A unified equation linking electrode geometry, dielectric material properties, excitation frequency, and load conditions to capacitive coupling power output

Capacitive coupling through dielectric barriers represents an important mechanism for electrical energy transfer between electrically isolated systems. This study presents a theoretical and conceptual framework for a low-cost dielectric-barrier capacitive coupling structure constructed using conductive foil electrodes separated by an insulating medium such as wax or polymer dielectric layers. The proposed configuration is intended to investigate field-mediated electrical energy transfer in systems where direct conductive pathways are unavailable or undesirable. The model is formulated using classical electrostatic and electromagnetic field theory. When a voltage is applied to the primary electrode, an electric field is established across the dielectric barrier, resulting in dielectric polarization and induced charge redistribution on the secondary electrode. Under time-varying excitation conditions, displacement current can propagate through the electric field across the dielectric interface, enabling capacitive energy coupling between the two electrically isolated circuits. The coupling strength and resulting electrical response are governed by the effective capacitance of the structure, expressed as C=εrε0A/d where AA represents the effective electrode overlap area, d is the dielectric thickness, and εr is the relative permittivity of the insulating medium. The frequency-dependent behavior of the system is characterized by capacitive reactance XC=1/2πfC which determines the magnitude of displacement current and the achievable coupling efficiency under alternating or pulsed excitation conditions. The proposed framework systematically analyzes the influence of electrode geometry, dielectric material properties, barrier thickness, excitation frequency, and load impedance on coupling efficiency and power transfer capability. Preliminary theoretical analysis indicates that increasing electrode area, reducing dielectric thickness within safe breakdown limits, and operating at higher excitation frequencies can significantly enhance capacitive coupling strength. This work does not propose energy generation or violation of conservation laws; instead, it provides a physically consistent theoretical basis for investigating dielectric-mediated electrical coupling mechanisms. The conceptual framework may support the development of low-cost capacitive coupling systems for applications such as insulated signal transmission, electrostatic sensing, contactless energy transfer prototypes, and educational demonstrations of electromagnetic field-based energy interaction. Future work will involve controlled experimental validation including capacitance measurement, dielectric leakage characterization, frequency response analysis, and load-dependent power transfer evaluation to determine the practical performance limits of the proposed dielectric-barrier coupling architecture. Please check the attachment for details