Generating nearly optimally compact models from Krylov-subspace based reduced-order models

Automatic model reduction of chip, package, and board interconnect is now typically accomplished using moment-matching techniques, where the matching procedure is computed in a stable way using orthogonalized or biorthogonalized Krylov-subspace methods. Such methods are quite robust and reasonably efficient, though they can produce reduced-order models that are far from optimally accurate. In particular, when moment-matching methods are applied to generating a reduced-order model for interconnect which exhibits skin effects, the generated models have many more states than necessary. In this paper, we describe our two-step strategy in which we first compute medium-order models using an efficient moment-matching method, and then nearly optimally reduce the medium-order models using truncated balanced realization. Results on a spiral inductor and a package example demonstrate the effectiveness of the two-step approach.