Fully-Adaptive and Semi-Adaptive Frequency Sweep Algorithm Exploiting Loewner-State Model for EM Simulation of Multiport Systems
Shilpa T. N., Rakesh Sinha
TL;DR
This work introduces fully adaptive and semi-adaptive frequency sweep strategies based on Loewner-matrix (LM) state models to accelerate EM simulations of multiport systems. By constructing two LM pencils (with identical or different orders) and using small frequency perturbations, the methods adaptively select sampling points to minimize model error, terminating when the actual error meets a user-defined tolerance with memory. The framework covers SISO and MIMO cases via vector- and matrix-format tangential interpolation, includes data partitioning and reduced-order modeling via SVD, and employs pseudo-error-driven adaptive sampling. Four EM examples demonstrate significant speedups and accurate results with far fewer samples than traditional approaches, outperforming Pradovera's and Stoer-Bulirsch methods in both speed and sample efficiency. This LM-based approach provides a practical, scalable pathway for rapid EM simulations of planar multiport PCBs and large-scale networks.
Abstract
This paper employs a fully adaptive and semi-adaptive frequency sweep algorithm using the Loewner matrix-based state model for the electromagnetic simulation. The proposed algorithms use two Loewner matrix models with different or the same orders with small frequency perturbation for adaptive frequency selection. The error between the two models is calculated in each iteration, and the next frequency points are selected to minimize maximum error. With the help of memory, the algorithm terminates when the error between the model and the simulation result is reached within the specified error tolerance. In the fully adaptive frequency sweep algorithm, the method starts with the minimum and maximum frequency of simulation. In the semi-adaptive algorithm, a novel approach has been proposed to determine the initial number of frequency points necessary for system interpolation based on the electrical size of the structure. The proposed algorithms have been compared with the Stoer-Bulirsch algorithm and Pradovera's minimal sampling algorithm for electromagnetic simulation. Four examples are presented using MATLAB R2024b. The results show that the proposed methods offer better performance in terms of speed, accuracy and the requirement of the minimum number of frequency samples. The proposed method shows remarkable consistency with full-wave simulation data, and the algorithm can be effectively applicable to electromagnetic simulations.