Nonreciprocal Filtering Power Divider Using Mixed Static and Time-Modulated Resonators: Numerical Design Approach and Experimental Validation

This paper presents detailed design methodology and the experimental validation of a nonreciprocal power divider $(|S_{21}|\neq|S_{12}|$ and $|S_{31}|\neq|S_{13}|)$ using mixed static and time-modulated resonators. The nonreciprocal response is achieved by modulating its constituent resonators with a sinusoidal signal with progressive phase shift. The mixed static and time-modulated resonators are used to achieve a wider bandwidth for the reverse isolation $(|S_{12}|$ and $|S_{13}|)$ while using fewer time-modulated resonators. The analytical spectral S-parameters of the nonreciprocal power divider have been derived to simplify the design method. General empirical design equations for the modulation parameters are derived from numerical simulations, which enable the proposed nonreciprocal power divider with the desired specifications. For experimental validation, a nonreciprocal filtering power divider with an equal power division ratio was designed and fabricated at center frequency of 1.45 GHz. The measured results confirmed the accuracy of the analytical design equations.