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This model approximates the behaviour of an inductor with the influence of saturation, i.e., the value of the inductance depends on the current flowing through the inductor (Fig. 1). The inductance decreases as current increases. Note, that hysteresis is not taken into account.

The approximation of the flux linkage is based on the atan function with an additional linear term, as shown in Fig. 2:

Psi = Linf*i + (Lzer - Linf)*Ipar*atan(i/Ipar)
L = Psi/i = Linf + (Lzer - Linf)*atan(i/Ipar)/(i/Ipar)

This approximation is with good performance and easy to adjust to a given characteristic with only four parameters (Tab. 1).

Tab. 1: Characteristic parameters of the saturating inductor model

Variable	Description
Inom.	Nominal current
Lnom	Nominal inductance at nominal current
Lzer	Inductance near current = 0; Lzer has to be greater than Lnom
Linf	Inductance at large currents; Linf has to be less than Lnom

The parameter Ipar is calculated internally from the relationship:

Lnom = Linf + (Lzer - Linf)*atan(Inom/Ipar)/(Inom/Ipar)

Fig. 1: Actual inductance Lact versus current i

Fig. 2: Actual flux linkage Psi versus current i

The flux slope in Fig. 2 is equal to Lzer for small currents. The limit of the flux slope is Linf as the current i approaches infinity. The nominal flux is indicated by the product of the nominal inductance Lnom and the nominal current Inom.

Inom	Value: Type: Current (A) Description: Nominal current
Lnom	Value: Type: Inductance (H) Description: Nominal inductance at Nominal current
Lzer	Value: Type: Inductance (H) Description: Inductance near current=0
Linf	Value: Type: Inductance (H) Description: Inductance at large currents