Finite difference coefficient

Polder tensor is a tensor used in description of magnetic permeability of ferrites. The tensor notation needs to be used because ferrimagnetic materials become anisotropic in the presence of magnetizing field.

The tensor is described mathematically as:

$B=\left[\begin{array}{ccc}\mu & j\kappa & 0\\ -j\kappa & \mu & 0\\ 0& 0& {\mu }_0\end{array}\right]H$

where:

$\mu ={\mu }_0(1+\frac{{\omega }_0{\omega }_m}{{\omega }_0^2-{\omega }^2})$

$\kappa ={\mu }_0\frac{\omega {\omega }_m}{{{\omega }_0}^2-{\omega }^2}$

${\omega }_0=\gamma {\mu }_0{H}_0$

${\omega }_m=\gamma {\mu }_{0}M$

and $\gamma =17.6\cdot g$ [kHz/(A/m)] is a gyromagnetic ratio and g is a factor between 1.9-2.4 depending on ferrite material. Magnetizing frequency (f) is expressed as $\omega =2\pi f$, H₀ is a bias field, M is magnetization and ${\mu }_0$ is magnetic permeability of free space.

References

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