In this paper we present a passive reduced order modeling algorithm for linear multiport interconnect structures. The proposed technique uses rational fitting via semidefinite programming to identify a passive transfer matrix from given frequency domain data samples. Numerical results are presented for a power distribution grid and an array of inductors, and the proposed approach is compared to two existing rational fitting techniques.

In this paper we present an efficient algorithm for extracting the complete statistical distribution of the input impedance of interconnect structures in the presence of a large number of random geometrical variations. The main contribution in this paper is the development of a new algorithm, which combines both Neumann expansion and Hermite expansion, to accurately and efficiently solve stochastic linear system of equations. The second contribution is a new theorem to efficiently obtain the coefficients of the Hermite expansion while computing only low order integrals. We establish the accuracy of the proposed algorithm by solving stochastic linear systems resulting from the discretization of the stochastic volume integral equation and comparing our results to those obtained from other techniques available in the literature, such as Monte Carlo and stochastic finite element analysis. We further prove the computational efficiency of our algorithm by solving large problems that are not solvable using the current state of the art.