Magnet-Less Circulators Based on Spatiotemporal Modulation of Bandstop Filters in a Delta Topology

In this paper, we discuss the design rationale and guidelines to build magnet-less circulators based on spatiotemporal modulation of resonant junctions consisting of first-order bandstop filters connected in a delta topology. Without modulation, the junction does not allow transmission between its ports; however, when the natural oscillation frequencies of the constituent LC filters are modulated in time with a suitable phase pattern, a synthetic angular-momentum bias can be effectively imparted to the junction and a transmission window opens at one of the output ports, thus realizing a circulator. We develop a rigorous small-signal linear model and find analytical expressions for the harmonic S -parameters of the proposed circuit, which significantly facilitate the design process. We validate the theory with simulations and further discuss the large-signal response, including power handling, nonlinearity, and noise performance. Finally, we present measured results with unprecedented performance in all metrics for a printed circuit board prototype using off-the-shelf discrete components.