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     

A closed-form formula for 2-D ohmic losses calculation in SMPStransformer foils

A new formula aimed at calculating ohmic losses in switch-mode power supply (SMPS) transformers is presented. It is based on intensive two-dimensional (2-D) finite element method (FEM) simulations, the results of which have been summarized in a closed-form formula following a “semi-empirical” approach. The main benefit of this new formula, specifically intended for industrial designers, is to combine the precision of 2-D models with the ease-of-use and speed of calculation of one-dimensional (1-D) models, on the whole frequency range. It accurately covers cases where the classical Dowell's formula significantly underestimated the losses, specifically those with significant edge effect in foil windings. Experimental validation and discussion of accuracy is provided. At the moment, the formula is only valid for one layer of foil located between a zero and a maximum of the magnetomotive force but a similar approach could be applied with success to other types of windings. Furthermore, the analytical expression proposed in the article, based on Maxwell equations, can be used as a stand-alone tool to model the real behavior of any type of winding. More accurate understanding of the 2-D field is also possible thanks to the direct link established between the losses and the geometrical data of the winding     

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.     

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     

A multiwinding modeling method for high frequency transformers and inductors

This paper presents a method to obtain an electric model for transformers and inductors, including both frequency and geometry effects in the windings, which can be linked with existing core models. One-dimensional distributions for magnetic and electric fields are assumed, and from Maxwell's equations an equivalent electric circuit is easily obtained. This equivalent circuit has been included in analog simulators (Spice, AnalogWorkBench, Saber ...), and comparisons between measured and simulated results are shown, both in time domain and in AC sweep, which verify the model accuracy. The model described in this paper allows designers to deal with key issues in the design of high-frequency magnetic components (copper losses, leakage inductance, skin and proximity effects) by using analog simulators, which are usually more familiar to them than finite-element analysis tools.     

Frequency-dependent resistance in Litz-wire planar windings for domestic induction heating appliances

In this paper, the frequency-dependent resistance in Litz-wire planar windings for domestic induction heating appliances is analyzed. For these inductors, in which the size is not an essential constraint, an analytical model is developed based on the superposition of different loss effects in the wire. Eddy current losses, including conduction losses and proximity-effect losses, both internal and external, were considered and modeled. The magnetic field necessary to evaluate the external proximity losses is as well analytically calculated considering the complete winding and load properties. To verify this model and its limitations, several inductors with different wires and numbers of turns were constructed and results with both non-loaded and loaded inductors are compared with theoretical predictions.     

A simple 2-D/3-D method for fast analysis of patch resonators withhigh accuracy

For a patch resonator, a two-dimensional (2-D) planar circuit analysis (modal or contour integral) has advantages of being simple and fast. However, this method does not account for perturbation of the fringe fields at the edge. A three-dimensional (3-D) analysis such as integral equation moment method has the advantage of accounting for the fringe fields at the edge, however, the disadvantage of having to long computation time and high truncation error. A better way is to make use of advantages of both and discard the disadvantages. The result is the combined 2-D/3-D method described in this paper. This method requires a few seconds of computer time, but gives errors of resonance frequency only around 0.5%. The errors in general are within the tolerances of presently available analysis and experiments. Field theory reasons accounting for such fast convergent and low error results, are explained and numerical examples are given     

Directional filtering in edge detection

Two-dimensional (2-D) edge detection can be performed by applying a suitably selected optimal edge half-filter in n directions. Computationally, such a two-dimensional n-directional filter can be represented by a pair of real masks, that is, by one complex-number matrix, regardless of the number of filtering directions, n. Specific calculations of the edge strength were conducted using a 2-D tridirectional filter based on a Petrou-Kittler (1991) one-dimensional (1-D) detector optimized for the ramp edges, which are characteristic of posterior eye capsule images that were used here as a test set. In applications to image segmentation, tridirectional filtering results in co-occurrence arrays of low dimensionality.     

Detection of composite edges

The paper presents a new parametric model-based approach to high-precision composite edge detection using orthogonal Zernike moment-based operators. It deals with two types of composite edges: (a) generalized step and (b) pulse/staircase edges. A 2-D generalized step edge is modeled in terms of five parameters: two gradients on two sides of the edge, the distance from the center of the candidate pixel, the orientation of the edge and the step size at the location of the edge. A 2-D pulse/staircase edge is modeled in terms of two steps located at two positions within the mask, and the edge orientation. A pulse edge is formed if the steps are of opposite polarities whereas a staircase edge results from two steps having the same polarity. Two complex and two real Zernike moment-based masks are designed to determine parameters of both the 2-D edge models. For a given edge model, estimated parameter values at a point are used to detect the presence or absence of that type of edge. Extensive noise analysis is performed to demonstrate the robustness of the proposed operators. Experimental results with intensity and range images are included to demonstrate the efficacy of the proposed edge detection technique as well as to compare its performance with the geometric moment-based step edge detection technique and Canny's (1986) edge detector.     

