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# How to configure a generalized mutual inductance

In Schematic Editor, there are two blocks to represent mutual inductances: “Single Phase Two Winding Mutual Inductance” and “Three Winding Mutual Inductance“.

However, such blocks have some limitations:

The three winding block have equal mutual terms.

The number of winding is limited to three;

In order to surpass such limitations, the following instructions shall be followed.

# Creating an unbalance 3-by-3 mutual inductance

The “Three Winding Mutual Inductance“ block implements is used to model a mutual inductance with equal mutual coupling.

The voltage-current relationship is given by the matrix differential equation:

as we can see, all non-diagonal terms of both matrices are equal (balanced mutual coupling).

In order to model a generalized 3-by-3 mutual inductance block with unbalanced coupling, described by the equation:

we use three two-windings blocks, associated as indicated in the figure below:

The parameters for the two-windings blocks are:

block “m12“:

block “m23“:

block “m13“:

# Creating a 4-by-4 mutual inductance

In a similar way, a four-windings inductance is defined by the following equation:

As for the blocks with three windings, we distinguish two possible configurations: balanced and unbalanced mutual inductance terms.

## Balanced 4-by-4 mutual inductance

When the mutual coupling terms are equal, the matrix differential equation becomes:

and we can model it with four mutual inductance blocks, one block containing three windings and three containing two windings, associated as indicated in the figure below:

The parameters for the three- and two-windings blocks are:

block “m123“:

block “m34“:

block “m24“:

block “m14“:

## Unbalanced 4-by-4 mutual inductance

If the mutual terms are unequal, we cannot use the three-winding block; instead, we use the equivalent one described in the previous section:

The configuration applied for the blocks “m34“, “m24“, and “m14“ remains the same, except for the fact that the mutual resistances and inductances are different:

block “m34“:

block “m24“:

block “m14“:

# Creating a generalized N-by-N mutual inductance

The same procedure described in the previous sections could be used recursively to create higher order blocks.

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