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The theoretical approach proposed here was aimed at accurately describing the electromagnetic response of self-biased Y-junction circulators made of polycrystalline hexaferrites. The accuracy of circulator response was enhanced by considering the real magnetization state of the material through a calculation of the permeability tensor; this tensor remains valid whatever the strength of the local effective dc field in the ferrite is. Moreover, the hysteresis phenomenon was introduced in the calculation of tensor through the use of the Stoner and Wolhfart [IEEE Trans. Magn. 27, 3475 (1948)] law; as a consequence, the tensor took into account the privileged direction of easy-axis distribution due to the manufacturing process, which allowed us to treat the polycrystalline hexaferrites as being magnetically self-biased. However, the results issued from our approach indicate that this higher accuracy is at the expense of Y-junction circulator performances, which are far from those reported in the literature or obtained with electromagnetic commercial simulators and based on the frequent assumption of saturated hexaferrite, even at the remanent state. [ABSTRACT FROM AUTHOR]

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 dc 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. [ABSTRACT FROM AUTHOR]

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 carded 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. [ABSTRACT FROM AUTHOR]