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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03 Sep 2015
TL;DR: In this paper, the design of a TSV based high-density 3D toroidal type inductor with two different ferromagnetic materials (nickel and Ni-Zn-ferrite) in the core is described.
Abstract: This paper describes the design of a Through-Silicon-Via (TSV) based high-density 3D toroidal type inductor with two different ferromagnetic materials (nickel and Ni-Zn-ferrite) in the core. 3D inductors with different structural dimensions are simulated and compared.
1 citations
13 May 2013
TL;DR: In this paper, the authors take the cost of power loss and core volume in the long term into consideration during selection of core size, shape and material to produce an efficient transformer.
Abstract: The high-frequency transformer design for switch mode power supplies consists of core and winding design It is necessary to take the cost of power loss and core volume in the long term into consideration during selection of core size, shape and material to produce an efficient transformer The proximity effect seen in the windings deteriorates the performance of the transformer and can be averted by using Litz wires and sandwich winding structure
1 citations
DOI•
TL;DR: In this paper , the authors proposed an innovative frequency analytical model permitting to simply and accurately compute the current distribution in the transformer windings, the ac resistance, and the leakage inductance.
Abstract: Regarding the ever-increasing switching frequency of power converters, there is a lack of tools to perform a quick and effective optimization of the high-frequency transformers embedded in isolated power converters. Indeed, at high operating frequency, the geometry of the core and windings deeply impacts the overall transformer performance. Specifically, assessing accurately the current distribution in parallel-connected windings is a challenging and key issue. Winding parallelization, frequently implemented in low-voltage and high-current applications so as to decrease Joule losses, may be an ineffective solution because of skin and proximity effects. They create an unbalanced current distribution in the parallel-connected windings, which greatly impacts the ac resistance and leakage inductance of the transformer. This article proposes an innovative frequency analytical model permitting to simply and accurately compute the current distribution in the transformer windings, the ac resistance, and the leakage inductance. The proposed approach is comprehensively presented, validated using both measurements and two-dimensional finite element analysis and analyzed giving guidelines to engineers designing high-frequency transformers.
1 citations
TL;DR: In this paper , an analytical model of the various components constituting an isolated DC-DC power supply was used to define a simplified but convincing and accurate model (successfully assessed on a wide bandwidth using an experimental setup).
1 citations
10 Dec 2020
TL;DR: In this article, a bi-directional CLLC converter with an integrated transformer for energy storage systems (ESS) applications (48 V batteries) is presented and simulated using 3D Finite Element Analysis (FEA).
Abstract: This paper presents the design of a bi-directional CLLC converter with an Integrated transformer for energy storage systems (ESS) applications (48 V batteries). As the distributed energy generation and storage are gaining momentum it Is required to have ESS that can regulate the power bi-directionally, presently the ESS are bulky in size, to enhance the power density and converter efficiency, an integrated transformer is introduced and simulated using 3D Finite Element Analysis (FEA). Essentially, a simple PI-based voltage/current control loop Is implemented on a 32-bit microcontroller (TMS320F28379D). Also, synchronous rectification (SR) Is implemented by controlling the turn-on and turn-off delays on rectifier sides, respectively. The design and control of the CLLC converter are verified through the experimental results. A 300 kHz, 700 W prototype Is built with the peak conversion efficiency of 96.6% while charging and 96.4% while discharging
1 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