No offense, but the whole "doubling down" discussion wins my award for the Most Useless Bit Of Armchair Technical Analysis . . . or the Most Misconstrewed Measurement Comparison . . . something that really shouldn't be paid hardly any attention to.
In this test, what is being compared is the the maximum power output of a given amplifier, before clipping, into a few various resistive load impedances. But there are several mechanisms by which an amplifier can be driven into clipping, so unless you know exactly how the given circuit is behaving for the test . . . the information is useless. It's even more useless when comparing two amplifiers of very different topologies (i.e. OTL tube vs. conventional emitter-follower Class AB SS), because they can behave so differently when overdriven.
Virtually all amplifiers can be driven into clipping by excessive voltage - that is, the output device(s) approach the power-supply rail(s) to the point where there simply isn't any more voltage available to transfer to the speaker. This is the case when an amplifier sees a high-impedance or open load.
But since the overwhelming majority of amplifiers use unregulated power supplies, as the load impedance to the amplifier is lowered, the power-supply rail(s) sag, which reduces the amount of voltage available. So even if the amplifier circuit was perfectly lossless, there still wouldn't be as much voltage available as the load decreased . . . thus there will be less than double the amount of power available if the load impedance is halved. THIS is how the whole "doubling-down" comparison started -- as a way to compare the power-supply robustness between similar solid-state amps.
A typical solid-state feedback amplifier has a very low output impedance, so into a "realistic" speaker load, it will indeed be the power-supply that determines its clipping output. But since we're basically testing the amplifier into two different resistive loads . . . this says NOTHING about the performance of the circuit itself into a "difficult", or reactive load.
But suppose instead of a "realistic" load . . . we're talking about a "super-demanding" load, maybe 1.5 ohms or so. For most conventional amplifiers, to drive such a load all the way to the power-supply rails puts the output devices into danger zone, so a current-limiting mechanism kicks in and makes the amplifier clip earlier. But this is still a resistive load, so we still know very little about how the circuit handles a "difficult" loudspeaker - the best we can infer is how much money was spent on the power tranformer, filter capacitors, and output silicon.
Now let's look at a single-ended Class A circuit, a la Nelson Pass. It can still voltage-clip at the supply rail with light loading, but as the load impedance is lowered, the amount of voltage available is ultimately limited by the standing current available in the output device(s) (by Ohm's Law), even assuming the power supply is perfectly regulated. So it's the "sag" in the amplifier circuit itself (that is, its high output impedance), that determines the clipping-power-vs.-load-impedance picture. And this amplifier will of course deal with a complex speaker load very differently than the conventional amplifier, but the "doubling-down" test reveals nothing about this.
The situation is very similar with a push-pull OTL amp, here (provided no feedback) the main limiting factor as the load decreases is the output tubes' plate resistance. But again, the "doubling-down" test can't reveal whether this is the result of a sagging power-supply or output stage, and says nothing about its performance into a loudspeaker load.
In a transformer-coupled tube amp the designer actually can make some trade-offs in this area - the load to the output tubes is commonly chosen to be a "sweet spot" to maximize power efficiency, while the output impedance is lowered by use of negative feedback. Thus, it will put out maximum power into the load impedance (or impedances, in the case of multiple taps) chosen by the designer. In this case, the "doubling down" test simply reveals to which output transformer tap the output leads are connected.
It seems that the real points of the Atma-Sphere "white paper" are about the disapproval of negative feedback, and tolerance of high output impedance. These are long-debated topics in audio, but the "doubling-down" test, and its discussion, is a very crude and inaccurate way of analyzing these characteristics and their effects.
