In one embodiment, a tuning network includes: a controllable capacitance; a first switch coupled between the controllable capacitance and a reference voltage node; a second switch coupled between the controllable capacitance and a third switch; the third switch coupled between the second switch and a second voltage node; a fourth switch coupled between the second voltage node and a first inductor; the first inductor having a first terminal coupled to the fourth switch and a second terminal coupled to at least the second switch; and a second inductor having a first terminal coupled to the second terminal of the first inductor and a second terminal coupled to the controllable capacitance.

A varainductor includes a signal line over a substrate. The varainductor further includes a first ground plane over the substrate. The varainductor further includes a first floating plane over the substrate, wherein the first floating plane is between the first ground plane and the signal line, and the first floating plane is a same distance from the substrate as the first ground plane. The varainductor further includes a first transistor configured to selectively electrically connect the first ground plane to the first floating plane. The varainductor further includes a second transistor configured to selectively electrically connect the first ground plane to the first floating plane, wherein a gate of the first transistor is connected to a gate of the second transistor.

A method using a phase locked loop (PLL) includes receiving a reference frequency. The method further includes generating a control signal based on the reference frequency. The method further includes adjusting an output signal based on the control signal. Adjusting the output signal includes operating a plurality of switches in response to the control signal, wherein operating the plurality of switches comprises selectively electrically connecting a first ground plane to a first floating plane, wherein the first floating plane is between the first ground plane and the signal line, and the first floating plane is a same distance from a substrate as the first ground plane.

In one embodiment, a tuning network includes: a controllable capacitance; a first switch coupled between the controllable capacitance and a reference voltage node; a second switch coupled between the controllable capacitance and a third switch; the third switch coupled between the second switch and a second voltage node; a fourth switch coupled between the second voltage node and a first inductor; the first inductor having a first terminal coupled to the fourth switch and a second terminal coupled to at least the second switch; and a second inductor having a first terminal coupled to the second terminal of the first inductor and a second terminal coupled to the controllable capacitance.

An apparatus and method for implementing a compact and tunable microwave resonator using NbN kinetic inductance, comprising: a DC source, an attenuator, an oxygen-free copper cavity, a superconducting coil, a first-stage amplifier, a second-stage amplifier, a vector network analyzer and a control computer, a small-sized tunable resonator whose size is reduced by 10-20 times as compared with an ordinary thin film microwave resonator is implemented in a microwave frequency band by using high kinetic inductance of an ultra-thin NbN thin film in a superconducting state, the tunability of the resonator lies in that the ultra-thin NbN thin film serves as the LC resonance circuit, a dc-SQUID is connected to the end of the resonator, and a change in the external magnetic field causes a change in the equivalent inductance of the dc-SQUID, thereby changing the total inductance of the resonator and modulating the resonant frequency of the resonance circuit.

An apparatus and method for implementing a compact and tunable microwave resonator using NbN kinetic inductance, comprising: a DC source, an attenuator, an oxygen-free copper cavity, a superconducting coil, a first-stage amplifier, a second-stage amplifier, a vector network analyzer and a control computer, a small-sized tunable resonator whose size is reduced by 10-20 times as compared with an ordinary thin film microwave resonator is implemented in a microwave frequency band by using high kinetic inductance of an ultra-thin NbN thin film in a superconducting state, the tunability of the resonator lies in that the ultra-thin NbN thin film serves as the LC resonance circuit, a dc-SQUID is connected to the end of the resonator, and a change in the external magnetic field causes a change in the equivalent inductance of the dc-SQUID, thereby changing the total inductance of the resonator and modulating the resonant frequency of the resonance circuit.

Devices, systems, and methods related to an energy-efficient machine learning framework which exploits structural and functional similarities between a machine learning network and a general electrical network satisfying the Tellegen's theorem are described.

In one embodiment, a tuning network includes: a controllable capacitance; a first switch coupled between the controllable capacitance and a reference voltage node; a second switch coupled between the controllable capacitance and a third switch; the third switch coupled between the second switch and a second voltage node; a fourth switch coupled between the second voltage node and a first inductor; the first inductor having a first terminal coupled to the fourth switch and a second terminal coupled to at least the second switch; and a second inductor having a first terminal coupled to the second terminal of the first inductor and a second terminal coupled to the controllable capacitance.

A varainductor includes a signal line over a substrate. The varainductor further includes a first ground plane over the substrate. The varainductor further includes a first floating plane over the substrate, wherein the first floating plane is between the first ground plane and the signal line, and the first floating plane is a same distance from the substrate as the first ground plane. The varainductor further includes a first transistor configured to selectively electrically connect the first ground plane to the first floating plane. The varainductor further includes a second transistor configured to selectively electrically connect the first ground plane to the first floating plane, wherein a gate of the first transistor is connected to a gate of the second transistor.

A varainductor includes a signal line, a ground plane, and a floating plane over a substrate. The ground plane is disposed on a side of the signal line, and the first floating plane is disposed between the ground plane and the signal line. An array of switches includes at least two switches configured to selectively electrically connect the ground plane to the floating plane.