Systems and methods for tuning resonators

A method, comprising:

• providing a resonator having a dielectric substrate, a liquid crystal dielectric and a plurality of conductive vias, the plurality of conductive vias extending through the dielectric substrate and forming an inductive coil embedded in the dielectric substrate, the plurality of conductive vias including at least a first conductive via and a second conductive via within a turn of the inductive coil, wherein the liquid crystal dielectric is embedded within the inductive coil between the first conductive via and the second conductive via, thereby forming a tunable capacitive component within the inductive coil in series with the first conductive via and the second conductive via;
• and
• controlling a resonance quality factor of the resonator, the controlling comprising biasing the tunable capacitive component with a bias signal, thereby varying a permittivity and capacitance of the tunable capacitive component.

A system, comprising:

• a resonator having a dielectric substrate and an inductive coil having at least one turn, the inductive coil comprising at least one conductor and a plurality of conductive vias, the plurality of conductive vias extending through the substrate and including at least a first conductive via, a second conductive via, and a third conductive via, wherein a liquid crystal dielectric is disposed between the first conductive via and the second conductive via and forms a capacitive element within the inductive coil in series with the first conductive via and the second conductive via;
• and
• a control element configured to transmit a bias signal to the inductive coil for biasing a capacitance of the capacitive element.