassis over and checking that for real, I would not take the circuit's word for it, partucularly condidering I will probably need to modify its design but preserve its function.
I assume the transformer died a horrid death because one of the doubler capacitors dried out and put some sort of nasty DC component of current through the secondary and saturated the core??
If the transformer in this were "beyond recovery" I'd rip it out, along with the doubler. I would preserve the HT RC filters in the upper right hand corner though. These days why would you use a doubler anyway, it produces double the ripple of a full-wave bridge and needs really big filter capacitors. These days I'm sure a higher voltage secondary transformer is no issue like it possibly was back then prompting the use of the doubler in the first instance.
I would also preserve the 18v, (actually more like 20v) heater supply and arrangement and just drive the bridge from a new and possibly separate transformer. There is a little heater-cathode insulation stuff going on here, particularly with the two valves in the centre with their pins 9 going back to the 18v, these have the highest heater voltage above ground and, as you said, they are the output cathode-follower buffers which would be expected to have a fairly high cathode voltage above ground....particularly if they are DC coupled to the previous stage...so the valves with the greatest quiescent DC cathode voltages above deck are also given the highest heater voltage above deck to minimize electrolysis of the zirconium dioxide insulation over the tungsten heater wires where it touches the inside of the nickel cathode tube.
I have a book somewhere, written by Philips in the mid '50's about their "SQ" series industrial valves, valves like the "E80F" an industrialized-ruggedized version of the EF80 or 6BX6, it has a whole chapter devoted to cathode heater voltage differences. I have a vague recollection that the cathode can be up to 150v or so above the heater, but only 15v or so below the heater because the ZrO2 sandwiched between tungsten and nickel acts as a sort of dry electrolyte electrolytic cell, so with one polarity, reduction of the ZrO2 to zirconium metal will be reduced, but with the other polarity it will be increased due to the dissimilar metals of tungsten and nickel on either side. In this regard peak AC voltages on the heater need to be taken into account, particularly in transformerless designs with high voltage heater valves all strung in series.
Here the design is very conservative by using DC on the heaters and keeping the h-k differences as low as possible.
So, preserve the heater supply as is. Build a new HT supply with a bridge rectifier and largish filter capacitor....you can then choose a transformer with sufficient secondary voltage that does not require stacking on top of the heater supply. Calculate the required voltage the HT supply has to reach by calculating the drop down to 310v across the first resister, R71 in the filter. If you don't know the current draw through this resistor "guesstimate" it from the (mains consumption minus valve heaters, not output to speakers) power rating of the amplifier and plug this into "P = V.I" So if it is 15w, then use 15 = 310 x I so I is about 50mA, then you can calculate the drop across that first resistor. V = I.R , V = 0.05.1500, or 75v! So your HT supply would need to be 385v and able to deliver 50mA if the guess of 15w is correct.
I recall that the 12Ax7 series of dual triodes are 300mA heater current, with the exception of the 12BH7 which is 600mA I think. So the heaters are 12 x 0.3W for each dual triode valve, or 21.6W fir all six valves.
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