Synthesis of Multi-Port Filtering Power Divider for Mixed Topology Using Matrix Optimization

In this brief, a direct synthesis method is proposed to extract the coupling matrix of multi-port filtering power divider (FPD) for mixed topology for the first time. Different from the existing cross-coupled configuration, extracted pole based topology containing non-resonating nodes (NRN) is introduced into the multi-port FPD network to eliminate some inherent limitations. All the elements of coupling matrix are obtained directly in the synthesis process by optimizing the cost function with the deigned Quantum Particle Swarm Optimization (QPSO) algorithm in this brief, avoiding evaluating the numerical value one by one from the conventional two-port filter synthesis method and eliminating the step of similarity transformations of the coupling matrix. Moreover, impedance matching has been considered to the FPD synthesis process to meet the comprehensive needs of more scenarios. Several numerical examples of FPD with equal/unequal power division ratios and arbitrary reference impedance, different responses for both symmetrical and asymmetrical mixed topologies are synthesized to verify the proposed synthesis method.