Single phase inductors have non-linear inductance values, and M-phase coupled inductors having non-linear leakage inductance values. Each inductor includes, for example, at least one of the following: a saturable magnetic element, a gap of non-uniform thickness, a core formed of a distributed gap material, or a non-homogeneous core. A DC-to-DC converter includes an inductor having a non-linear inductance value, a switching subsystem, and an output filer. Another DC-to-DC converter includes an output filter, a coupled inductor having non-linear leakage inductance values, and switching subsystems.

A direct current controller includes a rectifier configured to convert alternating current input into a direct current output. A converter electrically coupled to the rectifier generates a converted direct current voltage that regulates a converted direct current from the direct current output of the rectifier and synthesizes an ac component of an alternating current grid to counteract an induced back-emf. A direct current controller central controller coupled to the converter regulates the converted direct current.

A power managing apparatus, a DC-DC control circuit, and a method for enabling a chip are disclosed. The power managing apparatus has an enable pin and the enable pin is used to couple a first level control circuit. The power managing apparatus includes a second level control circuit and a level detecting circuit. The second level control circuit is coupled to the enable pin. The level detecting circuit is coupled to the enable pin and used to detect a control signal on the enable pin. The control signal is transmitted from the first level control circuit. The control signal has at least three levels according to operations of the first level control circuit and the second level control circuit.