I feel that the problem has been already verbosely discussed in your previous "coupled coil" threads
https://www.edaboard.com/showthread.php?t=365324
https://www.edaboard.com/showthread.php?t=365447
https://www.edaboard.com/showthread.php?t=368884
Generally, there's nothing specific about small signal versus large signal transfer function as long as long as involved magnetic cores are operated below saturation. The coupled coil equivalent circuit is a basic transformer circuit with low coupling coefficient k respectively high leakage inductance.