Inversely coupled inductors

Assuming that I have a three phase coupled inductor buck as the following


There are two ways to couple the iductors, direct coupling or inverse coupling.

I can do easily direct coupling in Q spice as shown in the picture. However, I am not sure how to simulate an inverse coupling in which between any two inductors the coupling would be as follow


When I tried doing that by having the coupling statement K1 L1 L2 L3 {-Kc}, it gives a message that it is physically impossible. Any hints?

How is your B source defined? You can define coupled inductors like K L1 L2 L3 1, it works for me or try to define inductors like in figure.

Best regards

Thanks for your reply.
This is not inversely coupled though.
I need to have between any two Inductors a negative coupling.

For this example, if L1 and L2 are negative coupled [V(b) reverse] and L1 and L3 are negative coupled [V(c) reverse], V(b) and V(c) are in same phase and they are positive coupled physically.
When you write Kx L1 L2 L3 -1, this represent

  • K1 L1 L2 -1
  • K2 L1 L3 -1
  • K3 L2 L3 -1

and therefore, Qspice return error that it is physically impossible.

I can agree with you in the case of perfect coupling (k=-1). However, for coupling less than 1, I think it is possible and it is already applied in multiphase buck while interleaving the switching signal of each.
Think about a core shaped as equilateral triangle whereas at each point you have an inductor while the return path of the flux in the middle to control the coupling coeff.
I tried with K= -0.7 and it still didn’t work and I don’t see it as physically impossible.

I investigated the topic more. Interestingly, for 3 coupled inductors you can go with coupling factor up to - 0.5 with no issues. Qspice worked for me with this limit.
The limit on K goes lower for higher number of coupled inductors.
I could realize this limit by looking into the canonical model outlined in this paper:

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