A New Principle for Eliminating the Ideal Transformer in Center-Tapped Circuit Analysis

In electrical circuit theory, the classical transformer equivalent circuit is well known, in which the secondary quantities are referred to the primary side (or vice versa) through the turns ratio, and the ideal transformer can be eliminated from the equivalent circuit, leaving both sides of the transformer connected galvanically. In electrical circuits with a center-tapped transformer, it is not so simple to eliminate the transformer by referring secondary quantities to the primary and considering the galvanic connection between both sides of the transformer; this is possible only for very simple examples. The literature contains known methods for replacing a center-tapped transformer in electrical circuits. The center-tapped transformer can be replaced in circuits with two appropriately connected single-phase transformers or gyrators, or with a voltage/current-dependent source. However, none of the mentioned methods connect the primary and secondary sides of the transformer galvanically, thereby simplifying the overall equivalent circuit; they even include voltage/current-dependent sources that complicate it further. In this article, a new principle is presented that is not known in the literature. The new principle shows how a center-tapped transformer can be eliminated fully from a nontrivial circuit and not only replaced with other elements. Additionally, the primary and secondary sides of the transformer become connected galvanically as a single circuit, which is sometimes easier to understand and analyze mathematically. To achieve this, some of the elements on the secondary side of the center-tapped transformer must be split and rearranged to use different connections. The new principle is explained first using a simple example with only resistors, and then a more complex circuit is presented that includes inductors and capacitors. Finally, the new principle is applied successfully to an equivalent circuit of a resistance spot-welding system that also contains nonlinear diodes.