A simple technique to evaluate winding losses includingtwo-dimensional edge effects

This paper presents a simple technique for evaluating the AC losses of magnetic windings including two-dimensional (2-D) edge effects. Although one-dimensional (1-D) analysis tools have been developed to evaluate winding losses in conductor windings, the additional AC losses due to 2-D edge effects are quite significant and cannot be predicted by the developed 1-D solutions. The proposed approach is based on introducing a set of correction factors for the 1-D analysis results to account for the 2-D edge effects. Finite-element analyses are utilized to validate the obtained results     

A practical approach to model long MIS interconnects in VLSI circuits

In this paper, a practical approach to model metal-insulator-semiconductor (MIS) interconnects is presented, with focus on the microstrip configuration. Starting from a one-dimensional (1-D) electromagnetic field analysis, we first extend the validity range of some closed-form expressions from 1-D to two-dimensional (2-D) and present an original RLCG-B model with five equivalent circuit parameters. These parameters, which depend on two effective widths of the physical metal strip, can be frequency dependent because of the skin effect and the dielectric losses. The original RLCG-B model is then modified and implemented with seven frequency-independent circuit parameters. These parameters are computed by analytical equations. Numerical simulations are used to validate the original and modified RLCG-B models. A formula to allow comparison of various interconnect models in the time domain is proposed. Comparisons based on this formula are presented for a single transmission line with source resistance, R/sub S/, and load capacitance, C/sub L/. Such comparisons are more meaningful in VLSI applications than comparisons of characteristics derived from swept-frequency per-unit-length parameters.     

A Semiempirical Model to Determine HF Copper Losses in Magnetic Components With Nonlayered Coils

While in numerous power electronics applications, transformers and inductors with nonlayered windings are used, the absence up until now of any theoretical or even empirical model for their HF effective resistance calculation leads magnetic component designers to make high-error approximations. The typical approach until now has been to consider them as layered and apply some of the existent relevant models. The present paper establishes a new semiempirical model for the accurate determination of HF copper losses in windings with the random conductor distribution, a case that cannot be treated by any analytical method. This model is based on the statistical treatment of numerical results coming from a large number of simulations carried out with finite-element analysis software, and incorporates only three easily determinable parameters. The selected range for each of these parameters ensures that the model is suitable for the majority of practical applications. The theoretical analysis is verified by experimental measurements on different forms of winding geometries. A detailed investigation of the new formula reveals its inherent advantages on copper loss calculation when designing nonlayered coils.      

Optimizing the AC resistance of multilayer transformer windingswith arbitrary current waveforms

AC losses due to nonsinusoidal current waveforms have been found by calculating the losses at harmonic frequencies when the Fourier coefficients are known. An optimized foil or layer thickness in a winding may be found by applying the Fourier analysis over a range of thickness values. This paper presents a new formula for the optimum foil or layer thickness, without the need for Fourier coefficients and calculations at harmonic frequencies. The new formula requires the RMS value of the current waveform and the RMS value of its derivative. It is simple, straightforward and applies to any periodic waveshape     

Optimal air-gap design in high-frequency foil windings

High-frequency AC losses are normally induced in transformer and inductor windings due to skin, proximity, fringing and other AC effects. In addition, the winding structure greatly affects the distribution of losses within the windings. Air gaps are usually placed in the core of magnetic devices to support the high magnetomotive force (MMF). Fringing fields can cause additional AC winding losses, and care must be taken to minimize these losses. In this paper, the effect of air-gap design on the induced losses is investigated. In particular, three air-gap designs-lumped, discretely distributed and uniformly distributed-are investigated and evaluated. Both one-dimensional (1-D) and finite-element analyses (FEAs) are used to investigate the different design structures     

