# 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

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TL;DR: In this paper, a systematic review of bridgeless power factor correction (PFC) boost rectifiers, also called dual-boost PFC rectifiers is presented, where loss analysis and experimental efficiency evaluation for both CCM and DCM/CCM boundary operations are provided.

Abstract: In this paper, a systematic review of bridgeless power factor correction (PFC) boost rectifiers, also called dual boost PFC rectifiers, is presented. Performance comparison between the conventional PFC boost rectifier and a representative member of the bridgeless PFC boost rectifier family is performed. Loss analysis and experimental efficiency evaluation for both CCM and DCM/CCM boundary operations are provided.

739 citations

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22 Jun 1997TL;DR: In this paper, the number and diameter of strands to minimize loss in a litz-wire transformer winding is determined, and a power law to model insulation thickness is combined with standard analysis of proximity effect losses to find the optimal stranding.

Abstract: The number and diameter of strands to minimize loss in a litz-wire transformer winding is determined. With fine stranding, the AC resistance factor can be decreased, but DC resistance increases as a result of the space occupied by insulation. A power law to model insulation thickness is combined with standard analysis of proximity-effect losses to find the optimal stranding. Suboptimal choices under other constraints are also determined.

683 citations

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07 May 2007TL;DR: In this article, a systematic review of bridgeless PFC boost rectifiers, also called dual boost PFC rectifiers is presented, where design considerations and experimental results in both CCM and DCM/CCM boundary operations are provided.

Abstract: In this paper, a systematic review of bridgeless PFC boost rectifiers, also called dual boost PFC rectifiers, is presented. Performance comparison between the conventional PFC boost rectifier and a representative member of the bridgeless PFC boost rectifier family is performed. Design considerations and experimental results in both CCM and DCM/CCM boundary operations are provided.

588 citations

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TL;DR: In this paper, the authors propose an orthogonality between skin effect and proximity effect to calculate the AC resistance of round conductor windings, which gives more accurate answers than the basic one-dimensional method because the exact analytical equations for round conductors can be used.

Abstract: The one well-known one-dimensional method for calculating the AC resistance of multilayer transformer windings contains a built-in orthogonality which has not been reported previously. Orthogonality between skin effect and proximity effect makes a more generalized approach for the analytical solution of AC resistance in windings possible. This includes a method to calculate the AC resistance of round conductor windings which is not only convenient to use, but gives more accurate answers than the basic one-dimensional method because the exact analytical equations for round conductors can be used. >

546 citations

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TL;DR: In this paper, a new method for predicting the stray capacitance of inductors is presented, which is based on an analytical approach and the physical structure of the inductors, where the inductor winding is partitioned into basic cells.

Abstract: A new method for predicting the stray capacitance of inductors is presented. The method is based on an analytical approach and the physical structure of inductors. The inductor winding is partitioned into basic cells-many of which are identical. An expression for the equivalent capacitance of the basic cell is derived. Using this expression, the stray capacitance is found for both single- and multiple-layer coils, including the presence of the core. The method was tested with experimental measurements. The accuracy of the results is good. The derived expressions are useful for designing inductors and can be used for simulation purposes.

393 citations

##### References

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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

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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

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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

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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