Rigorous Modal Circuit Synthesis Including Modal Coupling for Linear, Time-Invariant, and Passive Electromagnetic Systems

A novel and rigorous modal circuit-modeling approach for arbitrary linear, time-invariant, and passive electromagnetic systems, e.g., transmission lines, antennas, or printed circuit boards, is presented. Based on the discrete representation of the distributed system, e.g., by the method of moments, finite differences, or finite elements, the governing matrix equation is solved exactly by means of the eigenmodes of the quasi-static and lossless system. This is achieved by accounting for the mutual coupling of the modes, which has been omitted in all recently presented approaches and found to be responsible for the limitations, especially with regard to the radiation losses. The proposed circuit synthesis is based on the rational modeling of the fundamental system dynamic independent of the port positions. The latter correspond to modal weighting, modeled by a simple transformer network. The complexity of the network model is considerably reduced by an estimation of the dominant modal couplings and the representation of all subresonant modes by lumped elements. The versatility and accuracy of the proposed SPICE-compatible circuit model are demonstrated by full-wave reference simulations in frequency and time domain, including linear and nonlinear terminations.