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Model three coupled inductors

Passive Devices

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:

*V*is voltage across the_{i}th winding.*i**I*is current through the_{i}th winding.*i**L*is self inductance of the_{i}th winding.*i**M*is mutual inductance of the_{ij}th and*i*th windings, $${M}_{ij}={K}_{ij}\sqrt{{L}_{i}{L}_{j}}$$.*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.

**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.

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

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