If you pull a vacuum over a container of water, the water soaks up heat from it's local environment and begins to "boil". The USER work required to pull that vacuum is, at the most, about 14psi on the piston. The bulk of the vaporization energy comes from the space surrounding the water. This is the basis for heatpump theory. The amount of heat collected VS the work to pull the vacuum determines the C.O.P.
If you think of the Bedini system as an analog of a heatpump, then I becomes more clear what's going on; pulling a VOLTAGE VACUUM over the battery(my interpretation).
This is a method of producing a high floating voltage with a small current input. Hold the voltage high on the receiving battery, then wait as long as it takes for the battery to fully charge. The batteries don't usually "like" this much at first, improving over time. The biggest thing is that you SHOULD SEE the VOLTAGE hopping up on the receiving battery when you start the machine. This doesn't mean that the battery is INSTANTLY CHARGED, it just means you're holding the voltage high.
Once built and tuned, the motor/gen has a known, fixed power input every time you fire it up. This means that while you're "teaching" the batteries to accept this type of charging, you can run it from any 12v source you want to.
If the battery you're charging cannot be pulled up above 12.5v in a fairly short time by your charger, the charger isn't big enough for the batteries you're trying to use AND your battery is probably sulfating. In this case, you'll need to add more windings around the wheel.
Let's say you're stator design draws 80ma a peak tuning. Adding a few more identical windings will simply multiply that input requirement and also multiply the emf collected in the capacitor. This will give you increased capability for POPPING the voltage up on larger batteries.
You have to GIVE to GET in any system, even energy-collection systems. The BAIT is very small compared to the FISH that jumps on the hook.
Set a 1amp input Bedini motor next to a 1amp input commercial charger and then you'll see why it's different.
The small motor is a MODEL to learn from. But, if you build it correctly, there is plenty of room for expansion just by adding more stators and driver circuits.
If you look at the various machine pictures on Bedini's website, you'll see that there's NO FIXED COIL SPECIFICATIONS. You can build it with a variety of coil charactieristics. But, you MUST understand the process before you'll be able to modify anything with any success. Without that understanding, you'll head off into the the dark when you make changes.