Study of 3-D magnetic components by means of "double 2-D" methodology

The magnetic field in many magnetic components, namely toroids and EE cores, has a three-dimensional (3-D) distribution. Energy and losses calculation in these particular structures makes necessary the use of 3-D techniques that accounts for all 3-D effects. The calculation of the energy and losses is needed in order to obtain any transformer model. This paper presents a procedure that allows the calculation of energy and losses in 3-D structures using two-dimensional (2-D) approaches. This procedure accounts for 3-D effects, solving each magnetic component by means of two different analyses but using 2-D finite-element analysis (FEA) solvers instead of 3-D. The main advantages of this procedure are that all geometrical and frequency effects are taken into account using 2-D FEA solvers. 3-D FEA solvers are not applicable to analyze most practical cases because of the complexity in the geometry. Therefore, the use of this method is not only advantageous from the point of view of time reduction, but also it is a solution for many cases where 3-D solvers are not a feasible solution. Some experimental results illustrate the application of the methodology, which is especially useful to study the influence of the winding strategy in toroidal structures and to design integrated magnetics in order to adjust the coupling coefficient between each pair of windings before the component construction.     

Hierarchical 2-D DD and HD noise simulations of Si and SiGe devicesII. Results

For pt. I see ibid., vol. 49, pp. 1250-1257 (2002). Terminal current noise is investigated with Langevin-type drift-diffusion (DD) and hydrodynamic (HD) noise models for one-dimensional (1-D) N⁺ NN⁺ and P⁺ PP⁺ structures and a realistic two-dimensional (2-D) SiGe NPN HBT. The new noise models, which are suitable for technology computer aided design (TCAD), are validated by comparison with Monte Carlo (MC) device simulations for the 1-D structures including noise due to particle scattering and generation of secondary particles by impact ionization (II). It is shown that the accuracy of the usual approach based on the DD model in conjunction with the Einstein relation degrades under nonequilibrium conditions. 2-D MC noise simulations are found to be feasible only if the current correlation functions decay on a subpicosecond scale, what is not always the case     

Computationally efficient winding loss calculation with multiplewindings, arbitrary waveforms, and two-dimensional or three-dimensionalfield geometry

The squared-field-derivative method for calculating eddy-current (proximity-effect) losses in round-wire or litz-wire transformer and inductor windings is derived. The method is capable of analyzing losses due to two-dimensional and three-dimensional field effects in multiple windings with arbitrary waveforms in each winding. It uses a simple set of numerical magnetostatic field calculations, which require orders of magnitude less computation time than numerical eddy-current solutions, to derive a frequency-independent matrix describing the transformer or inductor. This is combined with a second, independently calculated matrix, based on derivatives of winding currents, to compute total AC loss. Experiments confirm the accuracy of the method     

Finite-element method modeling of superconductors: from 2-D to 3-D

A three-dimensional (3-D) numerical modeling technique for solving problems involving superconducting materials is presented. The model is implemented in finite-element method software and is based on a recently developed 3-D formulation for general electromagnetic problems with solid conductors. It has been adapted for modeling of superconductors with nonlinear resistivity in 3-D, characterized by a power-law E-J relation. It has first been compared with an existing and verified two-dimensional (2-D) model: Compared are the current density distribution inside the conductors and the self-field ac losses for different applied transport currents. Second, the model has been tested for computing the current distribution with typical 3-D geometries, such as corner-shaped and twisted superconductors. Finally, it has been used with two superconducting filaments in the presence of external magnetic field for verifying the existence of coupling currents. This effect deals with the finite length of the conductors and cannot be taken into account by 2-D models.     

Electrothermal analysis of the self-excited push-pull DC-DC converter

The SPICE-aided electrothermal analysis of a self-excited push-pull DC-DC converter is considered in the paper. The new electrothermal model of a pulse transformer, which constitutes the basic component element of the considered converter, is proposed. This model contains among others: two different temperatures of the windings and the core, the influence of temperature on losses in the core and in the windings, the dependence of the magnetization curve on the core temperature, the Curie temperature, selfheating and mutual thermal interactions between the core and the windings. The semiconductor devices are described with the use of the hybrid electrothermal models. The measurements and electrothermal calculations of the characteristics of the investigated converter with the use of the models proposed in the paper are performed. A good agreement between the results of the calculations and the measurements achieved with this model testifies to correctness of the presented models.     

