A Generalized Model for Linear-Periodically-Time-Variant Circulators

Magnetic-free non-reciprocity based on linear-periodically-time-variant (LPTV) circuits has received significant research and commercial attention since it could revolutionize wireless communications. LPTV circuits are formed by two main components: linear-time-invariant (LTI) networks and periodically-modulated switches. The modulated switches are the core elements to break the reciprocity of LTI networks. To understand and design LPTV circulators, a universal and intuitive analytical model is required. However, such model does not exist as it is extremely challenging to accurately model and fully understand the LPTV behaviour of energy storage networks. To address this limitation, this work introduces a novel analysis method, which is broadly applicable to any LPTV networks, and validates it experimentally. The novelty of this methodology comes from two main contributions: (1) modelling of the switch as a resistor in parallel with a current-controlled current source; (2) the decomposition of the LPTV network into the linear superposition of two LTI networks. We apply this technique to model the exact behaviour of an LPTV circulator in the frequency domain.