Three-dimensional analysis of scattering losses due to sidewall roughness in microphotonic waveguides

We present a three-dimensional (3-D) analysis of scattering losses due to sidewall roughness in rectangular dielectric waveguides valid for any refractive-index contrast and field polarization. The analysis is based on the volume current method and uses array factors to introduce significant mathematical simplifications to better understand the influence of individual waveguide parameters on scattering losses. We show that the typical two-dimensional (2-D) analyses can substantially overestimate scattering losses in small waveguides and that scattering losses exhibit considerable polarization dependence. We produce scattering-loss estimates for a wide variety of waveguides and provide guidelines for design of waveguide cross sections that are less sensitive to sidewall roughness.     

Improved analytical modeling of conductive losses in magneticcomponents

The one well-known one-dimensional method for calculating the AC resistance of multilayer transformer windings contains a built-in orthogonality which has not been reported previously. Orthogonality between skin effect and proximity effect makes a more generalized approach for the analytical solution of AC resistance in windings possible. This includes a method to calculate the AC resistance of round conductor windings which is not only convenient to use, but gives more accurate answers than the basic one-dimensional method because the exact analytical equations for round conductors can be used     

A new two-dimensional model for the potential distribution of shortgate-length MESFET's and its applications

A new analytical technique for calculating the 2-D potential distribution of a MESFET device operated in the subthreshold region is proposed, in which the 2-D Poisson's equation is solved by the Green's function technique. The potential and electric-field distributions of a non-self-aligned MESFET device are calculated exactly from different types of Green's function in different boundary regions, and the sidewall potential at the interface between these regions can be determined by the continuation of the electric field at the sidewall boundary. The remarkable feature of the proposed method is that the implanted doping profile in the active channel can be treated. Furthermore, a simplified technique is developed to derive a set of quasi-analytical models for the sidewall potential at both sides of the gate edge, the threshold voltage of short gate-length devices, and the drain-induced barrier lowering. Moreover, the developed quasi-analytical models are compared with the results of 2-D numerical analysis and good agreements are obtained     

Prior shape level set segmentation on multistep generated probability maps of MR datasets for fully automatic kidney parenchyma volumetry

Fully automatic 3-D segmentation techniques for clinical applications or epidemiological studies have proven to be a very challenging task in the domain of medical image analysis. 3-D organ segmentation on magnetic resonance (MR) datasets requires a well-designed segmentation strategy due to imaging artifacts, partial volume effects, and similar tissue properties of adjacent tissues. We developed a 3-D segmentation framework for fully automatic kidney parenchyma volumetry that uses Bayesian concepts for probability map generation. The probability map quality is improved in a multistep refinement approach. An extended prior shape level set segmentation method is then applied on the refined probability maps. The segmentation quality is improved by incorporating an exterior cortex edge alignment technique using cortex probability maps. In contrast to previous approaches, we combine several relevant kidney parenchyma features in a sequence of segmentation techniques for successful parenchyma delineation on native MR datasets. Furthermore, the proposed method is able to recognize and exclude parenchymal cysts from the parenchymal volume. We analyzed four different quality measures showing better results for right parenchymal tissue than for left parenchymal tissue due to an incorporated liver part removal in the segmentation framework. The results show that the outer cortex edge alignment approach successfully improves the quality measures.     

The Nitrogen Boil-Off Method for Measuring AC Losses in HTS Coils

We have developed a novel apparatus for applying a nitrogen boil-off method as a mean of making calorimetric measurements and allowing for simple measuring and evaluating of AC losses in HTS coils at liquid nitrogen temperature. With the ability to measure AC loss generated in superconductors directly, this method produces more reliable data than that obtained by general, electro-magnetic measurements. A sensitivity of about 0.1 W was achieved by improving sensitivity in measuring gas evaporation via the following three steps: (1) use of nonmetallic vessel, heat-insulated housing in which the sample is located; (2) optimization for sample vessel thickness and tube size; and (3) stabilization of evaporating gas emitted by the heater. It is widely expected that the proposed apparatus may be used for individual measurement of the magnetization loss and the transport current loss in HTS coils, as well as their total losses, in addition to the AC loss in irregularly shaped samples.     

Implementation of a forward-backward procedure for the fast analysis of electromagnetic radiation/scattering from two-dimensional large phased arrays

Forward-backward method (FBM) was successfully developed for the analysis of electromagnetic radiation/scattering from one-dimensional (1-D) phased array in an efficiency appealing fashion. The FBM applications to treat 2-D array problems are developed in this paper. Acceleration algorithm, performing better than the novel spectrum acceleration algorithm used for 1-D FBM computation, is also developed for this 2-D FBM so the unique advantages of high efficiency and O(N/sub tot/) computational complexity as in the 1-D problems can be retained where N/sub tot/ is the total number of array element. Numerical examples are presented to demonstrate its validity.     

