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Circuit models are developed from the physical behavior of transformers. The models contain passive elements and controlled sources which are directly useful in computer analysis programs, and which the designer can use a readily as transistor and vacuum-tube models. Linear models are developed for ideal and perfect transformers and for lossy transformers. A piecewise linear model is developed for saturable reactors. The development is carried out for the generalized n-winding transformer. The parameters of the circuit model are related to winding and core parameters to facilitate transformer selection and design.