Effects of eddy currents in transformer windings
01 Aug 1966-Vol. 113, Iss: 8, pp 1387-1394
TL;DR: In this article, the effect of eddy currents on transformer windings is considered and a method is derived for calculating the variation of winding resistance and leakage inductance with frequency for transformers with single-layer, multilayer and sectionalised windings.
Abstract: The effects of eddy currents in transformer windings are considered, and a method is derived for calculating the variation of winding resistance and leakage inductance with frequency for transformers with single-layer, multilayer and sectionalised windings. The method consists in dividing the winding into portions, calculating the d.c. resistances and d.c. leakage inductances of each of these portions, and then multiplying the d.c. values by appropriate factors to obtain the corresponding a.c. values. These a.c. values are then referred to, say, the primary winding and summed to give the total winding resistance and leakage inductance of the transformer. Formulas are derived and quoted for calculating the d.c. resistances and leakage inductances of the winding portions. Theoretical expressions are derived for the variation with frequency etc. of the factors by which the d.c. values must be multiplied to obtain the corresponding a.c. values. These expressions are presented in the form of graphs, permitting the factors to be read as required.
Citations
More filters
TL;DR: In this article , an intuitive circuit model is used to describe ECL and its superposition effect, and an optimal frequency to achieve the maximum dc-dc efficiency in the seawater is proposed.
Abstract: Wireless power transfer (WPT) technology is ideal for wireless charging of unmanned underwater vehicles (UUV). However, in underwater WPT systems, the eddy current loss (ECL) caused by the conductivity of seawater cannot be ignored. This paper obtains the expressions of the equivalent ECL resistance and mutual inductance by calculating the complex power generated by the current in the electric field. An intuitive circuit model is used to describe ECL and its superposition effect. Based on the system efficiency expressions, the influence of the medium conductivity, coil gap and operating frequency on the transmission efficiency is analyzed. Results show that there is an optimal frequency to achieve the maximum dc–dc efficiency in the seawater. Simulated and experimental results verify the validity of the method in calculating ECL and capturing the optimal transmission frequency.
1 citations
01 Sep 2019
TL;DR: In this article, a leakage inductance shield is proposed to reduce the leakage flux by means of Eddy current shielding, which can reduce leakage induction by almost 15 % in a transformer for a 100 W, 100 kHz flyback converter.
Abstract: This paper presents a novel technique to reduce the leakage inductance in transformers for switch mode power supplies. By introducing the leakage inductance shield, that reduces the leakage flux by means of Eddy current shielding, the leakage inductance is reduced by almost 15 % in a transformer for a 100 W, 100 kHz flyback converter. Analysis showed that this reduction in leakage flux is insufficient to fully mitigate the large voltage spikes and ringing in the circuits, caused by the leakage inductance. However, a small improvement in efficiency of a flyback converter can be achieved. It is concluded that the leakage inductance shield is simple to implement and can effectively decrease transformer leakage inductance, additional benefits to reduced electromagnetic interference can be expected as well, but were not proven in this paper.
1 citations
10 Oct 2021
TL;DR: In this paper, the authors proposed an accurate 2D model to calculate the winding loss of a single-layer multi-turn planar air-core PCB-inductor by incorporating the 2D edge effect in its formulation.
Abstract: Planar air-core PCB-inductors provide an opportunity to lower the weight and increase the power density of high-frequency switch-mode power applications. The difference between field distribution in cored and air-core inductors makes the conventional winding loss model no longer suitable for planar air-core PCB-inductors. Based on fundamental electromagnetic theory, this paper proposes an accurate 2D model to calculate the winding loss of a single-layer multi-turn planar air-core PCB-inductor by incorporating the 2D edge effect in its formulation. The proposed model's accuracy is validated over a wide frequency range by using 2D FEM simulation and experiment.
1 citations
15 Jun 2008
TL;DR: In this paper, a methodology for designing naturally cooled high frequency integrated magnetic component is presented, where the component geometry determines the maximal temperature on the surface of component by taking account the natural air convection and radiation effects.
