Effective Complex Permeability Research Articles

The influence of ambient temperature and X-band frequency on EMI shielding performance of graphene/silica nanocomposites

The electromagnetic interference (EMI) shielding devices fabricated by graphene-based nanocomposites are constantly exposed to high temperature and X-band frequency during service, but at present no theory can account for such environmental effects. In this work, a micromechanics-based theory is developed to address the influence of temperature and X-band frequency on EMI shielding of graphene/silica nanocomposites. First, the temperature-dependent electromagnetic constitutive relations are established for both graphene and silica, and then the temperature-dependent electromagnetic interface effects, including electron tunneling and hopping for the conductivity and dielectric polarization and relaxation for the permittivity, are introduced. With these constituent and interface properties, the effective complex permittivity and permeability of the nanocomposite are evaluated through the effective-medium approximation. The EMI shielding effectiveness (SE) in the X-band range is calculated from Maxwell's equations under the near-field wave source. The predicted complex permittivity and EMI SE are shown to agree with the experiments of rGO/silica nanocomposites over 320–480 K and 8–12 GHz. The X-band EMI SE enhances with the increase of temperature due to the increase of reflection loss, and the temperature influence increases with the sample thickness. Several other novel attributes are also discovered.

Broadband Applications of a Tunable Nano-Rod Metaferrite

The rigorous analytical model of broadband effective electromagnetic response of the two-component metaferrite is presented in this study in the range up to THz frequencies. The metaferrite is a square array of ferric or ferromagnetic infinitely long cylinders of circular cross section symmetrically imbedded into homogenous isotropic dielectric host medium. It is assumed that the cylinders are fully or partially magnetized by a dc biasing magnetic field directed along the cylinder axes. Expressions of the complex effective permeability and permittivity tensors are obtained in the study. Expressions of the complex effective relative permeability and permittivity transverse to the direction of magnetization are derived and analyzed as functions of the frequency of incident electromagnetic wave and constitutive parameters of the metaferrite.It is shown that tuning a dc biasing magnetic field enables to effectively change the transmittivity and reflectivity of the metaferrites in the considered frequency range. We were also able to show that a layer of the metaferrite can be used for exciting surface plasmons at GHz frequencies. Finally, we have discussed the principal possibility of usage of the considered metaferrite for fabricating the substrates of miniaturized patch antennas with improved performance.

Fundamental Noise Limits and Sensitivity of Piezoelectrically Driven Magnetoelastic Cantilevers

Magnetoelastic sensors for the detection of low-frequency and low-amplitude magnetic fields are in the focus of research for more than 30 years. In order to minimize the limit of detection (LOD) of such sensor systems, it is of high importance to understand and to be able to quantify the relevant noise sources. In this contribution, cantilever-type electromechanical and magnetoelastic resonators, respectively, are comprehensively investigated and mathematically described not only with regard to their phase sensitivity but especially to the extent of the sensor-intrinsic phase noise. Both measurements and calculations reveal that the fundamental LOD is limited by additive phase noise due to thermal-mechanical noise of the resonator, i.e. by thermally induced random vibrations of the cantilever, and by thermal-electrical noise of the piezoelectric material. However, due to losses in the magnetic material parametric flicker phase noise arises, limiting the overall performance. In particular, it is shown that the LOD is virtually independent of the magnetic sensitivity but is solely determined by the magnetic losses. Instead of the sensitivity, the magnetic losses, represented by the material's effective complex permeability, should be considered as the most important parameter for the further improvement of such sensors in the future. This implication is not only valid for magnetoelastic cantilevers but also applies to any type of magnetoelastic resonator.

Behavioral Modeling of Complex Magnetic Permeability With High-Order Debye Model and Equivalent Circuits

In this article, a systematic procedure to derive equivalent circuit networks accurately reproducing the frequency response of the input impedance of magnetic cores in a broad frequency range is presented. The proposed procedure foresees to represent the effective complex permeability spectra of a magnetic core (i.e., the permeability resulting from the superposition of intrinsic material properties and effects due to structural features of the core) by a high-order Debye series expansion, which is subsequently synthesized into suitable Foster and Cauer networks. Such networks can be implemented in any circuit simulator, and are particularly favorable for time-domain transient simulation since they can be easily combined with hysteresis models. Two nanocrystalline tape-wound cores and a commercial bulk current injection probe are used as test cases to prove the effectiveness of the proposed method both in terms of accuracy and ease of implementation.

