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Present 3D electromagnetic simulators have high accuracy but they are time and memory expensive. Owing to a fast and simple expression for inductance is also necessary for initial inductor design. In this paper, new efficient methods for total inductance calculation of meander inductor, are given. By using an algorithm, it is possible to predict correctly all inductance variations introduced by varying geometry parameters such as number of turns, width of conductor or spacing between conductors.

The starting point for the derivation of the recurrent formula is Greenhouse theory. Greenhouse decomposed inductor into its constituent segments. Meander inductor is divided into straight conductive segments. Then the total inductance of the meander inductor is a sum of self‐inductances of all segments and the negative and positive mutual inductances between all combinations of straight segments. The monomial equation for the total inductance of meander inductor has been obtained by fitting procedure. The fitting technique, using the method of least squares, finds the parameters of the monomial equation that minimize the sum of squares of the error between the accurate data and fitted equation. The paper presents new expression for inductance of meander inductor, in the monomial form, which is suitable for optimization via geometric programming. The computed inductances are compared with measured data from the literature.

The first, recurrent, expression has the advantage that it indicates to the designer how the relative contributions of self, positive, and negative mutual inductance are related to the geometrical parameters. The second expression presents the inductance of the meander inductor in the monomial form, so that the optimization of the inductor can be done by procedure of the geometric programming. Simplicity and relatively good accuracy are the advantages of this expression, but on the other hand the physical sense of the expression is being lost. Thus, the effects of various geometry parameters on inductance are analyzed using two expressions and the software tool INDCAL.

Applied flexible efficient methods for inductance calculation of meander inductor are able to significantly increase the speed of RF and sensor integrated circuit design.

For the first time a simple expression for fast inductance calculation for meander inductor in monomial form is presented. It is explained how such an expression is generated, which can be directly implemented in circuit simulators.

The purpose of this paper is to compare several methods to calculate solenoid inductances regarding their applicability to model the inductance of DC motor armature windings. Special attention is given to the influence of wiring insulation and current distribution and the axial length of the solenoid.

Expressions for the self‐ and mutual‐inductance of current filament and wire combinations are derived from basic inductance formulas. Combining these expressions allows expressing the inductance of arbitrary shaped solenoids (e.g. polygons).

Accurately describing self‐ and mutual‐inductances is a very complex topic. However, in the case of motor armature windings, several simplifications can be applied to lower the calculation cost significantly. Plus, differences in inductances between regular polygonial solenoids and similar circular shapes were found to be rather small. Thus, many windings' inductances can well be approximated by using expressions for circular solenoids.

A new way to calculate the inductance of arbitrary polygonial shapes is presented, and an example is given for hexagonal shapes.

The purpose of this paper is to minimize on‐chip inductance effect for modern very large‐scale integration (VLSI), ultra large‐scale integration (ULSI) systems.

As operating frequency increases, parasitic inductance has become a major concern for electronic design on both delay and coupling noises. The impacts of on‐chip inductance are strongly associated with higher frequency operation, denser interconnect geometry, reductions of resistance, and capacitance of interconnects. The paper presents a novel layout technique – opposing inter‐digitating routing, to generate magnetic fields in opposing directions; consequently, effective magnetic field is minimized, or inductance effect is reduced. To prove the effectiveness of these approaches, 3D field solver FastHenry is used to extract inductance data and verify the results.

Verification shows that this proposed method gives more than ten times reduction in self‐inductance while mutual inductance reduces even faster, without incurring any area and resource penalty.

The proposed technique can be used effectively to minimize inductance effects in the design of modern interconnect structures. This technique is shown to be highly effective for inductance reduction in wide signal buses which are used frequently in global buses, critical data path or clock distribution networks of VLSI and ULSI systems.

