Saturable Core
Purpose
Magnetic core element with saturation
Library
Magnetic / Components
Description
This component models a segment of a magnetic core. It establishes a non-linear relationship between the magnetic field strength \(H\) and the flux density \(B\) to model saturation effects. The user can choose between the following fitting functions:
- \(\tan^{-1}\) fit
The \(\tan^{-1}\) fit is based on the arctangent function:
\[B = \frac{2}{\pi} B_\mathrm{sat} \tan^{-1} \left( \frac{\pi H}{2 a} \right) + \mu_\mathrm{sat} H\]- \(\coth\) fit
The \(\coth\) fit was adapted from the Langevian equation for bulk magnetization without interdomain coupling, and is given as:
\[B = B_\mathrm{sat} \left( \coth \frac{3H}{a}-\frac{a}{3H} \right) + \mu_\mathrm{sat} H\]
Both fitting functions have three degrees of freedom which are set by the coefficients \(\mu_\mathrm{sat}\), \(B_\mathrm{sat}\) and \(a\). \(\mu_\mathrm{sat}\) is the fully saturated permeability, which usually corresponds to the magnetic constant \(\mu_0\), i.e. the permeability of air. \(B_\mathrm{sat}\) defines the knee of the saturation transition between unsaturated and saturated permeability:
The coefficient \(a\) is determined by the unsaturated permeability \(\mu_0\) at \(H=0\):
Fig. 279 illustrates the saturation characteristics for both fitting functions. The saturation curves differ only around the transition between unsaturated and saturated permeability. The \(\coth\) fit expresses a slightly tighter transition than the \(\tan^{-1}\) fit.
Fig. 279 Comparison of \(\coth\) and \(\tan^{-1}\) saturation characteristics
Parameters
- Fitting functions
Saturation characteristic modeled with \(\tan^{-1}\) or \(\coth\) fit.
- Cross-sectional area
Cross-sectional area \(A\) of the flux path, in square meters (\(\mathrm{m}^2\)).
- Length of flux path
Length \(l\) of the flux path, in meters (\(\mathrm{m}\)).
- Unsaturated rel. permeability
Relative permeability \(\mu_\mathrm{r,unsat} = \mu_\mathrm{unsat} / \mu_0\) of the core material for \(H \to 0\).
- Saturated rel. permeability
Relative permeability \(\mu_\mathrm{r,sat} = \mu_\mathrm{sat} / \mu_0\) of the core material for \(H \to \infty\).
- Flux density saturation
Knee \(B_\mathrm{sat}\) of the saturation transition between unsaturated and saturated permeability.
- Initial MMF
Magneto-motive force at simulation start, in ampere-turns (\(\mathrm{A}\)).
Probe Signals
- MMF
The magneto-motive force measured from the marked to the unmarked terminal, in ampere-turns (\(\mathrm{A}\)).
- Flux
The magnetic flux flowing through the component, in webers (\(\mathrm{Wb}\)). A flux entering at the marked terminal is counted as positive.
- Field strength
The magnetic field strength \(H\) in the core element, in amperes per meter (\(\mathrm{A}/\mathrm{m}\)).
- Flux density
The magnetic flux density \(B\) in the core element, in teslas (\(\mathrm{T}\)).