If you search the internet for “transformer equivalent circuits,” you’ll get five pages of over 100 small circuit diagrams. Figures 1 and 2 show two typical circuits, one that’s “referred to the primary” and the other that’s “referred to the secondary.” The Figure 2 circuit also has the mutual impedance in the primary. Most other circuits are variations of these.
1. This is a typical transformer equivalent circuit. (Source: Wikipedia)