Ceiling fan speed control

["Silver Surfer"]

My fairly old ceiling fan needs a speed control switch replacement.  It's a 
three-speed fan with a three wire switch.  There are no capacitors; instead 
it appears to use some kind of smallish transformer looking device for speed 
control.  My Googling to find what the circuit might look like has been 
fruitless.  Can someone point me toward an educational source of speed 
control schemes for these fans or else explain to me how mine works?