Non-magnetic four-port electronic circulators based on [Formula: see text] non-reciprocal phase-shifters

This paper presents a family of four-port electronic circulators adhering to a new topology symmetry that enables linear, low-loss transistor-based circuit implementations. The underlying principle of operation employs a property of the [Formula: see text] non-reciprocal phase shifter (NRPS) derived in this article. Under quadrature excitation, the NRPS transfers or reflects exciting signals depending on their respective phase lead. The fundamental topology consists of two back-to-back quadrature hybrid couplers with a [Formula: see text] NRPS connected in parallel over the line of symmetry, interrupting the circuit's reciprocity to achieve circular propagation by bypassing or reflecting at the NRPS but not through. We break down the circuit into three fundamental four-port sub-circuits. The transfer function of the cascaded sub-circuits enables an analysis with specific hybrid couplers. It also allows a synthesis of other four-port passive sub-circuits that, with an NRPS, achieve a four-port circulator transfer function by solving a matrix equation. Some of the mathematical solutions have circuit realizations, which are adjusted quadrature hybrid structures that differ from each other by the characteristic impedance of their arms. Two familiar solutions, including the standard quadrature hybrid and a modified design with equal [Formula: see text], [Formula: see text] arms, are simulated utilizing lossless lumped element arms and a 4-Path, 65-nm NMOS [Formula: see text] NRPS. The simulation results verify the theoretical analysis and enable a comparison between the performance of the two circuit solutions around 1 GHz. The four-port circulator with equal arms is implemented on a PCB and measured, yielding better than 1.5 dB insertion loss between the circulator ports, over 17 dB port-to-port reverse isolation, and better than 20 dBr port matching around 1 GHz.