Unequal Power Division Ratio Nonreciprocal Filtering Power Divider With Arbitrary Termination Impedance and Center Frequency Tunability
Girdhari Chaudhary, Yongchae Jeong
Abstract
This article presents RF design and practical implementation of a nonreciprocal filtering power divider that enables arbitrary power division ratio ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$k^{2}$ </tex-math></inline-formula> ) and center frequency tunability. By modulating resonators in the filtering power divider with progressive phase shift sinusoidal modulation signals, a nonreciprocal response ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\vert S_{21}\vert \ne \vert S_{12}\vert $ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\vert S_{31}\vert \ne \vert S_{13}\vert$ </tex-math></inline-formula> ) 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 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$k^{2}$ </tex-math></inline-formula> 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 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$k^{2}$ </tex-math></inline-formula> = 1 and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$k^{2}$ </tex-math></inline-formula> = 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 ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\vert S_{12}\vert $ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\vert S_{13}\vert$ </tex-math></inline-formula> ) higher than 20 dB at each center frequency tuning state.