Exact and approximate rebinning algorithms for 3-D PET data

This paper presents two new rebinning algorithms for the reconstruction of three-dimensional (3-D) positron emission tomography (PET) data. A rebinning algorithm is one that first sorts the 3-D data into an ordinary two-dimensional (2-D) data set containing one sinogram for each transaxial slice to be reconstructed; the 3-D image is then recovered by applying to each slice a 2-D reconstruction method such as filtered-backprojection. This approach allows a significant speedup of 3-D reconstruction, which is particularly useful for applications involving dynamic acquisitions or whole-body imaging. The first new algorithm is obtained by discretizing an exact analytical inversion formula. The second algorithm, called the Fourier rebinning algorithm (FORE), is approximate but allows an efficient implementation based on taking 2-D Fourier transforms of the data. This second algorithm was implemented and applied to data acquired with the new generation of PET systems and also to simulated data for a scanner with an 18° axial aperture. The reconstructed images were compared to those obtained with the 3-D reprojection algorithm (3DRP) which is the standard “exact” 3-D filtered-backprojection method. Results demonstrate that FORE provides a reliable alternative to 3DRP, while at the same time achieving an order of magnitude reduction in processing time     

Reconstruction algorithms: Transform methods

Transform methods for image reconstruction from projections are based on analytic inversion formulas. In this tutorial paper, the inversion formula for the case of two-dimensional (2-D) reconstruction from line integrals is manipulated into a number of different forms, each of which may be discretized to obtain different algorithms for reconstruction from sampled data. For the convolution-backprojection algorithm and the direct Fourier algorithm the emphasis is placed on understanding the relationship between the discrete operations specified by the algorithm and the functional operations expressed by the inversion formula. The performance of the Fourier algorithm may be improved, with negligible extra computation, by interleaving two polar sampling grids in Fourier space. The convolution-backprojection formulas are adapted for the fan-beam geometry, and other reconstruction methods are summarized, including the rho-filtered layergram method, and methods involving expansions in angular harmonics. A standard mathematical process leads to a known formula for iterative reconstruction from projections at a finite number of angles. A new iterative reconstruction algorithm is obtained from this formula by introducing one-dimensional (1-D) and 2-D interpolating functions, applied to sampled projections and images, respectively. These interpolating functions are derived by the same Fourier approach which aids in the development and understanding of the more conventional transform methods.     

快速二维直方图斜分最小误差的图像阈值分割

鉴于二维斜分法的优势,提出了一种快速二维直方图斜分最小误差的阈值分割方法。首先将二维直方图斜分原理运用到最小误差阈值法中使得分割更准确,然后对其阈值选取公式进行简化得到最简公式,并利用此公式导出其一般递推算法,最后将二维直方图概率分布特性与这种算法有机结合得到新型的递推算法来提高运行速度。实验结果表明,与二维直线型最小误差阈值分割法相比,算法效率更高,与其递推算法相比,所提出的新型递推算法的运行速度更快,约快4倍。     

Integrated planar L-C-T component: Design,Characterization and Experimental Efficiency analysis

In a resonant dc/dc converter, the major part of the volume is filled by passive components. Moreover, all these components have to support all the power flow. On the one hand, this leads to losses in these components and their connections and on the other hand to an important cost of the converter. Concept of integrated passive component, called inductor-capacitor-transformer (L-C-T), is now well known [1],[3] ,[4] ,[6],[8], and this paper will present a new prototype which permits to integrate in an unique part an inductor, a capacitor and a transformer. Because it uses only one core with three windings, this component will reduce the volume of the passive part of the converter. By reducing the number of connections it will, also, have a positive effect on losses. After a presentation of L-C-T components, this paper describes a design of this device, using new windings disposition. The proposed structure permits to adjust separately L and C values. Then, to validate the approach, a characterization is carried out, leading to a new model, including dielectric, iron and copper losses.     

