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
More filters
TL;DR: In this article, a 3D model for calculating magnetic fields in a power transformer and the effective parameters (inductance and resistance) of its windings is presented and the results of the calculations performed in the frequency range 10 Hz-10 MHz, and show that the largest variations of both the magnetic field and parameters of the windings take place at frequencies below ~10 kHz and at frequencies higher than 1 MHz.
Abstract: We present a 3-D model for calculating magnetic fields in a power transformer and the effective parameters (inductance and resistance) of its windings. The transformer is representative of large transformers with power ratings ranging from hundreds of kilovolt amperes to hundreds of megavolt amperes. The model accounts for anisotropic frequency-dependent properties of the laminated transformer core and eddy currents in the steel sheets. We discuss the results of the calculations performed in the frequency range 10 Hz-10 MHz, and show that the largest variations of both the magnetic field and parameters of the windings take place at frequencies below ~10 kHz and, at frequencies higher than 1 MHz, the magnetic core does not significantly affect the variation of the effective parameters
52 citations
TL;DR: In this paper, the design and implementation of a printed circuit board (PCB)-integrated flyback transformer for a 1-mm-thin single-phase power factor correction rectifier is investigated.
Abstract: In future applications, e.g., in ultra-flat OLED lamp drivers or flat screen power supplies, ultra-flat ac/dc and dc/dc converter systems are highly demanded. Therefore, the design and implementation of a printed circuit board (PCB)-integrated flyback transformer for a 1-mm-thin single-phase power factor correction rectifier is under investigation. In this paper, first an overview on several integration methods is given. It is shown that the PCB integration of magnetic cores allows us to achieve the required thickness of 1 mm and a high energy density. In a next step, the design and the realization of ultra-flat magnetic components with PCB-integrated cores are discussed in detail. The presented multi-objective design procedure determines the inductor and/or transformer setup optimal with respect to minimal losses and/or minimal footprint area; for this purpose, all required electrical, magnetic, and geometrical parameters of the magnetic component are considered in the design process. Furthermore, all specific implications entailed by the PCB-integrated core, e.g., the core setup, anisotropic core losses, the interleaving of windings, or an accurate reluctance model are treated. Finally, experimental results are used to verify the design procedure.
52 citations
TL;DR: In this article, the authors provide a technique for design optimization for maximizing power harvest, revealing a critical result: for any given core in any particular application, power harvest is maximized when the core is permitted to saturate at an opportune time in the line cycle.
Abstract: Energy harvesting offers an important design option for creating sensing and control elements without a requirement for custom wiring or batteries. An exciting possibility creates a “self-powered” sensor node with an integrated energy harvester that can extract power from the magnetic fields around a power line to a load, in the manner of a current transformer. However, this “current transformer” provides not just current sensing, but also power for a sensor package, all without ohmic contact. This paper provides a technique for design optimization for maximizing power harvest, revealing a critical result: For any given core in any particular application, power harvest is maximized when the core is permitted to saturate at an opportune time in the line cycle. Circuits for optimizing this power transfer window and experimental results supporting the analysis are presented in this paper.
52 citations
TL;DR: In this article, the effect of air-gap design on high-frequency AC losses in transformer and inductor windings was investigated and evaluated using finite element analysis (FEAs).
Abstract: High-frequency AC losses are normally induced in transformer and inductor windings due to skin, proximity, fringing and other AC effects. In addition, the winding structure greatly affects the distribution of losses within the windings. Air gaps are usually placed in the core of magnetic devices to support the high magnetomotive force (MMF). Fringing fields can cause additional AC winding losses, and care must be taken to minimize these losses. In this paper, the effect of air-gap design on the induced losses is investigated. In particular, three air-gap designs-lumped, discretely distributed and uniformly distributed-are investigated and evaluated. Both one-dimensional (1-D) and finite-element analyses (FEAs) are used to investigate the different design structures.
52 citations
TL;DR: In this paper, the authors developed an analytical model of solenoid coils that includes the impact of tissue and coating around the coils, verified through simulations and measurements, using the proposed model, under a given size restriction and a specific load, they found the optimal operating frequency and coil geometry to maximize a figure of merit (FoM) for the Rx that including the loaded quality factor and its internal efficiency as well as a factor related to the coupling coefficient.
Abstract: The new trend towards minimally invasive millimeter-sized and free-floating distributed implants promises to enable emerging applications, such as chronic neural recording with minimal damage to the surrounding tissue. However, wireless power transmission (WPT) to these medical devices is quite challenging. The magnetic field produced by external transmitter (Tx) coils at the position of small implants can be considered homogeneous to separate the optimization of Tx and receiver (Rx) coils for efficient WPT. This paper focuses on the optimization of the solenoid-type Rx coils, which are suitable for this application. We have developed an analytical model of solenoid coils that includes the impact of tissue and coating around the coils, verified through simulations and measurements. Using the proposed model, under a given size restriction and a specific load, we find the optimal operating frequency and coil geometry to maximize a figure of merit (FoM) for the Rx that includes the loaded quality factor and its internal efficiency as well as a factor related to the coupling coefficient. For a millimeter-sized coil, the optimal operating frequency for the Rx and the number of turns are found to be 500 MHz and six, respectively, if the coil is closely wound using AWG36 copper wires. If the pitch is also optimized, then 700 MHz and four turns provide the best FoM for the solenoid Rx.
51 citations
References
More filters
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