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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.

This paper seeks to consider the design of small, naturally cooled, and high‐frequency (in excess of 10 kHz) inductors. Its purpose is to show that the design of such inductors can be obtained from the solution of a signomial program. In its most general form, the signomial program calls for minimising the total mass (or cost) of the inductor whilst ensuring the satisfaction of the inductance value together with constraints imposed by the copper fill‐factor, the allowed temperature rise, Kirchhoff's mmf law, and the core flux density.

The signomial program is solved using a sequential geometric programming (SGP) approach specifically tailored to the inductor design problem. In essence, SGP seeks a constrained minimum mass (or cost) solution by optimally setting the inductor geometry parameters, the air‐gap length, and the relevant electrical and magnetic quantities.

Design results reveal that including the inductor geometry parameters in the set of problem variables leads to significant savings in the inductor mass (or cost).

In cases where there are restrictions on the inductor weight, the optimal solution of the signomial program can be used for manufacturing inductors having cores with non‐standard sizes. In other applications where core dimensions are chosen from the manufacturer's database, the SGP approach can be used to complete the design by either maximising the inductance value or minimising the total loss whilst enforcing a given inductance value.

This work presents a first attempt to optimise an inductor design via signomial programming. The proposed solution methodology is based on SGP, but specifically adapted to the inductor design problem.

Dielectric barrier discharge (DBD) is widely used in the treatment of skin disease, surface modification of material and other fields of electronics. The purpose of this paper is to design a high-performance power supply with a compact structure for excimer lamps in electronics application.

To design a high-performance power supply with a compact structure remains a challenge for excimer lamps in electronics application, a current-source type power supply in a single stage with power factor correction (PFC) is proposed. It consists of an excitation voltage generation unit and a PFC unit. By planning the modes of the excitation voltage generation unit, a bipolar pulse excitation voltage with a high rising and falling rate is generated. And a high power factor (PF) on the AC side is achieved by the interaction of a non-controlled rectifier and two inductors.

The experimental results show that not only a high-frequency and high-voltage bipolar pulse excitation voltage with a high average rising and falling rate (7.51GV/s) is generated, but also a high PF (0.992) and a low total harmonic distortion (5.54%) is obtained. Besides, the soft-switching of all power switches is realized. Compared with the sinusoidal excitation power supply and the current-source power supply, the proposed power supply in this paper can take advantage of the potential of excimer lamps.

A new high-performance power supply with a compact structure for DBD type excimer lamps is proposed. The proposed power supply can work stably in a wide range of frequencies, and the smooth regulation of the discharge power of the excimer lamp can be achieved by changing the switching frequency. The ideal excitation can be generated, and the soft switching can be realized. These features make this power supply a key player in the outstanding performance of the DBD excimer lamps application.

There are few reports that evolutional topology optimization methods are applied to the conductor geometry design problems. This paper aims to propose an evolutional topology optimization method is applied to the conductor design problems of an on-chip inductor model.

This paper presents a topology optimization method for conductor shape designs. This method is based on the normalized Gaussian network-based evolutional on/off topology optimization method and the covariance matrix adaptation evolution strategy. As a target device, an on-chip planer inductor is used, and single- and multi-objective optimization problems are defined. These optimization problems are solved by the proposed method.

Through the single- and multi-objective optimizations of the on-chip inductor, it is shown that the conductor shapes of the inductor can be optimized based on the proposed methods.

The proposed topology optimization method is applicable to the conductor design problems in that the connectivity of the shapes is strongly required.

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.

The purpose of this paper is to investigate a bi-objective optimization problem characterized by coupled field analysis. The optimal design of a pancake inductor for the controlled heating of a graphite disk is considered as the benchmark problem. The case study is related to the design of industrial applications of the induction heating of graphite disk.

The expected goal of the optimization process is twofold: to improve temperature uniformity in the disk and also electrical efficiency of the inductor. The solution of the relevant bi-objective optimization problem is based on multiphysics field analysis. Specifically, the direct problem is solved as a magnetic and thermal coupled problem by means of finite elements; a mesh-inspired definition of thermal uniformity is proposed. In turn, the Pareto front trading off electrical efficiency and thermal uniformity is identified exploiting evolutionary computing.

By varying the problem targets, different Pareto fronts are identified trading off thermal uniformity and electrical efficiency of the induction-heating device.

These results suggest how to improve the design of this kind of device for the epitaxial growth of silicon wafer; the advantage of using a magnetic concentrator placed close to the inductor axis is pointed out.