Efficient algorithm for 2-D arithmetic Fourier transform

This article presents an efficient algorithm for the two-dimensional (2-D) arithmetic Fourier transform (AFT) based on the Mobius inversion formula of odd number series. It requires fewer multiplications and has less complexity over previous algorithms. In addition, a technique is proposed to carry out the on-axis Fourier coefficients. A parallel VLSI architecture is developed for the new algorithm     

Generating 2-D FIR filter functions by Christoffel–Darboux formula for Chebyshev polynomials of the second kind

Global Christoffel–Darboux formula for different polynomials has already been used for the filter design. Here, this formula for orthonormal Chebyshev polynomials of the second kind and for two independent variables is applied in generating novel class linear-phase two-dimensional (2-D) finite impulse response (FIR) digital filter functions. In this way, 2-D filters with some specific features including economy, phase linearity, symmetry and selectivity are designed. Representative examples of the 2-D FIR digital filters of a new class obtained by the proposed approximation technique are given. A filter generated by the proposed approach is compared with the corresponding one generated by the procedure from literature.     

根据2G信号强度预测3G信号强度的方法

本文通过研究2G系统和3G系统的链路预算的差别,提出了根据2G信号强度估算3G信号强度的一种便捷方法,并对该方法进行了仿真论证,通过与流行的传播模式预测的结果和实测值进行比较,验证了该方法的可行性.该方法对于3G系统的初期规划具有很好的工程指导意义.     

ARMA-cepstrum Recursion Algorithm for the Estimation of the MA Parameters of 2-D ARMA Models

This paper considers the problem of estimating the moving average (MA) parameters of a two-dimensional autoregressive moving average (2-D ARMA) model. To solve this problem, a new algorithm that is based on a recursion relating the ARMA parameters and cepstral coefficients of a 2-D ARMA process is proposed. On the basis of this recursion, a recursive equation is derived to estimate the MA parameters from the cepstral coefficients and the autoregressive (AR) parameters of a 2-D ARMA process. The cepstral coefficients are computed benefiting from the 2-D FFT technique. Estimation of the AR parameters is performed by the 2-D modified Yule–Walker (MYW) equation approach. The development presented here includes the formulation for real-valued homogeneous quarter-plane (QP) 2-D ARMA random fields, where data are propagated using only the past values. The proposed algorithm is computationally efficient especially for the higher-order 2-D ARMA models, and has the advantage that it does not require any matrix inversion for the calculation of the MA parameters. The performance of the new algorithm is illustrated by some numerical examples, and is compared with another existing 2-D MA parameter estimation procedure, according to three performance criteria. As a result of these comparisons, it is observed that the MA parameters and the 2-D ARMA power spectra estimated by using the proposed algorithm are converged to the original ones     

Topological analysis of trabecular bone MR images

Recently, imaging techniques have become available which permit nondestructive analysis of the three-dimensional (3-D) architecture of trabecular bone (TB), which forms a network of interconnected plates and rods. Most osteoporotic fractures occur at locations rich in TB, which has spurred the search for architectural parameters as determinants of bone strength. In this paper, we present a new approach to quantitative characterization of the 3-D microarchitecture of TB, based on digital topology. The method classifies each voxel of the 3-D structure based on the connectivity information of neighboring voxels. Following conversion of the 3-D digital image to a skeletonized surface representation containing only one-dimensional (1-D) and two-dimensional (2-D) structures, each voxel is classified as a curve, surface, or junction. The method has been validated by means of synthesized images and has subsequently been applied to TB images from the human wrist. The topological parameters were found to predict Young's modulus (YM) for uniaxial loading, specifically, the surface-to-curve ratio was found to be the single strongest predictor of YM (r2 = 0.69). Finally, the method has been applied to TB images from a group of patients showing very large variations in topological parameters that parallel much smaller changes in bone volume fraction (BVF).     

Model identification of a noncausal 2-D AR process using a causal 2-D AR model on the nonsymmetric half-plane

If a noncausal two-dimensional (2-D) autoregressive (AR) process is bi-causal, there exists a causal 2-D AR process on the nonsymmetric half-plane having the same autocorrelations as the noncausal 2-D AR process. A formula is presented to relate the AR coefficients of the noncausal 2-D AR process with those of the causal 2-D AR process on the nonsymmetric half plane. The 2-D Yule-Walker equations are derived for causal 2-D AR models on the nonsymmetric half plane. A computationally efficient order-recursive algorithm is proposed to solve the 2-D Yule-Walker equations. Using the autocorrelation equivalence relation and the order-recursive algorithm, we can easily identify a noncausal 2-D AR process from its autocorrelations.