Inductor (Coupled)

Description

Set of two or more mutually coupled inductors.

The number of windings defines the size $n$ of the inductance matrix. Diagonal terms $L_i$ are the self inductances, and off-diagonal terms $M_{i,j}$ are the mutual inductances between windings.

The inductance matrix should not be singular in order to be invertible. In case of ideally coupled inductors, the inductance matrix can become singular and an ideal transformer component should be preferred to model these ones. The mutual inductances $M_{ i,j}$ can also be linked with a coupling factor $K_{i,j}$ such as: $M_{ i,j} = k_{ i,j} \sqrt{ L_i L_j}$.

Case of two coupled inductors

The electrical model of two coupled inductors is equivalent to a non-ideal transformer:

$L_m$: magnetizing inductance referred to the primary side.

$L_p$: leakage inductance on the primary side.

$L_s$: leakage inductance on the secondary side.

$m$: transformer ratio.

The corresponding two-inductor model is:

$L_m = \frac{M}{m}$

$L_p = L_1 - \frac{M}{m}$

$L_s = L_2 - m.M$

Case of three coupled inductors

The electrical model of three coupled inductors is also equivalent to a non-ideal transformer:

$L_m = \frac{M_{13} M_{12}}{M_{23}}$

$l_1 = L_1 - \frac{M_{13} M_{12}}{M_{23}}$

$l_2 = L_2 - \frac{M_{23} M_{12}}{M_{13}}$

$l_3 = L_3 - \frac{M_{23} M_{13}}{M_{12}}$

Library

Electrical > RLC

Parameters

Property	Display Name	Parameter Type	Description
NumberOfWindings	Number of Windings	IntParameter	Number of ideal inductors.
Inductance	Inductance Matrix [H]	DoubleMatrixParameter	The inductance matrix (H). In order to model a magnetic coupling between the windings, a square matrix must be entered.
Iinit	Initial current [A]	DoubleArrayParameter	Vector of Initial inductor currents (A). The vector size must be equal to the number of windings.

Pins

Property	Pin Name	Type	Description
-	W1P	Electrical	W1P
-	W1N	Electrical	W1N
-	W2P	Electrical	W2P
-	W2N	Electrical	W2N
-	W3P	Electrical	W3P
-	W3N	Electrical	W3N

Default Size

Width	Height
6	6