Permanent magnet (PM) brushless machines equipped with fractional‐slot concentrated‐windings (FSCW) have been receiving considerable attention over the past few years, due to the fact that they have short end‐windings, a high‐slot fill factor, a high efficiency and power density, and good flux‐weakening and fault‐tolerance capabilities. A key design parameter for such machines is the phase winding inductance since this has a significant impact on the performance, as well as on the magnitude of any reluctance torque. The purpose of this paper is to describe a detailed investigation of the various components of the winding inductance in machines equipped with both overlapping and non‐overlapping windings and different slot/pole number combinations. It also examines the influence of key design parameters, which affect the inductance components, with particular reference to the inductances of machines in which all the teeth are wound and those in which only alternate teeth are wound.

The paper analyzes and compares various inductance components which result from different winding configurations.

It is shown that the main component of the winding inductance is the relatively large slot‐leakage component. Both analytical and finite element models are employed and predicted results are validated on several prototype machines.

Such a thorough investigation of the various inductance components for these type of machines has not been presented before. The paper will serve as a good reference for engineers and researchers designing PM machines equipped with FECW.

The purpose of this paper is to present an accurate and efficient hybrid method for the calculation of the inductance of a coil and its inductance change due to deformed turns using numerical methods.

The paper opted for finite element method coupled with analytical method (FCA) to accurately calculate the inductance of a coil, which is used as reference value. An algorithm with a power function is presented to approximate the partial inductance matrix with the purpose of obtaining the percentage change of the inductance due to deformed turns by using the partial element equivalent circuit (PEEC) with an approximated model and an optimization process. The presented method is successfully validated by the numerical results.

The paper provides a systematic investigation of the inductance of an arbitrary shaped coil and shows how to accurately and efficiently evaluate the inductance change of a coil due to its deformed turns. It suggests that the inductance of a coil can be accurately calculated by using FCA and its percentage change due to deformed turns can be efficiently calculated by using the PEEC_Approximation.

As this research is for the magnetostatics, the skin- and proximity-effects have not been taken into account.

The paper includes implication for the worst-case analysis of the coil’s inductance due to mechanical damage or manufacturing tolerance.

This paper fulfills an identified need to study how the inductance change of a coil can be obtained accurately and efficiently.

Rectangular conductors play an important role in planar transmission line structures, multiconductor transmission lines, in power transmission and distribution systems, LCL filters, transformers, industrial busbars, MEMs devices, among many others. The precise determination of the inductance of such conductors is necessary for their design and optimization, but no explicit solution for the AC resistance and internal inductances per-unit length of a linear conductor with a rectangular cross-section has been found, so numerical methods must be used. The purpose of this paper is to introduce the use of a novel numerical technique, the proper generalized decomposition (PGD), for the calculation of DC and AC internal inductances of rectangular conductors.

The PGD approach is used to obtain numerically the internal inductance of a conductor with circular cross-section and with rectangular cross-section, both under DC and AC conditions, using a separated representation of the magnetic vector potential in a 2D domain. The results are compared with the analytical and approximate expressions available in the technical literature, with an excellent concordance.

The PGD uses simple one-dimensional meshes, one per dimension, so the use of computational resources is very low, and the simulation speed is very high. Besides, the application of the PGD to conductors with rectangular cross-section is particularly advantageous, because rectangular shapes can be represented with a very few number of independent terms, which makes the code very simple and compact. Finally, a key advantage of the PGD is that some parameters of the numerical model can be considered as additional dimensions. In this paper, the frequency has been considered as an additional dimension, and the internal inductance of a rectangular conductor has been computed for the whole range of frequencies desired using a single numerical simulation.

The proposed approach may be applied to the optimization of electrical conductors used in power systems, to solve EMC problems, to the evaluation of partial inductances of wires, etc. Nevertheless, it cannot be applied, as presented in this work, to 3D complex shapes, as, for example, an arrangement of layers of helically stranded wires.

The PGD is a promising new numerical procedure that has been applied successfully in different fields. In this paper, this novel technique is applied to find the DC and AC internal inductance of a conductor with rectangular cross-section, using very dense and large one-dimensional meshes. The proposed method requires very limited memory resources, is very fast, can be programmed using a very simple code, and gives the value of the AC inductance for a complete range of frequencies in a single simulation. The proposed approach can be extended to arbitrary conductor shapes and complex multiconductor lines to further exploit the advantages of the PGD.

