A Spacetime Energy-Density Approach to Circuit Modeling of Cylindrical EM Structures: Capacitive, Inductive, and Mutual Coupling Effects

This work introduces a unified, iterative circuit modeling framework for cylindrical electromagnetic structures, grounded in a spacetime energy-density formulation. By progressively expanding Maxwell’s equations in cylindrical coordinates, the method reveals the emergence of capacitive and inductive behaviors as natural consequences of boundary-driven energy confinement. Each iteration order yields a distinct equivalent circuit configuration—odd orders exhibit inductive dominance through vanishing electric fields, while even orders correspond to capacitive regimes via magnetic field cancellation. This duality enables accurate representation of both lumped and distributed effects within a single, physically consistent formalism. Going beyond traditional static analogies, the model offers a scalable tool for analyzing mutual coupling, reactive field interactions, and the conditions defining non-radiative behavior. The resulting circuit analogues enhance analytical clarity across frequency regimes, bridging energy-based electromagnetic theory with extended circuit design. This approach aims to support predictive modeling in high-density, near-field, and strongly coupled EM systems, including antennas and metasurface-based structures.