809 Copyright © 2009 IEICE EMC’09/Kyoto Modelling of Absorbing Material Containing Magnetic Platelets Marina Y. Koledintseva #1 , James L. Drewniak #2 , Yongxue He *3 , and Bill Matlin *4 # EMC Laboratory, Electrical and Computer Engineering Department, Missouri University of Science and Technology (MS&T), Rolla, Missouri, 65409-0040, U.S.A. 1 marinak@mst.edu; 2 drewniak@mst.edu * Laird Technologies 1200 E. 36 th St., Chattanooga, TN 37407, U.S.A. 3 yongxue.he@lairdtech.com; 4 Bill.Matlin@lairdtech.com Abstract— An analytical model for a composite material containing magnetic platelets is presented based on the modified asymmetric Bruggeman’s effective medium theory for permeability. The model takes into account crushing of bulk magnetic material and form factors of inclusions. Key words: magnetic platelets, permeability, shielding effectiveness I. INTRODUCTION Design of effective, compact, and economical non- conductive absorbing-type shielding materials is important for improvement of electronic equipment immunity in a wide frequency range. These materials are able to eliminate possible surface currents, which are culprits of undesirable emissions. Application of ferrites for developing absorbing materials is attractive, since they possess a unique combination of high permittivity, spontaneous magnetization, and extremely low d.c. conductivity [1-5]. When engineering ferrite-containing composites it is possible to control frequency dispersion of their complex permeability and permittivity by variation of chemical contents and crystalline structure of filler(s), size of inclusions, their concentrations, and morphology of mixtures through the alignment of inclusion particles. For absorption at frequencies above 2 GHz, hexagonal ferrite powders may be effective [6-8]. Hexaferrites have substantial internal field of crystallographic anisotropy and exhibit natural ferromagnetic resonance (NFMR) even without any bias magnetic field. For comparatively low-frequency applications, soft spinel ferrites (Ni-Zn, Mn-Zn, etc.), can be used [9-11]. They absorb electromagnetic energy due to a large P cc related to loss due to magnetic domain wall dynamics – relaxation and resonance. They have high permeability (up to several thousand) from d.c. up to a cut-off frequency determined by Snoek’s law [12]. This cut-off frequency, depending on the ferrite, is typically beyond a few dozen MHz [13]. Consequently, neither hexagonal ferrites, nor isotropically (arbitrarily, randomly) shaped spinels can effectively absorb energy in the frequency range from 100 MHz to 2.5 GHz, which is currently the most interesting range for high-speed electronics applications. However, if crystallographically “isotropic” particles of soft ferrites, like Ni-Zn, Mn-Zn, Mg-Zn, etc., are shaped as platelets, they may exhibit high field of form anisotropy due to demagnetization. This may substantially increase their frequency range of application in absorbing materials and overcome Snoek’s limit. It is important to have an analytical model to predict effective permeability of a composite that contains ferrite or conducting magnetic platelets (if concentration of the latter is less than percolation threshold, where the mixture may become conductive). In this model, an arbitrary concentration of magnetic inclusions is considered, assuming that they are either non-conductive (as ferrites), or coated with a dielectric shell (oxide) that prevents from electric percolation. At the same time, to avoid fragility, volume fraction of ferrite or magnetic material in a composite should not exceed ~50%. In this paper, it is assumed that platelet inclusions are oriented randomly, though their planes alignment might lead to some increase in static permeability. Alignment of magnetic inclusions may lead to their magnetic interaction and affect their domain structure, static magnetic properties, and high- frequency behavior. This will be a topic for another research. II. ANALYTICAL MODEL A. Crushed Magnetic Material- Isotropic Shape Inclusions Both permeability and permittivity of magnetic inclusions are considered frequency-dispersive. If there are ferrite (non- conductive) inclusions, then their permittivity would follow the Debye law [14] ( ) , 1 sf f f f fe j j H H H Z H ZW f f     (1) where sf H and f H f are static and “optic limit” permittivities of ferrite, respectively, and fe W is the Debye dielectric relaxation constant. If inclusions are conducting, their permittivity would be mainly imaginary, 0 ( ) , i m j j V H Z ZH  (2) 24P3-4