This paper aims to show the proposed energy method for inductance calculation is valid for any number of poles, phases and any winding layout.

A two-dimensional (2-D) analytical energy-based approach is presented to calculate self-inductances and mutual inductances of brushless surface-mounted permanent-magnet machines.

The proposed calculation procedure is valid for brushless permanent-magnet machines with slotted or slotless stator structure. Comparisons between energy method and flux linkage method are presented based on simulation and experimental results. It shows that the energy method has an excellent agreement with the result obtained from finite element method (FEM) and experimental study.

This paper compares energy-based method with flux linkage method and FEM for inductance calculations in slotless and slotted permanent-magnet motors. The relations for inductance calculation are presented which are obtained based on 2-D analytical representation of magnetic field.

The purpose of this paper is to develop a system for estimating the position of the active magnetic bearing (AMB) shaft. A new approach using the static and dynamic inductances and complex analytic signal to simplify the estimation procedure. Finite element (FE) simulations are introduced as a part of the system synthesis.

The paper presents an AMB displacement estimation system. The system is created with three inductive sensors. The position is computed from refined static and dynamic inductance obtained from complex analytic signals of flux and current. FE simulation is used to relate refined inductances to the displacement and to verify the model.

This paper shows the applicability of complex analytic signal transformation on estimation systems. The use of new refined inductance is presented in contrast to the classical approach of static and dynamic inductances. The paper shows that classical approach of static and dynamic inductance is not usable for the presented estimation system.

For the practical implementation of the presented system, it is necessary to know the exact dimensions of the AMB stator and the voltage and frequency used to supply the inductance estimation system.

The paper presents a system for estimating the displacement of AMB. The paper introduces the application of complex analytic signal to the estimation of AMB displacement. The mentioned signal is used to compute the new refined inductances. The comparison to the classical approach of static and dynamic inductances is given in this paper. The paper introduces FE simulations to the estimation system synthesis.

This paper aims to propose an effective method to verify poles polarities of switched reluctance motors (SRMs). Different from the ways of detection poles polarities by permanent magnet in SRMs, the difference of self-inductance between different winding connections is used to verify the pole polarity.

First, the winding connections with the forward and reverse series are proposed. The magnetic circuit models are established to analyze the flux linkage of different winding connections. Then, according to the difference of inductance characteristics, including the self-inductance and the mutual inductance affected by the adjacent poles, it is theoretically feasible to verify the polarity of each pole. Finally, the proposed method is verified by the simulation and experiment on a six-phase SRM.

First, compared to the reverse series, the forward series can produce larger self-inductance when one phase is excited at the same current excitation, which can be used to verify the poles polarities of one phase with different winding connection. Second, the mutual inductance can be used to distinguish the winding connections. Third, the difference of the maximum self-inductance of the winding, which is composed of two adjacent windings, can be used to verify the polarities of the adjacent poles.

This paper proposes an effective method to verify poles polarities of SRMs.

The purpose of this paper is to present and apply a parasitic extraction approach for the calculation of DC busbar inductances.

A computational approach based on the finite integration technique and computed magnetic energy is developed to extract parasitic inductances. The finite integration analysis is conducted via the magnetoquasistatic solver of CST EM Studio^® capturing the 3D geometrical effects of the design, as well as the skin and proximity effects.

The method is applied successfully to evaluate the leakage inductances of two printed circuit boards structures; a backplane sample for the verification purpose and a real DC bus employed in a three‐phase pulse width modulation inverter.

The paper demonstrates that the method calculates the loop inductances accurately. It does not, however, verify the used technique to split loop inductances into partial inductances.

The extraction method is easy‐to‐use and able to handle complex geometries within acceptable computation time and accuracy.

The paper introduces a way to compute the parasitic inductances from the results of a numerical electromagnetic field solver.