Proximity Effect Losses Research Articles

Modeling, Analysis, and Winding Loss Calculation of Different Litz and Solid Wire on Coupled Inductor in DC–DC Cuk Converter for DCM

In this article, the coupled inductor is designed using a litz wire, an enameled litz wire, and a solid wire separately. All the coupled inductors wound with litz and solid wires are tested in a Cuk converter operated in DCM with a 25 kHz switching frequency for 15 W power, and winding losses of each wire, including proximity and skin effect loss, are calculated analytically without using any software, by using different techniques presented in literature, and the results are compared. Also, state-space modeling of the converter using a coupled inductor for DCM is derived as a contribution of the article because such a modeling is not derived for the Cuk converter in the literature. Thanks to the applications, inductor currents, switch voltage, input–output voltage, and output current are measured for coupled inductors with different wires. In addition, FEM simulation and co-simulation of all coupled inductors are realized, and the results obtained by applications are verified by them. Besides, it is shown that while the number of turns is the same, increasing the bundle of wires increases efficiency and inductance, reducing the window area and coupling coefficient.

Study of the Applicable Frequency Band of the YBCO Coil

Nowadays, copper Litz wire is widely used in the electrical applications. This wire is a particular type of multistrand wire, which is designed to reduce the skin effect and proximity effect losses in conductors. As the frequency dependence of losses in YBCO coils and Litz coils is different, how to determine the frequency band in which superconducting coils have an efficiency advantage over copper coils is a problem that needs to be solved. In response to the above concerns, a theory of the applicable frequency band of YBCO coils are proposed. Both experimental and numerical methods are used to study the characteristics of the applicable frequency band. Results show that the applicable frequency band of the YBCO coil decreases as the transport current increases, while its dependence on the radius of the coil is small. The obtained conclusions can be used as a reference when superconducting coils are used to replace copper coils.

Winding loss analysis of planar spiral coil and its structure optimization technique in wireless power transfer system

Circular planar spiral coils are wildly used for the magnetic coupling system in a high-frequency wireless power transfer system. The loss of the magnetic coupling system usually takes dominance in the whole system. This paper built the calculation model of magnetic field strength and coil loss, the proposed calculation model can effectively consider the mutual influence between the transmitter and receiver coil and accurately calculated the AC loss of WPT coils. Then, the effect of turn spacing on the AC resistance of coil is analyzed. It reveals that the proximity effect loss is greater when the coil is tightly wound, and the AC loss can be optimized by designing the turn spacing. Based on the above analysis, a double-layer coil method is proposed. This method can reduce the AC loss and improve the quality factor (Q) without changing the mutual inductance and footprint of coil at high frequency. The AC resistance of the double-layer coil method can be greatly reduced compared with the general method through simulation and experiment. The work efficiency of WPT system is increased by 4.3%, which verifies the accuracy and flexibility of theoretical analysis.

An Efficient Method for Litz-Wire AC Loss Computation in Transient Finite Element Analysis

An efficient method is proposed to predict eddy current loss of Litz wire coils, or completely transposed multi-strand coils, in transient finite element analysis (FEA). The method is based on analytical solutions of eddy current loss in a solid wire due to skin effects and proximity effects. The bundle of Litz or solid wires is homogenized by introducing a fill factor to describe the conducting area ratio. The analytical solutions in the frequency domain for round, square, and rectangular wires are further expanded to those in the time domain. The wire length direction in each 3-D mesh is automatically detected so that the flux density vector in each mesh can be correctly decomposed to the orthogonal and tangential components for anisotropic proximity effect loss computation. The method is applied to calculating eddy current loss of a gapped inductor in both 2-D and 3-D, and the results are compared with that using real solid wires.

Analysis of Litz Wire Losses Using Homogenization-Based FEM

This article proposes a novel analysis method for the losses in a litz wire considering the circulating and eddy currents. In the proposed method, the macroscopic complex permeability is introduced to evaluate the eddy current loss owing to the proximity effect. Homogenization-based finite element analysis using the macroscopic complex permeability can effectively compute the proximity effect loss. The loss owing to the circulating currents is evaluated by solving the corresponding circuit equation. It is shown that the eddy current loss is dominant for the solenoidal and spiral coils without magnetic cores because of the uniform magnetic field distribution along the wire. Moreover, the magnetic reactors in which the circulating current loss cannot be ignored are analyzed using the proposed method. It is shown that the losses computed by the proposed method agree well with the measured results.

