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5k primary 600 secondary rated at +37dbm and 45ma ... I cannot find a triode that will get close to the +37dbm for the rated current of the transformer.
+37dBm is 5 Watts.
5K at 45mA is 225V. 225V at 45mA is 10.1 Watts. This would be the "optimum" device condition. You can however apply more voltage and heat.
On the face of it, they expect a Class A power stage with 10.1W input and 5W output, 49% efficiency.
A good pentode will do 40% efficient.
A good triode with efficient loading will do 20%-33%.
Therefore the specs do not directly give an optimum condition.
I'm sure the original application was
pentode 6V6, working at 45mA and perhaps 250V-275V supply, 15V-20V bias, 11W-12W dissipation, 36dBm output.
You can however apply more voltage and heat.
Still, +37dBm in 5K is 44.77mA peak AC. The idle DC is 45mA. The spec assumes you can swing 99.5% of the way to zero current. In hollow-state, that's not happening. However I would not obsess about a few mA and a dBm or two.
EL34 triode will make ~~2.3W, 33.6dBm, at 5K load, 45mA, 330V plate-cathode, -27V bias. 6550/KT88 will not be very different. The total 360V supply is in the zone of common "Champ" power transformers with neat filtering. But note that these big bottles need
three times the heater power of 6V6. A 6L6 is not radically different, though a somewhat poorer triode, at only twice the heat-power of 6V6.
Without plotting, I bet 2A3 will do the same, except with twice as much bias, drive, and appropriately higher total B+. 300B will also work, handsomely, if you are rich.
6080 is also possible, but will need
140V bias and drive. The strain in the preceding stage will smother the poor linearity of 6080, making a very tough design or a bad amplifier. (And 5 times the heater of a 6V6.)
I don't think '45 is readily available. Likewise a couple '10 at 400V will do +33 or +34dBm in 5K load, but healthy '10s are very-very-very rare.
Note that a triode into a transformer needs much cleaner B+ than a pentode. The PSRR of a transformer coupled power triode is about 3, of a pentode closer to 10. A Champ power supply is not adequate without a C-L-C filter or C-R-C with kilo-uFd caps.
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I cannot find a triode that will get close
WE 300, page 4, 350V, -76 bias, 50mA, 5000 load, 6.2 Watts, -30dB second, -45dB third. Knocking current down 10% would give 5 Watts or +37dBm on the nose, 3% 2nd, <1% 3rd. There is also a 400V 40mA 5K condition with more power at more distortion. If the iron is VERY old, it is possible this is the design target. But 6V6 (or broadcast-marked 6V6) has been popular for a very long time.
Why the heck would you want +37dBm in 600 ohms in this 21st century?