Rigorous design and experimental validation of non-reciprocal bandpass filter with ultrawide high reverse isolation bandwidth

This work presents a rigorous design and experimental validation of a non-reciprocal bandpass filter (NBPF) employing time-modulated resonators with progressive phase shift sinusoidal modulation signal to achieve low forward transmission insertion loss (IL) and ultrawide high reverse isolation bandwidth. Analytical design equations have been derived for numerical design of NBPF asl well as providing insights of nonreciprocal frequency response. Additionally, these proposed analytical spectral S-parameters offer the flexibility to design NBPFs with arbitrary termination port impedances. This work also demonstrates a systematic approach to find modulation parameters without relying on optimization methods. It has established empirical relationships between the modulation parameters and the filters specifications to achieve low forward transmission IL and reverse isolation exceeding 15 dB at entire frequency range. The accuracy of the proposed NBPF design has been confirmed by comparing with harmonic balance simulation results of microstrip line NBPF. For experimental validation, three prototypes of NBPF with different termination port impedances are designed, implemented, and manufactured. In experimental results, the frequency of NBPFs can be continously tuned from 1.62 GHz to 1.94 GHz (17.98 %) with maximum forward transmission IL (|S21|) of 5.40 dB and input/output return loss higher than 12 dB. For each frequency tuning state, the reverse isolation (|S12|) exceeds higher than 20 dB across the entire frequency range.