An Analytical Loss Model of Litz-Wire Windings for Transformers Excited by Converters With Winding Configurations Considered

An accurate analytical model for litz-wire (LW) winding loss calculation of power electronic transformers (PETs) was deduced. First, the skin effect and proximity effect losses at bundle levels of a single straight LW were introduced. Then, the proximity loss of an air-core LW winding was studied by adopting the coordinate transformation technique (CTT) considering helical winding (HW) configurations and twisting configurations (TCs). Last, a 2-D analytical model for LW windings considering magnetic materials, LW configurations, and winding configurations (WCs) was proposed with the help of CTT, Dowell method, and Roth’s method. This model is helpful for the design of LW windings considering more details such as the choices of WCs and LW configurations.

Eddy Current Losses Analysis and Optimization Design of Litz-Wire Windings for Air-Core Compulsators

Compulsators are popular choices for high-end railgun power supplies. In order to increase the power density, air-core compulsators are proposed by using composite materials instead of ferromagnetic materials. Compared with the conventional iron-core machines, armature conductors of the air-core machines are not surrounded by the ferromagnetic teeth, resulting in the conductors been exposed to highly dense revolving magnetic field, which causes eddy current losses in the conductor strands. On the other hand, high-frequency currents flow through the armature winding during the self-excitation and discharge process, which also causes skin effect and proximity effect losses. Therefore, an effective winding design is essential to ensure proper current density distribution and eddy current losses of armature conductors to avoid local overheating. This paper deduced the calculation model of eddy current losses of a single conductor under alternating magnetic fields and then established the eddy losses calculation model of the air-core compulsator’s armature winding. The expression indicates that the eddy current losses of a conductor are determined by both the radial and tangential components of the flux density, which can be obtained by finite-element analysis. Based on the calculation model, the performance of two particular armature designs (a solid conductor and a compacted type-8 litz wire with the same area) are analyzed and discussed. The conductor eddy current losses are estimated and compared for both designs. Finally, an optimization study is carried out to find the best choice of strand diameter to minimize the total losses.

Analytical Calculation of Proximity-Effect Resistance for Planar Coil With Litz Wire and Ferrite Plate in Inductive Power Transfer

Planar coils are popularly used in inductive power transfer applications. The coils’ efficiency is improved with litz wire by eliminating the winding's skin-effect loss, but the proximity-effect loss still needs to be considered. To calculate the proximity-effect resistance, the magnetic fields across the windings are required. During the coils’ optimization process, numerical methods of field calculation are too time-consuming due to the parametric sweep of physical parameters. The analytical calculation of the magnetic field is preferred in this scenario, but it becomes complex with the existence of the ferrite plate, which is used to increase the coils’ coupling. In this paper, the method of image is applied to simplify the analytical calculation, in which the magnetic fields across the windings are derived from Ampere's law and Biot–Savart law. The proximity-effect resistance is then calculated with these fields. The study also proves that the size of the ferrite plate has negligible influence on the proximity-effect resistance as long as it is larger than the size of the winding. A planar coil was fabricated and measured to verify the analytical calculation of the proximity-effect resistance, using litz wire composed of 100 strands with 0.1 mm diameter. A square plate of 3C96 ferrite with the dimensions of 100 mm × 100 mm × 5 mm was placed below the winding. The difference between calculation and measurement is less than 15%.

Compact Modeling of Proximity Effect in High- ${Q}$ Tapered Spiral Inductors

This letter presents a technique to accurately predict the proximity effect losses in spiral inductors with variable width and spacing (taper) across the turns. The change in magnetic flux in a spiral turn due to the nearby non-uniformly spaced traces is considered while developing expression that captures proximity effect. A broadband, scalable, and frequency-independent compact model is developed for tapered inductors using the proposed technique. Resistance, inductance, and quality factor ( ${Q}$ ) plots are shown for spiral inductors with different values of taper. Excellent agreement between model and EM simulated/measured data demonstrates the scalability of the proposed model. The proposed model can be used to accurately predict the high ${Q}$ possible with tapered inductors.

Design Optimization of Multiple-Layer PSCs With Minimal Losses for Efficient and Robust Inductive Wireless Power Transfer

Inductive wireless Power Transfer (IPT) is a promising technology for remote powering of a wide variety of applications of electronic devices. To design IPT systems with the highest power transfer efficiency and the maximal robustness to coupling factor variations between transmitter and receiver of printed spiral coils (PSCs), high quality factors ( Q-Factor ) of the utilized PSCs are required. Designing PSCs with high Q-Factor is limited by the eddy current, the proximity effect, and parasitic losses. In this paper, PSC parasitic losses are carefully analyzed and specific design solutions are proposed. Genetic algorithm optimizations are developed to accommodate the proposed design solutions in minimizing losses. Single and multiple layer variable width PSCs are optimally designed with eddy current and proximity effect losses minimized. The designed PSCs are fabricated and experimental measurements are performed. The validity of the proposed approach to largely improve both IPT efficiency and robustness are confirmed. Using multiple coil layers, the robustness to axial and lateral coupling variations between coils is highly improved. For a triple-layer PSC design case, up to 3.5-fold improved robustness are obtained in reference to conventional IPT systems. Compared with the previous state of the art IPT topologies, the highest Figure-of-Merit value is obtained using the proposed design solutions.

