Optimal design of a low power transformer

BACKGROUND: A low power transformer is one of the most common electromagnetic devices. They are used in special installations: aircraft, space or underwater vehicles, portable equipment, etc., as well as in stationary units and household devices. At the same time, the requirements for transformers vary greatly. Therefore, their optimal design is a relevant task.

AIM: Justified selection of optimization criteria when designing low–power transformers with minimum weight or minimum price.

METHODS: The optimal values of the criteria are obtained with mathematical analysis methods. If the weight and cost of insulating materials are not considered, a transformer consists of two components: a ferromagnetic (steel) core and copper (in some cases aluminum) windings. On the other hand, according to the law of electromagnetic induction, that the product of the number of windings turns and the cross–sectional area of the ferromagnetic core is constant, 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.

RESULTS: As a result of the analysis, for the minimum mass of the transformer, the optimal core and windings masses ratio was obtained as 1:1. For the minimum cost of the transformer, the optimal core and windings masses ratio depends on the price of the corresponding materials, and it is inversely proportional to the core and windings materials cost ratio.

CONCLUSION: The practical value of the research lies in the ability to design low-power transformers optimally for various applications.