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 , an improved two-dimensional analytical winding loss model for multilayered air-cored inductors with a single-turn per layer is proposed based on the fundamental electromagnetic field solution incorporating the 2-D boundary values and the edge effect in its formulation.
Abstract: Air-cored planar inductors play an important part in enabling high power-density, low weight, and low-profile design of high-frequency switched-mode power applications. However, the absence of ferromagnetic core in these inductors makes the magnetic field distribution in them different from that in the cored inductors and the transformers. Due to this difference, the conventional winding loss calculation models like the 1-D Dowell's model are not suitable for these inductors. Therefore, in this article, an improved two-dimensional analytical winding loss model for multilayered air-cored inductors with a single-turn per layer is proposed based on the fundamental electromagnetic field solution incorporating the 2-D boundary values and the edge effect in its formulation. The finite element method (FEM) simulation and experimental results validate the proposed model's high-accuracy and engineering precision over a wide frequency range (up to 10 MHz). Furthermore, the results ensure the proposed analytical model to be an efficient, easier, and better substitute for the FEM based calculation approach.
3 citations
15 Jun 2003
TL;DR: In this article, a planar litz structure was proposed to reduce the AC resistance of the planar conductor, which can result in lower AC resistance than is achieved with a solid conductor in a specific frequency range.
Abstract: The new trend in power converters is to design planar magnetic components that aim at a low profile. However, at high frequencies, AC losses induced in the planar inductor and transformer windings become significant due to the skin and proximity effects. The planar litz structure had been proposed previously to reduce the AC resistance of the planar conductor. A planar litz conductor can be constructed by dividing the wide planar conductor up into multiple lengthwise strands and weaving these strands in much the same manner as one would use to construct a conventional round litz wire. Each strand is subjected to the magnetic field everywhere in the winding window, thereby equalizing the flux linkage. 3D finite element modeling (FEM) was performed for some simple models. The simulation results showed that the planar litz conductor can result in lower AC resistance than is achieved with a solid conductor in a specific frequency range. The performance of the planar litz winding was also verified with measurements on the experimental prototypes.
3 citations
01 May 2016
TL;DR: In this paper, the series resistance of planar inductors is determined in three frequency domains: i) at very low frequencies, ii) at low frequencies (capacitive couplings are negligible), iii) at resonant frequencies, i.e. high frequencies.
Abstract: This paper presents a new approach in order to determine copper losses from measurements or simulations of planar inductors. Copper losses are modeled with a series resistance r(f) that depends on the frequency. Measured or simulated admittances of the inductors are used to determine the model parameters of the inductors. The resistance r(f) is determined in 3 frequency domains: i) at very low frequencies (or DC) ii) at low frequencies (capacitive couplings are negligible) iii) at resonant frequencies i.e. high frequencies. The presented approach is different as those encountered in literature and allows the series resistance from measured or simulated Sij parameters to be determined.
3 citations
07 Sep 2020
TL;DR: A 100 kW, isolated dc–dc converter was built over the course of one year, starting from a blank page, and reflects on the strengths and weaknesses of computer-based modelling and simulation tools.
Abstract: A 100 kW, isolated dc–dc converter was built over the course of one year, starting from a blank page. This paper details the design and manufacturing process, and reflects in particular on the strengths and weaknesses of computer-based modelling and simulation tools.
3 citations
01 Jun 2020
TL;DR: In this article, a method to determine winding losses from scattering matrix parameters in planar inductors is presented, where losses are separated in two parts for coreless inductors: skin effect and proximity effect.
Abstract: This paper presents a method to determine winding losses from scattering matrix parameters in planar inductors. Winding losses are taken into account by a dependent frequency resistance. This method allows losses to be separated in two parts for coreless inductors: skin effect and proximity effect. In high frequencies both software, like High Frequency Structure Simulator, and equipment, like Vector Network Analyzer, provide scattering parameters that allow both impedance or admittance matrices to be calculated. Then, parameters of an electric equivalent circuit can be calculated. The resistance value taking into account both skin and proximity effects is determined in three frequency domains. The first domain is at very low frequencies or at direct current. The second domain is at low-medium frequencies where the capacitive couplings are negligible. The last domain is at the resonant frequencies of the admittance matrix parameters, so at high frequencies. The presented approach is different from those encountered in literature and allows the series resistance from measured or simulated scattering matrix parameters to be determined.
3 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