以全域A r noldi演算法發展超大型類比積體電路巨觀模型的方法

A new method for MIMO RLCG interconnects model order reduction technique using the global Arnoldi algorithm is proposed. This algorithm is an extension of the standard Arnoldi algorithm for systems with multi-inputs and multi-outputs (MIMO). Under this framework, the input matrix is treated as a stacked vector form and the global Arnoldi algorithm will be the standard Arnoldi algorithm applied to a new matrix pair. It will be shown that this new matrix Krylov subspace, generated from the Frobenius orthonormalization process, indeed is the union of system moments. By employing the congruence transformation with this matrix Krylov subspace, the onesided projection method can be used to construct a reduced-order system. In comparison with the existing block Arnoldi algorithm, it can be proven that transfer matrices of both reduced system will be identical. However, the computation complexity of the global Arnoldi algorithm seems to be cheaper. Connections of the reduced system and the original RLCG interconnect circuits are developed. The transfer matrix residual error of the reduced system is derived analytically. This error information will be a guideline for the order selection scheme. Experimental results demonstrate the feasibility and the effectiveness of the proposed method.