The Duality between Interlinked Electric and Magnetic Circuits and the Formation of Transformer Equivalent Circuits

When making calculations on a circuit, containing both electric impedances and transformers, it is frequently desirable to consider the transformers removed and the constraints they impose replaced by a rearrangement of the impedances connected to their terminals. Such "equivalent circuits" may not always be found; the rules are here established for their formation, and also for checking, by inspection, whether the transformer constraints are removable in this way, in any particular case. It is shown that the equivalent electric circuit of a transformer, having any arrangement of magnetic paths, is derivable from its magnetic circuit by application of the topological principle of duality. This cannot be done if the magnetic circuit is non-planar, as in the case of a transformer possessing four or more windings with leakage couplings; a physically realizable circuit does not then exist. Under certain conditions the principle may be applied in reverse and the impedances in a given electric circuit may be coupled together by a suitable transformer, so that the various current and voltage constraints are unaltered.