In circuit simulation, a distinction is made between an ideal transformer and a perfect transformer.  

The perfect transformer has coils of specified inductance, no resistive losses and has perfect coupling between coils, i.e., completely coupled with k=1.  

The ideal transformer is an impedance transformer specified by a turns ratio (instead of specifying the primary and secondary inductances) and operates over infinite frequency, including DC.   The ideal transformer is very convenient for transforming impedance, but needs a DC block when used in simulations of DC biased circuits, e.g., amplifiers.  Just something to remember (or, more likely, to recall after one has made the mistake).

The Floating Admittance Matrix for flux-coupled inductors is derived in detail.   The floating admittance matrix (also known as the indefinite admittance matrix, or nodal matrix, or un-grounded matrix) is used to easily derive the  Y-Parameters for center-tapped transformers, auto-transformers, or other inductor configurations.