Magnetless 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 spatio-temporal 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 and non-linearity, and the noise performance. Finally, we present measured results with unprecedented performance in all metrics for a PCB prototype using a Rogers board and off-the-shelf discrete components.