DIY FSK RFID reader with arduino

The coil is just an air wound coil (3.25 inches diameter). I think a toroid implies that it has some sort of ferro-magnetic core or case (in which case I would agree) but the design has a coil that is big enough to function both as a transmitter of power and also as an antenna to pick up the generated disturbances of the transmitted signal, ie the data being transmitted.