# Mutual Inductor

Specifies coupling between two inductors.

In this topic:

## Netlist Entry

Kxxxx l1 l2 coupling_factor
 l1 Component reference of first inductor l2 Component reference of second inductor coupling_factor Coupling factor, K

If mutual inductance is M then:

$v_{L_1} = L_1 \frac{di_{L_1}}{dt} + M \frac{di_{L_2}}{dt}$

$v_{L_2} = L_2 \frac{di_{L_2}}{dt} + M \frac{di_{L_1}}{dt}$

$K = \frac{M}{\sqrt{L_1 \cdot L_2}}$

K cannot be greater than 1.

## Notes

You can only couple ideal inductors using this method. The saturable inductor devices may not be coupled in this way. See Inductor (Saturable) for more information.

To use the mutual inductor directly on a schematic you will need to add the device line to the netlist. See Adding Extra Netlist Lines for information about how to do this.

If you wish to couple more than two inductors, the coupling coefficient (K value) must be specified for every possible combination of two inductors. An error will result if this is not done.

For iron cored transformers values of K between 0.99 and 0.999 are typical. For ferrites lower values should be used. If the windings are concentric (i.e. one on top of the other) then 0.98 to 0.99 are reasonable. If the windings are side by side on a sectioned former, K values are lower - perhaps 0.9 to 0.95. The addition of air gaps tends to lower K values.

## Example

A transformer with 25:1 turns ratio and primary inductance of 10mH

** Inductors
Lprimary N1 N2 10m
Lsecondary N3 N4 16u

** Coupling of 0.99 typical for ungapped ferrite
K1 Lprimary Lsecondary 0.99