One can easily get too carried away with all the technicalities of how things work. I say rather than spend your time reading up about power supplies
(you need to be acquainted with electronics to fully get the most out of that sort of info and if you are not the you wont really benefit so much) spend your time making recordings instead with DI's and learn how to get the best out of them in terms of
where they are used in the signal chain. Much more important. Yes there are some issues for sure with DI's but they are not major in the end. I have used them live and in recording situations for years without any issue and always been happy with the signal that has arrived through a DI box.
The advantages of an active DI are firstly they are quick and easy to setup. Mostly they are pretty transparent in terms of what they do and because they don't have any controls and level settings and things on them it makes them easier and less prone to mis adjust. A preamp set wrongly is going to be a much worse scenario.
Also remember too
(and I don't think Mike is factoring this in so much) is that the clean DI signal that comes directly out of a guitar will most likely be processed pretty hard later on with an array of virtual amp and cabinet simulators so the sound of the original DI signal is going to be well and truly lost by the time it finds its way into your final stereo mix buss.
Is the listener going to say Oooh I don't like that guitar sound because it was recorded through a DI with an inferior power supply? If the guitar part is killer then the listener is going to really enjoy it don't you think. That is where it's at.
(Frank Gambale still sounds good through a DI. ANY DI!) I have got a box too that generates 48V DC from a 12V DC input (1 amp) so there are circuits that can step DC voltages up too. But I agree with
Mike in that I am not sure they are doing that inside many DI's though. It is quite a large and heavy unit and is designed for phantom powered devices that are connected to mixers that do not offer phantom power. Use phantom power where ever you can with any DI. It will perform better for sure and also it will never go flat either!