Mutual Inductor

Netlist Entry

Kxxxx L1 L2 [L3...] coupling_factor

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 it is desired to couple more than two inductors and different coupling factors are required for certain combinations, you can enter multiple K devices to define the coupling between inductors. However, a coupling factor must be defined for every combination of inductor pairs. For example, with three inductors, there must be a definition for L1-L2, L2-L3 and L1-L3.

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