Pseudo-Linear Time-Invariant Magnetless Circulators Based on Differential Spatiotemporal Modulation of Resonant Junctions

In this paper, we present voltage-mode and currentmode differential magnetless nonreciprocal devices obtained by pairing two single-ended (SE) circulators, each consisting of three first-order bandpass or bandstop LC filters, connected in either a wye or a delta topology. The resonant poles of each SE circulator are modulated in time with 120 degrees phaseshifted periodic signals, resulting in synthetic angular-momentum biasing achieved through spatiotemporal modulation (STM). We tailor the two SE circulators to exhibit a constant 180 degrees phase difference between their STM biases. Unlike conventional differential time-variant circuits, for which only the even or odd spurs are rejected, we show that the proposed configuration cancels out all intermodulation products, thus making them operate alike linear time-invariant (LTI) circuits for an external observer. In turn, this property enhances all metrics of the resulting circulator, overcoming the limitations of SE architectures, and improving insertion loss, impedance matching, bandwidth, and noise figure. We show that this differential architecture also significantly relaxes the required modulation parameters, both in frequency and amplitude. We develop a rigorous small-signal model to guide the design of the proposed circuits and to get insights into their pseudo-LTI characteristics. Then, we validate the theory with simulations and measurements showing remarkable performance compared to the current state-of-the-art of magnetless nonreciprocal devices.