Search

We describe a theoretical approach for determining the permeability tensor of polycrystalline ferrites regardless of their magnetization state. To take into account both the demagnetizing dynamic fields related to the magnetic domain and grain shapes and the magnetic interactions between adjoining domains and between adjoining grains, we transform the classical Landau-Lifschitz-Gilbert equation into a coupled two-equation system. We introduce statistical distribution laws for both the domain and grain demagnetizing coefficients into the calculation to take the domain and grain shape diversity into account and derive static vectorial quantities such as the internal magnetic dc field and magnetization in each domain that depends on the applied de magnetic field from the Stoner-Wohlfarth hysteresis model. We compare results with those for existing models for various magnetized states. Then we apply the model to predict the permeability tensor behavior of barium hexaferrite thin film, especially in the remanent state, which is of great interest for the design of self-biased Y-junction circulators in the millimeter-wave range. Index Terms--Anisotropic media, ferrites.

This paper describes a mathematical model enabling the calculation of the effective permeability tensor of heterogeneous magnetic materials set in various magnetization states. The theoretical approach we propose permits to predict the microwave behavior of unsaturated magnetic loaded composites as well as those of unsaturated polycrystalline ferrites. The model gives all the complex components of the permeability tensor in a single calculation phase whatever the magnetization state of the material is. This is useful for the computer-aided design of microwave magnetic devices. The calculation of the effective permeability tensor is carried out from a limited number of parameters: saturation magnetization, anisotropy field, damping factor, external dc field strength, concentration, and shape of the magnetic particles or domains. The model is predictive in the way that the magnetization state of the material is determined from the strength of the external dc magnetic field applied on the material. Index Terms--Magnetic anisotropy, magnetic hysteresis, nonhomogeneous media, permeability.

We compare the diagonal [micro] and off-diagonal [kappa] permeability tensor components of magnetized polycrystalline ferrites given by the theoretical model of Gelin and Berthou with experimental ones at microwave frequencies. We used a broad-band and noniterative measurement technique recently developed within our research group. Whatever the ferrite magnetization state is, simulated and measured [micro] and [kappa] points agree well. This study provides an experimental validation of the Gelin--Berthou model. Moreover, by using this characterization method, we show how the measurement of the magnetic properties can be affected by the size of the ferrite sample under test. Index Terms--Anisotropic media, demagnetizing fields, ferrites, permeability, scattering parameters.

This paper presents a physical model of the properties of polycrystalline ferrites below magnetic saturation, a common condition in many applications of ferrites in microwave devices. The properties are mainly characterized through the elements of the effective permeability tensor as functions of magnetization state, anisotropy field, and frequency. Partially magnetized states are characterized by a suitable distribution of magnetic domains over orientations. The magnetic domain shapes studied were cylinders and spheres. Homogeneity of the medium is obtained in the effective medium approximation, which allows us to treat heterogeneous magnetic materials as a function of the volume fraction of nonmagnetic matter present in the material. The model gives all the components of the permeability tensor in a single calculation phase. The paper presents results for different partially magnetized states at remanence (with no external field applied) and compares them with empirical formulations of permeability tensor components, in their domain of validity. Index Terms--Anisotropic media, ferrimagnetic materials, ferrites, permeability.

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. Index Terms - Anisotropic media, ferrites, microwave measurements, permeability measurement, waveguide discontinuities.

This paper outlines the finite-difference time-domain (FDTD) treatment of partially magnetized ferrites characterized by a permeability tensor model, which was recently published [15]. Its causal aspect makes this tensor well adapted to time-domain simulations. Validation is demonstrated for a resonant ferrite structure. Numerical and analytical results are compared, showing good agreement. Index Terms - FDTD, ferrite.

Partially magnetized ferrites play an important role in a large class of microwave devices. For instance, when the optimal design of circulators, which operate with ferrite in the low magnetic field region, and other ferrite devices (phase shifters, isolators etc.) are considered, permeability tensor is required for arbitrary magnetization. The existing models do not simultaneously provide all tensor components, and their validity domain is limited. The proposed model provides integral expressions for all permeability tensor components, which can be treated numerically without difficulties. The physical nature of the model enforces the causal aspect that is required when numerical time-domain methods (such as finite-difference time domain (FDTD), transmission-line matrix (TLM), time-domain finite-element method (TDFEM), etc.) are used. Finally, the comparison with measurements or specific cases, which can be treated by available models, demonstrates the validity of the proposed approach.

In order to examine guided wave propagation in unsaturated magnetized materials, it seems reasonable to consider an alternation of layers with antiparallel magnetization in a rectangular waveguide. This approach is coherent with Schlomann's model [1] which considers partially magnetized ferrites as an alternation of antiparallel coaxial cylinders. The finite-difference time-domain (FDTD) method had been used in the case of an homogeneously filled rectangular waveguide. It is adapted here to a guide partially filled with two antiparallel magnetization layers. The modification of the FDTD algorithm at the air/ferrite and ferrite/ferrite interfaces is presented. Results are compared with the ones obtained by a mode-matching technique.

The accurate electromagnetic analysis of discontinuities in a microstrip device, used for the broad band measurement of complex permittivity and permeability of materials, is presented. This analysis is based on the spectral domain approach together with the mode matching method which consists in the electromagnetic field matching at the discontinuities for each mode of the microstrip line. The study of the influence of higher order modes on the S-parameter measurements enabled us to determine the domain of validity of the transmission-line theory that has been used until now in the processing of the data. The use of the transmission-line theory for the description of the electromagnetic behavior of the cell discontinuities permits in the 45 MHz-14 GHz frequency band the achievement of a good precision (better than 5%) for the results on materials with low electromagnetic characteristics ([Epsilon][prime] 10 and [Mu][prime] < 10). The improvement in high frequencies of the results on materials with greater permittivity and permeability is provided by the calculation of higher order modes (about 10) in the analysis of the microstrip discontinuity.

The method presented here aims at determining the complex permeability [[Mu].sup.*] and permittivity of [[Epsilon].sup.*] with an automatic and broad band (45 MHz-18 GHz) system from the reflection-transmission measurement of the S-parameters of a microstrip test device. The complex values [[Epsilon].sup.*] and [[Mu].sup.*] are obtained with the S-parameters from a specific software created within the context of this work. Compared with previous methods, our measurement technique is fast, easy to implement and does not require any calibration test sample or pick-up coils. Lastly, an analysis of the error depending on the method used and the results found with bulk isotropic materials (dielectrics and ferrites) are presented.

The measurement method presented here permits the determination of the complex permeability [Mu]* and permittivity [Epsilon]* of rectangular samples of various thicknesses (0.1 [micro]m-1800 [micro]m) over the (130 MHz-7 GHz) frequency band. This method is based on the S-parameters measurements of an asymmetrical stripline containing the sample under test. It does not require any magnetic reference sample. The originality of this method is to reproduce the same environment for the material under test as encountered in microwave devices. The results given by this 'in situ' measurement technique are more useful to design microwave devices than those given by traditional measurement methods. Index Terms--Magnetic materials, permeability measurement, stripline, thin films.

To provide a broad-band 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. Index Terms--Anisotropic media, ferrites, inverse problem, microwave measurements, permeability measurement, waveguides.