# Mutual Inductor

Mutual inductor in electrical systems

• Libraries:
Simscape / Foundation Library / Electrical / Electrical Elements

## Description

The Mutual Inductor block models a mutual inductor, described with the following equations:

`$V1=L1\frac{dI1}{dt}+M\frac{dI2}{dt}$`
`$V2=L2\frac{dI2}{dt}+M\frac{dI1}{dt}$`
`$M=k\sqrt{L1·L2}$`

where:

• V1 is the voltage across the primary winding.

• V2 is the voltage across the secondary winding.

• I1 is the current flowing into the + terminal of the primary winding.

• I2 is the current flowing out of the + terminal of the secondary winding.

• L1, L2 are the winding self-inductances.

• M is the mutual inductance.

• k is the coefficient of coupling, 0 < k < 1.

• t is time.

Use this block to represent an AC transformer. If inductance and mutual inductance terms are not important in a model, or are unknown, you can use the Ideal Transformer block instead.

The two electrical networks connected to the primary and secondary windings must each have their own Electrical Reference block.

### Variables

To set the priority and initial target values for the block variables prior to simulation, use the Initial Targets section in the block dialog box or Property Inspector. For more information, see Set Priority and Initial Target for Block Variables.

Nominal values provide a way to specify the expected magnitude of a variable in a model. Using system scaling based on nominal values increases the simulation robustness. Nominal values can come from different sources, one of which is the Nominal Values section in the block dialog box or Property Inspector. For more information, see Modify Nominal Values for a Block Variable.

## Ports

### Conserving

expand all

Electrical conserving port associated with the positive terminal of the primary winding.

Electrical conserving port associated with the negative terminal of the primary winding.

Electrical conserving port associated with the positive terminal of the secondary winding.

Electrical conserving port associated with the negative terminal of the secondary winding.

## Parameters

expand all

Self-inductance of the primary winding.

Self-inductance of the secondary winding.

Coefficient of coupling, which defines the mutual inductance. The parameter value should be greater than zero and less than 1.

## Version History

Introduced in R2007a