Efficient stochastic transient analysis of high-speed passive distributed networks using Loewner Matrix based macromodels

Distributed networks with embedded parametric uncertainty can be characterized in the frequency-domain by tabulated augmented multiport S or Y-parameter responses based on a stochastic Galerkins formulation of the network equations. In this work, the Loewner Matrix approach is utilized to generate a compact SPICE-compatible macromodel of the stochastic distributed network from the tabulated frequency-domain data for transient analysis. The key attribute of this work is that the superior scaling of the computational complexity of the Loewner Matrix approach with respect to the augmented number of network ports allows for a more efficient generation of the macromodel than the classical Vector Fitting approach. This leads to faster transient analysis for problems involving large random spaces. The advantage of the proposed approach is validated using a numerical example.