Evaluation of absorptive properties and permeability of thin sheet magneto-dielectric materials Marina Y. Koledintseva n , Victor V. Khilkevich, Alexander G. Razmadze, Aleksandr G. Gafarov, Soumya De, James L. Drewniak EMC Lab, Missouri University of Science & Technology, 4000 Enterprise Dr., HyPoint Industrial Park, Rolla, MO 65401, USA article info Available online 25 February 2012 Keywords: Coaxial line Electromagnetic absorber Magneto-dielectric Thin coating S-parameters Permittivity Permeability Attenuation abstract An analytical model to evaluate attenuation on the coaxial line with the central conductor coated with a magneto-dielectric layer is proposed and validated by the experiments and numerical modeling. This model is convenient for comparing absorptive effectiveness of different materials, as well as of different thicknesses and lengths of the same material. The proposed model also lays the basis for the technique to extract permeability of thin sheet magneto-dielectric materials by wrapping them around a central conductor of the coaxial airline. & 2012 Elsevier B.V. All rights reserved. 1. Introduction Thin absorbing layers containing magnetic alloy or ferrite inclusions are widely used to solve various problems of electro- magnetic compatibility/immunity, e.g., reduction of common- mode currents on extended structures, which could be sources of unwanted radiation. It is important to efficiently compare absorptive effectiveness of different materials, as well as of different thicknesses and lengths of the same material, and to extract frequency dependencies of permeability of those materi- als exhibiting pronounced magnetic losses. Herein, an analytical model to evaluate attenuation on the line with the central conductor coated with a magneto-dielectric layer is proposed, and it also lays the basis for the technique to extract permeability of thin sheet magneto-dielectric materials by wrapping them around a central conductor of the coaxial airline. 2. Analytical model The proposed analytical model based on finding a complex propagation constant g and the corresponding surface impedance Z s associated with the TM z mode propagating along a coaxial line. This is an air-filled line, but its central conductor is coated with a thin magneto-dielectric layer. Frequency characteristics of e and m are supposed to be measured in advance, e.g., as in [1]. The proposed model is based on the vector potential matching on the interfaces between conductor and lossy material, and lossy material and air, and on the rigorous solution of the transcen- dental equation for wave numbers for the modes propagating in the air region at the boundary with the lossy magneto-dielectric medium [2,3]. The attenuation of the quasi-TEM mode propagat- ing in the air-filled coaxial line with the coated central conductor (CCC) is analyzed using the concepts of surface displacement [4]. The effective per-unit-length (p.u.l.) RLGC parameters of the structure with the CCC, different from those in a coaxial line with an uncoated central conductor (UCC), are then extracted. The S-parameters for a section of the coaxial line with the CCC can be calculated using the transition from the RLGC parameters to the ABCD matrix parameters. A number of commercially available thin sheet noise-suppressing magneto-dielectric materials have been tested, and good agreement of measured and modeled frequency dependences of attenuation for all of them was obtained. In this paper, results are presented for one test sample. This approach allows for comparing absorptive properties of different thin sheet materials, as well as sheets of the same material, but of different thickness or length. This is important for developing a metric of attenuation due to the presence of the noise-suppression material on a conducting surface. The analy- tical results for the transmission coefficient (S 21 ) are also com- pared with the numerical simulations over the frequency range of interest (herein, 900 MHz to 14 GHz). The longitudinal electric field component is non-zero, when the electromagnetic field penetrates inside a non-perfect electric conductor. This leads to the appearance of the non-zero surface Contents lists available at SciVerse ScienceDirect journal homepage: www.elsevier.com/locate/jmmm Journal of Magnetism and Magnetic Materials 0304-8853/$ - see front matter & 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2012.02.049 n Corresponding author. Tel.: þ1 573 341 6659; fax: þ1 573 341 4532. E-mail address: marinak@mst.edu (M.Y. Koledintseva). Journal of Magnetism and Magnetic Materials 324 (2012) 3389–3392