Circuit Transfer Matrix: A Novel Approach to Enhancing Circuit Analysis Efficiency by Extending the Transfer Matrix Method for Multibody System

To address the challenge of high computational complexity in large-scale circuit analysis, the Circuit Transfer Matrix Method is proposed, drawing on the strong parallels between electrical and mechanical systems. This method builds upon the Transfer Matrix Method for Multibody Systems, which has seen significant breakthroughs and widespread use in complex mechanical systems, extending its application to circuit analysis. Unlike traditional model-reduction techniques, the circuit transfer matrix method employs the concepts of ‘transfer’ of system state vectors and the ‘assembly’ of transfer matrices, effectively reducing the order of the system’s equations and significantly improving computational efficiency. This reduced-order model allows designers to analyze and synthesize a system’s dynamic behavior within a limited design cycle more efficiently. The text presents the computational workflow of the Circuit Transfer Matrix Method, from the definition of state vectors to the invocation and assembly of transfer matrices, followed by the solution of the transfer equations. The fundamental component transfer matrices are derived upon which the method for deriving the transfer matrices of combined elements is provided, along with a corresponding example. Subsequently, examples are provided to illustrate the detailed computational processes for linear AC analysis, transient analysis of linear chain systems, transient analysis of linear closed-loop systems, and transient analysis of general nonlinear systems. The accuracy of the algorithm is validated by comparisons with methods based on SPICE. Finally, a comparison of the algorithm speed with SPICE reveals that SPICE has an asymptotic time complexity of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$O(n^{3})$ </tex-math></inline-formula>, while the Circuit Transfer Matrix Method has a complexity of only <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$O(n)$ </tex-math></inline-formula>, significantly enhancing computational efficiency.