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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11 Jun 2008
TL;DR: In this article, the effect of the air-gap position on the winding losses in planar inductors and its practical applicability on the basis of real examples is presented. But this paper is restricted to a single series of planar cores.
Abstract: The development of power supply technology has always been associated with the need for further miniaturization. One aspect of this trend is a design based on mathematical and physical principles and the implementation of magnetic components. The use of planar inductors and transformers offers the best preconditions for realizing this objective as they allow the windings to be integrated directly in the circuit board. Even when only a single series of planar cores is used, exactly identical winding configurations may have different air-gap positions. Different winding losses then result as a function of this position. The following paper presents a procedure for determining the effect of the air-gap position on the winding losses in planar inductors and its practical applicability on the basis of real examples.
4 citations
24 Dec 2012
TL;DR: An analysis of the resistance of multi-track coils in printed circuit board (PCB) implementations, where the conductors have rectangular cross-section, for spiral planar coils is carried out, and it is concluded that for the range of frequencies, the coil dimensions and the planar configuration typically used in domestic induction heating, these analysis are unsatisfactory.
Abstract: In this paper, an analysis of the resistance of multi-track coils in printed circuit board (PCB) implementations, where the conductors have rectangular cross-section, for spiral planar coils is carried out. For this purpose, different analytical losses models for the mentioned conductors have been reviewed. From this review, we conclude that for the range of frequencies, the coil dimensions and the planar configuration typically used in domestic induction heating, the application in which we focus, these analysis are unsatisfactory. Therefore, in this work the resistance of multi-track winding has been calculated by means of finite element analysis (FEA) tool. These simulations provide us some design guidelines that allow us to optimize the design of multi-track coils for domestic induction heating. Furthermore, several prototypes are used to verify the simulated results, both single-turn coils and multi-turn coils.
4 citations
01 Jan 2013
4 citations
16 Jul 2007
TL;DR: In this article, the authors predicted the optimum notch radius for a specific inductor design using a calorimetric experiment and verified the predicted results with a specific design of a planar inductor.
Abstract: AC-losses in gapped-core planar inductor windings seem to be dominated by eddy losses induced by the time varying fringing flux near the air gap. Shaping the windings in the region of the gap reduces AC-losses but the reduction in width of planar foil conductors causes the DC-resistance to increase. The winding shape can be optimized using FEM-tools but the process is very time consuming. If the DC-resistance of the conductors is however kept constant by increasing its thickness a reduction in the AC-losses occurs continuously as the conductor tips are moved away from the gap. The optimum notch radius can now be predicted easily and is governed mainly by the geometry of the winding stack and core window. The predicted results are verified for a specific inductor design using a calorimetric experiment.
4 citations
01 Dec 2015
TL;DR: In this article, the authors developed a high frequency planar transformer model and compared the results of FEM simulation results and simulation model with a comparative study between FEM results and the simulation model and found excellent agreement.
Abstract: Planar magnetic components used for energy conversion is crucial elements in power conversion application. Particularly, planar transformer printed on circuit board is characterized by the high efficiency, high power density, low weight and small size. Therefore, designed power conversion systems are needs prototype. But, planar transformer model is still not available in power simulator tools. Therefore, there is a limitation during the simulation process of power systems. This paper focuses on the development of a high frequency planar transformer model. The planar transformer model remains a complex device to model, the magnetizing inductance, the leakage inductance of primary and secondary windings, the skin and proximity effects in windings and the parasitic capacitances effects are taken into account. A comparative study between FEM simulation results and simulation model is established and found excellent agreement. Validity domains are discussed.
4 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
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