A Macromodeling-Based Hybrid Method for the Computation of Transient Electromagnetic Fields Scattered by Nonlinearly Loaded Metal Structures

In this article, we present a hybrid numerical scheme to compute the transient electromagnetic fields scattered by a metallic structure loaded with lumped nonlinear loads. The proposed scheme is based on three successive steps. First, the field coupling problem to the structure with the nonlinear loads removed is solved in the frequency domain using a method-of-moments (MoM) formulation. The unloaded structure is thus characterized as a generalized multiport Thevenin equivalent, whose components are represented as time-domain operators by performing a set of rational approximations followed by closed-form Laplace transform inversion. Transient port voltages and currents in the presence of nonlinear loads are then computed using a standard circuit solver. As a last step, the substitution theorem is used to solve the radiation problem again in the frequency domain using a MoM solver, the results of which are then translated into the time domain by means of rational approximations and recursive convolution operations. The proposed method enables an accurate and efficient evaluation of the transient nonlinearly scattered fields by the loaded structure, with a good potential for scalability to large-scale high-complexity nonlinear shields. Extensive validations are provided to demonstrate the accuracy of the proposed method, which is here applied to the characterization of energy-selective shielding for protection of sensitive devices from high-intensity radiated fields.