Analytical Solution to EMI Response of High-Frequency Field-Line Coupling with Lumped-Load Based on Asymptotic Theory

Due to the complex propagation of high-frequency electromagnetic waves in transmission lines, classical transmission line theory or approximation methods can no longer be used to accurately calculate the electromagnetic response of transmission lines subject to high-frequency electromagnetic interference (EMI). The asymptotic method has emerged in recent years as a new approach to solve high-frequency field-line coupling models. However, it has only been applied to infinite-length transmission line, and the calculation of the current response for transmission lines with loads still relies on numerical methods. To address this issue, this paper establishes a fundamental model of a long straight conductor with lumped loads under high-frequency external field irradiation, and derives an analytical expression for the current distribution in the load section by using asymptotic theory. Based on an analysis of the main factors influencing the error in the approximation of the Pocklington equation, the amplitude of the approximate solution for the current along the conductor is corrected. The corrected analytical solution for the current response along the conductor with lumped loads is derived, and the results are validated by comparing them with numerical calculation results. The results obtained in this paper provides a quick and accurate way to calculate the current response in the load section, completing a fundamental theoretical work in the asymptotic method and contributing to the development of a comprehensive analytical approach for high-frequency field-line coupling models.