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A technique is presented for designing transformers with given size and type of structure to have maximum volt-ampere (VA) output while at the same time insuring the satisfaction of a number of design constraints. The technique is based on a mathematical optimization problem whose solution is a set of parameter values characterizing the maximum VA output design. The existence and uniqueness of the solution to this problem are established, and a set of closed-form expressions are presented for the optimum design parameter values. The resulting design technique eliminates overdesign problems in that the smallest physical size structure will result consistent with the design objectives. The results presented here also provide information on possible design trade-offs between various parameters. Although a graphical design procedure is illustrated here, the ultimate utility of this analytical technique will be in a comprehensive computer-aided design program.