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: An analytical design methodology for nonsaturated thermally limited high-frequency transformers/inductors with the objective of minimum core size and minimum power loss is proposed and an effective ac resistance factor in terms of all windings is proposed to model the winding loss.
Abstract: This article proposes an analytical design methodology for nonsaturated thermally limited high-frequency transformers/inductors with the objective of minimum core size and minimum power loss. The major challenge of analytical design methodologies is to simultaneously retain the optimality of design results, simplicity/ease of use, and generality of design methodologies. Most of the reported analytical methodologies have a limitation on optimality due to neglect of discreteness of design variables and have limitations on simplicity and generality because of a complicated winding loss model with the consideration of eddy current effects. To address these limitations, a further optimization process considering discreteness of design variables is proposed to improve the optimality of the design results. A concept of an effective ac resistance factor in terms of all windings is proposed to model the winding loss in a simple and general way so that simplicity and generality of the design methodology are ensured. To illustrate the methodology and its improvement on optimality, the methodology is used to design a 150-W 100-kHz forward transformer and is compared with the methodology without further optimization. Theoretical calculations and experiments both indicate a decrease of about 5 °C of the methodology in this article compared with the methodology without further optimization.
16 citations
06 Mar 2011
TL;DR: In this paper, the design and fabrication of coupled inductors with low profile, low cost, and high power density for tapped-inductor high-step-down dc-dc power converters in the very high frequency (30-300 MHz) range are presented.
Abstract: The design and fabrication of coupled inductors with low profile, low cost, and high power density for tapped-inductor high-step-down dc-dc power converters in the very high frequency (30–300 MHz) range are presented. The inductor consists of a multi-layer thin-polyimide printed circuit board (PCB) and nano-granular thin-film magnetic material deposited on both sides and on beveled cuts to form a fully linked closed core. The magnetic material Co-Zr-O has good soft magnetic properties, high resistivity and high flux density capability. Multi-layer Co-Zr-O/ZrO 2 thin films are used to improve the performance of the magnetic core. A winding loss model of this coupled inductor is presented. Coupled inductors with turns ratios 2 and 10 for several different converter applications have been fabricated.
16 citations
26 Mar 2017
TL;DR: In this paper, a matrix transformer structure is proposed to integrate four elemental transformers into one magnetic core with simple four-layer PCB windings, fully utilizing the available PCB copper and space, and further reduce core loss.
Abstract: Isolated high output current DC/DC converters are critical for future data center power architecture. LLC converters with matrix transformer are suitable for these applications due to its high efficiency and high power density. Different matrix transformer structures are investigated. Flux cancellation can be utilized to reduce core size and loss. Synchronous rectifiers and output capacitors can be integrated into the secondary windings to minimize leakage and termination loss. To further improve the current design practice, several efforts have been made and a detailed design procedure is provided in this paper. A novel matrix transformer structure is proposed to integrate four elemental transformers into one magnetic core with simple four-layer PCB windings, fully utilize the available PCB copper and space, and further reduce core loss. The proposed matrix transformer is superior to the state-of-art, due to the much reduced core loss, integrated magnetics and simple four-layer PCB winding. With the proposed matrix transformer, LLC converter can achieve both high efficiency and high power density by operating at MHz. A 1MHz 380V/12V 800W LLC converter with GaN devices is demonstrated. The prototype can fit into the quarter-brick footprint and achieves a peak efficiency of 97.6% and a power density of 900W/inch3.
16 citations
TL;DR: In this paper, an extremely low-profile frequency-tunable composite antenna with enhanced gain and an omnidirectional radiation pattern is presented, which is based on a very short two-legged monopole antenna and consists of one driven element and eight identical parasitic coupled elements.
Abstract: This paper presents an extremely low-profile frequency-tunable composite antenna with enhanced gain and an omnidirectional radiation pattern. The antenna is based on a recently developed very short two-legged monopole antenna and consists of one driven element and eight identical parasitic coupled elements. By utilizing the mutual coupling between elements, the radiation resistance of the antenna is significantly increased, leading to considerable gain enhancement and better matching performance. The composite antenna has the same height as the single monopole ( $\lambda _{0}/150$ ) but a larger lateral dimension ( $\lambda _{0}/16$ ). The performance of the proposed antenna is compared with that of a single monopole antenna. It is shown that the peak gain of the composite antenna is about 10 dB higher than that of the monopole antenna. The design is then modified for frequency tunability to achieve frequency agility and higher bandwidth for certain modulations like frequency hopping spread spectrum. The fractional bandwidth of the tunable antenna is 3.32%, and the gain is further improved at higher frequencies. A new method of effectively measuring a monopole antenna with an electrically small ground plane using cascaded transformers is also presented and discussed.
16 citations
20 Feb 2018
TL;DR: The design, the fabrication, and the test of an isolated DC-DC converter for renewable energy applications is presented and the experimental validation of the 100 kW prototype is presented.
Abstract: This article presents the design, the fabrication, and the test of an isolated DC-DC converter for renewable energy applications. The converter is based on the Dual Active Bridge topology and uses silicon carbide power semiconductors and a medium frequency transformer. The design process covers hardware ranging from the semiconductor die to the complete power converter. For the control, a rapid prototyping approach was used. The experimental validation of the 100 kW prototype is presented.
16 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