Passive multipoint moment matching model order reduction algorithm on multiport distributed interconnect networks

In this paper, we introduce a general method of interconnect simulation based on distributed circuits. The algorithm is very efficient and consists of two main steps. In the first step, each distributed line is modeled by a finite order system with passivity preservation and multipoint moment matching of its input admittance/impedance matrix. In the second step, an Arnoldi-based congruence transform is applied to the network to form its reduced order model. The main feature of the algorithm is in its first step, where a passive multipoint moment matching model of a distributed line can be generated without any discretization of the line. We provide an integrated-congruence transform which can be directly applied to the partial differential equations of a distributed line and generate a passive finite order system as its model. We also provide an algorithm based on the L² Hubert space theory so that exact moment matching at multiple points can be obtained. We demonstrate the accuracy of our method with examples and show the advantage of ours over conventional ones based on lumped circuit models.