Q-Based Design Equations and Loss Limits for Resonant Metamaterials and Experimental Validation

• Published in: IEEE transactions on antennas and propagation Vol. 56; no. 1; pp. 127 - 132
• Main Authors: Cummer, S.A., Popa, B.-I., Hand, T.H.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.01.2008; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Applied classical electromagnetism; Complex media; Design engineering; Electromagnetic wave propagation, radiowave propagation; Electromagnetism; electron and ion optics; Equations; Exact sciences and technology; Frequency estimation; Frequency measurement; Fundamental areas of phenomenology (including applications); Magnetic materials; Magnetic resonance; Mathematical analysis; Metamaterials; Ohmic; Particle measurements; Permeability; Permeability measurement; Permittivity; Permittivity measurement; Physics; Q factor; Q measurement; Simulation; Studies; Tangents; Lower bound; Design criterion; Frequency dependence; Parameter estimation; Electromagnetism; Q factor; S-parameters; metamaterials; Complex media; Simulation; Quality factor; Analytical method; Permittivity; Metamaterial
• ISSN: 0018-926X; 1558-2221
• DOI: 10.1109/TAP.2007.912959

Practical design parameters of resonant metamaterials, such as loss tangent, are derived in terms of the quality factor Q of the resonant effective medium permeability or permittivity. Through electromagnetic simulations of loop-based resonant particles, it is first shown that the Q of the effective medium response is essentially equal to the Q of an individual resonant particle. This implies that by measuring the Q of a single fabricated metamaterial particle, the effective permeability or permittivity of a meta-material can be estimated simply and accurately without complex simulations, fabrication, or measurements. Experimental validation shows that the frequency-dependent complex permeability analytically estimated from the measured Q of a single fabricated self-resonant loop agrees with the complex permeability extracted from S parameter measurements of a metamaterial slab to better than 20 %. This Q equivalence reduces the design of a metamaterial to meet a given loss constraint to the simpler problem of the design of a resonant particle to meet a specific Q constraint. The Q-based analysis also yields simple analytical expressions for estimating the loss tangent of a planar loop magnetic metamaterial due to ohmic losses. It is shown that tan delta ap 0.001 is a strong lower bound for magnetic loss tangents for frequencies not too far from 1 GHz. The ohmic loss of the metamaterial varies inversely with the electrical size of the metamaterial particle, indicating that there is a loss penalty for reducing the particle size at a fixed frequency.