I've never heard the term coefficiency (not a word according to the spell checker) before and I think what you are referring to is the coupling coefficient K that represents the deviation from ideality of a real transformer. It turns out that even when you specify K=1, what you actually get is just a small epsilon away from 1. It represents the leakage inductance present in all real transformers. There is an equivalence between the coupled inductor model and one that represents the magnetizing inductance, and the parasitic inductances of the primary and the secondary.
Glad you found the real problem.