A Wideband Model for On-Chip Interconnects With Different Shielding Structures

In this paper, a wideband model for on-chip interconnects with different shielding structures is proposed. In order to improve the performance of interconnects, solid ground, floating shields, and parallel ground shields are often employed in real applications. Based on the transmission line theory and electromagnetic wave theory, these three different shielding structures are analyzed and discussed. Also, many parasitic effects such as eddy current, skin effect, proximity effect, and substrate loss have been taken into consideration to improve the precision of the proposed model. It is shown that the simulated results of the model are in good agreement with the measured ones up to 110 GHz. The validity of the proposed model has been proven.

Improved method to calculate the high‐frequency eddy currents distribution and loss in windings composed of round conductors

With the switching frequency of power electronic devices increasing rapidly, the high-frequency loss in windings is becoming significant. The one-dimensional (1D) Dowell's method and 2D Ferreira's method are the most accepted methods used for winding loss calculation. Ferreira's method is used to calculate high-frequency loss in windings composed of round conductors. In this study, this method is modified and supplemented with a component called intra-layer proximity effect loss by considering the interaction between conductors in the same layer. The improved model gives much accurate prediction of 2D eddy current distribution in the cross-section of a round conductor with a wider band of frequency than Ferreira's method. On the basis of the eddy current distribution, the AC-to-DC winding resistance ratio is derived. The results of the improved method are verified by finite element method, and the error of loss calculation is <;0.6% when skin effect and proximity effect are very significant.

Wireless Power Transfer Using Selected Harmonic Resonance Mode

The smaller size of the coils is one of the major concerns in designing the wireless power transfer (WPT) systems. In the optimum design of a WPT system, imposing constraints on the physical dimensions of the coils results in more copper usage for certain efficiency. Increasing the operating switching frequency, however, mitigates the weight and copper usage, but it leads to more switching, skin, and proximity effect losses, which decrease the overall efficiency. In this paper, a novel approach using selected harmonic current of switching frequency has been introduced to design optimum coils. In this method, a high resonant frequency converter excited by a lower switching frequency has been developed. The proposed approach leads to lighter and smaller coils with higher efficiency. The proposed approach was verified using simulation and experimental results for a 3500-W WPT system to transfer power over a distance of 0.15 m at 425-KHz resonant frequency while the switching frequency was only 85 KHz.

6.78 MHz, 100 W, 30 cm 거리 무선 전력 전송 시스템의 전선별 손실 및 효율 비교

In MHz operating wireless power transfer systems, skin- and proximity-effect losses in the transmitter and the receiver coils dominate the coil-to-coil efficiency of the system. A Litz-wire was regarded as a common solution for minimizing such Ohmic losses in high frequencies. In this paper, equivalent series resistances of 12 different cables including Litz-wire and copper tubing have been calculated and measured for a 6.78 MHz, 100W, 30 cm wireless power transfer system. It has been shown that the copper tubing has lower resistances compared to the Litz-wire in that frequency and a wireless power transfer system with the copper tubing was able to achieve much higher efficiency than a system using the Litz-wire. Calculations of the resistances and efficiencies were accomplished with analytical equations and those calculations were evaluated by experimental results.

Series Stacked Multipath Inductor With High Self Resonant Frequency

In this brief, a novel combination of multilayer up-down series stacking and multipath architecture for equal path length is explored for the first time to improve the performance of on-chip inductors. The up-down series winding reduces the interlayer capacitance, thereby increasing both the peak quality-factor (Q) frequency ( f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Qmax</sub> ) and self resonant frequency (SRF). The crossover interconnection architecture ensures equal path length at every pair of spiral turns in the series stack. This architecture lowers skin and proximity effect losses in the spiral, increasing the slope of Q characteristics. Thus, using the proposed architecture, both the ac resistance and capacitance are simultaneously reduced while realizing higher inductance values. Implemented in a 0.18 μm high resistivity silicon-on-insulator technology using a dual thick metal stack, the proposed inductor achieves more than 10% improvement in peak-Q value, 50% improvement in f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Qmax</sub> , and 100% improvement in SRF values when compared with a conventional series stacked multipath inductor.

