Amazon had a sale on some Powermat kits (base, battery pack, and phone case) for $10, so I bought one. Unfortunately, only the base could be nondestructively torn down, but there's a teardown of the battery pack at
http://hardforum.com/showthread.php?t=1846962 .
Each active area of the base is just a high frequency resonant inverter with a Freescale chip controlling it. The coil is glued to the top surface, with a ferrite core glued to the other side.
The power supply for the base is an oddball 18V, so beware if you're planning to run it from some other power source like automotive power. It might work on 12V (haven't tried) with reduced performance.