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The purpose of this paper is twofold. First, it aims to study the proximity‐effect power loss in the foil, strip (rectangular), square, and solid‐round wire inductor windings. Second, it aims to optimize the thickness of the foil, strip, square wire windings, and the diameter of the solid‐round‐wire, the minimum of winding AC resistance and the minimum of winding AC power loss for sinusoidal inductor current.

The methodology of the analysis is as follows. First, the winding resistance of the single‐layer foil winding with a single turn per layer and uniform magnetic flux density B is derived. Second, the single‐layer foil winding with uniform magnetic flux density B is converted for the case, where the magnetic flux density B is a function of x. Third, the single‐layer winding is replaced by the winding with multiple layers isolated from each other. Fourth, transformation of the multi‐layer foil winding into different conductor shapes is performed. For the solid‐round‐wire windings, the results of the derivation are compared to Dowell's equation and verified by measurements.

Closed‐form analytical equations for the optimum normalized winding size (thickness or diameter) at the global or local minimum of winding AC resistance are derived. It has been shown that the AC‐to‐DC winding resistance ratio is equal to 4/3 (F_Rv=4/3) at the optimum normalized thickness of foil and strip wire winding h_opt/δ_w. The AC‐to‐DC winding resistance ratio is equal to 2 (F_Rv=2) at the local minimum of the square wire and solid‐round‐wire winding AC resistances. Moreover, it has been shown that for the solid‐round wire winding, the proximity‐effect AC‐to‐DC winding resistance ratio is equal to Dowell's AC‐to‐DC winding resistance ratio at low and medium frequencies. The accuracy of equation for the winding AC resistance of the solid‐round wire winding inductors has been experimentally verified. The predicted results were in good agreement with the measured results.

It is assumed that the applied current density in the winding conductor is approximately constant and the magnetic flux density B is parallel to the winding conductor (b>>h). This implies that a low‐ and medium‐frequency 1‐D solution is considered and allows the winding size optimization. This is because the optimum normalized winding conductor size occurs in the low‐ and medium‐frequency range. The skin‐effect winding power loss is much lower than the proximity‐effect winding power loss and therefore, it is neglected.

This paper presents derivations of closed‐form analytical equations for the optimum size (thickness or diameter) that yields the global minimum or the local minimum of proximity‐effect loss. A significant advantage of these derivations is their simplicity. Moreover, the paper derives equations for the AC‐to‐DC winding resistance ratio for the different shape wire windings, i.e. foil, strip, square and solid‐round, respectively.

The purpose of this paper is to present a method for calculating frequency-dependent resistance when multiple current-carrying conductors are present.

Analytical and numerical formulations are presented. Both skin- and proximity-effects are considered in the numerical approach, whereas only skin-effect can be taken into account in analytical equations. The calculation is done using a self-developed integral equation-based field solver. The results are benchmarked using professional software based on the finite element method (FEM).

Results from the numerical approach are in agreement with FEM-based software throughout the whole frequency range. Analytical formulations yield unsatisfactory results in higher frequency range. When multiple conductors are mutually relatively close, the proximity-effect has an impact on effective resistance and has to be taken into account.

The methodology is presented using axially symmetrical conductors. However, the same procedure can be developed for straight conductors as well.

Presented fast and stable procedure can be used in most electromagnetic devices when frequency-dependent resistance needs to be precisely determined.

The value of the presented numerical methodology lies in its ability to take both skin- and proximity-effects into account. As conductors are densely packed in most electromagnetic devices, both effects influence the effective resistance. The method can be easily implemented using a self-developed solver and yields satisfactory results.

The purpose of this paper is to propose a numerical procedure for the extraction of RL equivalent circuits of high frequency multi‐winding transformers with a low computational time.

Rigorous RL equivalent circuits of multi‐winding transformers can be obtained by performing open and short‐circuit tests. In this work, the finite element method (FEM) is employed as a virtual laboratory in order to derive such circuits. However, an accurate modeling of skin and proximity effects in the windings requires extremely dense meshes at high frequencies. Therefore, a 2D frequency‐domain homogenization of the windings, which conducts to coarser meshes, is applied in order to decrease the computational burden. The fine and homogenized models are compared in terms of simulation time as well as accuracy.

A significant decrease in simulation times is observed with the homogenized model (one order of magnitude at high frequencies for 2D models), while keeping acceptable relative error values (below 8 percent in the worst case, taking the fine model as reference). Furthermore, it is shown that the skin effect could contribute in a significant way to the total values of the circuit parameters, especially for high frequencies and for small fill factors. It should therefore not be neglected compared to the proximity effect when gathering such conditions, as commonly assumed in the literature.

