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SET amplifiers with more power been have produced by Cary and VAC using the exact method you mentioned. By running the tubes in parallel. Vaic/KR have produced tubes with more power and I believe there have been some KR amplifiers with higher power ratings also like around 40 to 50 watts.
Manufacturers of SET amplifiers have told me the transfomer is most important.
I use a pair of SET Cary 805AE's to drive my Maggie 3.6's occasionally. Cary claims either 50 or 70 wpc, depending whether you use the 845 or 211 output tube (1 tube per channel, no paralleling). I do 90% of my listening at low to mid volume levels and normally use Pass XA monos to drive them but I love the sound of SET's and took a chance on the Cary's working out. They do to my satisfaction.
I seem to remember ASL making a single ended KT88 amp some time ago. I think it only put out 12 or 15 watts though.
The actual answer to the question is that it has to do with the output transformer. There is a certain amount of DC current you can put through the transformer before it begins to distort, so building amps with parallel tubes gets tricky as what you are doing is adding more current when you parallel tubes.
So most manufacturers in building a larger SETs go for more voltage instead. This is why you see the more exotic transmitting triodes used in the higher power SETs.
Regardless, the other issue that you run into with output transformers in general, but particularly SETs, is that the more power you go for, the less bandwidth you get. In most cases, the 7W of a 300b is about as big as you can get and expect bandwidth that might be considered 'hifi'. This is also why the smaller SETs, the 2A3s, 45s and the like have the reputation for sounding better- they have greater bandwidth. Now you can fudge things a little- optimize for bass or highs (and since most high efficiency speakers have troubles making deep bass, the tendancy is to go for the highs rather than the bass) since you aren't going to get both.
Push-pull overcame a lot of these issues to a certain degree, with its own set of trade-offs. For example, an SET will have nearly unmeasurable distortion as the signal level heads towards zero, whereas a push-pull amplifier will usually see increased distortion (this is commonly attributed to an additional circuit in P-P amps called a phase splitter; its worthy of note that not all P-P amps have to have this as a separate circuit). This is where SETs get the magical midrange that they are known for- when distortion is reduced, detail is revealed.
You still have the issue of bandwidth with P-P, but in general you can have about 10X more power available compared to an SET with equivalent bandwidth.
You also don't have the DC saturation issue, as the DC currents used by the power tubes cancel in the core of the transformer. On top of that, even-ordered harmonics are also canceled in the load, making for an amp that should be more transparent at greater power outputs.
So it may be that there are 20 or 50 watt SETs, which all battle trade-offs in their design, but a 200-watt SET is a rare thing indeed.
One 6c33c in class A will provide you with something around 18 Watts. Two tubes theoretically will provide twofold increase, but only theoretically. To do this they must be supper precisely matched and for 6C33C it is practically impossible, so on peaks one tube with bigger current will swamp another. I believe you can get 30 Watts for from parallel 6c33c SET amp. The only way to get 3db increase of power from paralleling two tubes is to use two independent power supply , two output transformers and parallel the secondaries of the output transformers. The solution is very expensive.
Push/Pull amps make more power because they are more efficient, each tube only conducts for 180 degrees of the input signal hence the term push/pull. This allows each tube's plate to cool down while the other tube is conducting, giving greater average power. I doubt distortion is created by a properly designed phase splitter. The trick is avoiding crossover distortion. The area of zero conduction where the two halves of the sine wave are put together is the weakness of P/P designs. The way to overcome this nonlinear region is to make each tube of the P/P output ckt. conduct for slightly more than 180 degrees.
Tdelahanty, what you are describing is known as 'class B' operation. It is also possible to have a class A push-pull amp, where both tubes are always conducting throughout the entire signal, even at full power.
This makes for a better sounding amp, and is still more efficent than single-ended. The only way to avoid the degradation of the phase splitter is to build it into the voltage amplifier, IOW make the voltage amplifier fully balanced.
You can get big power SET's, but you'll pay a hefty price for them. All are of the parallel single ended design you mentioned. KR's various manifestations of the Kronzilla using the 1610 output tube can produce a lot of power, as does the Cary 1610. MastersounD's Evolution 845 makes 55 wpc. Their PF 100 Limited pumps out 117 wpc using a slew of 845 tubes. Don't ask how much these amps cost- it will make your skin crawl. But those amps are out there if you can afford them.