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 low-frequency, high-precision resonant capacitor bridge method based on a planar transformer is used for space gravitational wave detection in the frequency band of 10 mHz-1 Hz.
Abstract: In space gravitational-wave-detection missions, inertial sensors are used as the core loads, and their acceleration noise needs to reach 3×10−15 ms−2/Hz at a frequency of 0.1 mHz, which corresponds to the capacitive sensing system; the capacitive sensing noise on the sensitive axis needs to reach 1 aF/Hz. Unlike traditional circuit noise evaluation, the noise in the mHz frequency band is dominated by the thermal noise and the 1/f noise of the device, which is a challenging technical goal. In this paper, a low-frequency, high-precision resonant capacitor bridge method based on a planar transformer is used. Compared with the traditional winding transformer, the developed planar transformer has the advantages of low temperature drift and low 1/f noise. For closed-loop measurements of capacitive sensing circuits and sensitive structures, the minimum capacitive resolution in the time domain is about 3 aF, which is far lower than the scientific measurement resolution requirement of 5.8 fF for gravitational wave detection. The capacitive sensing noise is converted to 1.095 aF/Hz in the frequency band of 10 mHz–1 Hz. Although there is a gap between the closed-loop measurement results and the final index, the measurement environment is an experimental condition without temperature control on the ground; additionally, in China, the measurement integrity and actual measurement results of the capacitive sensing function have reached a domestic leading level. This is the realization of China’s future space gravitational wave exploration.
1 citations
29 Nov 2020
TL;DR: In this paper, a field shaping technique, dubbed the field-cannon-technique, is proposed to mitigate eddy current effects in high frequency transformers' foil windings.
Abstract: Minimizing transformer winding loss is a prominent factor to increase efficiency of power electronics converters. This is especially valid for modern switched-mode power supplies, where eddy current effects on windings become dominant due to continuously elevated switching frequency. In this paper, a field shaping technique, dubbed the field-cannon-technique, is proposed to mitigate eddy current effects in high frequency transformers’ foil windings. The basic principle and the implementation of the proposed technique is introduced. A model is derived using finite difference method, in order to calculate the distribution of the magnetic field within the transformers implemented with the field-cannon-technique. Finally, the technique is verified by experiments, where the winding resistance of the transformer is reduced by a factor of three.
1 citations
09 Nov 2020
TL;DR: This paper investigates the use of multi-phase and fractional-turn transformers in this application space and finds that they can offer significant miniaturization benefit especially in the 12V/1kW regime where a split-phase fractional turn transformer is estimated to operate with 3.1 times lower loss than a single-phase configuration.
Abstract: Data center servers represent an important and growing electrical load, and there is strong interest in miniaturizing the supplies that power them. This paper investigates the use of multi-phase and fractional-turn transformers in this application space and finds that they can offer significant miniaturization benefit especially in the 12V/1kW regime where a split-phase fractional turn transformer is estimated to operate with 3.1 times lower loss than a single-phase configuration.
1 citations
01 Sep 2020
TL;DR: In this paper, an optimization approach of high frequency transformers based on the calculation of the optimum number of turns is presented, and the relationship between the volume, the power and the frequency is also investigated.
Abstract: This paper presents an optimization approach of high frequency transformers based on the calculation of the optimum number of turns. The relationship between the volume, the power and the frequency is also investigated. The design approach considers the skin and proximity effects, the core geometry and the magnetic material.
1 citations
20 Jun 2022-Compel-the International Journal for Computation and Mathematics in Electrical and Electronic Engineering
TL;DR: The work presented here drastically improves the usability of this rapid prediction method by creating a software tool that can automatically generate winding configurations and analyze them at speeds of thousands-per-second.
Abstract: Transformer characteristics such as current distri-bution, loss, and leakage inductance are often predicted through hand calculations or FEA analysis, which are slow and labor-intensive. A recently-developed analysis technique can predict transformer characteristics six orders of magnitude faster than FEA and is promising for use in analysis and especially op-timization. The work presented here drastically improves the usability of this rapid prediction method by creating a software tool that can automatically generate winding configurations and analyze them at speeds of thousands-per-second. This paper covers the implementation of such a general software tool, called the Quick Simulator of High-Frequency Transformers (QuickSHiFT), demonstrates its user interface and utility for human analysis, and further provides examples of rapid brute-force optimization of 4-layer planar transformers.
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