In the above schematic, you see an 300B based cathode follower output stage being driven by an 300B based grounded-cathode amplifier, whose plate resistor is three times greater (3750 ohms) than the reflected impedance on the output transformer's secondary (1250 ohms; the 247 ohm biasing resistor's value will have to be added to the primary impedance, if this resistor is not bypassed). The key feature is that the grounded-cathode amplifier stage's idle current and cathode-to-plate voltage matches that of each output tube.
     The extra power supply voltage comes from a voltage doubler circuit, as shown below. Lest those who posses all-knowledge-of-all-that-is-worth-knowing-about-tube-electronics (a surprisingly small amount, it turns out, no more than can fill a few articles from the audiophile press and the odd rec.tube thread) lose their composure over the unseemly use of solid-state diodes, a tube rectifier can be easily used for the 400 vdc power supply voltage and, with some work, tube rectifiers could be used for the 800 volts power supply as well. 

    The 300B-based driver tube must realize a voltage swing large enough to drive the parallel cathode followers to full power output. Since the needed swing is not symmetrical, the potential swing need not be either. As configured, the driver stage can potentially swing down more voltage than up, which is what the output stage needs to see. This is the result of the triode requiring more voltage to turn it off than it requires to increase its conduction.
 

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