Spectral algorithm to compute and synthesize reduced order passive models for arbitrary RC multiports

In this article, we present a time domain method to compute synthesized reduced-order approximation of arbitrary linear RC multiports. If the given multiport is passive, then the computed approximation, with all its nodes accessible, is also proved to be passive. This ensures that the reduced order multiport is well behaved during circuit simulations when embedded back in the parent nonlinear circuit. The reduced-order multiport is synthesized as a passive RC circuit which can be analyzed directly with standard circuit simulators treating the latter as black boxes. The method is based on computing tests from the partial fraction expansion of the port admittance matrix. The computations are performed by writing state equations implicitly, wherein the Lanczos algorithm is used to compute eigenvalues and eigenvectors. The residue matrices are also computed implicitly. The notion of `relevance´ of an eigenvalue for reduced order model is emphasized. The method does not impose any topological constraints (such as prohibition of capacitor cutsets) on the multiport. All computations are performed implicitly through DC analyses of appropriately constructed networks. An efficient DC analysis algorithm is used for this. The implicit computation ideas presented in this paper could also be used for efficient spectral investigation of linear RC/RLC circuits