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 Apr 1988
TL;DR: In this paper, it is shown that distribution of the gaps uniformly around the core, which can be realized by using low-permeability magnetic material, reduces the AC-DC resistance ratio of series-connected windings to about two at large conductor width.
Abstract: Lumped gaps incur unacceptably high eddy-current loss in small high-frequency magnetic geometries because of their close proximity to the winding. The problem is studied for four simulated inductor structures, using finite-element analysis. It is shown that distribution of the gaps uniformly around the core, which can be realized by using low-permeability magnetic material, reduces the AC-DC resistance ratio of series-connected windings to about two at large conductor width. Measures to reduce the field nonuniformity, such as arranging the series turns in multiple layers so that the winding window has better aspect ratio, further reduce winding loss. Loss reduction due to more uniform field distribution offsets the loss increase due to multilayer arrangement, at least for a small number of turns. >
59 citations
TL;DR: In this article, a 3D thermal model based on finite-element modeling using I-DEAS is presented and the thermal behavior of the dc/dc converter system is simulated and analyzed.
Abstract: In this paper, thermal analysis for a 42-V/14-V bidirectional dc/dc converter with integrated inductors is performed. An interleaved dc/dc converter system with four channels was chosen for the automotive-converter topology with 42-V/14-V dual-output voltages. Coupled inductors were designed and used for the four-channel dc/dc converter. A 3-D thermal model based on finite-element modeling using I-DEAS is presented and the thermal behavior of the dc/dc converter system is simulated and analyzed. The thermal model includes a printed circuit board, integrated inductors, a heat sink, and switching devices (MOSFETs). The analyzed thermal result can help to design a converter system under severe ambient-temperature conditions
58 citations
TL;DR: It is shown that the pulsewidth modulation inverter-fed power line is a feasible medium for the transmission of modulated digital information at data rates of over 40 kb/s and that this transmission path provides a suitable alternative to the sensor cabling between the actuator and the controller of an encoder-based servosystem.
Abstract: It is shown that the pulsewidth modulation inverter-fed power line is a feasible medium for the transmission of modulated digital information at data rates of over 40 kb/s and that this transmission path provides a suitable alternative to the sensor cabling between the actuator and the controller of an encoder-based servosystem. The encoder data is modulated and transmitted from the actuator to the controller, over the inverter-fed power cable. The data is modulated using frequency-shift keying, based on a center frequency of 5 MHz. Specialized magnetics design techniques are outlined for the coupling and decoupling circuits which transfer the modulated digital information to and from the power lines. A software observer is employed to improve the velocity derived from the received position information, and this velocity is used in the motion control algorithm to generate a reference torque signal for the controller.
57 citations
TL;DR: In this article, the materials and the fabrication of planar magnetic components for switch mode power supplies (SMPSs) and other applications are reviewed and the advantages and disadvantages of such devices are introduced.
Abstract: The materials and the fabrication of planar magnetic components for switch mode power supplies (SMPSs) and other applications are reviewed. The advantages and the disadvantages of such devices are introduced. The magnetic materials used in the devices, such as ferrite, amorphous metallic glass, and thin and thick magnetic films, are detailed. The devices have varying degrees of planarization-partially planar devices with magnetic cores and planar windings and truly planar devices for integrated magnetic circuits with planar windings and planar magnetics. Devices of both types reported in the literature since 1979 are reviewed. The design of the planar magnetic components must be optimized with respect to losses, and design issues which relate to electrical, thermal, and mechanical performance are discussed. >
57 citations
22 Jun 2014
TL;DR: In this paper, a lumped circuit model was developed to capture the impact of skin and proximity effects on current distribution and electromagnetic fields in planar magnetics, which enables accurate predictions of impedances, losses, stored reactive energy and current sharing among parallel windings.
Abstract: Planar magnetic components using printed-circuit-board windings are attractive due to their high repeatability, good thermal performance and usefulness for realizing intricate winding patterns. To enable higher system integration at high switching frequency, more sophisticated methods that can rapidly and accurately model planar magnetics are needed. This paper develops a lumped circuit model that captures the impact of skin and proximity effects on current distribution and electromagnetic fields in planar magnetics. This enables accurate predictions of impedances, losses, stored reactive energy and current sharing among parallel windings. This lumped model is also a circuit domain representation of electromagnetic interactions. It can be used to simulate circuits incorporating planar magnetics, to visualize the electromagnetic fields, and to extract parameters for magnetic models by simulations. The modeling results match with previous theories and finite-element-modeling results. A group of planar magnetic devices, including transformers and inductors with various winding patterns, are prototyped and measured to validate the proposed approach.
56 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