Extraction of Magnetic Parameters for Elements of a Planar EMI Filter

The planar electromagnetic interference (EMI) filter has good application in aviation for its easy magnetic integration, small parasitic parameter, and strong anti-EMI ability. Based on the annular structure, the common-mode (CM) and difference-mode (DM) modules are proposed. The former is formed by “capacitance and inductance” (LC unit), while the latter is formed by an independent DM capacitor and the leakage inductance of the LC units. The extraction of the unit-length electromagnetic parameters is the foundation of analyzing the characteristics of the modules and further the whole EMI filter. The axisymmetric electrostatic field model of LC unit is established to extract the turn-to-turn partial capacitances. Considering the skin effect, proximity effect, and core loss, the model of harmonic magnetic field of LC unit is also established to extract the inductances and resistances. To obtain the leakage inductance that serves as the DM inductance, the model of harmonic magnetic field with a leakage layer between LC units is studied. The DM capacitance can be calculated directly using the approximate expression of a parallel plate. Finally, the impedances of the LC units can be drawn out with the obtained distributed parameters under the appreciate boundary conditions, and they are compared with the measured results. The results verify the accuracy of the extracted parameters and the validity of the proposed extraction method.

Computationally-Efficient, Generalized Expressions for the Proximity-Effect in Multi-Layer, Multi-Turn Tubular Coils for Wireless Power Transfer Systems

Wireless power transfer (WPT) based on magnetic induction is used in numerous applications where physical contact between the power source and the load is not desired. For efficient power transfer, the resonant coils should have a low equivalent series resistance at the resonant frequency and have a high packing factor while being simple to manufacture. Coils made from hollow copper tubes might be an acceptable alternative to Litz wire designs due to low skin-effect resistance, easy manufacturing, and simplicity in implementing active cooling; however, the lack of an analytical model for complex coil designs poses a difficulty in systematically assessing its benefits and limitations. This paper presents a new method, based on the Fourier series, for evaluating proximity-effect losses in a multi-turn, multi-layer tubular coil. The model evaluates the proximity factor G <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sub> as a function of coil and tube parameters, which can be incorporated into the design and optimization procedures. The derivations are supported by simulations that compare analytic and finite element models (FEM) of current density distribution in the coil. The model is further validated via experimental measurements of the resulting equivalent series resistance for two prototype coils.

Analysis of the Double-Layer Printed Spiral Coil for Wireless Power Transfer

As a critical part of the wireless power transfer system via strongly coupled magnetic resonances, the resonant coils must be cautiously designed for the specific resonant frequency and high quality factor. There are some issues needed to be considered and studied in the coil design, such as the coil structure, parasitic parameter extraction, and optimizing. In this paper, the double-layer printed spiral coil is used, which could fully take advantage of the limited space and make larger parasitic capacitance for lower resonant frequency. Using the simplified partial element equivalent circuit method and finite element method, the circuit model with consideration of parasitic parameters and high-frequency losses is built, and the impedance characteristic of coil is simulated, which coincides well with the measurement result. In addition, several elements affecting the high-frequency loss, including the skin effect, proximity effect, and dielectric loss, are discussed for reaching higher quality factor, which is critical for the power transfer system.

Double-π fully scalable model for on-chip spiral inductors

A novel double-π equivalent circuit model for on-chip spiral inductors is presented. A hierarchical structure, similar to that of MOS models is introduced. This enables a strict partition of the geometry scaling in the global model and the model equations in the local model. The major parasitic effects, including the skin effect, the proximity effect, the inductive and capacitive loss in the substrate, and the distributed effect, are analytically calculated with geometric and process parameters in the local-level. As accurate values of the layout and process parameters are difficult to obtain, a set of model parameters is introduced to correct the errors caused by using these given inaccurate layout and process parameters at the local level. Scaling rules are defined to enable the formation of models that describe the behavior of the inductors of a variety of geometric dimensions. A series of asymmetric inductors with different geometries are fabricated on a standard 0.18-μm SiGe BiCMOS process with 100 Ω/cm substrate resistivity to verify the proposed model. Excellent agreement has been obtained between the measured results and the proposed model over a wide frequency range.

An improved continuum skin and proximity effect model for hexagonally packed wires

This work presents approximate but closed-form expressions for “effective” complex-valued magnetic permeability and electric conductivity that represent the effects of proximity and skin effect losses in wound coil with hexagonally packed wires. Previous work is extended by providing improved accuracy versus finite element results for effective permeability and by providing an expression for effective conductivity, which was previously neglected. These material properties can then be used in 2D/axisymmetric finite element models in which the coil is modeled as a coarsely meshed, homogeneous region (i.e., removing the need for modeling each turn in the coil).