A novel method for the synthesis of magnetically coupled networks considering the frequency-dependence of the impedances

A new methodology for the representation of a set of magnetically coupled coils by means of an equivalent circuit is presented in this paper. The proposed method makes use of an equivalent circuit made up of a primary group of RL branches, which are the input terminals-pairs of the model, and a group of RL loops that are magnetically coupled with the primary branches, constituting a multiport model of a system of coupled coils that allows representing its frequency-behavior very accurately. This can be seen as a generalization of the classic methodology for the synthesis of RL driving-point impedances (developed by Foster and Cauer) considering the more general case of having multiple input terminals-pairs. This paper contributes an appropriate tool for the accurate modeling of transformer windings, a historically very difficult problem due to the frequency-dependence of the inductances and losses. The new method is first applied to the simple case of a single coil and was used afterward to the representation of a coil system, proving in both cases the mathematical validity of the method. The usefulness of the method is shown through its application to the modeling of a transformer winding.