Complex Permeability Tensors Research Articles

Microwave Measurements of Electromagnetic Properties of Materials.

A review of measurement methods of the basic electromagnetic parameters of materials at microwave frequencies is presented. Materials under study include dielectrics, semiconductors, conductors, superconductors, and ferrites. Measurement methods of the complex permittivity, the complex permeability tensor, and the complex conductivity and related parameters, such as resistivity, the sheet resistance, and the ferromagnetic linewidth are considered. For dielectrics and ferrites, the knowledge of their complex permittivity and the complex permeability at microwave frequencies is of practical interest. Microwave measurements allow contactless measurements of their resistivity, conductivity, and sheet resistance. These days contactless conductivity measurements have become more and more important, due to the progress in materials technology and the development of new materials intended for the electronic industry such as graphene, GaN, and SiC. Some of these materials, such as GaN and SiC are not measurable with the four-point probe technique, even if they are conducting. Measurement fixtures that are described in this paper include sections of transmission lines, resonance cavities, and dielectric resonators.

A probabilistic model for the interaction of microwaves with 3-dimensional magnetic opal nanocomposites

The complex diagonal and off-diagonal components of the effective permeability tensor were calculated for the case of a realistic 3D opal, infiltrated with Ni0.7Zn0.3Fe2O4 nanoparticles. First, an accurate electrodynamic effective medium permeability tensor approach is formulated. Next, Maxwell`s equations were solved rigorously for the case of an interacting systems of ferrite particles in the opal matrix, having a normal distribution of the ferromagnetic resonance fields. The method is demonstrated by calculating the bias field dependence of the components of the complex permeability tensor at 26 GHz, and a good agreement with recent experimental data was obtained.

A modified model of GMI effect in amorphous films with transverse magnetic anisotropy

Compared with a simple model of giant magneto-impedance (GMI) effect in amorphous films we proposed recently (J. Magn. Magn. Mater. 250 (2002) 288), a new modified model by introducing a longitudinal residual stress and a three-dimensional magnetic field, and thus the expressions of complex permeability tensor and impedance are more accurately deduced. The numerical calculation illustrates that the agreement between the simulation results and experimental data is more satisfactory. Besides, the dependence of GMI effect on the frequency of alternating current and the thickness of the film is discussed with the present model, showing results similar to experiments.

Automatic measurement of complex tensorial permeability of magnetized materials in a wide microwave frequency range

This paper describes a microwave measurement technique enabling the automatic and broad-band determination of the complex permeability tensor components /spl mu/, /spl kappa/ of magnetized materials. The method is applicable to ferrites, as well as magnetic composite materials. The measurement cell is composed of a nonreciprocal strip transmission line partly filled with the sample that is to be characterized. The data-processing program based on a quasi-static approach is valid whatever the magnetization state of the material is from the total demagnetization state to the saturation. The scattering matrix of the cell is measured in a wide frequency range (130 MHz-6 GHz) with a network analyzer setup. The stripline is set in the air gap of an electromagnet to magnetize the material. The electromagnetic parameters of the sample under test are deduced from the scattering matrix using analytical relations. General equations for /spl mu/ and /spl kappa/ are proposed. Some measurements of magnetized ferrites are reported and compared with values predicted by Polder's relations to validate the technique in the saturation state. To our knowledge, this is the first noniterative measurement method giving /spl mu/ and /spl kappa/ simultaneously in a wide range of frequency.

New method for determining the permeability tensor of magnetized ferrites in a wide frequency range

To provide a broadband method for measuring the complex permeability tensor components of magnetized ferrites we have realized a nonreciprocal rectangular waveguide cell. A network analyzer setup is used to measure the scattering parameters of the cell over a wide range of frequencies. The nonreciprocity of the cell permits the determination of the permeability tensor components in a single experimental phase. Complex permittivity and complex components of the permeability tensor are computed from a data-processing program, taking into account higher order modes excited at the cell discontinuities and using a numerical optimization procedure to match calculated and measured values of the S-parameters. We have studied the convergence of the calculated S-parameters as the number of modes taken into account in the calculations. Sensitivity to the input parameters for the optimization algorithm is discussed. A thru-reflect-line calibration in conjunction with a specific sample holder is used to eliminate systematic errors inherent in the S-parameter measurements. Measured complex permeability tensor components data for microwave ferrites are presented at X-band frequencies (8-12 GHz). Experimental results are in good agreement with theoretical results given by the ferromagnetic material theory.

Nonreciprocal cell for the broadband measurement of tensorial permeability of magnetized ferrites: direct problem

In this paper, a broad-band characterization method for measuring the complex permeability tensor components and complex scalar permittivity of magnetized ferrites is described. The technique is based on the reflection/transmission measurement of a rectangular waveguide partly filled with the ferrite that is to be characterized. The fundamental principle of the measurement consists in using the anisotropy of the material to lead to the nonreciprocity of the device in order to have the same number of measurable parameters (the S-parameters of the cell) for the characteristics we want to determine. Here, we will recall the principle of the mode-matching method used for the electromagnetic analysis of the cell (direct problem). We will bring to the fore the difficulties linked to the determination of the complex propagation constants of the different modes and will present a calculation procedure that makes this determination in a wide-frequency range easier. We will then compare at X-band frequencies (8-12 GHz) the theoretical S-parameters with those measured for ferrites of well-known properties in order to validate the direct problem. The determination of the permittivity and permeability values from the measured parameters (inverse problem) is not addressed here.

