A novel linear equivalent circuit of a transformer winding considering the frequency-dependence of the impedances

A new methodology for the representation of a transformer winding or any set of magnetically coupled coils by means of an equivalent circuit is presented in this paper. This circuit is suitable for the representation of the frequency-behavior of a system of coils at high frequencies and it consists of RL coupled circuit elements. The frequency-behavior representation of the actual impedances is accomplished by means of additional RL loops. Therefore, the circuit synthesis theory takes a step beyond the RL Foster or Cauer equivalent circuits, which were developed to represent only a single inductive element. Starting from the proposed equivalent circuit, the matrix equation of the system of coupled inductive branches is derived and their equivalence with the characteristic equations of the real system is proved. Finally, the method is applied to the modeling of transformer windings.