The Multiple Point Global Lanczos Method for MIMO Interconnect Model-Order Reductions

The global Lanczos algorithm for solving the RLCG interconnect circuits is presented in this paper. This algorithm is an extension of the standard Lanczos algorithm for multiple-inputs multiple-outputs (MIMO) systems. By employing the congruence transformation with the matrix Krylov subspace, the two-side oblique projection-based method can be used to construct a reduced-order system. It will be shown that the system moments is still matched. The error of the 2q-th order system moment will be derived analytically. Furthermore, a novel model-order reduction technique called the adaptive-order global Lanczos (AOGL) algorithm which is based on the multiple point moment matching is proposed. The frequency responses using the AOGL algorithm have higher coherence to the original system than those using the single point expansion method. Finally, simulation results on both frequency domain and time domain will illustrate the feasibility and the efficiency of the proposed method.