Hierarchical Space Mapping With Group Delay Optimization for Microwave Filter Design

Group delay plays a critical role in filter synthesis design of practical physical structures. Initial syntheses based on step-by-step single-port group delay optimization often fail to meet the requirements of the final design. Space mapping (SM) has become one of the most widely used optimization techniques to bridge the gap between theoretical models and optimal designs. In this article, a novel hierarchical SM (HSM) technique is proposed for group delay optimization in microwave filter design. At each step, SM is employed to reduce the error between the theoretical and actual group delays. However, the effectiveness of each step using SM is limited by the quality of the starting point. To address the issue of the poor starting point, an adaptive differential approximation derivative-based hierarchical modification method is proposed. Compared with direct electromagnetic (EM) optimization and existing SM methods, the proposed algorithm reduces the number of iterations and optimization time. The effectiveness of the proposed technique is demonstrated through three progressively complex group delay design examples.