Hmmph! Learned something today. Thanks.
There are "DC transformers" sold, but I found this:
For a transformer to work, the current in one coil has to somehow make current flow in the other coil and the circuit it's connected to. A DC current in one coil will make a magnetic field on the other coil, but a magnetic field by itself won't drive any electrons around. A CHANGING magnetic field, however, does create an electric force which will accelerate those electrons in the other coil into carrying a current. This process is described by Faraday's law of induction. You get a changing field from an AC current, since the current which makes the field is changing.
It's been a LONG time since my electronics courses...