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.In electrical engineering a toroidal inductor is used to measure or monitor the electric currents of an AC power circuit as a function of the harmonic distortion [1,2]. A galvanically isolated current measurement is required, such that the advantages of lower losses nd measurement signals processed directly must be attained [3]. The ferrite core toroid inductors produces a reduced current accurately proporonal to the measured current. The toroidal inductor can be also commonly used for feedback control, and other applications 

The design method for an anti interference toroidal inductor is proposed as an alternative to power-quality evaluation. The method is based on well-known tools by the engineers in which is presented the relationships that exist between equivalent circuit and transfer function of a toroidal inductor. The proposed design method has been explained with normalized functions based on physical parameters of a toroidal inductor. This work presents the main arguments of the suggested methodology and as demonstration of the design method as function of normalized parameters, is developed a current-signal sensor which has been validated in the laboratory by the EN-50160-2-2 standard to evaluate the power quality in home use loads.

In this work a method of design based on normalized parameters for a high flux toroidal inductor were proposed. Based on proposed method a current-signal sensor was designed to monitoring of the AC current waveforms.Two normalized functions have been found. One is the magnetizing inductance, Lm(α), another is magnetizing impedance, Zm(α). These parameter leads to obtain in general an optimal design of any toroidal inductor as a function of α parameter.A toroid was built with recycled grain-oriented silicon-iron foils. From the results was observed that the home use loads do not satisfy the EN-50160-2-2 standard which should be corrected in the future. Also, with some suggestions, the proposed method can be expanded to special design of toroidal inductors for other applications.