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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 describes a microwave measurement technique enabling the automatic and broad-band determination of the complex permeability tensor components [mu] [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 [mu] and [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 [mu] and [kappa] simultaneously in a wide range of frequency. Index Terms--Anisotropic media, ferrites, microwave measurements, permeability measurement.

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.

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.