Design and Synthesis of Reconfigurable Filtering Phase Shifter Using Optimization of Coupling Matrix

In this article, a design and synthesis method to realize filtering phase shifter with tunable insertion phase and passband center frequency is proposed. The filtering phase shifter is based on a circuit consisting of three resonators in a triplet topology. Coupling matrix analysis is employed to obtain the detailed relationship between the insertion phase and the amplitude response of the filter. Then, differential evolution (DE) algorithm-based optimization method is proposed to obtain the coupling matrix with an arbitrary prespecified insertion phase. The proposed optimization method can not only obtain the coupling matrix with desired insertion phase but also can align the phase slope of different phase states, resulting in a low-phase error over the filter passband. Furthermore, a method is proposed to extend the phase shift range to full 360<inline-formula> <tex-math notation="LaTeX">$^{\circ}$</tex-math> </inline-formula> by switching the signs of specific terms in the coupling matrix, significantly simplifying the required optimization procedure. Finally, a filtering phase shifter using lumped elements is designed, fabricated, and measured to validate the design concept. The phase-shifting range of the circuit can achieve 360<inline-formula> <tex-math notation="LaTeX">$^{\circ}$</tex-math> </inline-formula> with continuously reconfigurable center frequency covering from 650 to 860 MHz.