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 article, a detailed analysis of high-frequency leakage inductance and an accurate prediction methodology is proposed, where the highfrequency eddy current effects cause a reduction in leakage induction and the proximity effect between adjacent layers is responsible for the reduction of leakage induction.
Abstract: Frequency-dependent leakage inductance is often observed. The high-frequency eddy current effects cause a reduction in leakage inductance. The proximity effect between adjacent layers is responsible for the reduction of leakage inductance. This paper gives a detailed analysis of high-frequency leakage inductance and proposes an accurate prediction methodology. High-frequency leakage inductances in several interleaved winding configurations are also discussed. Interleaved winding configurations actually give a smaller degree of reduction of leakage induction at high frequency. Finite-element analysis simulation and measurement validate the models.
134 citations
07 Jul 2011
TL;DR: In this article, the impact of peak-to-peak flux density ΔB, frequency f, DC premagnetization H DC, temperature T, core shape, minor and major loops, flux waveform, and material on core loss calculation is considered.
Abstract: Loss models of inductive components are thoroughly investigated, thereby all different aspects of loss modeling are considered. The impact of peak-to-peak flux density ΔB, frequency f, DC premagnetization H DC , temperature T, core shape, minor and major loops, flux waveform, and material on core loss calculation are considered. In order to calculate winding losses, formulas for round conductors and litz wires, each including skin- and proximity effects (including the influence of an air-gap fringing field) are included. A high level of accuracy is achieved by combining the best state-of-the-art approaches and by embedding newly-developed approaches into a novel loss calculation framework. The loss models are verified by FEM simulations and experimental measurements.
134 citations
TL;DR: In this article, the authors developed a numerical model for calculation of eddy-current losses in a multiturn winding of a high-frequency transformer, which assumes periodic arrangement of conductors, and uses the repeat elementary cell concept.
Abstract: This paper develops a numerical model for calculation of eddy-current losses in a multiturn winding of a high-frequency transformer. The model assumes periodic arrangement of conductors, and uses the repeat elementary cell concept. The paper proposes analytical expressions and graphic dependences to determine effective frequency-dependent resistance of the winding. It computes the leakage field in the transformer window, taking into consideration the effective magnetic permeability of the multiturn winding as a heterogeneous medium. Finally, it analyzes the values of the resistance at various frequencies for two types of winding (solid conductor winding and Litz wire winding) by numerical and experimental methods.
132 citations
TL;DR: In this paper, the high-frequency power-transformer design equations for winding and core losses and temperature rise were reviewed from literature and formulated for spreadsheet calculations using material (Steinmetz loss coefficients, ferrite resistivity, copper resistivity), geometry (core area, core length, winding area, winding length), winding (number of primary turns, copper fill factor, primary to secondary area ratio) and excitation (input voltage, switching frequency, duty cycle, current harmonic components) parameters.
Abstract: The high-frequency power-transformer design equations for winding and core losses and temperature rise were reviewed from literature and formulated for spreadsheet calculations using material (Steinmetz loss coefficients, ferrite resistivity, copper resistivity), geometry (core area, core length, winding area, winding length), winding (number of primary turns, copper fill factor, primary to secondary area ratio) and excitation (input voltage, switching frequency, duty cycle, current harmonic components) parameters. The accuracy of each design issue was first validated and quantified separately using regression analysis. Calculated core losses, winding AC-resistance equations and heat transfer capacity calculations were compared with the results from calibrated heat sink measurements, finite-element method (FEM) analysis and measurements using thermal test blocks, respectively. Finally three EFD20 type transformers (solid wire, noninterleaved foil and interleaved foil winding) were fitted into an active clamp forward converter (100-300 kHz switching frequency, 0-78 W throughput power) for comparison between the theory and experiments. Standard error of predicted core losses and heat transfer capacity were determined to be 0.0581 and 0.15 W, respectively. The results of the in circuit tests suggests that the transformer total losses can be predicted with the average standard error below 0.2 W with datasheet type information only. The most significant uncertainty was heat conduction through and losses generated in the interconnecting wires between the test transformer and other converter components.
127 citations
TL;DR: In this article, a novel PCB winding based magnetic structure is proposed to integrate both inductor and transformer into one component, which can be easily controlled by changing the cross-sectional area of the core or the length of the air gap.
Abstract: The momentum toward high power density high-efficiency power converters continues unabated. The key to reducing the size of power converters is high-frequency operation and the bottleneck is the magnetic components. With the emerging widebandgap devices, the switching frequency of power converters increases significantly, to hundreds of kilohertz, which provides us the opportunity to adopt printed circuit board (PCB) winding planar magnetics. Compared with the conventional litz-wire-based magnetics, planar magnetics can not only effectively reduce the converter size, but also offer improved reliability through automated manufacturing process with repeatable parasitics. Another way to reduce the number of magnetic components and shrink the size of power converters is through the magnetic integration. In this paper, a novel PCB winding based magnetic structure is proposed to integrate both inductor and transformer into one component. In this structure, the inductor value can be easily controlled by changing the cross-sectional area of the core or the length of the air gap. A 6.6-kW 500-kHz CLLC resonant converter prototype with 98% efficiency and 130-W/in3 (8 kW/L) power density is built to verify the feasibility of the proposed PCB winding based magnetic structure.
124 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