Time-domain analysis methodology for large-scale RLC circuits and its applications

With soaring work frequency and decreasing feature sizes, VLSI circuits with RLC parasitic components are more like analog circuits and should be carefully analyzed in physical design. However, the number of extracted RLC components is typically too large to be analyzed efficiently by using present analog circuit simulators like SPICE. In order to speedup the simulations without error penalty, this paper proposes a novel methodology to compress the time-descritized circuits resulted from numerical integration approximation at every time step. The main contribution of the methodology is the efficient structure-level compression of DC circuits containing many current sources, which is an important complement to present circuit analysis theory. The methodology consists of the following parts： 1） An approach is proposed to delete all intermediate nodes of RL branches. 2） An efficient approach is proposed to compress and back-solve parallel and serial branches so that it is error-free and of linear complexity to analyze circuits of tree topology. 3） The Y to πtransformation method is used to error-free reduce and back-solve the intermediate nodes of ladder circuits with the linear complexity. Thus, the whole simulation method is very accurate and of linear complexity to analyze circuits of chain topology. Based on the methodology, we propose several novel algorithms for efficiently solving RLC-model transient power/ground （P/G） networks. Among them, EQU-ADI algorithm of linear-complexity is proposed to solve RLC P/G networks with mesh-tree or mesh-chain topologies. Experimental results show that the proposed method is at least two orders of magnitude faster than SPICE while it can scale linearly in both time- and memory-complexity to solve very large P/G networks.