Suggestions:
1. Reference
Gordon R. Slemon "Magnetoelectric Devices, Transducers, Transformers and Machines," John Wiley and Sons, Inc., New York, 1966, Section 3.2.2 Variable Frequency Operation (under Operating Characteristics of Transformers) generally analyzes the transformer dependency on frequency. A graph of |Eload/Esource| versus frequency is provided. The distributed capacitances between the primary and secondary windings becomes influential at higher frequencies.
2. Traditionally, the analysis of a transfer function is in relationship with the input type, i.e.
Iout(s) = H(s) x Iin(s)
For all practicall purposes, the Iin(s) is different from 1 in Laplace s-domain or Dirac function delta(t) in the time domain. Usually, Iin(s)= w/(s**2 + w**2) ~ sin(wt) or Iin(s)=s/(s**2 + w**2) ~ cos(wt) for the fundamental waveform (no harmonics involved). The harmonics somewhat complicate the Laplace analysis approach; however, it can be used with the nonlinear approach to the modeling via the multidimensional Laplace transform.