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Journal ArticleDOI

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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Journal ArticleDOI
TL;DR: In this article, the authors presented a method for predicting parasitic capacitances of solenoid HF inductors made of one layer of turns with circular cross sections, uniformly wound around a cylindrical nonconductive core.
Abstract: This paper presents a method for predicting parasitic capacitances of solenoid HF inductors made of one layer of turns with circular cross sections, uniformly wound around a cylindrical nonconductive core. The method is based on an analytical approach to obtain the turn-to-turn and turn-to-shield capacitances of coils. The influence of the wire insulation is taken into account. An equivalent lumped parallel capacitance is derived. The method was tested by experimental measurements. The calculated and measured values were in good agreement in the considered cases. The derived expressions are useful for designing HF inductors and can also be adopted for modeling and simulation purposes.

236 citations

Journal ArticleDOI
TL;DR: In this article, a graphical and numerical method of calculating and minimizing losses in windings, that generalizes previous findings, has been introduced using electromagnetic theory and MMF diagrams in both space and time.
Abstract: A graphical and numerical method of calculating and minimizing losses in windings, that generalizes previous findings, has been introduced Using electromagnetic theory and MMF diagrams in both space and time a method is proposed that provides insight into the mechanism of skin and proximity effect losses and that also yields quantitative results Using this method, several winding geometries for various topologies are covered The analysis and optimization process is experimentally verified using an interleaved flyback transformer The mathematical treatment justifying the use of the field method and which is essential in arriving at any numerical result is presented are more general equations for the calculation of copper losses are derived The relation between the fields in the transformer and copper losses is emphasized Also, the tools necessary to derive optimization diagrams are provided >

233 citations

Journal ArticleDOI
TL;DR: In this article, a procedure for the optimum design of a high-power, high-frequency transformer is presented based on both electrical and thermal processes in the power transformer and identifies: (a) the VA-rating of ferrite cores in relation to the operating frequency; (b) the optimum flux density in the core; and (c) the optimal current densities of the windings providing maximum transformer efficiency.
Abstract: A procedure for optimum design of a high-power, high-frequency transformer is presented. The procedure is based on both electrical and thermal processes in the power transformer and identifies: (a) the VA-rating of ferrite cores in relation to the operating frequency; (b) the optimum flux density in the core; and (c) the optimum current densities of the windings providing maximum transformer efficiency. Since the transformer is the major contributor to the volume and weight of the power supply, the results of transformer analysis can be used for entire power supply optimization as well. Two high-power, high-frequency transformers are optimally designed, built, and tested. Practical results show good agreement with the theory.

217 citations

Journal ArticleDOI
TL;DR: The major advantages and disadvantages in the use of planar magnetics for high-frequency power converters are covered in this paper, and a detailed survey of winding conduction loss, leakage inductance, and winding capacitance for planar magnetic technologies is presented.
Abstract: The momentum toward high efficiency, high frequency, and high power density in power supplies limits wide use of conventional wire-wound magnetic components This paper gives an overview of planar magnetic technologies with respect to the development of modern power electronics The major advantages and disadvantages in the use of planar magnetics for high-frequency power converters are covered, and publications on planar magnetics are reviewed A detailed survey of winding conduction loss, leakage inductance, and winding capacitance for planar magnetics is presented so power electronics engineers and researchers can have a clear understanding of the intrinsic properties of planar magnetics

208 citations

Journal ArticleDOI
TL;DR: In this paper, an approximate model for multi-strand wire winding, including litz-wire winding, is presented, which takes into account the existence of proximity effect within the litzwire bundle between the strands and between the bundles, as well the skin effect.
Abstract: This study presents an approximate model for multi-strand wire winding, including litz-wire winding. The proposed model is evaluated using Dowell's equation. The model takes into account the existence of proximity effect within the litz-wire bundle between the strands and between the bundles, as well the skin effect. The expressions for optimum strand diameter and number of strands at which minimum winding AC resistance is obtained for the litz-wire windings are derived. The boundary frequency between the low-frequency and the medium-frequency ranges are given for both litz-wire and solid-round wire inductors. Hence, the low-frequency ranges of both wire windings are determined. It is shown that litz-wire is better than the solid wire only in specific frequency range. The model has been verified by the measurements, and the theoretical results were in good agreement with those experimentally measured. Comparison of the theoretical predictions of the proposed approximate litz-wire model with models proposed in other publications and with experimental results is given.

193 citations

References
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Journal ArticleDOI
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

Journal ArticleDOI
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

Journal ArticleDOI
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

Journal ArticleDOI
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