Three-dimensional source localization in a waveguide

This paper deals with three-dimensional (3-D) passive localization of a narrowband point source in a 2½-dimensional waveguide using an array of sensors. Two different maximum likelihood (ML) procedures for estimating the source range, depth, and direction-of-arrival (DOA) based on the normal mode representation of the received data are studied. In the first procedure, ML estimation of range and depth is applied on the data collected by a vertical array, and DOA is estimated using the ML algorithm on the data received by a separate, horizontal array. In the second procedure, the ML algorithm is applied on the data received by a two-dimensional (2-D), hybrid array for simultaneously estimating of all three source location parameters. Our study shows that although a horizontal array is sufficient for 3-D localization, to reduce sensitivity of the localization algorithm, a 2-D array should be used. The presented performance analysis of the two algorithms enables one to determine the performance losses in using the stage-wise, suboptimal algorithm relative to the optimal one in any given scenario. Numerical examples with channel parameters, which are typical to shallow water source localization, show performance losses of 0-3 dB. Simulation results of the two ML algorithms and their comparison with the Cramer-Rao bound (CRB) support the theory     

多胞型二维多项式的Schur稳定性

本文提出多胞型二维多项式的Schur稳定的充分必要条件。我们揭示多胞型二维多项式的系数具有线性仿射特性。基于这一仿射特性,将多胞型二维多项式视为具有复变系数的多胞型一维多项式,我们证明多胞型二维多项式的稳定性可由其有限的棱边多项式的稳定性保证。我们提供了一种棱边多项式的稳定性检验算法。     

High-Efficiency Isolated Boost DC–DC Converter for High-Power Low-Voltage Fuel-Cell Applications

A new design approach achieving very high conversion efficiency in low-voltage high-power isolated boost dc–dc converters is presented. The transformer eddy-current and proximity effects are analyzed, demonstrating that an extensive interleaving of primary and secondary windings is needed to avoid high winding losses. The analysis of transformer leakage inductance reveals that extremely low leakage inductance can be achieved, allowing stored energy to be dissipated. Power MOSFETs fully rated for repetitive avalanches allow primary-side voltage clamp circuits to be eliminated. The oversizing of the primary-switch voltage rating can thus be avoided, significantly reducing switch-conduction losses. Finally, silicon carbide rectifying diodes allow fast diode turn-off, further reducing losses. Detailed test results from a 1.5-kW full-bridge boost dc–dc converter verify the theoretical analysis and demonstrate very high conversion efficiency. The efficiency at minimum input voltage and maximum power is 96.8%. The maximum efficiency of the proposed converter is 98%.      

Control algorithms and circuit designs for optimal flyback-chargingof an energy-storage capacitor (e.g., for flash lamp or defibrillator)

A flyback-type of a transformer-coupled DC/DC power converter supplies a train of current pulses to charge an energy-storage capacitor to a desired high voltage, converting input DC power obtained from a lower voltage DC source. The energy-storage capacitor is charged to a specified voltage within a specified time with minimum peak and RMS currents in the transistor, the rectifier diode, the transformer windings and the DC power source, minimizing the i²R losses. This is done by generating: (1) energy-storage current pulses in the power transistor and the transformer primary winding in which the current increment from the beginning to the end of a pulse is only a small fraction of the final (peak) value; and (2) energy-delivery flyback current pulses in the capacitor and the transformer secondary winding in which the current decrement from the beginning to the end of a pulse is only a small fraction of the initial (peak) value. Recommended methods are: (1) hysteretic current-mode control with current sensing in both transformer windings; (2) peak-current-commanding current-mode control with switching frequency or transistor-nonconducting time varying in a prescribed way during the charging; or (3) valley-current-commanding current-mode control with switching frequency or transistor-conducting time varying in a prescribed way during the charging. Compared with one nonoptimal method, peak currents are reduced by a factor of about 2 and i²R power losses are reduced by a factor of about 1.33     

Antiresonant reflecting optical waveguide-type vertical-cavity surface emitting lasers: comparison of full-vector finite-difference time-domain and 3-D bidirectional beam propagation methods

The cold-cavity modal characteristics of an antiresonant optical waveguide-type cylindrical vertical-cavity surface-emitting laser (VCSEL) are investigated through numerical simulations using a three-dimensional (3-D) bidirectional beam propagation method (BD-BPM) and a full-vector axisymmetric finite-difference time-domain (FDTD) method. Good agreement between the BPM- and FDTD-computed radial mode profiles as well as the mode-dependent radiation losses is obtained. The results of this paper establish the accuracy of the BD-BPM technique for simulating this class of devices and confirm effective-index method predictions that antiresonance conditions for cylindrical geometry devices (i.e., VCSELs) differ from those of planar geometry devices (i.e., edge emitters).