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Calculation Inductance of Toroidal Inductor Wound by Rectangular Cross-Sectional Wire
In this article, we present two methods for calculation of the inductance of toroidal core power inductors wound by rectangular cross-sectional wire, considering that the current density is inversely proportional to the circular coil radius. The first method is to simplify the helical toroidal coil into a thick-walled toroidal, and based on Grover’s toroidal inductor formula, the inductance is obtained by calculation the magnetic flux and the calculation method is simple, but the applicability is poor. The second method is to simplify the helical toroidal coil into a collection of self-closing circular coils, the calculation method is complex but has high accuracy, and the mutual inductance between the circular coils is calculated by the filament method based on the adjusted Grover’s mutual inductance of circular coils with inclined axes. We verify the adjusted Grover’s mutual inductance of filamentary circular coils with inclined axes and the mutual inductance between inclined circular coils with a rectangular cross section. Finally, we compared and analyzed the results calculated by the two methods proposed in this article and the results calculated by the finite element method.
The various advantages of toroidal inductors, which are cooler, smaller and more EMI-resistant are discussed. With toroidal inductors, there is an advantage to maintaining a single layer of windings due to which the inductor behaves closer to an ideal component of lower levels of parasitic capacitance. Multi-layer toroidal inductors involve both turn-to-turn capacitance and layer-to-layer capacitance and a very significat start/finish gap capacitance since there is no start/finish gap. This increases the total amount of parasitic capacitance by orders of magnitude.
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