Passive Interconnect Macromodeling Via Balanced Truncation of Linear Systems in Descriptor Form

Abstract

In this paper, we present a novel passive model order reduction (MOR) method via projection-based truncated balanced realization method, PriTBR, for large RLC interconnect circuits. Different from existing passive truncated balanced realization (TBR) methods where numerically expensive Lur'e or algebraic Riccati (ARE's) equations are solved, the new method performs balanced truncation on linear system in descriptor form by solving generalized Lyapunov equations. Passivity preservation is achieved by congruence transformation instead of simple truncations. For the first time, passive model order reduction is achieved by combining Lyapunov equation based TBR method with congruence transformation. Compared with existing passive TBR, the new technique has the same accuracy and is numerically reliable, less expensive. In addition to passivity-preserving, it can be easily extended to preserve structure information inherent to RLC circuits, like block structure, reciprocity and sparsity. PriTBR can be applied as a second MOR stage combined with Krylov-subspace methods to generate a nearly optimal reduced model from a large scale interconnect circuit while passivity, structure, and reciprocity are preserved at the same time. Experimental results demonstrate the effectiveness of the proposed method and show PriTBR and its structure-preserving version, SP-PriTBR, are superior to existing passive TBR and Krylov-subspace based moment-matching methods.