Fully integrated parity-time symmetric electronics

A Parity-Time (PT) symmetric integrated circuit configured to generate a broadband nonreciprocal microwave transmission, the PT symmetric integrated circuit comprising:

• a first resonator having a first terminal and a second terminal, the first resonator comprising an active gain resistor, a gain capacitor, and a gain inductor in parallel and electrically coupling the first terminal with the second terminal, wherein the gain inductor includes a first coil tap;
• a second resonator having a third terminal and a fourth terminal, the second resonator comprising a loss resistor, a loss capacitor, and a loss inductor in parallel and electrically coupling the third terminal with the fourth terminal, wherein the loss inductor includes a second coil tap electrically coupled to the first coil tap of the gain inductor;
• and
• at least one coupling element selectively coupling at least one of the first terminal with the third terminal, and the second terminal with the fourth terminal, wherein each coupling element comprises at least one capacitor in series with a switch,
• wherein a negative resistance of the active gain resistor is approximately equal to a magnitude of a resistance of the loss resistor,
• wherein an inductance of the gain inductor is approximately equal to an inductance of the loss inductor, and
• wherein a capacitance of the gain capacitor is approximately equal to a capacitance of the loss capacitor.

A Parity-Time (PT) symmetric integrated circuit, comprising:

• a first resonator having a first terminal and a second terminal, the first resonator comprising an active gain resistor, a gain capacitor, and a gain inductor in parallel and electrically coupling the first terminal with the second terminal, wherein the active gain resistor has a negative resistance, wherein the gain inductor includes a first coil tap;
• a second resonator having a third terminal and a fourth terminal, the second resonator comprising a loss resistor, a loss capacitor, and a loss inductor in parallel and electrically coupling the third terminal with the fourth terminal, wherein the second terminal is electrically coupled to the fourth terminal at a ground node for the first resonator and the second resonator, wherein the loss inductor includes a second coil tap electrically coupled to the first coil tap of the gain inductor;
• and
• a coupling element selectively coupling the first terminal of the first resonator with the third terminal of the second resonator, the coupling member comprising at least one capacitor in series with a switch,
• wherein the negative resistance of the active gain resistor is approximately equal to a magnitude of a resistance of the loss resistor,
• wherein an inductance of the gain inductor is approximately equal to an inductance of the loss inductor, and
• wherein a capacitance of the gain capacitor is approximately equal to a capacitance of the loss capacitor.