IEEE TRANSACTIONS ON MAGNETICS, VOL. 46, NO. 6, JUNE 2010 1687 Generalized Measurement Method for the Determination of the Dynamic Behavior of Magnetic Materials in Any Magnetization State Jorge Enrique Lezaca, Patrick Quéffélec, and Alexis Chevalier Lab-STICC UMR 3192, Université de Bretagne Occidentale, Université Européen de Bretagne, Brest, France A broad-band characterization method based on the junction of the full-wave analysis of a nonreciprocal strip transmission line with a predictive permeability tensor model is presented. The aim of this method is the direct measurement of the permeability tensor compo- nents spectra of magnetized thick samples, whatever their magnetization state is. The propagation constants of the dominant transverse electromagnetic (TEM) and higher order modes inside the measurement cell are obtained along with its scattering parameters (S-pa- rameters). The apparition of magnetostatic modes and the nonreciprocal nature of the structure are probed. Procedures based on the use of this method to find accurate values of gyromagnetic resonance and the resonance line width are proposed. The direct analysis is validated by comparison of the calculated S-parameters with those obtained with an electromagnetic field simulator based on finite element methods (FEM). Index Terms—Magnetic resonance, magnetic variables measurement, nonreciprocal wave propagation, permeability, scattering pa- rameters. I. INTRODUCTION F ERRITE materials are widely used for microwave appli- cations; their good insulating behavior in high frequencies and their static magnetic field-dependent permeability make them suitable for several signal processing functions. On one side, some reciprocal devices (tunable filters, commutators and phase shifters) are based on the variation of the microwave response of ferrites under the action of a static magnetic field. On the other side, nonreciprocal devices like isolators and circulators exploit the magnetic field-induced anisotropy of ferrites. Fig. 1 shows the different magnetization states (M) found in some of the microwave devices mentioned. The dynamic behavior of magnetized ferrites must be repre- sented by a tensorial quantity: the permeability tensor (1) (1) where , and are complex values, is the frequency and is the static magnetic field strength. In order to assist the design of this type of devices, the per- meability of magnetized magnetic materials must be fully char- acterized; that is why the need to develop a characterization method enabling the determination of the dynamic behavior of magnetized materials, whatever its magnetization state is. II. PREVIOUS WORKS Currently there are different methods to characterize mi- crowave magnetic materials. For the case of demagnetized Manuscript received October 30, 2009; revised December 15, 2009; accepted December 21, 2009. Current version published May 19, 2010. Corresponding author: J. E. Lezaca (e-mail: jorge.lezaca@gmail.com; zaca82@yahoo.com). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMAG.2009.2039776 Fig. 1. Magnetization states (M) for different microwave applications. materials transmission line-based methods are widely used [1]. For a magnetized sample, whose permeability is a tensor quantity, these methods give the effective scalar permeability (2) where and are the diagonal and off-diagonal components of the permeability tensor (1). This effective value (2) does not show neither the same magnitude nor the same gyromagnetic resonance frequency of the tensor components and in (1). For the case of saturated materials the cavity resonators are used [2]. These methods give the resonance line width (normally at 9.4 GHz) to characterize the losses of ferrites. Measurements of this parameter at high or low frequencies are impractical due to the cavities size constraints. Moreover, they are related to Polder’s formulations [3] of the permeability tensor components which are only valid for an infinite saturated medium. In practice ferrites are not always used in a saturated state (tunable filters, self-biased circulators, etc.), even in con- ventional circulators where non saturated regions appear in the ferrite puck as demonstrated in [4]. In such a context a broad-band characterization method has been developed in our laboratory [5]. This method is based on the use of a microstrip coupled with a generalized quasi-trans- verse electromagnetic (quasi-TEM) approach. Its domain of validity is limited from the theoretical point of view by the quasi-TEM approximation to 3 GHz. From the experimental 0018-9464/$26.00 © 2010 IEEE Authorized licensed use limited to: Universite de Bretagne Occidentale. Downloaded on June 02,2010 at 14:39:14 UTC from IEEE Xplore. Restrictions apply.