The improvement and implementation of theory of Maxwellian circuit

Abstract

The classical transmission line (TL) equations are constrained by the quasi-TEM (Transverse Electromagnetic) approximation. The Theory of Maxwellian Circuit (TMC) establishes a generalized TL equation. It employs full-wave analysis results to fit the distributed parameters of the TL equation, thereby determining a generalized TL equation form that is not limited to the quasi-TEM approximation. TMC can be regarded as a data-driven modeling approach. Furthermore, the TL equation formulated by TMC can serve as a reference for other generalized TL equations in terms of both equation form and parameters, including coefficient terms and inhomogeneous terms. This paper analyzes the distributed parameters and source terms in the differential equations of TMC and improves the form of the source terms, which implies corresponding changes in the values of the distributed parameter terms. Numerical simulations reveal that the improved TMC model offers improved accuracy in predicting current distribution along TLs. Furthermore, several technical details related to the numerical implementation of TMC are presented, including avoiding dealing directly with non-smooth positions in TLs, using a set of boundary conditions with weak ill-conditioning, and choosing the range of [λ/40, λ/20] as the length of segments based on computational accuracy and efficiency. These considerations represent novel contributions not previously mentioned. These studies will aid in applying machine learning to transmission line modeling and analysis and advance the development of generalized TL equations and theory.