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Metamaterials (MTMs) are very promising in engineering applications because they can be used to easily manipulate the spatial and temporal distributions of electromagnetic fields and waves. Nevertheless, studies on MTMs have been directed primarily toward high-frequency electromagnetics and optics. Consequently, the development and applications for MTMs in low-frequency electromagnetics still face some bottleneck problems and challenges. For example, deteriorated resonance strength and large unit dimensions are inevitable for low-frequency MTM unit cells. Moreover, the existing analytical, computational, and experimental methodologies for MTMs are not applicable for low-frequency cases. To address these problems, one-dimensional compact stacking miniaturized MTM bulk in the kHz frequency band, which is the lowest resonance frequency for passive MTMs reported to date in the literature, is proposed and fabricated. This work develops a miniaturized and high performance low-frequency MTM unit cell using a unit topology that consists of two spiral structures connected with a via and a lumped chip capacitor. A numerical model is proposed for performance simulations of the MTM unit cell, and a quality factor equivalence-based method is introduced. An experimental–numerical methodology is developed to extract the complex permeability of the MTM bulk. Comprehensive numerical computations and experimental studies significantly impact the investigation of the extraordinary performance of MTM-based near-field electromagnetic devices. Both numerical and experimental results have confirmed the feasibility and applicability of the presented work, which reveals the extraordinary physical properties of novel MTM-based electromagnetic devices.

Metamaterials (MTMs) with extraordinary electromagnetic properties are recently applied to wireless power transfer (WPT) systems to improve power transmission efficiency. Although theoretical progress has been made on MTMs in low frequency near field, in the operation frequency of most WPT systems (usually MHz), the design of MTMs still utilizes the model used in high-frequency applications. Therefore, a practical model of MTMs in low MHz band is proposed in this work. The resonance frequency and quality factor are used to describe the characteristics of an MTM slab. The near field WPT systems with MTMs are then modeled as electric circuits, the system efficiency is explicitly deduced, and optimization algorithms are employed to optimize the MTM resonance frequency and maximize the system efficiency. The proposed practical model is validated via a prototype wireless power transfer system operating at 6.78 MHz. Experiments show that the proposed MTM model has good accuracy for low MHz WPT systems compared with the high-frequency model. The proposed practical model of MTMs provides an accurate way to analyze the performance of MTM at low MHz frequencies and greatly benefits the future exploitation of MTM-based low-frequency near field applications.

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