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The ideal four-port hybrid transformer is characterized by the following desirable properties: a biconjugacy between alternate sets of ports, an impedance match at each port, the ability to split power in any desired proportion between two receiving ports without incurring internal losses, and a 180° phase inversion in one of the four possible transmission voltage ratios. The necessary and sufficient conditions for obtaining these properties are reviewed for a number of useful configurations, which range from a simple tapped autotransformer to a two-core multiwinding device. Although these criteria are developed for an ideal transformer, it is possible to construct practical hybrid transformers, which exhibit satisfactory performance over one or more decades of bandwidth. Some of the problems in designing such transformers as well as additional useful applications of balanced winding transformers are discussed in brief.