A brushless, self-excited synchronous field winding machine is presented. The AC stator is configured with four or more phases to produce independent magnetic fields at different spatial harmonics. Windings in the rotor are configured to magnetically couple to the different spatial harmonics produced by the AC stator. More specifically, an oscillating field generated by the stator magnetically couples to the excitation winding on the rotor. This induces an AC voltage which results in current flowing through the field winding of the rotor. The magnitude of the field current is therefore controlled by the magnitude of the oscillating field. The AC stator also produces a magnetic field at a different spatial harmonic which magnetically couples to field winding of the rotor. This component will interact with the field current to produce torque. With this approach, the power density of the electric machine is significantly increased as compared to conventional field winding designs.