Frequency characteristics of single-phase two-winding transformers using distributed-parameter modeling

Using modal analysis and modeling results from transmission-line theory, closed-form s-domain expressions are derived for the spatial voltage and current distributions along the primary and secondary windings of a single-phase two-winding transformer. These expressions take into account both of the inductive and capacitive coupling between the two windings, in addition to inter-turn coupling within each winding. The frequency characteristics of the transformer input impedance under different loading conditions are obtained, which can be useful in identifying the resonant frequencies of the transformer. The results are compared with those obtained from the well-known circuit simulation program SPICE.