Broad-Band Measurement of all Complex Permeability Tensor Components and Complex Permittivity of Ferrites using a Rectangular Waveguide

We have worked out a broad-band characterization method for magnetized ferrimagnetic materials. The technique is based on the reflection/transmission measurement of the S-parameters of a rectangular waveguide partly loaded with a ferrite that is to be characterized. The device is set in between the poles of an electromagnet to magnetize the sample. The fundamental principle of the measurement consists in using the anisotropy of the material to lead to the non-reciprocity of the cell (S 11 ¬=S 22 and S 21 ¬=S 12 ) in order to have the same number of information that for the characteristics we want to determine (complex permittivity and all complex permeability tensor components). In this paper, we will compare in the X-band (8 - 12.4 Ghz) the theoretical S-parameters of the cell with those measured by the network analyzer for different ferrites of well-known properties in order to validate the electromagnetic analysis of the cell. We will underscore the importance of the losses which are entirely responsible for the non-reciprocity of the S-parameters modulus. To conclude we will suggest a strategy to resolve the inverse problem with an optimization method.

A new frequency domain symmetrical condensed TLM node

This paper reports the development of a new symmetrical condensed TLM node derived directly in the frequency domain. The new node can accommodate a graded mesh and can model lossy anisotropic media described by a static conductivity tensor along with complex permittivity and complex permeability tensors. The frequency domain TLM method is used to generate modal dispersion curves for microwave and millimeter wave guiding structures. The results compare the new node to existing time domain symmetrical condensed nodes. >

Measurements of all complex permeability tensor components and the effective line widths of microwave ferrites using dielectric ring resonators

A method of measuring all the complex permeability tensor components of microwave ferrites using a single cylindrical ferrite sample is described. Two dielectric ring resonators having the same height and internal diameter but different external diameters, operating on HE/sub 111//sup +or-/ and H/sub 011/ modes respectively, are applied for these measurements. Permeability tensor components are computed from the measured resonant frequencies and Q factors of these resonators with and without the ferrite sample. Computations are based on the exact eigenvalue equations for these modes. Measurements of all permeability tensor components versus static magnetic field intensity, performed for different ferrite materials, generally confirm results obtained by earlier researchers, but they also contain certain aspects concerning relations between particular permeability tensor components below saturation.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Acoustic multipole logging in transversely isotropic poroelastic formations

The properties of the modes generated by multipole sources in a fluid-filled borehole embedded in (radially layered) formations that include transversely isotropic poroelastic layers are investigated. These layers are modeled following Biot’s and homogenization theories, under the assumption that the principal axes of symmetry of both the transversely isotropic skeleton and the complex permeability tensor are parallel to the vertical axis of the borehole. A general formulation based on the Thomson–Haskell method accounts for any combination of fluid, elastic, and poroelastic layers, either isotropic or transversely isotropic. The investigation is achieved through the computation of dispersion and attenuation curves, and frequency-dependent sensitivity coefficients with respect to the parameters. In the presence of a fast or slow radially semi-infinite transversely isotropic poroelastic formation with an impermeable borehole wall, the shear-wave transverse isotropy of the skeleton can be determined using the low-frequency parts of the fundamental modes generated by a monopole source and one of higher order. With a permeable interface, the fluid flow effects refer to the horizontal mobility (horizontal permeability/saturant fluid viscosity) and disables the determination of the shear-wave transverse isotropy. Without this information, any horizontal mobility determination is incorrect. Whatever the nature of any fluid–poroelastic interface, the presence of radial layering decreases the reliability of any estimation of parameter related to the virgin formation except for the velocity and attenuation of the vertically propagating SV wave. Whatever the configuration, the transverse isotropy of the compressional wave velocity cannot be determined nor can that of the complex permeability tensor or the anelastic attenuation due to the polarization of the (quasi) body waves involved. The results of this work also show that, in contrast to the pure elastic situation, a transverse isotropy of the complex permeability tensor leads to slightly different quasi-SV-wave velocities along the principal directions of propagation at ultrasonic frequencies.

Selection of ferrite materials for microwave device applications

This paper deals with some general rules for selecting materials for linear ferrite devices. Four steps are required for material definition. 1) An analysis which relates device performance to the intrinsic complex permeability tensor [μ] and to the complex permittivity <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\epsilon = epsilon' - j\epsilon"</tex> of the material. 2) A determination of the internal biasing field in the ferrite from the applied biasing field and shape-dependent demagnetizing factors. 3) An estimate of the required saturation magnetization M <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</inf> based on a consideration of lowest operating frequency, peak RF power level, and maximum desirable biasing field. 4) A specification of ferrite composition and mechanical properties resulting from consideration of magnetic loss, temperature-dependence of the device, peak-power capability, and mechanical stability. Materials selection is done from the particular ferrite system which comes closest to the required saturation magnetization and offers the best compromise with respect to magnetic loss, temperature stability, and peak-power handling capability.