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Please someone explains the main parameters used in the k_linear part in pspice , more specifically what is L1 , L2 , L3 and designators in its parameters?

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The k_linear is a parameter to describe the coupling between inductors with 1 being a perfect coupling/transformer. Its sub-parameters L1, L2 etc. describes which inductors is coupled. As an example, if you have 2 inductors forming an transformer, and their reference designator was L6 and L7, you would specify L1=L6 and L2=L7, to let the simulator know that these is physically coupled(Like on a transformer core):

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