A Novel FDFD-TL Method for the Coupling Analysis of Multi-Conductor Transmission Lines

A novel frequency domain field-to-line hybrid method consisting of the Finite Difference Frequency Domain (FDFD) method and transmission line (TL) equations (FDFD-TL) is proposed, which can address the coupling problems of multi-conductor transmission lines (MTLs) excited by long-duration electromagnetic signals rapidly. First, the coupling model of long-duration interference signals to the MTLs is constructed via the TL equations combined with the analytical solutions of the excitation fields of MTLs. Then, the FDFD method is applied to solve these TL equations, and new FDFD schemes are developed for calculating the currents on the MTLs and their loads. Additionally, a new FDFD-TL matrix equation is formulated. Finally, the conjugate gradient method, enhanced by the OpenMP parallel technique, is employed to rapidly solve this matrix equation, thereby obtaining the current responses on the MTLs and their terminal loads. The advantages of this method include avoiding late-time instability and lengthy computation times associated with time-domain simulations for long-duration signals, while effectively calculating current responses along MTLs without directly modeling the MTL structures. Numerous coupling simulations of ideal transmission lines and actual power lines excited by various long-duration electromagnetic pulses are presented and compared to the results obtained using the method of moments (MoM) and FDTD-TL method, demonstrating the accuracy and efficiency of the proposed method.