Computational Study and Experimental Verification of the Effective EM Properties of a Particle-Matrix Composite

We present a simulation of the effective electromagnetic (EM) parameters of a carbonyl iron (CI) powder - polyurethane (PU) composite based on a realistic micrometer-level 3-dimensional model by fractions. CI particles, 10 × 10 × 10, were randomly modeled in a PU matrix, and the optimized meshing condition was adapted to simulation. The calculated effective complex permittivity and permeability were compared with the classical mixing formulas and measurements of prepared CI-PU samples to verify the simulation results. Studies of the local EM field distribution and a parametric analysis of the composite revealed how the randomly distributed particles behaved differently than periodic particles. This study shows the possibility of designing a composite material based on a full-wave simulation.

Effective Medium Model of Periodic Nanolayered Transparent Shields

An innovative effective medium model based on the transfer matrix method is proposed for the simulation of 1D-periodic subwavelength metal–dielectric laminated structures excited by TM- or TE-polarized plane wave with oblique incidence angles. The homogeneous medium of each period is characterized by TM or TE complex effective permeability and conductivity. The resulting effective single layer (ESL), having the same total thickness of the multilayer laminate, is represented by a transfer matrix given by the product of the transmission matrices of the periods composing the structure. Notice that this model allows the homogenization of n -layer periods, while the effective medium approximation method is formulated for only two-layer periods. The ESL is used to compute the transmission and reflection coefficients and the shielding effectiveness of 1D-periodic nanolayered transparent coatings made by alternating layers of silver, zinc oxide, or titanium dioxide films, in the frequency range from 100 MHz up to 10 THz. The propagating wave performances of the ESL are compared with the ones given by the rigorous multilayer model. Finally, two different screens made of transparent coatings over glass are proposed and analyzed.

Electrodynamic Calculation of Effective Electromagnetic Parameters of a Dielectric Medium with Metallic Nanoparticles of a Given Size

The frequency dependence of the effective complex permittivity and effective complex permeability of a heterostructure based on a dielectric medium containing metallic nanoparticles of spherical shape is calculated by an original method. In contrast to the Bruggeman [21] and the Maxwell Garnett [17] approaches, which use the quasi-static approximation in calculations, a nonuniform distribution of electromagnetic fields inside metallic particles is calculated, which allows the analysis of the electromagnetic parameters of the heterostructure not only as a function of frequency but also as a function of the nanoparticle size. It is shown that the plasmon resonant frequency decreases with increasing both the size and the concentration of particles in the heterostructure. It is also shown that a dielectric medium containing nonmagnetic metallic nanoparticles exhibits diamagnetic properties. In this case, the position of the maximum on the frequency dependence of the imaginary part of the magnetic susceptibility coincides with the relaxation frequency of charge carriers. The calculated spectra of the real and imaginary components of the permittivity of the heterostructure with a size of metallic particles less than 10 nm are in good agreement with Bruggeman calculations; however, the agreement with Maxwell Garnett calculations is observed only at nanoparticle concentrations lower than 10–6.

Probing split-ring resonator permeabilities with loop-gap resonators

A method is proposed to experimentally determine the effective complex permeability of split-ring resonator (SRR) arrays used in the design of metamaterials at microwave frequencies. We analyze the microwave response of a loop-gap resonator (LGR) whose bore has been partially loaded with one or more SRRs. Our analysis reveals that the resonance frequency, magnetic plasma frequency, and damping constant of the effective permeability of the SRR array can be extracted from fits to the reflection coefficient (S11) of an inductively coupled LGR. We propose LGR designs that would allow both a one-dimensional array of SRRs and small three-dimensional arrays of SRRs to be characterized. Finally, we demonstrate the method using a toroidal LGR loaded with a single extended SRR of length z.

Effective High-Frequency Permeability of Compacted Metal Powders

We propose a model for determination of the effective complex permeability of compacted metal-powder media. It is based on the equality of the magnetic moment in a given volume of the media with the desired effective permeability to the total magnetic moment of metal particles in the external high-frequency magnetic field, which arises due to excitation of electric eddy currents in the particles. Calculations within the framework of the proposed model allow us to refine the values of the real and imaginary components of the permeability of metal powder compacts in the microwave band. The conditions of applicability of the proposed model are formulated, and their fulfillment is verified for metal powder compacts in the microwave and millimeter wavelength bands.

