Magnetic Field Penetration Into a Metal Enclosure Using an ELF/VLF Loop Antenna

Abstract

The ability of extremely and very low frequency (ELF/VLF, 0-30 kHz) radio waves to penetrate conductive media is well established. Magnetic field penetration into a thin but highly conductive box using an ELF/VLF loop antenna transmitter is investigated. The work is relevant for electromagnetic shielding of ELF/VLF sensors, defect detection, inductive power transfer, and through container imaging. Analytical solutions are reviewed for related shielding problems, however, determining the penetration through a realistic shield geometry and finite sized near-field source requires a numerical approach. Surface integral equation (SIE) methods are well suited for shield modeling due to the low surface area to volume ratio of the shield. Method of moment techniques have been successfully applied to solving SIEs in the past, however, enforcing algorithm stability at low frequencies is known to require considerable effort. To alleviate the low-frequency concerns, a high-order locally corrected Nyström (LCN) scheme is utilized to solve an SIE based on an augmented Müller formulation of Maxwell's equations. To validate the LCN simulations, an experiment is conducted using a loop antenna inside a 1.2 m aluminum cube of 2.7 mm thickness with an external ELF/VLF loop transmitter. Experimental results are shown to match within 3 dB of the LCN code predictions.