Modeling of a coil system considering frequency-dependent inductances and losses I. Analysis of the impedance matrix characteristics

A general equivalent circuit for the modeling of a system of magnetically coupled coils including the losses is presented. This equivalent circuit includes two parts: a subsystem of primary branches whose terminals correspond with those of the real coils, and a secondary network which allows the representation of frequency-dependent inductances and resistances. An analysis of the equations of the proposed circuit is carried out and an expression of the frequency-dependent impedance matrix as seen by the primary coils is determined. The properties of the mathematical expression are analyzed. The proposed equivalent circuit allows representing the dependence of inductances and resistances on the frequency. The expression of the impedance is the starting point for the synthesis of an equivalent circuit, which is carried out in a separate article.