Synthetic helicoidal rotation of a quasielectrostatic ring resonator for ultrabroadband magnet-free nonreciprocity

Suitably tailored forms of spatiotemporal modulation in electronic circuit networks have been recently employed to overcome fundamental challenges in modern electronic systems, including breaking reciprocity, squeezing the footprint of high-Q resonators, and overcoming the delay-bandwidth limit. Rotating patterns of temporal modulations have been used to synthesize angular momentum, which replaces magnetic bias to break reciprocity in integrated circuits. However, this approach is limited by trade-offs between modulation speed, footprint, and bandwidth of operation. Rotating switching patterns in commutated capacitor networks also enables compact filters and quasielectrostatic wave propagation, overcoming the delay-bandwidth limit. In this paper, we combine these mechanisms in an integrated-circuit ring that synthetically rotates in two dimensions, realizing an effective helicoidal motion that provides ultrabroadband quasielectrostatic nonreciprocal responses fitting within a theoretically infinitesimal size. We also analyze the impact of modulation signal noise on time-modulated nonreciprocal components and unveil the role of a dynamic noise mechanism based on which the noise level increases in the presence of a strong signal passing through the component, along with methods to mitigate this effect. We experimentally verify these principles in a three-port integrated circulator based on a 65-nm CMOS process that operates from dc to 1 GHz with a miniaturization factor of 2 ×{} 10⁶.