Impedance-Feature-Based Gauss–Newton Optimization Incorporating MOR and FFS Sensitivity for Waveguide Filters

Using <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</i>-parameter features to assist or even directly drive the optimization of microwave filters (the latter often called as cognition-driven optimization) has proven to be an effective approach when the initial design is suboptimal. However, the robustness of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</i>-parameter feature extraction tends to degrade significantly when the initial design deviates further from the target. Recently, an impedance-feature-based cognition-driven space mapping (SM) optimization method has been proposed to address this limitation, which demonstrates superior robustness in the case of poor initial designs and provides more accurate optimization guidance compared with <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</i>-parameter-based methods. This article proposes an impedance-feature-based Gauss–Newton optimization algorithm incorporating model order reduction (MOR) and fast frequency sweep (FFS) sensitivity. The impedance features are extracted directly through an MOR process based on the finite element method (FEM) and the inherent properties of impedance. Subsequently, the physical expressions of the derivatives of impedance features under the FEM are derived. Due to the severe numerical deviations caused by the high sensitivity of impedance features near resonance, a modified fast derivative formula is proposed. In combination with the derived FFS sensitivity expression of the impedance parameters, the proposed method achieves sensitivity calculations with the same accuracy as finite-difference derivatives but with significantly improved efficiency. Based on the obtained sensitivity information of the impedance features, a trust-region-based Gauss–Newton optimization formulation is developed, enabling faster and more robust optimization compared with previous work. The proposed approach is validated and compared through two illustrative examples.