Optimal Transformer Design Low Power

The article considers the problem of choosing criteria for optimal design of low-power transformers. Two criteria have been selected as the main criteria: the minimum mass of the transformer and the minimum cost of the transformer. If you do not take into account the mass and cost of insulating materials, the transformer consists of two components: a ferromagnetic (steel) core and copper (sometimes aluminum) windings. On the other hand, it follows from the law of electromagnetic induction that the product of the number of turns of the windings per the cross–sectional area of the ferromagnetic core is a constant value, since it is specified by the technical specification. These two ratios can be used to obtain optimal values for the selected criteria. Equations from two variables were compiled, the solution of which made it possible to obtain the optimal ratio of the mass of the ferromagnetic core and the mass of the windings. The optimal values of the criteria were obtained by mathematical analysis methods. As a result of the analysis, for the minimum mass of the transformer, the optimal ratio of the mass of the core and the mass of the windings was obtained as 1:1. For the minimum cost of the transformer, the optimal ratio of the mass of the core and the mass of the windings was obtained, which depends on the price of the corresponding materials, and it is inversely proportional to the ratio of the price of the core material and the price of the winding material.