Tunable inductor and methods to realize tunable inductor

A tunable inductor comprising:

• a core having a closed shape and comprising a first leg, a second leg, and a third leg between the first leg and the second leg;
• a first winding wound around the first leg;
• and
• a second winding wound around the second leg, wherein a first winding direction of an upper half of the second winding is opposite to a second winding direction of a lower half of the second winding,
• wherein:
• the first winding is coupled to a controller configured to provide DC power to the first winding, and the first winding is configured to generate a DC flux in a DC flux path in response to the DC power, the DC flux path passing through the first leg, the third leg, and the second leg;
• and
• the second winding is coupled to an AC power source configured to provide AC power to the second winding, and the second winding is configured to generate AC flux in a plurality of AC flux paths in response to the AC power, wherein:
• a first AC flux path of the plurality of AC flux paths passes through an upper portion of the core and returns via a path perpendicular to the third leg;
• and
• a second AC flux path of the plurality of AC flux paths passes through a lower portion of the core and returns via a second path perpendicular to the third leg.

A tunable inductor comprising:

• a core having a closed shape and comprising a first leg and a second leg;
• a first winding wound around the first leg;
• and
• a second winding wound around the second leg, wherein a first winding direction of an upper half of the second winding is opposite to a second winding direction of a lower half of the second winding,
• wherein:
• the first winding is coupled to a controller configured to provide DC power to the first winding, and the first winding is configured to generate a DC flux in a DC flux path in response to the DC power, the DC flux path passing through the first leg and the second leg;
• and
• the second winding is coupled to an AC power source configured to provide AC power to the second winding, and the second winding is configured to generate AC flux in a plurality of AC flux paths in response to the AC power, wherein:
• a first AC flux path of the plurality of AC flux paths passes through an upper leg of the core and returns via a path perpendicular or almost perpendicular to the first leg and the second leg;
• and
• a second AC flux path of the plurality of AC flux paths passes through a lower leg of the core and returns via a second path perpendicular or almost perpendicular to the first leg and the second leg.