Wei Liu

This letter proposes a novel resonance degree discrimination algorithm for the systematic compact embedded neuro-transfer function (SC-TF) parametric modeling method. As the variation range of geometrical parameters expands, the electromagnetic (EM) responses of microwave components exhibit stronger fluctuations, which lead to the emergence of abnormal pole–residue pairs and inconsistent distributions of high- and low-resonance sub-TFs under different geometrical parameters. To address these issues, a three-step strategy is introduced, which incorporates preliminary pole–residue classification, sub-TF scaling, and adaptive pole–residue tracking. The proposed algorithm effectively improves the modeling accuracy and applicability range of the SC-TF method. The effectiveness of the proposed algorithm is verified through two microwave filter examples.

The vector fitting (VF) technique is popularly used in neural network-transfer function (neuro-TF) modeling methods for electromagnetic (EM) behaviors of microwave filters. However, VF often produces nonsmooth and discontinuous transfer function (TF) coefficients under large geometrical variations, which degrade training stability and model accuracy. To address this issue, this article proposes a novel autoencoder-based neural network-TF (AENN-TF) parametric modeling method for EM behavior of microwave filters. In the proposed method, an advanced autoencoder (AE)-based feature parameter extraction technique is incorporated to develop a smooth relationship of TF parameters with respect to geometrical variables. This smooth relationship improves the neural network training accuracy, consequently improving the overall AENN-TF modeling accuracy for EM behavior. Novel derivative formulations are derived for the proposed model structure in order to perform fast gradient-based overall model training. Furthermore, we develop a novel four-step training framework with detailed modeling processes for the proposed AENN-TF modeling method. Compared to existing neuro-TF methods with the VF technique, the proposed AENN-TF method achieves better accuracy and robustness. The superior performance of the proposed method over existing neuro-TF methods is further demonstrated through two microwave application examples.

In modern RF and microwave systems, the electromagnetic environment is increasingly congested. Demand for massive data throughput and ultra-high-resolution sensing has driven systems to higher frequency bands. Beyond 30 GHz (subterahertz and above), dielectric loss becomes the primary bottleneck limiting system noise figure improvement and power efficiency. At these frequencies, traditional planar transmission lines, such as microstrip lines and substrate-integrated waveguides, degrade significantly due to increased dielectric loss and radiation leakage. Traditional metal waveguides offer excellent power-handling capability and near-zero dielectric loss. However, they are highly dependent on high-precision computer numerical control milling, resulting in bulky, heavy, high-cost structures that are incompatible with miniaturization of modern satellite payloads and mobile terminals.

Space mapping (SM) accelerates full-wave electromagnetic (EM) optimization, but its efficiency depends strongly on the quality of the coarse model. In reduced-order modeling (ROM)-based SM, a reduced basis constructed at a nominal design may lose approximation capability under geometric deviations, thereby restricting the validity region of the reduced-order coarse model (ROCM). To address this issue, this article presents a common projection subspace (CPS)-based reduced-order coarse-modeling approach for ROM-based SM. By constructing a CPS from reduced bases extracted at multiple neighboring geometries, the proposed method improves the local modeling validity of the ROCM over the sampled neighborhood within each SM iteration while preserving high computational efficiency. Combined with mesh-deformation techniques, the method enables efficient coarse-model updating without repeated remeshing. Three representative microwave design examples, together with comparisons against direct EM optimization, mesh SM (MSM), aggressive SM (ASM), and nominal-basis ROM-SM, demonstrate that the proposed coarse-modeling strategy can reduce the number of SM iterations and total CPU cost in the tested cases while maintaining comparable final design accuracy.

When the performances of microwave waveguide filters are obviously influenced by thermal effects, designers have to consider and analyze the multiphysics coupling effect in devices. Most existing parametric modeling techniques based on pure electromagnetic (EM) are not suitable for multiphysics scenarios. Among the available approaches, vector fitting-based neuro-transfer functions (neuro-TFs) represent one of the techniques compatible with multiphysics parametric modeling due to their data-driven characteristics. However, vector fitting-based neuro-TF inherently suffers from discontinuities in the transfer function parameters caused by order changing. For pure EM problems, physics-driven transfer functions can be derived using finite element methods (FEMs) and model order reduction (MOR), which significantly improves the continuity of the extracted transfer function parameters and thereby enhances modeling accuracy. However, in the case of multiphysics problems, it is currently infeasible to extract physics-driven transfer function parameters. In this article, we propose an implicit iterative formulation for extracting multiphysics transfer function parameters based on FEM and MOR in the EM-thermal-mechanical multiphysics. The continuity of the multiphysics transfer function parameters is ensured through mesh deformation, and an iterative convergence criterion is established. Based on the extracted multiphysics transfer function parameters, a pole-zero neuro-TF method for multiphysics parametric modeling is developed. The proposed method is validated through two high-power filter examples. Compared with existing conventional neuro-TF and multiphysics modeling methods, the proposed multiphysics parametric modeling approach achieves significantly higher model accuracy.

Recent research has demonstrated the exponential potential of hybrid quantum–classical algorithms (HQAs) in solving electromagnetic (EM) problems. However, the optimization objective of HQAs typically focuses on the magnitude of electric fields in EM problems, neglecting phase information. Consequently, the resulting quantum solution is inherently normalized to unity and subject to a global phase offset. This limitation prevents the calculation of the correct magnitude and phase of S-parameters. To address this challenge, we propose a block-encoding-based HQA (BEHQA) integrating a specialized quantum method for S-parameter extraction with magnitude and phase. The proposed method employs the specialized quantum method to reconstruct both the magnitude scaling and the phase offset, ensuring correct S-parameter extraction. Besides, HQAs fundamentally operate on unitary matrices, necessitating the explicit decomposition of nonunitary finite element method (FEM) matrices into many unitary operators. To mitigate the overhead associated with matrix decomposition, we introduce the block-encoding to embed the FEM matrix directly as a sub-block within a unitary operator. This strategy eliminates the need for decomposing FEM matrices to unitary operators, thereby reducing circuit complexity. For efficient optimization, we also derive a novel cost function specifically designed for the proposed BEHQA. The algorithm employs a strongly entangling ansatz (SEA) and gradient-based optimization to minimize the loss function. The effectiveness of BEHQA is demonstrated through its application to two microwave components, showcasing its feasibility for quantum-driven EM simulations.

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.

This study proposes an equivalent circuit-fitting-based neural transfer function modeling method (ECFB neuro-TF) to enhance the robustness, interpretability, and capability of handling nonideal factors in parametric modeling of coupled resonator microwave bandpass filters. Unlike previous approaches that rely on vector fitting (VF), this method introduces physical constraints through equivalent circuit (EC) mapping. Compared with the previous systematic neuro-transfer function method based on a compact embedded format (SCEF neuro-TF), this work includes the following advances: First, constraining pole/residue extraction via predefined circuit topology, effectively overcoming VF’s inherent issues of order inconsistency and parameter discontinuity. Second, establishing a complex exponential phase shift function through theoretical and experimental validation, providing accurate quantification of port effects. Furthermore, demonstrating the pole uniqueness and parameter continuity under perturbation from filter synthesis theory. The developed neuro-TF model incorporates these circuit-based features while employing neural networks to correct residual nonideal effects. Experimental results demonstrate that our method achieves superior accuracy over broader parameter ranges compared to both VF-based and multilayer perceptron (MLP) approaches, offering an efficient and reliable solution for complex electromagnetic (EM) modeling scenarios.