Transfer Matrix Method for Circuit a Cross-disciplinary Extension from Transfer Matrix Method for Multibody Systems

Transfer matrix method for multibody systems (MSTMM) has attracted much attention in mechanical systems for its ability to efficiently handle complex dynamics problems. In this paper, we extend its theoretical framework to the field of circuits and propose a transfer matrix-based circuit simulation method. By analyzing the similarity between mechanical systems and circuit systems in terms of component equations and topologies, a transfer matrix library applicable to circuit components is constructed, and a program framework containing model preprocessing, transfer matrix construction and system solving is designed. The correctness and computational efficiency of the method are verified by taking the circuits containing multi-pulse discharge units and the equivalent circuits of high-voltage transmission lines as examples. The results show that compared with the traditional Simulation Program with Integrated Circuit Emphasis (SPICE) method, the circuit transfer matrix method significantly reduces the computational complexity in large-scale circuit simulation, and the computation time increases linearly rather than exponentially with the number of components. This study provides new ideas for the fast simulation of complex circuit systems and theoretical support for the feasibility of cross-domain method migration.