Unequal Power Division Ratio Nonreciprocal Filtering Power Divider With Arbitrary Termination Impedance and Center Frequency Tunability

This article presents RF design and practical implementation of a nonreciprocal filtering power divider that enables arbitrary power division ratio ( $k^{2}$ ) and center frequency tunability. By modulating resonators in the filtering power divider with progressive phase shift sinusoidal modulation signals, a nonreciprocal response ( $\vert S_{21}\vert \ne \vert S_{12}\vert $ and $\vert S_{31}\vert \ne \vert S_{13}\vert$ ) is achieved. The analytical spectral S-parameters of nonreciprocal filtering power divider have been derived for insight analytical nonreciprocal frequency response and practical implementation. The proposed analytical equations can be applied to design a nonreciprocal filtering power divider with arbitrary $k^{2}$ and any arbitrary termination port impedances. Center frequency tunability can be achieved by tuning the resonant frequencies of time-modulated resonators. For experimental validation, prototypes of nonreciprocal filtering power dividers with $k^{2}$ = 1 and $k^{2}$ = 0.5 are designed, implemented, and manufactured. The measured results confirm the accuracy of the analytical design equations. In the experimental results, the center frequency of nonreciprocal filtering power dividers is tuned from 1.66 to 1.98 GHz (17.58%) with a maximum forward insertion loss of 4.95 dB and reverse isolation ( $\vert S_{12}\vert $ and $\vert S_{13}\vert$ ) higher than 20 dB at each center frequency tuning state.