An intuitive explanation of the multiphase Buck Trans-Inductor voltage regulator (TLVR) 

Will see

Thanks

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I was carried away. I hope to return to it soon.

see www.tdcommons.org/cgi/viewcontent.cgi?article=6147&context=dpubs_series

Interesting concept. Using the same magnetic cores for the transformers, you can either double the wire cross section with the same turns, keeping inductance the same which should halve the resistance, or double the turns quadrupling the inductance. The later is a bad idea, so relatively speaking the ESR loss from the transformer regulator will be twice as high in the primary as the conventional regulator, however the secondary will also have losses. It would seem that in the worst case the secondary current will be approximately 1/N times the current carried in the primary, so this can be minimized with a large number of phases. These sorts of regulators usually suffer from large switching losses in the half-bridges, to keep the switching speeds high enough to satisfy the di/dt requirements. Effectively doubling(or N times, in your theoretical “nonlinear controller”) the di/dt using this technique might mean lower switching frequency (and higher inductor core losses) or fewer phases (and higher conduction losses) I can see where the trade offs may pay to use this method, but it’s not trivial to compare without a detailed optimization for both designs.

there would be no filtration, as the core would see pure DC and there would be no magnetic field collapse to drive the flyback cycle

@@two_number_nines Good point.

This will have no series to parallel amplification

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I think it is a matter of convention. The sign is meaningless until you define and mark the positive polarity of the terminal.