Some years ago I installed (by myself) a 300 cfm range hood.  One night I noticed that the #2 speed did not work.  I thought the motor was the problem, but there could be other components at fault, so I bought a damaged unit for cheap.

I replaced parts until I found out it was a transformer that determined fan speed, through a control board.

So, the transformer supplies DC to the motor.  Would a transformer rated different from the one I have in it, make a 400 cfm motor out of a 300 cfm motor?

Yes, English is my first language although I didn't use it well tonight  

A transformer does not convert AC to DC, it merely "transforms" the AC line voltage into whatever AC voltage the manufacturer wants. Diodes convert AC to DC namely silicon rectifier diodes. Most often the 117 volt line voltage is stepped down (transformed) and then rectified to DC with diodes and sometimes regulated as well.
ETA - Most appliance motors are AC motors and speed is regulated by how many of the windings are powered up. Usually controlled by a simple switch.

Why do you think it is a DC motor?

It is possible it's DC but I think it's unlikely.

Honestly, you need to post a schematic or photos of the unit.

By varying the number of stator poles you  an design an induction motor for limited variable steps.

At least put a volt meter with an AC and DC mode and see what it says in each mode on the control output.