enough.
Midpoint Ground Connection
   In the case where ground is referenced to the midpoint between the output cathodes, no sampling of the cathode's output is needed, just a balanced input signal for the output stage's grids. Differential amplifiers have been used, for they not only yield a balanced output, but also allow for a balanced input. Additionally, cascoding has often been also used with the Differential amplifier to

burden.
  One answer to these problems would be to use a simple non-cascoded Differential amplifier without the long tail (a large valued cathode resistor and a negative power supply). Because even the highest mu triodes (6SL7, 12AX7) could not alone yield enough gain to drive the output tubes, an additional input stage will be needed to feed the Differential amplifier. If a balanced input is desire, another Differential amplifier could be used. Or, if an unbalanced input is needed, a Split Load phase splitter could be introduced between input stage and Differential amplifier as was done in the Williamson amplifier.
   In fact, a conventional looking feedback network can even be used with the Williamson circuit, as the output stage's floating power supplies are only referenced to ground at the center of a two resistor voltage divider that spans the output cathodes. In other words, balanced feedback loops are not needed, as each leg of the output is identical to the other, differing only in phase no matter how unbalanced the output tubes or drive signals for these tubes, as no current flows from the ground connection into the output triodes and the voltage divider only splits what signal is present across the outputs regardless how asymmetrical that signal might be.
   If you are still puzzled, then you are probably imagining an output stage power supply referenced to ground and not a floating one. Here is a thought experiment: imagine a pocket radio that runs off batteries. Now imagine a two resistor voltage divider that spans the speaker terminals within the radio. If a scope's ground is attached to the center of the voltage divider and a probe is attached to one terminal and then the other, the trace on the scope will show the same signal in phase and out of phase in both cases. This would not be the case if the scope's ground were attached to the amplifier ground and the probe was attached to one leg of the Differential amplifier and then the other, as the triodes may be poorly matched or even differing in types.

increase the amount of gain from the circuit.
   The cascoded Differential amplifier offers high gain, but it requires a very high power supply rail voltage to realize a sufficiently large drive voltage, as a large portion of the available power supply voltage is used across the bottom tubes. This circuit also requires that care be taken not to exceed the tube's heater-to-cathode maximum voltage rating, as the top tubes' cathodes are at a much greater voltage than the bottom tubes. In addition, the need for a clean negative power supply is an further

Williamson front end on a Circular/Bridge/Balanced amplifier with ground referenced to the midpoint between cathodes.

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