NHAR: A non-homogeneous Arnoldi method for fast simulation of RCL circuits with a large number of ports

摘要

Large-scale RCL circuits with a large number of ports have been widely employed to model interconnect circuits, such as the power/ground networks, clock distribution networks and large data buses in VLSI. The input-dependent moment-matching technique, which takes the input excitations into account when constructing the projection matrices for the reduced-order systems, has been proposed to simulate this type of circuits. The existing input-dependent moment-matching methods suffer from either numerical instability in the case of extended Krylov subspace (EKS) and improved extended Krylov subspace (IEKS) methods, or unbearable memory consumption and CPU cost for the EXPanded LINearization (EXPLIN) method. In this paper, a Non-Homogeneous ARnoldi (NHAR) process, which consists of a memory-saving and computation-efficient linearization scheme and a numerical stable partial orthogonalization Arnoldi method, is proposed for the generation of the orthonormal projection matrix. By applying the obtained projection matrix to generate the reduced-order model, we derive the NHAR method for the model-order reduction of large-scale RCL circuits with a large number of ports. The proposed NHAR method can guarantee moment matching, numerical stability and passivity preserving. Compared with the EXPLIN method, NHAR can remarkably reduce the size of the linearized system and therefore can greatly save the memory consumption and computational cost with almost the same accuracy. Moreover, NHAR is numerically stable and can achieve higher accuracy with approximately the same computational cost compared with the EKS and IEKS methods.