Equivalent circuits which capture the skin and proximity effects are obtained at an acceptable computational cost, thanks to the use of homogenization techniques in FE simulations. To the best of the authors knowledge, such a procedure has not yet been published.

Previous research on salesperson-customer proximity has yielded mixed results, with some studies documenting positive proximity effects on shopping responses and others demonstrating the reverse. To reconcile such mixed findings, this paper aims to test whether and how salesperson proximity influences a series of key customer outcomes in actual retail settings using sample sizes that are considerably larger than most former investigations.

We conducted two high-powered field studies (N = 1,312) to test whether salesperson‐customer proximity influences consumers’ purchase behavior and store loyalty. Moreover, we investigated whether the short-term effects on purchase behavior were moderated by the extent to which the consumption context had a clear connection to consumers’ own bodies.

Salesperson proximity increased purchase incidence and spending in consumption contexts with a bodily basis (e.g. clothes, beauty, health), suggesting that consumers “buy their way out” in these contexts when a salesperson is violating their personal space. If anything, such proximity had a negative impact on consumers’ purchase behavior in contexts that lacked a clear bodily connection (e.g. building materials, furniture, books). Moreover, the link between proximity and consumer responses was mediated by discomfort, such that a salesperson standing close-by (vs farther away) increased discomfort, with negative downstream effects on shopping responses. Importantly, the authors found opposite proximity effects on short-term metrics (purchase incidence and spending) and long-term outcomes (store loyalty).

Drawing on the nonverbal communication literature and theories on processing fluency, the current work introduces a theoretically relevant boundary condition for the effects of salesperson-customer proximity on consumers’ purchase behavior. Specifically, the bodily basis of the consumption context is discussed as a novel moderator, which may help to explain the mixed findings in this stream of research.

Salesperson-customer proximity may serve as a strategic sales tactic to improve short-term revenue in settings that are closely tied to consumers’ own bodies and characterized by one-time purchases. However, as salesperson proximity was found to be associated with lower store loyalty, irrespective of whether the shopping setting had a bodily basis, the risk of violating consumers’ personal space may have costly consequences from a long-term perspective.

The present field studies make three central contributions. First, we introduce a novel moderator for proximity effects in various sales and service settings. Second, we test the focal hypotheses with much higher statistical power than most existing proximity studies. Finally, we document that salesperson-customer proximity ironically yields opposite results on short-term metrics and long-term outcomes, thus underscoring the importance of not solely focusing on sales effectiveness when training frontline employees.

To develop a subdomain perturbation technique to calculate skin and proximity effects in inductors within frequency and time domain finite element (FE) analyses.

A reference limit eddy current FE problem is first solved by considering perfect conductors via appropriate boundary conditions. Its solution gives the source for eddy current FE perturbation subproblems in each conductor with its actual conductivity. Each of these problems requires an appropriate mesh of the associated conductor and its surrounding region.

The skin and proximity effects in inductors can be accurately determined in a wide frequency range, allowing for a precise consideration of inductive phenomena as well as Joule losses calculations in thermal coupling.

The developed subdomain method allows to accurately determine the current density distributions and ensuing Joule losses in conductors of any shape, not only in the frequency domain but also in the time domain. It extends the domain of validity and applicability of impedance boundary condition techniques. It also allows the solution process to be lightened, as well as efficient parameterized analyses on signal forms and conductor characteristics.

The purpose of this paper is threefold. First, an analytical model based on one-dimensional Dowell’s equation for computing ac-to-dc winding resistance ratio FR of litz wire is presented. The model takes into account proximity effect within the bundle and between bundle layers as well as the skin effect. Second, low- and medium-frequency approximation of Dowell’s equation for the litz-wire winding is derived. Third, a derivation of an analytical equation is given for the optimum strand diameter of the litz-wire winding independent on the porosity factor.

The methodology is as follows. First, the model of the litz-wire bundle is assumed to be a square shape. Than the effective number of layers in the litz wire bundle is derived. Second, the litz-wire winding is presented and an analytical equation for the winding resistance is derived. Third, analytical optimization of the strand diameter in the litz-wire winding is independent on the porosity factor performed, where the strand diameter is independent on the porosity factor. The boundary frequency between the low-frequency and the medium-frequency ranges for both solid-round-wire and litz-wire windings are derived. Hence, useful frequency range of both windings can be determined and compared.

Closed form analytical equations for the optimum strand diameter independent of the porosity factor are derived. It has been shown that the ac-to-dc winding resistance ratio of the litz-wire winding for the optimum strand diameter is equal to 1.5. Moreover, it has been shown that litz-wire winding is better than the solid-round-wire winding only in specific frequency range. At very high frequencies the litz-wire winding ac resistance becomes much greater than the solid-round-wire winding due to proximity effect between the strands in the litz-wire bundle. The accuracy of the derived equations is experimentally verified.

