Nonlinear Core

Symbol

Description

Model of an nonlinear magnetic core. It represents a nonlinear relationship between the magnetic flux $\Phi$ and the magneto-motive force $\mathcal{F}$ .

$\dot{\phi} = P(\mathcal{F}) * d\mathcal{F}/dt$

where, $P(\mathcal{F})$ : Peremeance, inverse of reluctance

The nonlinear core device supports two BH data types: Table and Function. The Table option uses a BH point array to represent the core’s nonlinearity. In the meantime, the Function option represents the BH curve using fitting equations defined by a few user-specified parameters, such as the magnetic flux density at the knee point, the permeability before saturation and the permeability after saturation. In the Function option, two fitting functions, coth and atan are available.

When the table is selected,

$P(\mathcal{F}) = \mu_{table} (H) * Area / L$

When the coth function is selected,

$P(\mathcal{F}) = ( -3.0/a * Bsat * 1/(sinh^2(3.0*H/a)) + Bsat * a/3.0 *1/H^2 + Musat ) * Area /L$

When the atanh is selected,

$P(\mathcal{F}) = {(Bsat/a * 1/ ( (\pi*(H)/(2*a) )^2 + 1) + \mu_{sat})} *Area / L$

Where, $H$ is the magnetic field, $Bsat$ is the magnetic flux density at the knee point, $\mu_{unsat}$ is the permeability before saturation, $\mu_{sat}$ is the peremeability after saturation, $Area$ is the area of cross section of the core, and $L$ is the length of the core.

$a$ is a helper parameter calculated from the user input

$a = Bsat/(\mu_{unsat} - \mu_{sat})$

Library

Magnetic > Branches

Pins

Name	Description
P	Positive Pin (●)
N	Negative Pin

Parameters

Name	Description
Area	Cross-sectional area, in m^2
Length	Length of flux path, in m
BHDataType	BH data type
BHCurve	BH data point array
FunctionType	Nonlinear Core Function type
B_sat	Saturated magnetic flux density
Mu_unsat	Permeability before saturation
Mu_sat	Permeability after saturation