Modeling of the ferrite for microwave applications

Modeling the electromagnetic (EM) properties of ferrites placed in their application environment (circulator, isolator, phase shifter, miniature antenna, tunable filter, etc.) remains, despite the current abundance of software on offer, a tricky step for the microwave device designer. To understand this, we must first recall a specificity of these materials: their response to EM excitation depends on their shape, and varies within the material as soon as its shape differs from the ellipsoid of revolution, which is most often the case in practice with the common use of wafers, washers, toroids, thick films or thin layers. To date, no commercial EM simulator is capable of describing a ferrite integrated into a circuit with sufficient realism to avoid the "cut and try" approach that component manufacturers now follow, in spite of themselves. Indeed, in the absence of accurate simulation tools, the engineer in charge of optimizing the performance of a ferrite device has to make many costly round trips between the design and production phases.

Various models have been developed in the past to predict the dynamic behavior of magnetic materials as a function of signal frequency and applied static bias field strength. Unfortunately, the validity of these models is limited to specific magnetization states, and none of them takes into account hysteresis or the polycrystalline nature of the materials used.

To fill this gap, we have proposed a new theoretical approach with the aim of predictively calculating, whatever the magnetization state of the ferrite, its permeability, which is a tensor quantity as soon as the material is polarized. With reference to the state of the art, the advantage of the model developed, in addition to its general character linked to its ability to handle any type of polarization (demagnetized, partially magnetized, saturated, remanent states), lies in three key features. It quantitatively takes into account: (i) the dynamic interactions between magnetic domains and between grains, known as the Polder-Smit effect; (ii) the hysteresis phenomenon, by linking the internal magnetization of the medium to the external static field applied; (iii) the shape of the sample, through rigorous calculation of the demagnetizing field. The validity of this model has been demonstrated by comparison with experiments. However, before engineers can use it in the design of microwave devices, there is an important step to be taken: its integration into an EM simulator. First, the permeability model needs to be adapted for local use within each mesh of the EM simulator. This work constitutes the first section of this article.

The second section describes how to process the data from the general tensor permeability model so that it can be used with...