PLECS 3.3 Online Help

Saturable Core

Purpose

Magnetic core element with saturation

Library

Magnetic

Description

pict

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:

atan fit

The atan fit is based on the arctangent function:

              (    )
B = 2Bsattan-1  πH-  + μsatH
    π           2a

coth fit

The coth fit was adapted from the Langevian equation for bulk magnetization without interdomain coupling, and is given as:

        (             )
              3H-  -a-
B = Bsat  coth  a - 3H   + μsatH

Both fitting functions have three degrees of freedom which are set by the coefficients μsat  , Bsat   and a  . μsat   is the fully saturated permeability, which usually corresponds to the magnetic constant μ0  , i.e. the permeability of air. Bsat   defines the knee of the saturation transition between unsaturated and saturated permeability:

                ||
Bsat = (B - μsatH)|
                 H→ ∞

The coefficient a   is determined by the unsaturated permeability μunsat   at H  = 0  :

a = Bsat∕(μunsat - μsat)

The figure below 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 atan fit.

pict

Parameters

Fitting functions
Saturation characteristic modeled with atan or coth fit.
Cross-sectional area
Cross-sectional area A   of the flux path, in m2  .
Length of flux path
Length l   of the flux path, in m.
Unsaturated rel. permeability
Relative permeability μr,unsat = μunsat∕μ0   of the core material for H → 0  .
Saturated rel. permeability
Relative permeability μr,sat = μsat∕μ0    of the core material for H → ∞ .
Flux density saturation
Knee Bsat    of the saturation transition between unsaturated and saturated permeability.
Initial MMF
Magneto-motive force at simulation start, in ampere-turns (A).

Probe Signals

MMF
The magneto-motive force measured from the marked to the unmarked terminal, in ampere-turns (A).
Flux
The magnetic flux flowing through the component, in webers (Wb). A flux entering at the marked terminal is counted as positive.
Field strength
The magnetic field strength H   in the core element, in A/m.
Flux density
The magnetic flux density B   in the core element, in teslas (T).