Efficient model reduction of interconnect via approximate system gramians

Krylov-subspace based methods for generating low-order models of complicated interconnect are extremely effective, but there is no optimality theory for the resulting models. Alternatively, methods based on truncating a balanced realization (TBR), in which the observability and controllability gramians have been diagonalized, do have an optimality property but are too computationally expensive to use on complicated problems. In this paper we present a method for computing reduced-order models of interconnect by projection via the orthogonalized union of the approximate dominant eigenspaces of the system´s controllability and observability gramians. The approximate dominant eigenspaces are obtained efficiently using an iterative Lyapunov equation solver, Vector ADI, which requires only linear matrix-vector solves. A spiral inductor and a transmission line example are used to demonstrate that the new method accurately approximates the TBR results and gives much more accurate wideband models than Krylov subspace-based moment matching methods.