Analytic Iterative Solution of Electromagnetic Pulse Coupling to Multiconductor Transmission Lines

This paper provides an efficient iterative solution in the frequency domain for electromagnetic pulse (EMP) radiated field coupling to multiconductor transmission lines (MTLs) based on distributed analytical representation of the exciting sources and iterative technique originated from waveform relaxation. The method consists of two kinds of iterations, the first is that the incoming EMP wave couples to each conductor while the effects of neighboring conductors were neglected; the second is that each conductor will be not only subject to the illumination of the EMP wave, but also influenced by the virtual sources which are the induced voltages and currents of the neighboring conductors at the previous iteration. The key highlights of the proposed method are that the induced voltage and current at each iteration are considered as the virtual distributed exciting sources for next iteration, and the integrals were solved analytically by the Baum-Liu-Tesche equation, leading to a pretty good efficiency and quick convergence for most real cases. The validation results over a wide range show that the proposed method could efficiently handle EMP coupling to MTLs with a large number of conductors and the accuracy of the solutions is closely related to the number of iterations allowing the flexibility to choose between the accuracy and the time cost.