WITHDRAWN: Study of Composite material on volume fraction using analytical Model

Abstract In order to solve the practical engineering problem in calculating the effective permittivity and permeability of composites, this paper introduced the dilution process model (DPM) which sets the composite with the highest particle volume concentration as new matrix medium. With DPM, complex permittivity and permeability of composites could be calculated by using the Maxwell Garnett (MG) formula, the Bruggeman (BG) formula and the generalized effective medium theory (GEMT) with a fitting parameter of V which is a second-degree polynomial of new particle volume fraction. With the proposed method, the effective complex permittivity and permeability of composites consisting of isotropic spherical carbonyl iron particles or the anisotropic carbonyl iron particles embedded in the paraffin are calculated and comparisons between calculated results and experimental results are made. The results indicate that the calculated results using the GEMT formula with DPM are in better agreement with the measured results than that using the MG formula and BG formula. The achievement of this paper has important theoretical significance and engineering application value.

Calculating the Effective Permittivity and Permeability of Composites Based on the Dilution Process Model

In order to solve the engineering problem of calculating the effective permittivity and permeability of composites, this paper introduced a dilution process model (DPM) which sets the composite of the highest particle volume fraction as the new matrix medium and the old matrix medium as the inclusion. With DPM, complex permittivity and permeability of composites could be calculated by the Maxwell Garnett (MG) formula, the Bruggeman (BG) formula and the generalized effective medium theory (GEMT) with a fitting parameter of V which is a second-degree polynomial of new particle volume fraction. With the proposed method, the effective complex permittivity and permeability of composites consisting of isotropic spherical carbonyl iron particles (SCIPs) or anisotropic flaky carbonyl iron particles (FCIPs) embedded in paraffin are calculated. Comparisons are performed among the calculated results by different formulae and the measured results. It indicates that the calculated results by the GEMT formula with DPM are in great agreement with the measured results. The achievement of this paper has am important theoretical significance and engineering application.

Engineering approach to calculate the effective permeability of a composite material with unbiased ferrimagnetic nanoparticles

A step-by-step engineering approach offering a model for the characterization of magnetic composite materials is presented. The modelling of composite materials containing unbiased ferrites is a subject of great interest, due to extended range of applications, such as hyperthermia and microwave absorbers. Here, unbiased ferrites simplify the application structure, as they do not require a biasing field, while they can resonate at low microwave frequencies due to their innate magnetocrystalline anisotropy field. However, so far there has not been an explicit organized step-by-step engineering modelling approach. The homogenization approximation formula is used in conjunction with Landau–Lifshitz–Gilbert equation solution to systematically compute the complex effective permeability and compare it with published measurements, from an engineer's result-focused perspective. For further validation, simulations of these composite materials as periodic structures are carried out, which additionally provide useful insight on the electromagnetic field distributions within the composites and are often more accurate. The results of the proposed procedure show good agreement with the experimental ones, which validate it, while the relatively greater error appears for the imaginary parts. The EM field distributions suggest that better focusing around the nanoparticles is achieved when those are large enough to form magnetic domains.

Tunable Electromagnetic and Microwave Absorption Properties of Ba3Co2Fe24O41/P(VDF-TrFE) Composites

The electromagnetic and microwave absorption properties of polymer-based Ba3Co2Fe24O41/P(VDF-TrFE) composites were investigated. The effective complex permeability and permittivity of the two-phase composites can be manipulated by either varying the Ba3Co2Fe24O41 content or applying the dc magnetic field ( H dc). The composite containing 90 wt% Co2Z obtains a maximum reflection loss (RL) due to a proper impedance match and relatively high magnetic loss. In addition, it is found that the position of RL peak was tuned from 5.5 to 7 GHz with H dc up to 50 mT, whereas the intensity obtains a remarkable enhancement of 67% at 15 mT. These results reveal great potential for the applications of ferroelectric–ferromagnetic composites with tunable microwave absorption.

Dielectric and magnetic properties of substituted Li–Zn ferrite thick films clouded over a half wavelength microstrip rejection filter

Li0.35–0.5xMgxZn0.3Fe2.35–0.5xO4 nanoparticles (x = 0, 0.14, 0.28, 0.42, 0.56, and 0.70) were prepared by low-cost combustion synthesis at relatively low temperature. Thick films of Li–Mg–Zn ferrite were prepared by screen printing method and characterized by XRD and microwave characteristics at microwave frequencies (within X- and Ku-bands) by overlay technique using λ/2 rejection filter. The influence of magnesium content x on the resonance frequency, quality factor, effective dielectric constant, complex permittivity, complex permeability, microwave conductivity, and penetration depth was explored.

