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
01 Jan 2005
TL;DR: In this paper, a closed-form formula that calculates the 2D high-frequency ohmic losses (skin and proximity effects) in round wire windings has been provided by overwriting the classical definition (shown to be erroneous) of the layer copper factor introduced in 1D analytical theories.
Abstract: We provide a new closed-form formula that instantly calculates the 2D high-frequency ohmic losses (skin and proximity effects) in round wire windings It has been obtained by overwriting the classical definition (shown to be erroneous) of the layer copper factor introduced in 1D analytical theories Compared to similar previous formulas, the average error is divided by a factor of thousand Experimental validation is provided
6 citations
22 Jun 1997
TL;DR: In this paper, a technique to reduce high frequency AC losses in foil windings is presented, by shaping and controlling the field distribution in a given foil design, the current distribution can be improved which results in an improvement in the winding losses.
Abstract: High frequency foil windings offer a good solution to realize high power/high frequency magnetic components. The surface area available for cooling is quite large thus improving the thermal capacity of these windings and allowing higher current densities. However, at high frequencies, additional losses are incurred within foil windings due to the eddy currents induced by skin, proximity, fringing and other AC effects. In addition, the winding structure greatly affects the distribution of losses within the windings. This paper presents a technique to reduce high frequency AC losses in foil windings. By shaping and controlling the field distribution in a given foil design, the current distribution can be improved which results in an improvement in the winding losses.
6 citations
TL;DR: In this article, an analytical model for calculating the ac resistance due to the proximity effect in thick coil integrated spiral inductors is proposed, and the model is compared with both numerical simulations and experimental results.
Abstract: In this paper, an analytical model for calculating the ac resistance due to the proximity effect in thick coil integrated spiral inductors is proposed. Based on 2-D Maxwell’s equations, the redistribution of magnetic field and current in the coils caused by the proximity effect is modeled, and the ac resistance of the inductor is extracted. The analytical model is compared with both numerical simulations and experimental results. The ac resistance calculated by the model is good (within 14.8% discrepancy) up to the frequency of the peak quality factor for thick coil integrated spiral inductors.
6 citations
16 Mar 2014
TL;DR: In this article, an analysis of different planar windings configurations focusing on dc and ac resistances in order to achieve highly efficiency in dc-dc converters is presented, where different copper thicknesses form 70 μm up to 1500 μm are considered taking into account manufacturing complexity and challenges.
Abstract: Efficiency is one of the main concerns during the design phase of switch mode power supply. Planar magnetics based on PCB windings have the potential to reduce the magnetic manufacturing cost however, one of their main drawbacks comes from their low filling factor and high stray capacitance. This paper presents an analysis of different planar windings configurations focusing on dc and ac resistances in order to achieve highly efficiency in dc-dc converters. The analysis considers different copper thicknesses form 70 μm up to 1500 μm (extreme copper PCB) taking into account manufacturing complexity and challenges. The analysis is focused on a high current inductor for a dc-dc converter for fuel cell applications and it is based on FEM simulations. Analysis and results are verified on a 6 kW dc-dc isolated full bridge boost converter prototype based on fully planar magnetics achieving a peak efficiency of 97.8%.
6 citations
TL;DR: In this article, two dimensional simulations based on finite element method are done for investigation of current distribution in high power, high frequency transformers, and parallelized interleaved winding is presented for reducing the high frequency effect.
6 citations
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