Abstract
At high frequency, power losses of a winding due to eddy currents becomes significant. Moreover, the skin and proximity AC resistances are influenced by the width of printed circuit board (PCB) conductors and distance between the adjacent tracks which causes many difficulties to design windings with lowest AC resistances. To clarify this phenomenon, this paper focuses on modeling the influence of skin and proximity effects on AC resistance of planar PCB winding, thereby providing guidelines to reduce the winding AC resistance. An approximate electromagnetic calculation method is proposed and it shows that when the winding proximity AC to DC ratio ( F p r o x i m i t y ) is equal to 1 3 the AC on DC ratio caused by skin effect ( F s k i n ) , the winding is optimized and it has lowest AC resistance. 3-D finite element simulations of 3, 7 and 10-Turn windings, which are divided into 3 groups with the same footprint, are presented to investigate the lowest AC resistance when the track width varies from 3 mm to 5 mm and the frequency range is up to 700 kHz. In order to verify the theoretical analysis and simulation results, an experiment with 3 simulated groups, (9 prototypes in total) is built and has a very good fit with simulation results. Experimental results show that at the optimal width, the AC resistance of the windings can be reduced up to 16.5 % in the frequency range from 200 kHz to 700 kHz.
Highlights
Printed circuit board (PCB) winding has been widely used in high frequency electromagnetic devices including planar transformers and spiral coils because of its flexibility in design and high reproducibility
A procedure to optimize planar PCB winding is recommended in the discussion Section and a summary is drawn in the Conclusion
Equation (9) points out the relationship between the proximity ratio and track width with an idea that a slight change in track width will cause a significant change of proximity ratio
Summary
Printed circuit board (PCB) winding has been widely used in high frequency electromagnetic devices including planar transformers and spiral coils because of its flexibility in design and high reproducibility. Reference [4] optimized the quality factor of a predefined footprint spiral coil by changing the number of turns and distance between adjacent tracks. This approach will change the inductance of the winding and the operating frequency must be changed to accommodate the new inductor. A 2-dimensional model mentioned in Reference [9] and numerical solution presented in [10] were effective methods to calculate the AC resistance of long copper track. The paper is organized as follows—in Section 2, an approximate calculation analysis is performed with some assumptions to find the relationship between the skin and proximity effects of copper track, thereby, pointing out the optimal point. A procedure to optimize planar PCB winding is recommended in the discussion Section and a summary is drawn in the Conclusion
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