Derived equations takes into account the losses due to induced eddy-currents caused by the applied current. Equations does not take into account the losses caused by the fringing flux, curvature, edge and end winding effects.

This paper presents derivations of the closed-form analytical equations for the optimum bare strand diameter of the litz-wire winding independent on the porosity factor. Significant advantage of derived equations is their simplicity and easy to use for the inductor designers.

This paper seeks to develop a sub‐domain perturbation technique to efficiently calculate strong skin and proximity effects in conductors within frequency and time domain finite element (FE) analyses.

A reference eddy current FE problem is first solved by considering perfect conductors. This is done via appropriate boundary conditions (BCs) on the conductors. Next the solution of the reference problem gives the source for eddy current FE perturbation sub‐problems in each conductor then considered with a finite conductivity. Each of these problems requires an appropriate volume mesh of the associated conductor and its surrounding region.

The skin and proximity effects in both active and passive conductors can be accurately determined in a wide frequency range, allowing for precise losses calculations in inductors as well as in external conducting pieces.

The developed method allows one to accurately determine the current density distributions and ensuing losses in conductors of any shape, not only in the frequency domain but also in the time domain. Therefore, it extends the domain of validity and applicability of impedance‐type BC techniques. It also offers an original way to uncouple FE regions that allows the solution process to be lightened, as well as efficient parameterized analyses on the signal form and the conductor characteristics.

This study seeks to apply finite element analysis to study the proximity effect in a multi‐pickup inductively coupled power transfer system, quantify the effect and propose improved pick‐up configurations.

A mixture of approximate analytical formulae and accurate finite‐element simulations has been used as a tool for qualitative and quantitative analysis. Simplified consideration of magnetic flux paths aids understanding, whereas detailed numerical computation provides reliable performance prediction.

It is shown that a multi‐pickup formation of conventional E‐pickups may lead to power loss due to negative coupling between neighbouring pickups and that the phenomenon is nonlinear. Thus, two novel configurations for multi‐pickup systems have been proposed, an alternately‐directed Z‐pickup and a spilt‐type E‐pickup, both showing improved linearity, increased total power and more efficient use of ferromagnetic material.

The investigation aimed mainly at the electromagnetic performance, while economic issues will still need to be addressed.

The proposed pick‐up configurations may be very helpful in systems where improved performance is needed but space or configuration limitations restrict or eliminate the possibility of using other designs.

The finite‐element aided magnetic field simulation has proved invaluable in achieving difficult design objectives. The combination of a simplified analytical approach and detailed numerical analysis has provided a reliable tool for accomplishing improved designs.

The purpose of this paper is the presentation of an electrical equivalent circuit for inductive components as well as the methodology for electrical parameter extraction by using a 3 D finite element analysis (FEA) tool.

A parameter extraction based on energies has been modified for three dimensions. Some simplifications are needed in a real model to make the 3 D finite element method (FEM) analysis operative for design engineers. Material properties for the components are modified at the pre-modeling step and a corrector factor is used at the post-modeling step to achieve the desired accuracy.

The current hardware computational limitations do not allow the 3 D FEA for every magnetic component, and due to the component asymmetries, the 2 D analysis are not precise enough. The application of the new methodology for three dimensions to several actual components has shown its usefulness and accuracy. Details concerning model parameters extration are presented with simulation and measurement results at different operation frequencies from 1 kHz to 1 GHz being the range of switching frequencies used by power electronic converters based on Si, SiC or GaN semiconductors.

This new model includes the high-frequency effects (skin effect, proximity effect, interleaving and core gap) and other effects can be only analyzed in 3 D analysis for non-symmetric components. The electrical parameters like resistance and inductance (self and mutual ones) are frequency-dependent; thus, the model represents the frequency behavior of windings in detail. These parameters determine the efficiency for the inductive component and operation capabilities for the power converters (as in the voltage boost factor), which define their success on the market.

The user can develop 3 D finite element method (FEM)-based analyses with geometrical simplifications, reducing the CPU time and extracting electrical parameters. The corrector factor presented in this paper allows obtaining the electrical parameters when 3D FE simulation would have developed without any geometry simplications. The contribution permits that the simulations do not need a high computational resource, and the simulation times are reduced drastically. Also, the reduced CPU time needed per simulation gives a potential tool to optimize the non-symmetric components with 3 D FEM analysis.

We examine the role of past litigation in the selection of independent auditors. Using a sample of persons typically involved in auditor selection, we find that any litigation announcement alleging audit improprieties greatly reduces the auditor’s likelihood of hire regardless of the type of legal action announced or the degree of direct involvement by the auditor. Based on these findings, litigation imposes an indirect (and potentially substantial) cost by impeding the CPA’s ability to attract new clients.