Analysis and design of frequency tunable magnetless circulator using spatiotemporal modulated mixed static and time-modulated resonators

Abstract This paper presents a comprehensive analysis and radio frequency (RF) design methodology for frequency tunable circulator using spatiotemporal modulation technique. By combining static resonator and spatiotemporal modulated time-modulated resonator in each branch, the proposed circulator can achieve low transmission insertion loss (IL) with a flat passband response and sharp roll-off in stopband. For comprehensive analysis, the analytical spectral S -parameters are derived, providing insight into the nonreciprocity mechanism of the circulator in the absence of any magnetic materials. Simulation results demonstrate that the proposed circulator exhibits two reverse isolation nulls and two reflection pole frequency characteristics within the passband. The static resonators function as a bandpass filter, providing a flat passband response, and as a bandstop filter for intermodulation (IM) frequencies, resulting in a significant reduction in IM signal power. For proof-of-concept, a frequency-tunable circulator is designed and fabricated using microstrip resonators loaded with varactor diodes, showing continuous frequency tuning from 1.45 to 1.70 GHz. Measured IL varies between 3.95 and 4.60 dB, and reverse isolation ranges from 19 to 40 dB at the center frequency.