# Three-Winding Mutual Inductor

Three coupled inductors

**Libraries:**

Simscape /
Electrical /
Passive /
Transformers

## 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:

*V*is voltage across the_{i}*i*th winding.*I*is current through the_{i}*i*th winding.*L*is self inductance of the_{i}*i*th winding.*M*is mutual inductance of the_{ij}*i*th and*j*th 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.

## Examples

## Ports

### Conserving

## Parameters

## Extended Capabilities

## Version History

**Introduced in R2008a**

## See Also

Inductor | Mutual Inductor | Variable Inductor | Center-Tapped Transformer