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| A Winding Width Optimization Method for Planar Transformer with Uniform Distribution of Current Density |
| An Shaoliang1, Wu qing1, Wang Boyan1, Xu Yixuan1, Wu Hongfei2 |
1. School of Electrical Engineering Xi’an University of Technology Xi’an 710000 China;
2. College of Automation Engineering Nanjing University of Aeronautics and Astronautics Nanjing 211106 China |
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Abstract In recent years, with the continuous expansion of the market demand for consumer electronic products, various types of small and medium-power switch-mode power supplies have emerged. Particularly in modern small-power switch-mode power supplies, topologies represented by flyback converters play a crucial role in practical applications. In such power systems, the transformer, as one of the core components, significantly affects the overall system efficiency and power density. Planar transformers have attracted considerable attention due to their low height and leakage inductance characteristics.
When the transformer operates under high-frequency conditions, the skin effect and proximity effect prevent the current from distributing uniformly across its cross-section. In flyback converters, the primary winding has a large number of turns, and the intensified proximity effect further exacerbates the uneven distribution of current density in each winding, concurrently reducing the efficiency of the transformer. This paper proposes a winding-width optimization method for planar transformers to achieve uniform distribution of current density.
First, a quantitative method for measuring the current density of windings is discussed. The root mean square (RMS) value of the winding current density within a single switching cycle is time-invariant, which leads to the use of Ohm's Law to calculate its RMS value. Subsequently, through theoretical analysis, it is determined that when the operating conditions of the transformer are constant, the main factors affecting the winding current density are its geometric parameters. The constraints on the inner and outer diameters of the winding are derived to achieve the most uniform current density distribution. Considering the inevitable presence of winding clearances in practical engineering, the formula is adjusted to calculate the optimal inner-to-outer diameter ratio. Furthermore, an in-depth analysis explores the inherent relationship between winding current density distribution and winding losses. A comparison with the literature reveals that the constraints on winding width for uniform current density distribution and minimal losses are consistent. It is indicated that the influencing mechanisms for factors are related to the uniformity of impedance values for AC and DC components.
Taking the Hengdian Group DMEGC Magnetics standard core ECW32C as an example, the widths of individual windings on the same PCB layer are calculated using two methods: winding width in proportion and constant winding width. Under the same excitation conditions, a comparative analysis of current density and winding losses is conducted through finite element simulation. The results indicate that the design with proportional distribution of inner and outer winding radius leads to a more uniform current density distribution and minimized winding losses. Two prototypes of 30 W flyback converters are constructed, and experimental results confirm that the proportional distribution of inner and outer winding radius is more conducive to improving the transformer's heat dissipation characteristics. Since the calculation of winding current density effective value is not affected by the working conditions of the transformer, this method is practical under various power electronic topologies.
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Received: 06 February 2024
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2025, Vol. 40 
