Multiorder Arnoldi Approach for Model Order Reduction of PEEC Models With Retardation

This paper presents an efficient algorithm to create reduced-order models of large linear networks that contain delay elements. The proposed algorithm is based on a multiorder Arnoldi algorithm used to implicitly calculate the moments with respect to frequency. This procedure generates reduced-order models that preserve the structure of the original system, without having to introduce any extra state variables to calculate the moments. In addition, it is shown that the orthonormal subspace of the system, built by introducing extra state variables, is embedded in the subspace constructed by the multiorder Arnoldi approach. Numerical examples of distributed interconnects modeled by partial element equivalent circuits that include retardation effects are described to illustrate the validity of the proposed reduction technique.