# Three-Winding Mutual Inductor

Model three coupled inductors

Passive Devices

## Description

The Three-Winding Mutual Inductor block represents a set of three coupled inductors or windings. The voltage across the three windings is

`$\begin{array}{l}{V}_{1}={L}_{1}\frac{d{I}_{1}}{dt}+{M}_{12}\frac{d{I}_{2}}{dt}+{M}_{13}\frac{d{I}_{3}}{dt}\\ {V}_{2}={M}_{12}\frac{d{I}_{1}}{dt}+{L}_{2}\frac{d{I}_{2}}{dt}+{M}_{23}\frac{d{I}_{3}}{dt}\\ {V}_{3}={M}_{13}\frac{d{I}_{1}}{dt}+{M}_{23}\frac{d{I}_{2}}{dt}+{L}_{3}\frac{d{I}_{3}}{dt}\end{array}$`

where:

• Vi is voltage across the ith winding.

• Ii is current through the ith winding.

• Li is self inductance of the ith winding.

• Mij is mutual inductance of the ith and jth windings, ${M}_{ij}={K}_{ij}\sqrt{{L}_{i}{L}_{j}}$.

In the preceding equations, currents are positive when flowing into the positive node of their respective inductor terminals.

When you run a simulation that includes this block, the software checks the specified parameter values to ensure that the resulting device is passive. If it is not, the software issues an error.

## Dialog Box and Parameters

Inductance L1

The self inductance of the first winding. The default value is `0.001` H.

Inductance L2

The self inductance of the second winding. The default value is `0.001` H.

Inductance L3

The self inductance of the third winding. The default value is `0.001` H.

Coefficient of coupling, K12

The coefficient that defines the mutual inductance between the first and second windings. The default value is `0.9`. The absolute value must be between 0 and 1, exclusive.

Coefficient of coupling, K13

The coefficient that defines the mutual inductance between the first and third windings. The default value is `0.9`. The absolute value must be between 0 and 1, exclusive.

Coefficient of coupling, K23

The coefficient that defines the mutual inductance between the second and third windings. The default value is `0.9`. The absolute value must be between 0 and 1, exclusive.

Specify initial condition

Select one of the following options for specifying an initial condition:

• `No` — Do not specify an initial condition for the model. This is the default option.

• `Yes` — Specify the initial inductor currents.

Initial current port 1, IC1

The current flowing through the first winding at the start of the simulation. This parameter is only visible when you select `Yes` for the Specify initial condition parameter. The default value is `0` A.

Initial current port 2, IC2

The current flowing through the second winding at the start of the simulation. This parameter is only visible when you select `Yes` for the Specify initial condition parameter. The default value is `0` A.

Initial current port 3, IC3

The current flowing through the third winding at the start of the simulation. This parameter is only visible when you select `Yes` for the Specify initial condition parameter. The default value is `0` A.

## Ports

The block has the following ports:

`1+`

Positive electrical voltage of the first mutual inductor

`1-`

Negative electrical voltage of the first mutual inductor

`2+`

Positive electrical voltage of the second mutual inductor

`2-`

Negative electrical voltage of the second mutual inductor

`3+`

Positive electrical voltage of the third mutual inductor

`3-`

Negative electrical voltage of the third mutual inductor