Enhanced microwave absorption of multiferroic Co2Z hexaferrite–BaTiO3 composites with tunable impedance matching

The microwave absorbing properties of multiferroic particulate composites consisting of Co2Z hexaferrite and BaTiO3 (BT) were investigated over a frequency range of 2–18GHz. The effective complex permeability and permittivity of Co2Z–BT composites are shown to be effectively manipulated by varying the weight ratio of the two phases, which consequently demonstrates a strong tunability in the optimal working frequency and minimum reflection loss (RL). For the optimal Co2Z–10BT composite, the RL peak at a thickness of 2.0mm was enhanced by 97.8% in comparison with that of the single phase Co2Z hexaferrite. Moreover, the impedance-matched RL characteristics below 10GHz show a substantial improvement in both thickness and bandwidth with increasing BT content. This work clearly shows the potential to tune the impedance matching and microwave absorption performances of multiferroic composites.

Broadband impedance-matched electromagnetic structured ferrite composite in the megahertz range

A high refractive-index structured ferrite composite is designed to experimentally demonstrate broadband impedance matching to free-space. It consists of an array of ferrite cubes that are anisotropically spaced, thereby allowing for independent control of the effective complex permeability and permittivity. Despite having a refractive index of 9.5, the array gives less than 1% reflection and over 90% transmission of normally incident radiation up to 70 MHz for one of the orthogonal linear polarisations lying in a symmetry plane of the array. This result presents a route to the design of MHz-frequency ferrite composites with bespoke electromagnetic parameters for antenna miniaturisation.

Microwave characterization of vertically aligned multiwalled carbon nanotube arrays

Vertically aligned multiwalled carbon nanotube (VACNT) films have been characterized by rectangular waveguide measurements. The complex scattering parameters (S-parameters) are measured by a vector network analyzer at X-band frequencies. The effective complex permittivity and permeability of the VACNT films have been extracted. The extracted parameters are verified by full wave simulations and very good agreement has been obtained. The results of the systematic error analysis are presented and the errors are within the acceptable range. The performance of VACNT films as an absorber is examined, and comparison with the conventional carbon loaded materials shows that a 90% size reduction is possible while maintaining the same absorption level.

Complex permeability and microwave absorption properties of planar anisotropy Ce 2Fe 17N 3−δ particles

The effective complex permeability of Ce 2Fe 17N 3−δ particles/epoxy resin composites with various volume concentrations p were measured in the frequency range of 0.1–15 GHz. The intrinsic quasi-static permeability μ ′ 0 , i of Ce 2Fe 17N 3−δ particle was calculated by Bruggerman's (BG) effective medium theory. Meanwhile, the effective quasi-static permeability μ ′ 0 , e of composites were calculated by the BG theory and modified Bruggerman's (MBG) effective medium theory, respectively. Through analyzing the experiment data, the effective shape factors of Ce 2Fe 17N 3−δ composites were determined. The intrinsic natural resonance frequency of Ce 2Fe 17N 3−δ was obtained using Landua–Lifshitz–Gilbert (LLG) equation. The minimum EM absorbing values with RL ≤ −30 dB are observed for all the volume concentrations.

The Influence of Complex Permeability on the Broadband Frequency Response of a Power Transformer

This paper considers the effect of the complex permeability of a power transformer core on the frequency response analysis (FRA) test spectrum. Current work in FRA generally neglects the core beyond a few hundred kHz. This research demonstrates that the effective complex permeability is significant at 1 MHz and greater than unity at frequencies exceeding 15 MHz. The paper also shows that for broadband small signal testing, such as FRA, the low field conditions induced by the injected signal result in a relative permeability that approaches the initial permeability of the core. This ensures that the relative permeability remains approximately constant over a large range of frequencies and will have a degree of independence with respect to the amplitude of the injection voltage.

Synthesis and microwave electromagnetic properties of CoFe alloy nanoflakes prepared with hydrogen-thermal reduction method

CoFe alloy nanoflakes (NFs) with diameter and thickness on nanoscale were prepared by hydrogen-thermal reduction in CoFe2O4 flakes at 400 °C for 60 min. The effective complex permittivity and permeability of CoFe alloy NFs/paraffin composites were measured and compared with that of CoFe alloy nanoparticles (NPs)/paraffin composites. Due to the two-dimensional shape character, the real part of permittivity and permeability of CoFe alloy NFs was rather higher than that of CoFe alloy NPs. Electromagnetic wave absorbing (EMA) performance of both CoFe alloy NFs and NPs was evaluated by using transmission line theory. The effective EMA band position of the coating with CoFe alloy NFs as fillers was found to locate in the range of 2–4 GHz, while the effective EMA band position of the coating containing CoFe alloy NPs as fillers was located in the range 8–18 GHz. A maximum reflection loss (RLmax) of −57.8 dB was achieved in a coating containing CoFe alloy NFs as fillers, which is much higher than the −16.6 dB of coatings with CoFe alloy NPs.