Abstract: A methodology for designing naturally cooled high frequency integrated magnetic component is presented. Windings losses are analytically estimated, and then improved using finite elements calculation. The component geometry determines the maximal temperature on the surface of component by taking account the natural air convection and radiation effects. During its thermal stability, a magnetic component (windings, core, and isolation) could have a homogenous temperature in all its parts because of the good thermal conductivity of copper and ferrites. A prototype of 500 W, 48V half bridge integrated current- doubler rectifier is implemented. Component temperature was simply detected using infrared camera. This methodology could easily be integrated in computer aided design tools recently developed for designing magnetic component.
References
More filters
TL;DR: In this article, a multilayer winding carrying an alternating current, such as the windings illustrated in figures 1, 2, and 3, each layer of copper lies in the alternating magnetic field set up by the current in all the other layers.
Abstract: IN any multilayer winding carrying an alternating current, such as the windings illustrated in figures 1, 2, and 3, each layer of copper lies in the alternating magnetic field set up by the current in all the other layers. Eddy currents are set up in each layer in a direction to partly neutralize the magnetic intensities in the interior of the copper wire in each layer. As a result of the eddy-current losses in the copper, the effective resistance of the winding to the alternating current it carries may be many times its resistance to continuous currents.
103 citations
TL;DR: In this article, the authors discuss the more important causes of eddy currents in heavy conductors carrying alternating currents and surrounded on three sides by iron, and propose a method to identify the most important causes.
Abstract: The object of the present paper is the discussion of the more important causes of eddy currents in heavy conductors carrying alternating currents and surrounded on three sides by iron.
93 citations
64 citations
TL;DR: In this article, it is shown that a considerable proportion of the effective resistance of inductive coils when used at radio frequencies is caused by the eddy-currents set up in the wires of the coils by the alternating magnetic field in which they are situated, and that in extreme cases the alternating current resistance may amount to more than one hundred times the direct current resistance.
Abstract: It is well-known that a considerable proportion of the effective resistance of inductive coils when used at radio frequencies is caused by the eddy-currents set up in the wires of the coils by the alternating magnetic field in which they are situated, and that in extreme cases the alternating current resistance may amount to more than one hundred times the direct current resistance. It is therefore important to have reliable formulae for the eddy-current resistance of such coils in order to determine the conditions which will reduce the eddy-current losses to a minimum. The simplest case, that of a long straight cylindrical wire under the action of its own current, has been treated by Kelvin, Rayleigh, Heaviside, and others. The general effect is known as the “skin effect,” because the current tends to concentrate more and more upon the skin of the conductor as the frequency increases.
49 citations
TL;DR: In this article, the authors show how hyperbolic functions of complex angles may be applied to the solution of the problem of heat losses in rectangular conductors that are embedded in open slots.
Abstract: The principal object of this paper is to show how hyperbolic functions of complex angles may be applied to the solution of the problem of heat losses in rectangular conductors that are embedded in open slots. A certain knowledge of the functions themselves is presupposed. Inasmuch, however, as they are handled like trigometric functions of real angles?except in regard to the plus and minus signs?it is a simple matter to acquire the requisite technical skill to use them. The hyperbolic function of a complex angle, consisting as it does of a real and an imaginary part, may represent a vector?the real part being the component of the vector along the horizontal, and the imaginary part, component along the vertical. Thus, for example, A sinh (x + j x) represents a vector just as A e j ? A/?, A (cos ? + j sin ?) represent vectors. Considerable experience has shown that the vector method for handling a-c. problems is much superior to the original method in which simple trigonometric functions were used. With this lesson before us, it should require but little contact with the problem at hand to demonstrate the superiority of the vector method, even though it employs the possibly unfamiliar hyperbolic quantities. These hyperbolic vectors have been used for a number of years in the analysis of problems involving a-c. circuits, which have distributed inductance and capacitance, and have proved their usefulness.
27 citations