The coupling of a multiphysics direct problem with a multiobjective inverse problem is presented as a benchmark problem and accordingly solved. The benchmark provides a simple analysis problem that allows testing various optimization algorithms in a comparative way.

The appropriate selection of a testing method largely determines the accuracy of a measurement. Parasitic effects associated with test fixture demand a significant consideration in a measurement. The purpose of this paper is to introduce a measurement procedure which can be used for the characterization of surface mount devices (SMD) components, especially devoted to SMD inductors.

The paper describes measurement technique, characterization, and extracting parameters of SMD components for printed circuit board (PCB) applications. The commercially available components (multi‐layer chip SMD inductors in the ceramic body) are measured and characterized using a vector network analyzer E5071B and adaptation test fixture on PCB board. Measurement results strongly depend on the choice of the PCB; the behaviour of the component depends on the environment where the component is placed.

The equivalent circuit parameters are extracted in closed form, from an accurate measurement of the board‐mounted SMD inductor S‐parameters, without the necessity for cumbersome optimization procedures, which normally follow the radio frequency circuit synthesis.

It this paper, a new adaptation test fixture in PCB technology is realized. It is modeled and it has provided the extraction of parameters (intrinsic and extrinsic) of SMD inductor with great accuracy.

In surface mount assembly (SMA) process, small components are subjected to high temperature variations, which result in components’ deformation and cracking. Because of this phenomenon, cracks are formed in the body of carbonyl powder ceramic inductor (CPCI) in the preheat and cooling stages of the reflow oven. These cracks become the main cause of board failure in the ageing process. The purpose of this paper is to ascertain the thermal stress, thermal expansion of carbonyl iron ceramics and its effects on crack commencement and proliferation in the preheat stage of reflow oven. Moreover, this paper also categorized and suggested important parameters of reflow profile that could be used to eliminate these thermal shock failures.

In this paper, two different reflow profiles were studied that evaluate the thermal shock of CPCI during varying ΔT at the preheat zone of the reflow oven. In the first profile, the change in temperature ΔT at preheat zone was set to 3.26°C/s, which has resulted in a number of device failures because of migration of micro cracks through the CPCI. In the second profile, this ΔT at preheat stage is minimized to 2.06°C/s that eliminated the thermal stresses; hence, the failure rates were significantly reduced.

TMPC0618H series lead (Pb)-free CPCI is selected for this study and its thermal expansion and thermal shock are observed in the reflow process. It is inferred from the results that high ΔT at preheat zone generates cracks in the carbonyl powder-type ceramics that cause device failure in the board ageing process. Comparing materials, carbonyl powder ceramic components are less resistant to thermal shock and a lower rate of temperature change is desirable.

The proposed study presents an experimental analysis for mitigating the thermal shock defects. The realization of the proposed approach is validated with experimental data from the printed circuit boards manufacturing process.

This work aims to study a new design of linear permanent magnet transverse flux induction heating devices of nonmagnetic parallelepipedic workpiece. In these topologies, the permanent magnet inductor produces a static magnetic field, and the workpiece to be heated is subjected to a linear movement. To study the magnetothermal process, a new analytical coupling method between the magnetic and thermal phenomena is developed. This analytical model described in this study takes into account the variation of the physical properties of the heated workpiece. The analytical results are compared with good agreement to those issued from finite elements simulations, as well as those issued from measurements on an actual prototype.

The research methodology is based on analytical development of coupled problem, including the electromagnetic and thermal boundary problems. A strongly coupled magneto-thermal analytical model is developed; the time dependent magnetic problem is first solved by using the separation of variables method to evaluate the induced currents in the nonmagnetic plate and the resulting power density loss distribution. The plate temperature profile is then obtained, thanks to strong involvement of this magnetic model in a new analytical thermal model based on a synergy of separation of variables method and Green’s function transient regime analysis method.

The results show that an efficient transient magneto-thermal analytical model was developed allowing fast analysis of permanent magnet induction heater for deep heating of parallelepipedic workpieces. Developed model allows also fast and precise simulations of nonlinear and transient magneto-thermal phenomena for different types of permanent magnet induction heating devices.

The developed magneto-thermal analytical model can be used for fast designing of permanent magnet linear induction heating devices for moving parallelepipedic nonmagnetic workpiece.

A new analytical coupled model, including the electromagnetic and transient thermal boundary problem with additional algebraic equations and taking into account the nonlinearity, has been developed. The developed model accuracy was validated with a permanent magnet linear induction heating device. Developed coupled analytical model allows fast analysis and designing of such permanent magnet linear induction heating devices.