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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 aims to investigate the influence of structure parameters on giant-magnetoimpedance (GMI) effect measured by non-contact method.

The GMI sensor contains a Co-based internal magnetic core fabricated by laser cutting and an external solenoid. The influences of magnetic permeability of magnetic core and structure parameters on GMI effect were calculated in theoretical model. The output impedance, resistance, reactance and GMI ratio were measured by non-contact method using impedance analyzer.

Enhancing external magnetic field intensity can decrease the magnetic permeability of core, which has vital influences on the magnetic property and the output response of GMI sensor. In addition, increasing the width of magnetic core and the number of solenoid turns can increase the maximum GMI ratio. The maximum GMI ratio is 3,230% with core width of 6 mm and solenoid turns of 200.

Comparing with traditional contact-measured GMI sensor, the maximum GMI ratio and the magnetic field sensitivity are improved and the power consumption is decreased in non-contact measured GMI sensor. GMI sensor measured by non-contact method has a wide range of potential applications in ultra-sensitive magnetic field detection.

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.

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 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.

This paper aims to overcome the lack of methodologies for optimizing the volume of bulky low-frequency inductors that the authors came across with when working on the design of hybrid active power filters. Sound work was published concerning this well-known technology, but it became evident that the mentioned optimization topic was left unaddressed.

Using the Lagrange multipliers optimization method combined with the electromagnetic laws of inductor design, it was possible to establish a new design method to determine the optimal solutions that fulfil any given scenario of specifications. In other words, it is now possible to obtain the inductor’s geometric and electric parameters that not only satisfy the system’s electromagnetic requirements but also lead to smaller, lighter or economical solutions.

A generalized set of equations was obtained to facilitate the calculations of all the inductor-building parameters. As expected, these equations take as inputs the inductor’s required inductance, its maximum current and the desired resistance, but also a customizable cost function. The later cost function will optimize the inductor’s volumes of copper and iron and can be settled, among other purposes, for minimizing the total weight, volume or cost.

All the mathematical expressions to obtain the general optimal solutions are given as well as practical graphics for the three above-mentioned optimization criteria. Using these charts, the reader will be able to obtain by simple inspection the optimal solutions for a large, generalized universe of intended specifications.

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.

Introduces papers from this area of expertise from the ISEF 1999 Proceedings. States the goal herein is one of identifying devices or systems able to provide prescribed performance. Notes that 18 papers from the Symposium are grouped in the area of automated optimal design. Describes the main challenges that condition computational electromagnetism’s future development. Concludes by itemizing the range of applications from small activators to optimization of induction heating systems in this third chapter.

The results of an empirical investigation into the design and fabrication of high frequency planar thick‐film transformers for use in resonant mode power supplies are reported. A 50 W planar transformer design which realises efficiencies in excess of 90% is presented. The findings are used in order to establish an understanding between winding topologies and dimensions and the physical planar transformer parameters.

The purpose of this paper is to introduce a novel research area involved in fast compute‐online and electronic design automation (EDA) realization, so‐called COMPOL project or COMPOL software tool online (www.compute‐online.com) that is applied to designs of radio frequency integrated circuits/monolithic microwave integrated circuits (RFIC/MMIC) passive components.

This research work will present an interactive software package that has been fitted and verified by the results based on full‐wave full domain Lagrange differential (FDLD) method and experimental approach to realize EDA of RFIC RFIC/MMIC passive components. The developed web platform is based on browser/server pattern, by use of VisualStudio.NET and ASP.NET technologies.

Its functionality may include analysis, synthesis, optimization, interpolation, and modeling of spiral inductors and coplanar waveguide (CPW) with any shape on any material substrate for microwave and wireless applications. Through the complete online processing of the inductors and CPW designs, it is approvable to expand to design applications of other passive components such as resistor (R), capacitor (C), transmission line and connector, etc.

This compute‐online algorithm is first developed by the use of the originally established numerical method – FDLD makes one case design possible to be done online in the time range of seconds.